**Meet the editor**

Sebastiano D'Amico (PhD) has been working as Research Officer III at the Physics Department, University of Malta, since 2010. He was enrolled in the Physics program of the University of Messina where he was awarded the title of "Dottore in Fisica". In 2005, Dr D'Amico moved to Rome where he joined the Istituto Nazionale di Geofisica e Vulcanologia (INGV) and, in

2007, he married Rosarianna and moved to the United States to join the Earth and Atmospheric Sciences Department at Saint Louis University. His research interests are in the applied aspects of earthquake seismology and he has authored several publications in this field. Dr D'Amico is particularly interested in seismicity and tectonics of the Central Mediterranean, earthquake ground motion and seismic hazard, earthquake moment tensor solutions, and ambient noise measurements on soil and buildings.

Contents

**Preface VII**

**Lessons Learnt 21**

Mario Fernandez Arce

Sebastiano D'Amico

Zonghu Liao and Ze'ev Reches

Chapter 1 **A Review of the 1170 Andújar (Jaén, South Spain) Earthquake, Including the First Likely Archeological Evidence 1**

Martínez Solares and C. López Casado

Chapter 2 **Global Climatic Changes, a Possible Cause of the Recent**

Chapter 4 **Seismotectonic and the Hipothetical Strike – Slip Tectonic**

Chapter 5 **Modeling Dynamic-Weakening and Dynamic-Strengthening of Granite in High-Velocity Slip Experiments 107**

Chapter 6 **Characterizing the Noise for Seismic Arrays: Case of Study for**

Chapter 7 **Parameters Identification of Stochastic Nonstationary Process**

Giuseppe Carlo Marano, Mariantonietta Morga and Sara Sgobba

Septimius Mara and Serban-Nicolae Vlad

Chapter 3 **Scaling Properties of Aftershock Sequences in Algeria-Morocco Region 39** M. Hamdache, J.A. Pelàez and A. Talbi

**Boundary of Central Costa Rica 77**

**the Alice Springs ARray (ASAR) 127**

**Used in Earthquake Modelling 147**

J.A. Peláez, J.C. Castillo, F. Gómez Cabeza, M. Sánchez Gómez, J.M.

**Increasing Trend of Earthquakes Since the 90's and Subsequent**

### Contents

#### **Preface XI**



Preface

ical facilities.

led to the realization of this book.

The purpose of this book is to present 9 scientific papers focusing on new research and re‐ sults on earthquake seismology. Chapters of this book focus on several aspect of seismology ranging from historical earthquake analysis, seismotectonics, and damage estimation of crit‐

The first chapter presents a critical review of the Andújar earthquake, a historical event in the 12th century in southern Spain. Chapters 2 and 3 describe some statistical analysis on global earthquake activity and scaling properties of seismic sequences in Algeria. Chapter 4 reports a seismotectonic survey carried out in Central Costa Rica to evaluate a hypothetical strike-slip tectonic boundary between the Caribbean plate and the Panama Block. Chapter 5 presents a study on modeling dynamic-weakening and dynamic-strengthening of granite fault in high-velocity slip experiments. The sixth chapter presents a study conducted using seismic arrays. A new deterministic modulation function for defining evolutionary stochas‐ tic processes that model seismic ground motion accelerations is presented in Chapter 7. The last two chapters present respectively studies on the daily variation of the detection capabili‐ ty of earthquakes and its quantitative evaluation, and damage estimation improvement of

As the Editor of this book, I would like to thank InTech - Open Access Publisher for all the support during the publishing process and authors for their efforts in order to produce high quality works. I would like also to express my special thanks to Ms Danijela Durinc for her professional assistance and technical support during the entire publishing process that has

> **Sebastiano D'Amico** Research Officer III Physics Department University of Malta

> > Malta

electric power distribution equipment using multiple disaster information.

### Preface

Chapter 8 **Daily Variation in Earthquake Detection Capability: A**

Chapter 9 **Damage Estimation Improvement of Electric Power**

**Distribution Equipment Using Multiple Disaster**

**Quantitative Evaluation 167**

Takaki Iwata

**VI** Contents

**Information 185** Yoshiharu Shumuta

> The purpose of this book is to present 9 scientific papers focusing on new research and re‐ sults on earthquake seismology. Chapters of this book focus on several aspect of seismology ranging from historical earthquake analysis, seismotectonics, and damage estimation of crit‐ ical facilities.

> The first chapter presents a critical review of the Andújar earthquake, a historical event in the 12th century in southern Spain. Chapters 2 and 3 describe some statistical analysis on global earthquake activity and scaling properties of seismic sequences in Algeria. Chapter 4 reports a seismotectonic survey carried out in Central Costa Rica to evaluate a hypothetical strike-slip tectonic boundary between the Caribbean plate and the Panama Block. Chapter 5 presents a study on modeling dynamic-weakening and dynamic-strengthening of granite fault in high-velocity slip experiments. The sixth chapter presents a study conducted using seismic arrays. A new deterministic modulation function for defining evolutionary stochas‐ tic processes that model seismic ground motion accelerations is presented in Chapter 7. The last two chapters present respectively studies on the daily variation of the detection capabili‐ ty of earthquakes and its quantitative evaluation, and damage estimation improvement of electric power distribution equipment using multiple disaster information.

> As the Editor of this book, I would like to thank InTech - Open Access Publisher for all the support during the publishing process and authors for their efforts in order to produce high quality works. I would like also to express my special thanks to Ms Danijela Durinc for her professional assistance and technical support during the entire publishing process that has led to the realization of this book.

#### **Sebastiano D'Amico**

Research Officer III Physics Department University of Malta Malta

**Chapter 1**

**A Review of the 1170 Andújar (Jaén, South Spain)**

**Evidence**

C. López Casado

**1. Introduction**

evidence remains of it.

restructured and extended in different epochs.

http://dx.doi.org/10.5772/54864

J.A. Peláez, J.C. Castillo, F. Gómez Cabeza,

M. Sánchez Gómez, J.M. Martínez Solares and

Additional information is available at the end of the chapter

**Earthquake, Including the First Likely Archeological**

The origin of the town of Andújar (figures 1 and 2), in southern Spain, is likely a Roman settlement, as suggested by certain archaeological evidence in its historical center (figure 2). Andújar was probably founded to control a significant strategic route on the edge of the Guadalquivir River and ending in Córdoba. The town was a flat settlement, without natural shelters, presumably defended in this epoch by a defensive wall or fortification, although no

The first clear reference to the defensive wall of Andújar is a request from the emir *'Abd Allah* to the governor of the region, in the year 888, asking for aid to fortify the fort of *An‐ duyar* (Andújar) to protect the population from insurgents opposing the government of the Umayyad dynasty [1]. Subsequent archeological evidences indicate this fortification was

Based on information gathered from various archaeological digs in the historical center of Andújar (figure 2), we propose the following construction stages in its walled compound.

*a)* The emiral-caliphal town walls (the word emiral comes from Emirate, and caliphal from Caliphate, the two political systems existing during this epoch). They were built in the 9th and 10th centuries, when the presumable early fortification was established and extended to protect the population of the region. After that time, Andújar became one of the main towns in the countryside of Jaén, in the Guadalquivir Basin, significantly increasing in population,

> © 2013 Peláez et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2013 Peláez et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

## **A Review of the 1170 Andújar (Jaén, South Spain) Earthquake, Including the First Likely Archeological Evidence**

J.A. Peláez, J.C. Castillo, F. Gómez Cabeza, M. Sánchez Gómez, J.M. Martínez Solares and C. López Casado

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54864

**1. Introduction**

The origin of the town of Andújar (figures 1 and 2), in southern Spain, is likely a Roman settlement, as suggested by certain archaeological evidence in its historical center (figure 2). Andújar was probably founded to control a significant strategic route on the edge of the Guadalquivir River and ending in Córdoba. The town was a flat settlement, without natural shelters, presumably defended in this epoch by a defensive wall or fortification, although no evidence remains of it.

The first clear reference to the defensive wall of Andújar is a request from the emir *'Abd Allah* to the governor of the region, in the year 888, asking for aid to fortify the fort of *An‐ duyar* (Andújar) to protect the population from insurgents opposing the government of the Umayyad dynasty [1]. Subsequent archeological evidences indicate this fortification was restructured and extended in different epochs.

Based on information gathered from various archaeological digs in the historical center of Andújar (figure 2), we propose the following construction stages in its walled compound.

*a)* The emiral-caliphal town walls (the word emiral comes from Emirate, and caliphal from Caliphate, the two political systems existing during this epoch). They were built in the 9th and 10th centuries, when the presumable early fortification was established and extended to protect the population of the region. After that time, Andújar became one of the main towns in the countryside of Jaén, in the Guadalquivir Basin, significantly increasing in population,

**Figure 1.** Regional setting of the study region. Ellipse shows the likely epicentral area of the Andújar earthquake.

formed by mud-walls composed of small stones and lime in the externalmost part, and a

**Figure 2.** Current Andújar map. Historical center is enhanced showing the approximate extent of the different stages

A Review of the 1170 Andújar (Jaén, South Spain) Earthquake, Including the First Likely Archeological Evidence

http://dx.doi.org/10.5772/54864

3

*c)* The *Ibn Hamusk*-Almohad stage (*Ibn Hamusk* was an insurgent who governed the region in agreement with Almoravids and Almohads, according to his interests). This was the most significant rearrangement of the wall system, carried out in the second half of the 12th and the beginning of the 13th centuries. Most remains discovered in the town are from this epoch [2,3]. Built structures at this stage are very homogeneous, constituting strongly tamped mud-wall made with lime, small stones, and sand. It is similar to those used in other fortifications in the northern Guadalquivir Basin (*e.g.*, Baños de la Encina, Giribaile and Santa Eufemia castles). In the northern sector of this wall system, in the most strategic spot, an alcazar (citadel) was built, which lasted until the beginning of the 20th century [5]. We are confident that this extensive rebuilding arose due to the deplorable conservation of the defensive wall system after the town was besieged and attacked various times in the second half of the 12th century and specially

*d)* Christian stage or consolidation phase. Andújar was reconquered in 1225 by *Ferdinand III of Castile* and until the 15th century the ramparts were lightly repaired numerous times. Works mainly focused on cladding the most important structures of the defensive system, basically the towers and gateways, with sandstone ashlar. There are scarce elements remaining from

mixture of materials inside, primarily dirt [4].

of ramparts and location of the archeological dig.

as a result of damage after the 1170 earthquake [6].

and acquiring the condition of *Iqlim* (administrative district). The wall system is documented in an excavation carried out in the north of the town (figure 2) and revealing the ruins of a trapezoidal turret and several mud-walls of mortar with solid towers [2,3]. This mortar is extremely compacted gravel and lime, primarily white.

*b)* The taifa-Almoravid ramparts (taifas were small kingdoms in *Al-Andalus*, and the Almora‐ vids were a Berber dynasty invader of Iberia, like the Almohads). During the 11th and the first half of the 12th centuries, the previous wall system was rearranged to incorporate the suburbs (recycling part of the obsolete emiral-caliphal walls) and thereby improving the security of the defensive system. These extensive works are an indication of the strategic nature of Andújar. Some ruins of the walls from this period have been documented in an archeological survey in the south of the town (figure 2). It includes a set of fortifications around one of the main gates of the city wall, the so-called *Puerta del Alcázar* (Alcazar gateway), the gateway for those entering town from the *Puente Romano* (Roman bridge). In this stage, the wall system was A Review of the 1170 Andújar (Jaén, South Spain) Earthquake, Including the First Likely Archeological Evidence http://dx.doi.org/10.5772/54864 3

**Figure 2.** Current Andújar map. Historical center is enhanced showing the approximate extent of the different stages of ramparts and location of the archeological dig.

formed by mud-walls composed of small stones and lime in the externalmost part, and a mixture of materials inside, primarily dirt [4].

*c)* The *Ibn Hamusk*-Almohad stage (*Ibn Hamusk* was an insurgent who governed the region in agreement with Almoravids and Almohads, according to his interests). This was the most significant rearrangement of the wall system, carried out in the second half of the 12th and the beginning of the 13th centuries. Most remains discovered in the town are from this epoch [2,3]. Built structures at this stage are very homogeneous, constituting strongly tamped mud-wall made with lime, small stones, and sand. It is similar to those used in other fortifications in the northern Guadalquivir Basin (*e.g.*, Baños de la Encina, Giribaile and Santa Eufemia castles). In the northern sector of this wall system, in the most strategic spot, an alcazar (citadel) was built, which lasted until the beginning of the 20th century [5]. We are confident that this extensive rebuilding arose due to the deplorable conservation of the defensive wall system after the town was besieged and attacked various times in the second half of the 12th century and specially as a result of damage after the 1170 earthquake [6].

and acquiring the condition of *Iqlim* (administrative district). The wall system is documented in an excavation carried out in the north of the town (figure 2) and revealing the ruins of a trapezoidal turret and several mud-walls of mortar with solid towers [2,3]. This mortar is

**Figure 1.** Regional setting of the study region. Ellipse shows the likely epicentral area of the Andújar earthquake.

*b)* The taifa-Almoravid ramparts (taifas were small kingdoms in *Al-Andalus*, and the Almora‐ vids were a Berber dynasty invader of Iberia, like the Almohads). During the 11th and the first half of the 12th centuries, the previous wall system was rearranged to incorporate the suburbs (recycling part of the obsolete emiral-caliphal walls) and thereby improving the security of the defensive system. These extensive works are an indication of the strategic nature of Andújar. Some ruins of the walls from this period have been documented in an archeological survey in the south of the town (figure 2). It includes a set of fortifications around one of the main gates of the city wall, the so-called *Puerta del Alcázar* (Alcazar gateway), the gateway for those entering town from the *Puente Romano* (Roman bridge). In this stage, the wall system was

extremely compacted gravel and lime, primarily white.

2 Earthquake Research and Analysis - New Advances in Seismology

*d)* Christian stage or consolidation phase. Andújar was reconquered in 1225 by *Ferdinand III of Castile* and until the 15th century the ramparts were lightly repaired numerous times. Works mainly focused on cladding the most important structures of the defensive system, basically the towers and gateways, with sandstone ashlar. There are scarce elements remaining from this epoch, with the *Turret of Tavira* and the *Tower of 'de la Fuente la Sorda'* being worthy of note (figure 2) [5].

intensity (MM scale) equal to X. In contrast, in reference [12] authors place the epicenter at

A Review of the 1170 Andújar (Jaén, South Spain) Earthquake, Including the First Likely Archeological Evidence

http://dx.doi.org/10.5772/54864

5

It is important to note, as he states in his manuscript, that *Averroes* did not feel the mainshock himself, but several aftershocks when he went back to Córdoba from Sevilla. Concerning effects, it appears clear after reading the manuscript that: *a)* there was destruction and deaths, and *b)* there were aftershocks for three years. In addition, some statements suggest that the meisoseismal area, and presumably the epicentral area, is east of Córdoba, in the region of Andújar: *a)* effects were stronger east of Córdoba, and *b)* there were reported seismogeological

The second Arabic manuscript referring to this earthquake was written by *'Abd al-Malik b. Muhammad b. Ibn Sāhib al-Salā* (ms. number 2 in Appendix), an Arab chronicler contemporary of the event, and known by his translators for his explicitness, precision and fluency with respect to historical descriptions [13]. It is not totally clear but, it seems that *Ibn Sāhib al-Salā* was accompanying the caliph *Yūsuf I* and his brother the prince *Abū Sa'īd* on a journey throughout *Al Andalus*; accordingly, he probably felt the main quake or the aftershocks. In his manuscript, referring to events in the year 565 of the Arab calendar (September 25th, 1169 to September 13th, 1170), *Ibn Sāhib al-Salā* dramatically relates notable effects in Andújar: *a)* significant destruction, and *b)* a mainshock felt over a large region (the whole of *Al-Andalus*,

The manuscript by *Ibn Sāhib al-Salā* has been selected to assign a date for this earthquake. He provides a detailed description for each year of the most important historic events in *Al-Andalus*. It is precisely this systematization in the timing of the related events that leads us to consider this date (January-February, 1170), as previously considered by the author in

There are only two known works written by *Ibn Sāhib al-Salā* and only the second one, specifically the second volume of three of the second opus, called *Almohad caliphate history*, is currently preserved nowadays (in the Bodleian Library). This volume, which includes the manuscript referring to the Andújar event, covers 1159 to 1173. The only things known concerning the life of *Ibn Sāhib al-Salā* is what he relates about himself in this manuscript. Further support as to the importance of this text and its chronicler, as stated in reference [13], is the fact that another contemporary historian, *Ibn 'Idārī*, copied and extracted literally (ms. number 3 in Appendix) the *Ibn Sāhib al-Salā* writings. Although it must be taken into account that the information in a derived source cannot always be considered confirmed information,

Apart from these texts, there is no evidence of more reliable chronicles related to the event. A very short text (ms. number 4 in the Appendix) included in the so-called *Anales Toledanos* (Annals of Toledo), transcribed and compiled in reference [15], is the only other one worthy of note. They are contemporary medieval chronicles, characterized by extreme brevity and

Some researchers in the Spanish historic seismicity consider that this citation likely refers to the Andújar earthquake [7,16], inferring that the quoted date is just the date of the event. In

Andújar, assigning it a felt intensity (MCS scale) equal to IX.

effects in Andújar (*i.e.*, ground failure and/or ground liquefaction).

and specifically in Córdoba, Granada and Sevilla).

in this case we agree with the author's [13] criterion.

conciseness, reporting the most important occurrences of the time.

reference [14].

As mentioned above, after the taifa-Almoravid improvement and enlargement of the defensive wall system, a moderate earthquake struck this region. In the most recent Spanish earthquake catalog [7], it is termed the 1169, Andújar (Jaén) earthquake, the most destructive shock known in the whole Iberian Peninsula until the 1396, Tavernes de Valldigna (Valencia) earthquake (VIII-IX, macroseismic *MW* 6.7) [8]. In the international scientific literature, the earthquake is known as the 1170, Córdoba earthquake [9]. This is due to the fact that these authors used only one of the contemporary manuscripts to catalog the event (ms. number 1 in Appendix), where Córdoba city is cited because it was much more important than Andújar and only 65 km away. In fact, Córdoba was the capital of the Emirate (750-929) and Caliphate (929-1031) of Córdoba, seat of emirs and caliphs. In the caliphate epoch, Córdoba reached a population of about 400000 inhabitants [10].

Although there is scarce information about the true effects of the earthquake, as we will see below, there is no doubt that there was a heavily damaging to destructive earthquake in Andújar. Moreover, in this paper we present what we consider to be the first archeo‐ logical proof of this earthquake after interpreting the results obtained at an archeological site in the town. In archeoseismological studies, scientists must work bearing in mind the old rewrote saying: the presence of evidence is not evidence of presence. Considering contemporary documents of the event together with what we presume to be a recent ar‐ cheoseismological result, we argue that in this case archeology supports the occurrence of this event.

This historical earthquake should be taken into account for future seismic hazard assessments in this region. If there is a moderate earthquake in an area, then there is a geological structure, known or unknown, that hosted it. Therefore, it is capable of being triggered again in future.

#### **2. Contemporary written sources — Estimating effects and size**

Three Arabic documents are the contemporary documentary evidence reporting the effects of this earthquake. They are two original manuscripts and a clear plagiarized summary of one of them providing no further information.

The best-known manuscript is that written by *Abû l-Walîd Muhammad Ibn Ahmad*, known during his lifetime as *Ibn Rushd* (the grandson), and later known in European literature as *Averroes*, a very important Andalusian philosopher and physician, among other activities. The text (ms. number 1 in Appendix) is included in his work *De Meteoris*, where the author revises different Aristotelian concepts. It must be taken into account that this text is not in fact a historic description of the incident, as in the other two manuscripts.

This is the only text considered in the historical seismicity works including this shock in references [9,11,12]. In reference [9], authors place the epicenter at Córdoba, assigning it a felt intensity (MM scale) equal to X. In contrast, in reference [12] authors place the epicenter at Andújar, assigning it a felt intensity (MCS scale) equal to IX.

this epoch, with the *Turret of Tavira* and the *Tower of 'de la Fuente la Sorda'* being worthy of note

As mentioned above, after the taifa-Almoravid improvement and enlargement of the defensive wall system, a moderate earthquake struck this region. In the most recent Spanish earthquake catalog [7], it is termed the 1169, Andújar (Jaén) earthquake, the most destructive shock known in the whole Iberian Peninsula until the 1396, Tavernes de Valldigna (Valencia) earthquake (VIII-IX, macroseismic *MW* 6.7) [8]. In the international scientific literature, the earthquake is known as the 1170, Córdoba earthquake [9]. This is due to the fact that these authors used only one of the contemporary manuscripts to catalog the event (ms. number 1 in Appendix), where Córdoba city is cited because it was much more important than Andújar and only 65 km away. In fact, Córdoba was the capital of the Emirate (750-929) and Caliphate (929-1031) of Córdoba, seat of emirs and caliphs. In the caliphate epoch, Córdoba reached a population of about 400000

Although there is scarce information about the true effects of the earthquake, as we will see below, there is no doubt that there was a heavily damaging to destructive earthquake in Andújar. Moreover, in this paper we present what we consider to be the first archeo‐ logical proof of this earthquake after interpreting the results obtained at an archeological site in the town. In archeoseismological studies, scientists must work bearing in mind the old rewrote saying: the presence of evidence is not evidence of presence. Considering contemporary documents of the event together with what we presume to be a recent ar‐ cheoseismological result, we argue that in this case archeology supports the occurrence

This historical earthquake should be taken into account for future seismic hazard assessments in this region. If there is a moderate earthquake in an area, then there is a geological structure, known or unknown, that hosted it. Therefore, it is capable of being triggered again in future.

Three Arabic documents are the contemporary documentary evidence reporting the effects of this earthquake. They are two original manuscripts and a clear plagiarized summary of one

The best-known manuscript is that written by *Abû l-Walîd Muhammad Ibn Ahmad*, known during his lifetime as *Ibn Rushd* (the grandson), and later known in European literature as *Averroes*, a very important Andalusian philosopher and physician, among other activities. The text (ms. number 1 in Appendix) is included in his work *De Meteoris*, where the author revises different Aristotelian concepts. It must be taken into account that this text is not in fact a historic

This is the only text considered in the historical seismicity works including this shock in references [9,11,12]. In reference [9], authors place the epicenter at Córdoba, assigning it a felt

**2. Contemporary written sources — Estimating effects and size**

of them providing no further information.

description of the incident, as in the other two manuscripts.

(figure 2) [5].

4 Earthquake Research and Analysis - New Advances in Seismology

inhabitants [10].

of this event.

It is important to note, as he states in his manuscript, that *Averroes* did not feel the mainshock himself, but several aftershocks when he went back to Córdoba from Sevilla. Concerning effects, it appears clear after reading the manuscript that: *a)* there was destruction and deaths, and *b)* there were aftershocks for three years. In addition, some statements suggest that the meisoseismal area, and presumably the epicentral area, is east of Córdoba, in the region of Andújar: *a)* effects were stronger east of Córdoba, and *b)* there were reported seismogeological effects in Andújar (*i.e.*, ground failure and/or ground liquefaction).

The second Arabic manuscript referring to this earthquake was written by *'Abd al-Malik b. Muhammad b. Ibn Sāhib al-Salā* (ms. number 2 in Appendix), an Arab chronicler contemporary of the event, and known by his translators for his explicitness, precision and fluency with respect to historical descriptions [13]. It is not totally clear but, it seems that *Ibn Sāhib al-Salā* was accompanying the caliph *Yūsuf I* and his brother the prince *Abū Sa'īd* on a journey throughout *Al Andalus*; accordingly, he probably felt the main quake or the aftershocks. In his manuscript, referring to events in the year 565 of the Arab calendar (September 25th, 1169 to September 13th, 1170), *Ibn Sāhib al-Salā* dramatically relates notable effects in Andújar: *a)* significant destruction, and *b)* a mainshock felt over a large region (the whole of *Al-Andalus*, and specifically in Córdoba, Granada and Sevilla).

The manuscript by *Ibn Sāhib al-Salā* has been selected to assign a date for this earthquake. He provides a detailed description for each year of the most important historic events in *Al-Andalus*. It is precisely this systematization in the timing of the related events that leads us to consider this date (January-February, 1170), as previously considered by the author in reference [14].

There are only two known works written by *Ibn Sāhib al-Salā* and only the second one, specifically the second volume of three of the second opus, called *Almohad caliphate history*, is currently preserved nowadays (in the Bodleian Library). This volume, which includes the manuscript referring to the Andújar event, covers 1159 to 1173. The only things known concerning the life of *Ibn Sāhib al-Salā* is what he relates about himself in this manuscript.

Further support as to the importance of this text and its chronicler, as stated in reference [13], is the fact that another contemporary historian, *Ibn 'Idārī*, copied and extracted literally (ms. number 3 in Appendix) the *Ibn Sāhib al-Salā* writings. Although it must be taken into account that the information in a derived source cannot always be considered confirmed information, in this case we agree with the author's [13] criterion.

Apart from these texts, there is no evidence of more reliable chronicles related to the event. A very short text (ms. number 4 in the Appendix) included in the so-called *Anales Toledanos* (Annals of Toledo), transcribed and compiled in reference [15], is the only other one worthy of note. They are contemporary medieval chronicles, characterized by extreme brevity and conciseness, reporting the most important occurrences of the time.

Some researchers in the Spanish historic seismicity consider that this citation likely refers to the Andújar earthquake [7,16], inferring that the quoted date is just the date of the event. In fact, as mentioned, in the recent Spanish earthquake catalog it is identified as the 1169, Andújar earthquake. Although it is quite possible that the Andújar earthquake was felt in the center of the Iberian Peninsula, we cannot guarantee that this sole reference in the *Anales Toledanos* can be taken as definitive proof for considering them to be the same event.

**3. Seismic and geological framework**

only 0.05g.

crust [27].

aforesaid continental collision.

The only shock that stands out in the area is the studied earthquake. Seismicity is very scarce near Andújar, which is characteristic of the northern Guadalquivir Basin. Even within the basin, only a few minor earthquakes (4.0 ≤ *M* ≤ 5.0) are located. This region is therefore considered to have a low seismic hazard [21]. In fact, the design acceleration (called basic acceleration) for a return period of 500 years in the Spanish building code [22] for Andújar is

A Review of the 1170 Andújar (Jaén, South Spain) Earthquake, Including the First Likely Archeological Evidence

http://dx.doi.org/10.5772/54864

7

The work in reference [21], using the spatially smoothed seismicity approach, includes a model with the most significant earthquakes in the Iberian Peninsula over the last 300 years. On the other hand, the design acceleration considered in the Spanish building code was computed through a typical zonified method using a broad seismic zone including the whole Guadal‐ quivir Basin. Neither of these two assessments properly included the 1170 Andújar earthquake.

The only instrumental shock in this region deserving of mention is the March 10th, 1951 Linares earthquake (*MD* 4.8, VIII), 25 km NE of Andújar [23]. In a recent work [24] this event is reevaluated (*MS* 5.4, VI-VII, *h* = 30 km) and relocated to 20 km ESE of Andújar. These authors host this event at the base of the crust, in some deep fault near the southern boundary of the Paleozoic Iberian Massif related to the bending of the Paleozoic basement under the Neogene Guadalquivir Basin. More recently, in [25] has been reevaluated this earthquake once again (*MW* 5.2, *h* = 20 km), relocating it to 70 km SSW of Andújar (*i.e.*, distancing it from Andújar). In this last work, the authors cannot explain the known macroseismic intensity distribution for

The presumed mesoseismal area of the Andújar earthquake (figures 1 and 3) involves three tectonic and geographic domains (figure 3). The first, just north of Andújar, is the Paleozoic Iberian Massif, structured during the Variscan orogeny. The Iberian Massif has a flat topog‐

The second domain is the Guadalquivir Basin, which is a classic foreland basin [26] formed by the collision of the Internal Zones of the Betic Cordillera with the southern paleomargin of the Variscan Iberian Massif. The Andújar area is located on the north side of the basin, at the piedmont of Sierra Morena. This range, along the Variscan border, has recently been inter‐ preted as a flexural fore-bulge formed by the overload of the Betic chains above the Iberian

The third tectonic domain is the frontal thrust belt (Subbetic and Prebetic) of the Betic Cordil‐ lera, which delineates an evident mountain front 40 km south of Andújar, a result of the

The most active stage of the continental collision occurred in the region between 20 and 7 Ma ago (Burdigalian-Tortonian) [28]. Nevertheless, there is clear evidence of recent tectonic activity along the Betic Mountain Front [29,30] that may account for its limited seismicity. This tectonic and regional seismic activity is probably related to the ongoing Africa-Iberia collision, with a convergence rate of 4-5 mm/year [31]. However, the Andújar region and the Betic

this event after the epicenter relocation. Neither is a tectonic origin proposed.

raphy, with the exception of its southern edge, which has a smooth slope.

Evidently, the scarce documentary sources of this earthquake are a real problem in accurately dating the event. This lack also prevents researches from estimating with greater detail effects on buildings and people, establishing the meisoseismal area, and determining its impact on the society.

In a recent and comprehensive work [7], used as a basic historic seismic catalog in seismicity and seismic hazard studies in Spain, it is catalogued with a maximum intensity equal to VIII-IX (EMS-98 scale, used henceforth; [17]). As mentioned, it appears that there was ground liquefaction, implying at least a degree of intensity VIII. Nonetheless, this value must be supported independently of other effects. The intensity IX is sustained by the presumed effects on buildings, the result of considering that many houses were destroyed or collapsed and that many people died. Using the EMS-98 scale, this implies that many buildings of vulnerability class A (masonry structures of rubble stone, fieldstone, or adobe) sustained damage of grade 5 (total or near-total collapse). Quoted effects concerning mosque minarets described by *Ibn Sāhib al-Salā*, or damages in the ramparts, described below, as is well known, are very difficult to use for intensity assignment due to their complex structure and irregular behavior during an earthquake.

Using the empirical relationship among intensity and surface magnitude for the Mediterra‐ nean area in [18] gives *MS* 6.0 ± 0.6 for this shock. In this estimate, evidently, possible site effects are not included.

An unpublished geophysical exploration test recently carried out by the authors in an alluvial terrace at the same level as Andújar using the H/V spectral ratio approach based on ambient vibrations, showed resonance frequencies in the range of 5-8 Hz, clearly related to very shallow structures, specifically a shallow sandy sedimentary layer. The potential amplification of earthquake motion by sediments in this area, using this or other approaches, must be explored in depth by future projects. Potential site effects in Andújar are expectable, increasing the seismic hazard in this location, but presumably decreasing the afore-mentioned expectable magnitude for the Andújar earthquake.

There are four fluvial terraces and the present flood plain in the Andújar area, with ele‐ vations above the river channel on the order of 55, 25, 13, and 6 m, from oldest to youngest [19,20]. These terraces comprise alluvial sediments from the Guadalquivir River with thicknesses ranging from approximately 5 to 10 m. They show a conglomeratic lith‐ ology with a silty mud-matrix that becomes sandy mud-matrix at the top of each terrace level. In general, the lower part of the terraces portrays the channel infilling and bar bed‐ form, and the upper part shows the alluvial flood plain. The ages of these terraces range from the Holocene to 600 ka.

#### **3. Seismic and geological framework**

fact, as mentioned, in the recent Spanish earthquake catalog it is identified as the 1169, Andújar earthquake. Although it is quite possible that the Andújar earthquake was felt in the center of the Iberian Peninsula, we cannot guarantee that this sole reference in the *Anales Toledanos* can

Evidently, the scarce documentary sources of this earthquake are a real problem in accurately dating the event. This lack also prevents researches from estimating with greater detail effects on buildings and people, establishing the meisoseismal area, and determining its impact on

In a recent and comprehensive work [7], used as a basic historic seismic catalog in seismicity and seismic hazard studies in Spain, it is catalogued with a maximum intensity equal to VIII-IX (EMS-98 scale, used henceforth; [17]). As mentioned, it appears that there was ground liquefaction, implying at least a degree of intensity VIII. Nonetheless, this value must be supported independently of other effects. The intensity IX is sustained by the presumed effects on buildings, the result of considering that many houses were destroyed or collapsed and that many people died. Using the EMS-98 scale, this implies that many buildings of vulnerability class A (masonry structures of rubble stone, fieldstone, or adobe) sustained damage of grade 5 (total or near-total collapse). Quoted effects concerning mosque minarets described by *Ibn Sāhib al-Salā*, or damages in the ramparts, described below, as is well known, are very difficult to use for intensity assignment due to their complex structure and irregular behavior during

Using the empirical relationship among intensity and surface magnitude for the Mediterra‐ nean area in [18] gives *MS* 6.0 ± 0.6 for this shock. In this estimate, evidently, possible site effects

An unpublished geophysical exploration test recently carried out by the authors in an alluvial terrace at the same level as Andújar using the H/V spectral ratio approach based on ambient vibrations, showed resonance frequencies in the range of 5-8 Hz, clearly related to very shallow structures, specifically a shallow sandy sedimentary layer. The potential amplification of earthquake motion by sediments in this area, using this or other approaches, must be explored in depth by future projects. Potential site effects in Andújar are expectable, increasing the seismic hazard in this location, but presumably decreasing the afore-mentioned expectable

There are four fluvial terraces and the present flood plain in the Andújar area, with ele‐ vations above the river channel on the order of 55, 25, 13, and 6 m, from oldest to youngest [19,20]. These terraces comprise alluvial sediments from the Guadalquivir River with thicknesses ranging from approximately 5 to 10 m. They show a conglomeratic lith‐ ology with a silty mud-matrix that becomes sandy mud-matrix at the top of each terrace level. In general, the lower part of the terraces portrays the channel infilling and bar bed‐ form, and the upper part shows the alluvial flood plain. The ages of these terraces range

be taken as definitive proof for considering them to be the same event.

6 Earthquake Research and Analysis - New Advances in Seismology

the society.

an earthquake.

are not included.

magnitude for the Andújar earthquake.

from the Holocene to 600 ka.

The only shock that stands out in the area is the studied earthquake. Seismicity is very scarce near Andújar, which is characteristic of the northern Guadalquivir Basin. Even within the basin, only a few minor earthquakes (4.0 ≤ *M* ≤ 5.0) are located. This region is therefore considered to have a low seismic hazard [21]. In fact, the design acceleration (called basic acceleration) for a return period of 500 years in the Spanish building code [22] for Andújar is only 0.05g.

The work in reference [21], using the spatially smoothed seismicity approach, includes a model with the most significant earthquakes in the Iberian Peninsula over the last 300 years. On the other hand, the design acceleration considered in the Spanish building code was computed through a typical zonified method using a broad seismic zone including the whole Guadal‐ quivir Basin. Neither of these two assessments properly included the 1170 Andújar earthquake.

The only instrumental shock in this region deserving of mention is the March 10th, 1951 Linares earthquake (*MD* 4.8, VIII), 25 km NE of Andújar [23]. In a recent work [24] this event is reevaluated (*MS* 5.4, VI-VII, *h* = 30 km) and relocated to 20 km ESE of Andújar. These authors host this event at the base of the crust, in some deep fault near the southern boundary of the Paleozoic Iberian Massif related to the bending of the Paleozoic basement under the Neogene Guadalquivir Basin. More recently, in [25] has been reevaluated this earthquake once again (*MW* 5.2, *h* = 20 km), relocating it to 70 km SSW of Andújar (*i.e.*, distancing it from Andújar). In this last work, the authors cannot explain the known macroseismic intensity distribution for this event after the epicenter relocation. Neither is a tectonic origin proposed.

The presumed mesoseismal area of the Andújar earthquake (figures 1 and 3) involves three tectonic and geographic domains (figure 3). The first, just north of Andújar, is the Paleozoic Iberian Massif, structured during the Variscan orogeny. The Iberian Massif has a flat topog‐ raphy, with the exception of its southern edge, which has a smooth slope.

The second domain is the Guadalquivir Basin, which is a classic foreland basin [26] formed by the collision of the Internal Zones of the Betic Cordillera with the southern paleomargin of the Variscan Iberian Massif. The Andújar area is located on the north side of the basin, at the piedmont of Sierra Morena. This range, along the Variscan border, has recently been inter‐ preted as a flexural fore-bulge formed by the overload of the Betic chains above the Iberian crust [27].

The third tectonic domain is the frontal thrust belt (Subbetic and Prebetic) of the Betic Cordil‐ lera, which delineates an evident mountain front 40 km south of Andújar, a result of the aforesaid continental collision.

The most active stage of the continental collision occurred in the region between 20 and 7 Ma ago (Burdigalian-Tortonian) [28]. Nevertheless, there is clear evidence of recent tectonic activity along the Betic Mountain Front [29,30] that may account for its limited seismicity. This tectonic and regional seismic activity is probably related to the ongoing Africa-Iberia collision, with a convergence rate of 4-5 mm/year [31]. However, the Andújar region and the Betic

Another plausible seismic origin are the faults that fragmented the south Iberian crust during the Mesozoic, creating several blocks that produced swells and troughs in the marine paleo‐ margin [36]. These faults and their lateral ramps were tectonically inverted during the buildup of the Betic Cordillera (Miocene compression) and reutilized mainly as thrusts [37] until nowadays [38]. Thus, they continue to comprise crustal weak zones locally focusing the present crustal stress to host moderate earthquakes [30]. Most of these faults, seemingly with low slip rates, are now covered by the Guadalquivir Basin sediments (figures 1 and 3) and are difficult

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9

No Quaternary active faults have been described until now in the region and no clear limits can be traced at the lithospheric scale that could cluster the stress in the area. Nonetheless, any of the faults of these systems could explain a *MS* 6.0 earthquake such as the Andújar event. Further work should look for active faults bordering rigid crustal blocks of the Variscan basement accommodating some of the present convergence be‐

A recent unfinished archeological survey in the south of Andújar, as previously mentioned, has revealed the ruins of a fortification that underwent rebuilding (figure 4). We presume that

to recognize, even by geophysical exploration methods [39].

tween the Africa and Iberia plates.

**4. Archeological evidence**

these repairs are related to the 1170 earthquake.

**Figure 4.** Current general view of the archeological site.

**Figure 3.** Tectonic sketch of the study region.

Mountain Front are relatively far from the current plate boundary. On the other hand, the Betic thrusts in the area are relatively shallow and detached from the Variscan Basement through the plastic Triassic materials (Keuper). Keuper sediments are rich in clay and gypsum, displaying very plastic behavior and lacking enough strength to accumulate a large amount of stress. Nevertheless, active Betic thrusts can account for small shallow earthquakes along the Betic Mountain Front [30].

Other tectonic structures near Andújar capable of accumulating enough stress to trigger moderate earthquakes, or at least displaying geomorphologic evidence of recent tectonic activity must also be considered. One possible source of the 1170 earthquake is the flexure of the entire lithosphere. It can cause moderate to strong earthquakes [32], but only from the beginning of the orogenic overload (Lower Miocene) until viscoelastic stress relaxation and equilibrium was reached, a few million years ago [33]. However, the present intraplate compression could lead to the amplification of the initial flexural foreland loading [34,35] and consequently the reactivation of seismic faults.

Another plausible seismic origin are the faults that fragmented the south Iberian crust during the Mesozoic, creating several blocks that produced swells and troughs in the marine paleo‐ margin [36]. These faults and their lateral ramps were tectonically inverted during the buildup of the Betic Cordillera (Miocene compression) and reutilized mainly as thrusts [37] until nowadays [38]. Thus, they continue to comprise crustal weak zones locally focusing the present crustal stress to host moderate earthquakes [30]. Most of these faults, seemingly with low slip rates, are now covered by the Guadalquivir Basin sediments (figures 1 and 3) and are difficult to recognize, even by geophysical exploration methods [39].

No Quaternary active faults have been described until now in the region and no clear limits can be traced at the lithospheric scale that could cluster the stress in the area. Nonetheless, any of the faults of these systems could explain a *MS* 6.0 earthquake such as the Andújar event. Further work should look for active faults bordering rigid crustal blocks of the Variscan basement accommodating some of the present convergence be‐ tween the Africa and Iberia plates.

#### **4. Archeological evidence**

Mountain Front are relatively far from the current plate boundary. On the other hand, the Betic thrusts in the area are relatively shallow and detached from the Variscan Basement through the plastic Triassic materials (Keuper). Keuper sediments are rich in clay and gypsum, displaying very plastic behavior and lacking enough strength to accumulate a large amount of stress. Nevertheless, active Betic thrusts can account for small shallow earthquakes along

Other tectonic structures near Andújar capable of accumulating enough stress to trigger moderate earthquakes, or at least displaying geomorphologic evidence of recent tectonic activity must also be considered. One possible source of the 1170 earthquake is the flexure of the entire lithosphere. It can cause moderate to strong earthquakes [32], but only from the beginning of the orogenic overload (Lower Miocene) until viscoelastic stress relaxation and equilibrium was reached, a few million years ago [33]. However, the present intraplate compression could lead to the amplification of the initial flexural foreland loading [34,35] and

the Betic Mountain Front [30].

**Figure 3.** Tectonic sketch of the study region.

8 Earthquake Research and Analysis - New Advances in Seismology

consequently the reactivation of seismic faults.

A recent unfinished archeological survey in the south of Andújar, as previously mentioned, has revealed the ruins of a fortification that underwent rebuilding (figure 4). We presume that these repairs are related to the 1170 earthquake.

**Figure 4.** Current general view of the archeological site.

This archeological dig proves the existence of an early alcazar built in the 11th century, in the taifa-Almoravid stage, used approximately until the first half of the 12th century. In this epoch, it was replaced by a new alcazar located in the northern part of the town, built in the second half of the 12th and first half of the 13th centuries. After this, the early and obsolete alcazar was used only as a guard gate and control point of one of the main gateways (figure 5).

and another more complex one to the south (figure 5). This second tower had a room inside

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**Figure 6.** Details of the rectangular building within walls (3a and 3b in figure 5). Ordered fallen blocks of the collapsed

with a flat roof connecting the wall walks.

wall are visible over the rubble bench.

**Figure 5.** Reconstruction of the taifa-Almoravid (top) and *Ibn Hamusk*-Almohad (bottom) remains in the archeological site. 1a. Northern square solid tower. 1b. Reinforcement at the foundation of the tower. 2a. Southern complex tower. 2b. Reconstructed northwestern corner of tower. 3a. Rectangular building with adobe pillars. 3b. Reconstructed build‐ ing, now including a dividing wall. 4. Gateway (Alcazar gateway). 5. Ramparts. 6. Western tower. 7. Courtyard. 8. Tow‐ er gate.

The defensive walls and towers of the early alcazar were built using a matrix of lime, sand, and small stones outside, and dirt and rubbish inside. This construction technique is unques‐ tionably quick and cheap. However, although fillings of dirt and rubbish involve lower cost they also entail structural weakness, particularly for ground shaking during earthquakes. Two towers were excavated during the archeological survey, a small solid square tower to the north and another more complex one to the south (figure 5). This second tower had a room inside with a flat roof connecting the wall walks.

This archeological dig proves the existence of an early alcazar built in the 11th century, in the taifa-Almoravid stage, used approximately until the first half of the 12th century. In this epoch, it was replaced by a new alcazar located in the northern part of the town, built in the second half of the 12th and first half of the 13th centuries. After this, the early and obsolete alcazar was used only as a guard gate and control point of one of the main gateways (figure 5).

10 Earthquake Research and Analysis - New Advances in Seismology

**Figure 5.** Reconstruction of the taifa-Almoravid (top) and *Ibn Hamusk*-Almohad (bottom) remains in the archeological site. 1a. Northern square solid tower. 1b. Reinforcement at the foundation of the tower. 2a. Southern complex tower. 2b. Reconstructed northwestern corner of tower. 3a. Rectangular building with adobe pillars. 3b. Reconstructed build‐ ing, now including a dividing wall. 4. Gateway (Alcazar gateway). 5. Ramparts. 6. Western tower. 7. Courtyard. 8. Tow‐

The defensive walls and towers of the early alcazar were built using a matrix of lime, sand, and small stones outside, and dirt and rubbish inside. This construction technique is unques‐ tionably quick and cheap. However, although fillings of dirt and rubbish involve lower cost they also entail structural weakness, particularly for ground shaking during earthquakes. Two towers were excavated during the archeological survey, a small solid square tower to the north

er gate.

**Figure 6.** Details of the rectangular building within walls (3a and 3b in figure 5). Ordered fallen blocks of the collapsed wall are visible over the rubble bench.

Inside the alcazar, there was a large courtyard or ward where a simple rectangular building was probably used as a storehouse and/or kitchen (figures 5 and 6). The fact that it is not decorated suggests that it was not a room belonging to a palace or a residence. This building, attached to the eastern rampart, is 6.15 m wide, with an ashlar wall 1 m wide parallel to the rampart. The total length of this building is not completely known at the moment because the ends have not yet been excavated. Inside the building were found adobe pillars in a central position, probably related to the inward division and the roof support. Also, a rubble bench attached to the ashlar wall. The building was likely a space without interior walls divided into two rooms separated only by central pillars. These pillars held up central beams forming part of a roof of wood and tiles.

The southern tower (figures 8 and 9) was also damaged. Specifically, its northwest corner was destroyed, likely the weakest part due to the opening of the gate. It was repaired, replacing the mud-wall by a tamped dirt wall, remodelling and decreasing the room inside it. The

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13

**Figure 8.** Details of the southern complex tower (2a in figure 5) showing the reconstructed corner. View from the

The rectangular building inside the alcazar underwent near-total collapse (figure 6). The archeological dig found that the unattached western wall (1 m wide) of this building toppled inwards, to the east, and the fallen blocks are aligned the length of the wall. Fallen rocks tumbled on the rubble bench attached to the wall and on the floor. After the collapse, instead of cleaning out the blocks to the original floor, only a shallow cleaning was made. Therefore, collapsed blocks were buried, raising the level for a new floor. Moreover, previous pillars, likely very damaged or collapsed, were replaced by a dividing wall parallel to the fortification and to the front. From this dividing wall, the room was partitioned into four compartments

courtyard.

after its reconstruction.

remodelled tower shows support with medium-sized rocks, barely preserved.

The 1170 earthquake affected (figure 5) both the fortification and the attached building, as we show below.

The northern tower was heavily damaged. In fact, later reinforcement of its foundation can be observed (figure 7). The reinforcement was made by means of a wall of tamped dirt 0.4 m wide and 1.1 m high surrounding the tower at a distance of 1.6 m. The space between the tower and the wall was filled in with cobblestones, two layers of dirt, and another of adobe. At present, the reinforcement can be clearly seen only in the southern part of the tower, but it apparently bordered the entire tower. Thus, the final surface of the tower was quite extended.

**Figure 7.** Detail of the uncovered reinforcement at the foundation of the northern tower (1b in figure 5).

The southern tower (figures 8 and 9) was also damaged. Specifically, its northwest corner was destroyed, likely the weakest part due to the opening of the gate. It was repaired, replacing the mud-wall by a tamped dirt wall, remodelling and decreasing the room inside it. The remodelled tower shows support with medium-sized rocks, barely preserved.

Inside the alcazar, there was a large courtyard or ward where a simple rectangular building was probably used as a storehouse and/or kitchen (figures 5 and 6). The fact that it is not decorated suggests that it was not a room belonging to a palace or a residence. This building, attached to the eastern rampart, is 6.15 m wide, with an ashlar wall 1 m wide parallel to the rampart. The total length of this building is not completely known at the moment because the ends have not yet been excavated. Inside the building were found adobe pillars in a central position, probably related to the inward division and the roof support. Also, a rubble bench attached to the ashlar wall. The building was likely a space without interior walls divided into two rooms separated only by central pillars. These pillars held up central beams forming part

The 1170 earthquake affected (figure 5) both the fortification and the attached building, as we

The northern tower was heavily damaged. In fact, later reinforcement of its foundation can be observed (figure 7). The reinforcement was made by means of a wall of tamped dirt 0.4 m wide and 1.1 m high surrounding the tower at a distance of 1.6 m. The space between the tower and the wall was filled in with cobblestones, two layers of dirt, and another of adobe. At present, the reinforcement can be clearly seen only in the southern part of the tower, but it apparently

bordered the entire tower. Thus, the final surface of the tower was quite extended.

**Figure 7.** Detail of the uncovered reinforcement at the foundation of the northern tower (1b in figure 5).

of a roof of wood and tiles.

12 Earthquake Research and Analysis - New Advances in Seismology

show below.

**Figure 8.** Details of the southern complex tower (2a in figure 5) showing the reconstructed corner. View from the courtyard.

The rectangular building inside the alcazar underwent near-total collapse (figure 6). The archeological dig found that the unattached western wall (1 m wide) of this building toppled inwards, to the east, and the fallen blocks are aligned the length of the wall. Fallen rocks tumbled on the rubble bench attached to the wall and on the floor. After the collapse, instead of cleaning out the blocks to the original floor, only a shallow cleaning was made. Therefore, collapsed blocks were buried, raising the level for a new floor. Moreover, previous pillars, likely very damaged or collapsed, were replaced by a dividing wall parallel to the fortification and to the front. From this dividing wall, the room was partitioned into four compartments after its reconstruction.

the thorniest aspects of archeoseismology: to ascribe to historical attested earthquakes

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15

For this shock in southern Spain, only historical/documentary records have been available until now. Initially, a review of the scarce contemporary manuscripts was done, estimating some effects and justifying the presumed size. Then, damaged archeological structures and different repairs and reinforcements revealed in an archeological survey are proposed as true earthquake-related damages. In this case, in addition to the observed reinforcements and damages, there is the supporting evidence [42] of the historical record. We are confident that repairs and reinforcements in the two discovered and excavated towers, as well as the remodelling of a building attached to the rampart, including tumbled blocks along the length of its wall, are archeoseismological evidence. But it is still not possible from these effects to derive a better earthquake intensity estimate than that from contemporary manuscripts. In any case, we expect further results in future surveys, trusting that the site preserves additional

The question still remains as to which geological structure hosted this shock. As discussed above, with no more plausible candidates, we suggest hidden faults bordering blocks of the

Evidently, additional historical, archeological, and geological studies must be undertaken to

Anyone who saw with his own eyes the earthquake which occurred at Córdoba in the year 566 [September 14th, 1170 - September 3th, 1171] has received confirmation [of the Aristotelian theory of earthquakes]. I was not at Córdoba at the time, and when I arrived, I heard the rumble which preceded the earthquake; people thought the rumble came from the west. I saw the earthquake being generated by the progressive movement of west winds. These earthquakes persisted at Córdoba throughout the year, and only ceased after about three years. The first earthquake caused great destruction and killed many people; it was said that at a place near Córdoba called Andujira [Andújar], the earthquake caused the earth to split open and something similar to ashes and sand came out of the fissure. To the east of Córdoba the effects

estimate the size, effects and future implications of this earthquake.

source: *Taljīs kutub Aristātālīs fīl-Hikma*. Cairo National Library

were even more violent, whereas they were slighter to the west.

author: *Abû l-Walîd Muhammad Ibn Ahmad*, *Ibn Rushd* (the grandson) or *Averroes*

observed damages or effects in archaeological digs.

traces of seismic activity in the ground.

basement as the most likely hypothesis.

**Appendix**

Manuscript number 1

Manuscript number 2

transcription: reference [43]

used translation: references [12,44]

**Figure 9.** Details of the southern complex tower (2a in figure 5), showing the reconstructed corner. Opposite view of figure 8. 1. Early taifa-Almoravid wall and tower. 2. Reconstructed Ibn Hamusk-Almohad tower. 3. Christian period.

Some authors have used ordered fallen blocks as seismic-related kinematic indicators [40,41], among others effects, in order to determine, for example, the direction of seismic wave propagation or the degree of seismic shaking. In our case, the occurrence of just one episode unfortunately does not allow any conclusions to be inferred.

Since that time, this defensive complex likely had other functions, mainly as dwellings with rooms, kitchens, stables, and so on, as inferred from the archeological material found. This new use is supported by the fact that in the Almohad epoch, as noted previously, the alcazar was relocated to the northern part of the town, in a more strategic site [4].

Until now, these damages, reconstructions, and reinforcements could not be accurately dated. In any case, the fact that they occurred during the The *Ibn Hamusk*-Almohad stage (the second half of the 12th and the beginning of the 13th centuries), together with the documented date of the Andújar earthquake and the fact that no other likely historical explanation exists, supports a link between damages and the shock.

#### **5. Summary and conclusions**

In this paper we have presented a case study in seismic archeology that we believe to be the first likely archeological evidence of the 1170 Andújar earthquake. This case concerns one of the thorniest aspects of archeoseismology: to ascribe to historical attested earthquakes observed damages or effects in archaeological digs.

For this shock in southern Spain, only historical/documentary records have been available until now. Initially, a review of the scarce contemporary manuscripts was done, estimating some effects and justifying the presumed size. Then, damaged archeological structures and different repairs and reinforcements revealed in an archeological survey are proposed as true earthquake-related damages. In this case, in addition to the observed reinforcements and damages, there is the supporting evidence [42] of the historical record. We are confident that repairs and reinforcements in the two discovered and excavated towers, as well as the remodelling of a building attached to the rampart, including tumbled blocks along the length of its wall, are archeoseismological evidence. But it is still not possible from these effects to derive a better earthquake intensity estimate than that from contemporary manuscripts. In any case, we expect further results in future surveys, trusting that the site preserves additional traces of seismic activity in the ground.

The question still remains as to which geological structure hosted this shock. As discussed above, with no more plausible candidates, we suggest hidden faults bordering blocks of the basement as the most likely hypothesis.

Evidently, additional historical, archeological, and geological studies must be undertaken to estimate the size, effects and future implications of this earthquake.

### **Appendix**

**Figure 9.** Details of the southern complex tower (2a in figure 5), showing the reconstructed corner. Opposite view of figure 8. 1. Early taifa-Almoravid wall and tower. 2. Reconstructed Ibn Hamusk-Almohad tower. 3. Christian period.

Some authors have used ordered fallen blocks as seismic-related kinematic indicators [40,41], among others effects, in order to determine, for example, the direction of seismic wave propagation or the degree of seismic shaking. In our case, the occurrence of just one episode

Since that time, this defensive complex likely had other functions, mainly as dwellings with rooms, kitchens, stables, and so on, as inferred from the archeological material found. This new use is supported by the fact that in the Almohad epoch, as noted previously, the alcazar

Until now, these damages, reconstructions, and reinforcements could not be accurately dated. In any case, the fact that they occurred during the The *Ibn Hamusk*-Almohad stage (the second half of the 12th and the beginning of the 13th centuries), together with the documented date of the Andújar earthquake and the fact that no other likely historical explanation exists,

In this paper we have presented a case study in seismic archeology that we believe to be the first likely archeological evidence of the 1170 Andújar earthquake. This case concerns one of

unfortunately does not allow any conclusions to be inferred.

14 Earthquake Research and Analysis - New Advances in Seismology

supports a link between damages and the shock.

**5. Summary and conclusions**

was relocated to the northern part of the town, in a more strategic site [4].

Manuscript number 1

author: *Abû l-Walîd Muhammad Ibn Ahmad*, *Ibn Rushd* (the grandson) or *Averroes*

source: *Taljīs kutub Aristātālīs fīl-Hikma*. Cairo National Library

transcription: reference [43]

used translation: references [12,44]

Anyone who saw with his own eyes the earthquake which occurred at Córdoba in the year 566 [September 14th, 1170 - September 3th, 1171] has received confirmation [of the Aristotelian theory of earthquakes]. I was not at Córdoba at the time, and when I arrived, I heard the rumble which preceded the earthquake; people thought the rumble came from the west. I saw the earthquake being generated by the progressive movement of west winds. These earthquakes persisted at Córdoba throughout the year, and only ceased after about three years. The first earthquake caused great destruction and killed many people; it was said that at a place near Córdoba called Andujira [Andújar], the earthquake caused the earth to split open and something similar to ashes and sand came out of the fissure. To the east of Córdoba the effects were even more violent, whereas they were slighter to the west.

Manuscript number 2

author: *'Abd al-Malik b. Muhammad b. Ibn Sāhib al-Salā*

source: History of the Almohad Caliphate. Manuscript number 433. Bodleian Library. Oxford University

**Author details**

C. López Casado6

**References**

J.A. Peláez1\*, J.C. Castillo2

, F. Gómez Cabeza3

\*Address all correspondence to: japelaez@ujaen.es

1 Dpt. of Physics, University of Jaén, Jaén, Spain

4 Dpt. of Geology, University of Jaén, Jaén, Spain

1952; XVII 155-166 (*in Spanish*).

Vol. III, p276-291 (*in Spanish*).

Spain (*in Spanish*).

2 Dpt. of Historical Heritage, University of Jaén, Jaén, Spain

3 CAAI (Andalusian Center of Iberian Archaeology), Jaén, Spain

6 Dpt. of Theoretical Physics, University of Granada, Granada, Spain

1989. Sevilla, Spain: 1991. Vol. III, p319-327 (*in Spanish*).

Madrid: Instituto Geográfico Nacional; 2002 (*in Spanish*).

5 Section of Geophysics, IGN (National Geographical Institute), Madrid, Spain

[1] Guraieb JE. Al-Muqtabis de Ibn Hayyan (translation). Cuadernos de Historia de España

[2] Salvatierra V, Castillo JC, Pérez MC, Castillo JL. The urban development in al-Andalus: The case of Andújar (Jaén). Cuadernos de Madinat al Zahra' 1991; 2 85-107 (*in Spanish*).

[3] Choclán C, Castillo JC. Immediate archaeological excavation in a property at 3 San Francisco St. and 12 Juan Robledo St., Andújar. In: Anuario Arqueológico de Andalucía,

[4] Castillo JC. Immediate archaelogical excavation carried out in a property located between the Alcázar, Altozano Deán Pérez de Vargas and Parras streets, in the town of Andújar (Jaén). In: Anuario Arqueológico de Andalucía, 1989. Sevilla, Spain: 1991.

[6] Peláez JA, Castillo JC, Sánchez Gómez M, Martínez Solares JM, López Casado C. The 1170 Andújar, Jaén, earthquake. A critical review. In: proceedings of the Fifth Spanish-Portuguese Meeting on Geodesy and Geophysics, 30 January - 3 February 2006, Sevilla,

[7] Martínez Solares JM, Mezcua J. Seismic catalog of the Iberian Peninsula (880 B.C.-1900).

[5] Eslava J. Castles in Jaén. Jaén, Spain: University of Jaén; 1999 (*in Spanish*).

, M. Sánchez Gómez4

A Review of the 1170 Andújar (Jaén, South Spain) Earthquake, Including the First Likely Archeological Evidence

, J.M. Martínez Solares5

http://dx.doi.org/10.5772/54864

and

17

used transcription and translation: reference [13]

In the same year, the rain for the laid fields in al-Andalus was delayed until the Christian month of December, 1169, and [then] it rained and people sown. In this year big earthquakes hap‐ pened at dawn and when noon declined in the month of *Ŷumadā al-ūlà* in the year that we chronicle [January 21th to February 19th, 1170], and they continued in the Andújar town for several days, until it almost dissapeared, and it was swallowed by the ground, and they continued, after this, in the Córdoba, Granada and Sevilla cities, and all *Al-Andalus*, and the eyewitness saw that walls of the houses shaken and sloped towards the ground, then they straighten and return to its position by the goodness of *Allah*, and because of that a lot of houses were destroyed in the quoted regions, and the minarets of the mosques.

Manuscript number 3

author: *Ibn 'Idārī*

source: *Al-Bayān al-Mugrib*. Manuscript discovered in a Koranic school in Tamagrūt, near Zagora, in the Draa Valley (Morocco)

used transcription and translation: reference [45]

In this year, a big earthquake happened, at dawn and at the end of the month of *Ŷumadā alūlà*, in part of *Al-Andalus*; the eyewitness sawn that walls were shaken and sloped towards the ground, but then they straighten and return to its position by the goodness of *Allah*. A lot of houses and minarets were destroyed in the Córdoba, Granada and Sevilla cities.

Manuscript number 4

source: vanished codex

used transcription: reference [15]

Toledo was shaken on February XVIII, MCCVII [February 18th, 1169] [The quoted data in the text concern to the Spanish or Hispanic era, or Era of the Caesars, beginning in the year 38 B.C.].

#### **Acknowledgements**

This work was mainly supported by the Seismic Hazard and Microzonation Spanish research group. The authors are grateful to Emanuela Guidoboni for their constructive comments in an early version of this manuscript.

#### **Author details**

author: *'Abd al-Malik b. Muhammad b. Ibn Sāhib al-Salā*

16 Earthquake Research and Analysis - New Advances in Seismology

used transcription and translation: reference [13]

University

Manuscript number 3

Manuscript number 4

source: vanished codex

**Acknowledgements**

early version of this manuscript.

B.C.].

used transcription: reference [15]

Zagora, in the Draa Valley (Morocco)

used transcription and translation: reference [45]

author: *Ibn 'Idārī*

source: History of the Almohad Caliphate. Manuscript number 433. Bodleian Library. Oxford

In the same year, the rain for the laid fields in al-Andalus was delayed until the Christian month of December, 1169, and [then] it rained and people sown. In this year big earthquakes hap‐ pened at dawn and when noon declined in the month of *Ŷumadā al-ūlà* in the year that we chronicle [January 21th to February 19th, 1170], and they continued in the Andújar town for several days, until it almost dissapeared, and it was swallowed by the ground, and they continued, after this, in the Córdoba, Granada and Sevilla cities, and all *Al-Andalus*, and the eyewitness saw that walls of the houses shaken and sloped towards the ground, then they straighten and return to its position by the goodness of *Allah*, and because of that a lot of houses

source: *Al-Bayān al-Mugrib*. Manuscript discovered in a Koranic school in Tamagrūt, near

In this year, a big earthquake happened, at dawn and at the end of the month of *Ŷumadā alūlà*, in part of *Al-Andalus*; the eyewitness sawn that walls were shaken and sloped towards the ground, but then they straighten and return to its position by the goodness of *Allah*. A lot of

Toledo was shaken on February XVIII, MCCVII [February 18th, 1169] [The quoted data in the text concern to the Spanish or Hispanic era, or Era of the Caesars, beginning in the year 38

This work was mainly supported by the Seismic Hazard and Microzonation Spanish research group. The authors are grateful to Emanuela Guidoboni for their constructive comments in an

houses and minarets were destroyed in the Córdoba, Granada and Sevilla cities.

were destroyed in the quoted regions, and the minarets of the mosques.

J.A. Peláez1\*, J.C. Castillo2 , F. Gómez Cabeza3 , M. Sánchez Gómez4 , J.M. Martínez Solares5 and C. López Casado6


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A Review of the 1170 Andújar (Jaén, South Spain) Earthquake, Including the First Likely Archeological Evidence

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and rheology: neotectonic controls on Europe's intraplate continental topography. Quaternary Science Reviews 2005; 24 241-304.

**Chapter 2**

**Global Climatic Changes, a Possible Cause of the Recent**

Over 1 million earthquakes a year can be felt by people on Earth. Large earthquakes and related effects rank among most catastrophic environmental events. Both tectonically active areas of lithospheric plates interactions along their boundaries and intra-plate fault displacements are responsible for rupture yielding seismic waves that shake the ground. Devastating effects of the earthquakes that occurred during the last decades underlines the necessity of a multi-hazard approach regarding the subsequent effect of the tremor waves, such as tsunami waves (Sumatra – Andaman Islands, 2004, NE Japan 2011), soil subsi‐ dence and major accidents at nearby chemical facilities (Turkye, Kocaeli, 1999), explosions at petrochemical and nuclear plant, after failure of the cooling system due to power failure, following the 10 meters tsunami wave (NE Japan 2011), submarine landslides (northern coast of Papua New Guinea, 1998), or landslides and soil liquefaction ("earthquake lake" at Sichuan, China, 2008, Christchurch, New Zeeland, 2011). The multi-hazard concept represents a new direction of research in an integrated manner, with applied global implications. The frequency of the disasters appears to increase in the last decades (Fig. 1,2), and the communities became more vulnerable to the natural hazards, generally due to the complex aspects generated by increased urbanization, land planning and environmental changes. The uncertainties involving the relations between different components of the surrounding environment made more difficult the investigation of each category of natural hazards [1]. Consequently it is necessary to study groups of hazards, not just a single case, and the interaction among them in order to have a clear view of the internal processes and causative factors of the disasters. From this point of view, the disaster seems to be more

> © 2013 Mara and Vlad; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Mara and Vlad; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Increasing Trend of Earthquakes Since the 90's and**

**Subsequent Lessons Learnt**

http://dx.doi.org/10.5772/55713

**1. Introduction**

Septimius Mara and Serban-Nicolae Vlad

Additional information is available at the end of the chapter


## **Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of Earthquakes Since the 90's and Subsequent Lessons Learnt**

Septimius Mara and Serban-Nicolae Vlad

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/55713

#### **1. Introduction**

and rheology: neotectonic controls on Europe's intraplate continental topography.

[36] Vera JA. Evolution of the South Iberian Continental Margin. Mémories Musseum

[37] Azañón JM, Galindo Zaldíbar J, García Dueñas V, Jabaloy A. Alpine tectonics II: Betic Cordillera and Balearic Islands. In: Gibbons W, Moreno T (eds.) Geology of Spain.

[38] García Tortosa FJ, Sanz de Galdeano C, Sánchez Gómez M, Alfaro P. Recent tectonics in the Betic thrust front. The Jimena and Bedmar deformations (Jaén province, Spain).

[39] Ruano P, Galindo Zaldívar J, Jabaloy A. Recent tectonic structures in a transect of the Central Betic Cordillera. Pure and Applied Geophysics 2004; 161 541-563.

[40] Omuraliev M, Korjenkov A, Mamyrov E. Location of earthquake epicenters by nontraditional seismologic data. In: proceedings of the III Seminar "Non-Traditional Methods of Heterogeneity Study of the Earth Crust", Moscow, Russia. 1993 (*in Russian*).

[41] Korjenkov AM, Mazor E. Seismogenic origin of the ancient Avdat ruins, Negev Desert,

[42] Marco S. Recognition of earthquake-related damage in archaeological sites: Examples

[43] Allah SF, Razik SA, editors (1994). Al-jawâmi\_'fî l-falsafa: Kitâb al-âthâr al-'ulwîya.

[44] Puig J (1998). Averroes, judge, physician, and Andalusian philosopher. Sevilla: Consejería de Educación y Ciencia (Junta de Andalucía); 1998 (*in Spanish*).

[45] Huici A. Ibn 'Idari: Al-Bayān al-Mugrib. New Almoravid and Almohad fragments.

from the Dead Sea fault zone. Tectonophysics 2008; 453 148-156.

Valencia: Medieval texts collection, number 8; 1963 (*in Spanish*)

Quaternary Science Reviews 2005; 24 241-304.

20 Earthquake Research and Analysis - New Advances in Seismology

National Histoire Naturelle 2001; 186 109-143.

London: Geological Society; 2002. p401-416.

Geogaceta 2007; 44 59-62 (*in Spanish*).

Israel. Natural Hazards 1999; 18 193-226.

Cairo; 1994.

Over 1 million earthquakes a year can be felt by people on Earth. Large earthquakes and related effects rank among most catastrophic environmental events. Both tectonically active areas of lithospheric plates interactions along their boundaries and intra-plate fault displacements are responsible for rupture yielding seismic waves that shake the ground. Devastating effects of the earthquakes that occurred during the last decades underlines the necessity of a multi-hazard approach regarding the subsequent effect of the tremor waves, such as tsunami waves (Sumatra – Andaman Islands, 2004, NE Japan 2011), soil subsi‐ dence and major accidents at nearby chemical facilities (Turkye, Kocaeli, 1999), explosions at petrochemical and nuclear plant, after failure of the cooling system due to power failure, following the 10 meters tsunami wave (NE Japan 2011), submarine landslides (northern coast of Papua New Guinea, 1998), or landslides and soil liquefaction ("earthquake lake" at Sichuan, China, 2008, Christchurch, New Zeeland, 2011). The multi-hazard concept represents a new direction of research in an integrated manner, with applied global implications. The frequency of the disasters appears to increase in the last decades (Fig. 1,2), and the communities became more vulnerable to the natural hazards, generally due to the complex aspects generated by increased urbanization, land planning and environmental changes. The uncertainties involving the relations between different components of the surrounding environment made more difficult the investigation of each category of natural hazards [1]. Consequently it is necessary to study groups of hazards, not just a single case, and the interaction among them in order to have a clear view of the internal processes and causative factors of the disasters. From this point of view, the disaster seems to be more

internationalized, due to global factors which interact and affect the population and the environmental factors.

earthquake on Richter scale, where is produced, depending of the distance from the source. Therefore the data taken into consideration in the present earthquake evaluation includes just important earthquakes, which can produce significant damage (above level of stronger earthquakes, with the magnitude over 6 on Richter scale). As a conclusion, the thesis stipulating that just in the recent year the global network of seismographs was completed and that's why we have the "felling" of an increased trend of the earthquakes, and therefore the study of the past earthquake data didn't reflect complete the reality, because of "missing" earthquake, is falls. According with this theory, the same increasing pattern of the earthquakes should be observed since 80's, but as observed in the evolution trend of the similar earthquake magni‐ tudes over each separate decade (in 80's and 90's), are significantly different, in both of magnitudes range and increasing trend from one year to another (please see below Fig.1.a-d, of evolution including subsequent linear trends). Should be noticed that only for the decade 1980-1990, the trend line is decreasing, compared with the period intervals of 1990-2000 and 2000-2010, when the evolution trend of earthquake frequency and magnitude, in visible

Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of…

http://dx.doi.org/10.5772/55713

23

increasing.

(b)

(a)

)

#### **2. Problem statement**

Recently it became relevant that, despite frequent large earthquakes, several countries located in prone areas didn't have strong building codes and many houses are built out of mud bricks and un-reinforced masonry, which do not stand up well to earthquakes. Mud brick didn't resist to the earthquake stress and too heavy tile and cement roofs generally collapsed into many houses. Other factors contribute to the severity of a quake, but earthquake resistant buildings can make a huge difference in the number of damages [2]. As a result, casualties and damage are much higher than similar earthquakes elsewhere in the world. Therefore recent major earthquakes such as Guarajat, India (2001), Bam-Iran (2003), Sumatra – Andaman Islands (2004), Kashmir-Pakistan (2005), South of Java – Indonesia (2006) or Sichuan, China (2008) led to heavy human casualties, compared with other similar earthquakes all over the world. The same magnitude earthquakes, for example the Northridge quake in Los Angeles in 1994 killed only 57 people and in Kobe Japan in 1995 a similar quake killed about 5,000. Another example could be the earthquake –magnitude 7 - from Haiti, at Port-au-Prince in January 2010, with almost 220,000 casualties compared with a similar earthquake in the next month, in Chile, magnitude 8.8, 500 times higher than the previous one in Haiti, resulted in less than 600 casualties. In case of major tsunamis, which cross an entire Ocean, or so called "tele-tsunamis", i.e the greater earthquake ever recorded by instruments, with a 9.5 magnitude, in Valvidia, Chile (1960), which produced damage in Hawaii and alarm in Japan, it became obviously the "globalisation" of the subsequent effects of the tremors. They can reach any coastal areas all over the world, not necessarily earthquake prone areas, and request dedicated building codes. A similar effect took place following the recent great earthquakes at Sumatra – Andaman Islands (2004), 9.1 magnitude, with damages 1 mile inside the affected coastal areas, with a maximum height of the tsunami wave up to 30m, or the recent NE of Japan (2011), magnitude 9, where tsunami waves inflicted severe damages 9 miles inside the coast areas. The recent catastrophe in Japan exceeds the worst case scenarios previously estimated in prevention measures, especially at the nuclear plants. The maximum possible height of a tsunami wave was estimated at 6 meters high, whereas the height of the wave reached 10 m (the maximum recorded height was 23m for the NE of Japan).

#### **3. Application area**

The present analysis is based on data regarding the earthquake frequency and magnitude the world over, (Fig. 2), i.e. USGS (United States Geological Service) data base during the last 30 years [4]. It has to be specified that the earthquake monitoring activity network was used during the cold war [3], since 50's, to identify and localise nuclear tests all over the world, taking into account that a nuclear detonation is detected generally less than a 6 magnitude earthquake on Richter scale, where is produced, depending of the distance from the source. Therefore the data taken into consideration in the present earthquake evaluation includes just important earthquakes, which can produce significant damage (above level of stronger earthquakes, with the magnitude over 6 on Richter scale). As a conclusion, the thesis stipulating that just in the recent year the global network of seismographs was completed and that's why we have the "felling" of an increased trend of the earthquakes, and therefore the study of the past earthquake data didn't reflect complete the reality, because of "missing" earthquake, is falls. According with this theory, the same increasing pattern of the earthquakes should be observed since 80's, but as observed in the evolution trend of the similar earthquake magni‐ tudes over each separate decade (in 80's and 90's), are significantly different, in both of magnitudes range and increasing trend from one year to another (please see below Fig.1.a-d, of evolution including subsequent linear trends). Should be noticed that only for the decade 1980-1990, the trend line is decreasing, compared with the period intervals of 1990-2000 and 2000-2010, when the evolution trend of earthquake frequency and magnitude, in visible increasing.

internationalized, due to global factors which interact and affect the population and the

Recently it became relevant that, despite frequent large earthquakes, several countries located in prone areas didn't have strong building codes and many houses are built out of mud bricks and un-reinforced masonry, which do not stand up well to earthquakes. Mud brick didn't resist to the earthquake stress and too heavy tile and cement roofs generally collapsed into many houses. Other factors contribute to the severity of a quake, but earthquake resistant buildings can make a huge difference in the number of damages [2]. As a result, casualties and damage are much higher than similar earthquakes elsewhere in the world. Therefore recent major earthquakes such as Guarajat, India (2001), Bam-Iran (2003), Sumatra – Andaman Islands (2004), Kashmir-Pakistan (2005), South of Java – Indonesia (2006) or Sichuan, China (2008) led to heavy human casualties, compared with other similar earthquakes all over the world. The same magnitude earthquakes, for example the Northridge quake in Los Angeles in 1994 killed only 57 people and in Kobe Japan in 1995 a similar quake killed about 5,000. Another example could be the earthquake –magnitude 7 - from Haiti, at Port-au-Prince in January 2010, with almost 220,000 casualties compared with a similar earthquake in the next month, in Chile, magnitude 8.8, 500 times higher than the previous one in Haiti, resulted in less than 600 casualties. In case of major tsunamis, which cross an entire Ocean, or so called "tele-tsunamis", i.e the greater earthquake ever recorded by instruments, with a 9.5 magnitude, in Valvidia, Chile (1960), which produced damage in Hawaii and alarm in Japan, it became obviously the "globalisation" of the subsequent effects of the tremors. They can reach any coastal areas all over the world, not necessarily earthquake prone areas, and request dedicated building codes. A similar effect took place following the recent great earthquakes at Sumatra – Andaman Islands (2004), 9.1 magnitude, with damages 1 mile inside the affected coastal areas, with a maximum height of the tsunami wave up to 30m, or the recent NE of Japan (2011), magnitude 9, where tsunami waves inflicted severe damages 9 miles inside the coast areas. The recent catastrophe in Japan exceeds the worst case scenarios previously estimated in prevention measures, especially at the nuclear plants. The maximum possible height of a tsunami wave was estimated at 6 meters high, whereas the height of the wave reached 10 m (the maximum

The present analysis is based on data regarding the earthquake frequency and magnitude the world over, (Fig. 2), i.e. USGS (United States Geological Service) data base during the last 30 years [4]. It has to be specified that the earthquake monitoring activity network was used during the cold war [3], since 50's, to identify and localise nuclear tests all over the world, taking into account that a nuclear detonation is detected generally less than a 6 magnitude

environmental factors.

22 Earthquake Research and Analysis - New Advances in Seismology

**2. Problem statement**

recorded height was 23m for the NE of Japan).

**3. Application area**

**Figure 2. Earthquake trend evolution since 80's** (blue thick line represents the increased linear trend and the col‐

Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of…

http://dx.doi.org/10.5772/55713

25

The paper evaluate records of seismographs belonging to the international survey network over the last 30 years, assessing earthquakes frequency in order to detect evolution tendencies to be drawn. A simple linear correlation was used to categorize the trend of the seismic activity all over the world. Commonly the Earth seismic activity is almost constant in terms of frequency of earthquakes [3]. A possible increased tendency of earthquake activity was revealed studying the frequency of the principal earthquake types (such as: great, with the magnitude over 8, major with the magnitude of 7 - 7.9, and strong earthquake type of 6 - 6.9 magnitude on Richter scale), taking into consideration that an earthquake measuring 8 on the Richter scale is 10 times larger in term of ground motion than a 7 magnitude tremor, or 100 times larger than an earthquake measuring 6 magnitude, and so on. The results indicated an

oured lines the frequency evolution for each type of earthquake category, strong, major or great):

**4. Research course**

**Figure 1.** a. The strong earthquake type of 6 - 6.9 magnitude on Richter scale:b. The major earthquake type with the magnitude of 7 - 7.9 magnitude on Richter scale:c. The great earthquake type, with the magnitude over 8 magnitude on Richter scale:d. The great, major and strong earthquakes types, with the relative magnitude of 6-6.9 magnitude on Richter scale (combined).

Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of… http://dx.doi.org/10.5772/55713 25

**Figure 2. Earthquake trend evolution since 80's** (blue thick line represents the increased linear trend and the col‐ oured lines the frequency evolution for each type of earthquake category, strong, major or great):

#### **4. Research course**

**Figure 1.** a. The strong earthquake type of 6 - 6.9 magnitude on Richter scale:b. The major earthquake type with the magnitude of 7 - 7.9 magnitude on Richter scale:c. The great earthquake type, with the magnitude over 8 magnitude on Richter scale:d. The great, major and strong earthquakes types, with the relative magnitude of 6-6.9 magnitude on

Richter scale (combined).

24 Earthquake Research and Analysis - New Advances in Seismology

The paper evaluate records of seismographs belonging to the international survey network over the last 30 years, assessing earthquakes frequency in order to detect evolution tendencies to be drawn. A simple linear correlation was used to categorize the trend of the seismic activity all over the world. Commonly the Earth seismic activity is almost constant in terms of frequency of earthquakes [3]. A possible increased tendency of earthquake activity was revealed studying the frequency of the principal earthquake types (such as: great, with the magnitude over 8, major with the magnitude of 7 - 7.9, and strong earthquake type of 6 - 6.9 magnitude on Richter scale), taking into consideration that an earthquake measuring 8 on the Richter scale is 10 times larger in term of ground motion than a 7 magnitude tremor, or 100 times larger than an earthquake measuring 6 magnitude, and so on. The results indicated an unusual increased seismic activity since the 90's, which is in contradiction with the generally constant trend of the previous decade. Based on lessons-learning approach, the activity of implementation of an earthquake resilient activity worldwide at local, regional or national level in the areas prone to earthquakes have to be assured by taking into account valuable recommendations of the risk managers involved into decisional planning, as indicated in the research paper.

structural changes implemented over the lifecycles of schools or other public buildings which can weaken the building strength have to be avoided. Therefore an increased activity of inspection should be undertaken regularly, according with the building code in force, in order to interdict any possibility for improvisation or structural changes, mainly for the public buildings. In areas prone to natural hazards, including earthquakes and tsunamis, it is necessary to constantly review and implement the proper building codes for constructions. In particular, the presence of adobe-built houses or improvised makeshift shelters can become

Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of…

http://dx.doi.org/10.5772/55713

27

In the coastal areas prone to tsunamis, it is necessary to implement prevention measures such as structural ones: tsunamis walls, sea walls, beach-long protection wall, automatic and manual closing water gates, evacuation routes and signing, establishing safer distances between different land use categories and the coastal line, depending to their economical activity, for minimizing the impact of possible tsunamis, or inexpensive protective lines of trees and dense vegetation, by planting local resistant trees species (for example mangroves

In addition, non-structural measures involve elaboration of tsunami vulnerability and risk maps, implementation of building codes and land use planning in order to define safe areas, education of the population regarding the behaviour in case of a tsunami wave, implementa‐ tion of a seismic observation network system in relation to the possible detection of the tsunami generated by earthquakes, coupled with installation of alarming systems for the early warning of the population, studies for mapping the hazard vulnerability in the coastal areas character‐

Early disaster events could be further analysed having a look at underwater sedimentary deposits in order to get a full picture of the vulnerability (including the case of marine deltas where new settled sediments once loosing stability can trigger tsunamis waves on the nearby

Although relatively reduced vulnerability of Stromboli type island (prone to underground landslides due to volcano material flow during eruptions) could be high due to holiday seekers and volcano tourists. Therefore the continuous activities of the volcano should seriously be watched and appropriate vulnerability analyses be performed. The focus should be put on landslides and/or lava flows due to volcanic activities; in addition, a multi-hazard approach could be useful as small earthquakes and/or tremors together with landslides trigger local tsunamis whose potential of destruction should not be underestimated. In the case of Stromboli one could promote structural actions (enforcing parts of the shoreline) and non-structural actions (educating the local population and especially instructing non-residents like tourists of potential signs of tsunamis). In the particular case of Stromboli volcano, which is of small size and not flat, it would be more efficient to manage an easy but effective concept of earlywarning system (for ex., the use of loudspeakers, sirens) together with an evacuation system

that allows moving the local population towards safer places in extremely short time;

The recurrence maximum time period, taken into consideration by nuclear engineers for a tremor in relation with a nuclear facility, that is the 10,000 years quake event, does not

disastrous;

coastal areas);

in the tropical regions, coconut trees, etc.);

ized by intense socio-economical activity;

#### **5. Method used**

Decision makers begin to understand that to save lives, they have to adopt an integrated, comprehensive and multi-hazard strategy for disaster risk reduction, regardless the type of the disaster management procedure. This strategy includes prevention, mitigation, prepared‐ ness, response, recovery and rehabilitation, therefore the following lessons learnt can be drawn:

#### **5.1. Prevention measures**

The latest tragedies highlighted the importance of the addressing of public buildings (such as: hospitals, schools, fire-fighter units, etc.) in the national earthquake protection policies;

A multi-hazard approach (earthquake plus tsunami) should be envisaged when response actions are planned. For example, access routes could have survived the earthquake but not the impact of the tsunami or some areas may remain flooded and therefore not able for rescue operations;

The constructions located in earthquake prone areas, erected before the last building regulation was put into force, have to be inspected in case of not complying with the norms, then have to be retrofitted or rebuild. A special attention should be done for retrofitting the construction for the most vulnerable socio-economical activities, which in case of earth‐ quake could lead to severe loss of life, due to increased damages to the most vulnerable public areas (such as schools, fire-fighters units, hospitals, etc.), and interruption of public services (transportation, gas, electricity, water supply) by damaging the bridges, fall of power lines, pipelines rupture, etc;

The retrofitting works for all old buildings should take into account the new changing in the building resilience due to earthquake activity, taking into account the building codes for the specific earthquake area wherein the construction is located (for example, in Europe, the general rules for the assessment and strengthening of structures are available in the European Standard, Part 1-4 of Euro code 8, prEN 1998-3, and for other countries, the available guidelines in force). The designers and the constructors of the public units should pay more attention to structural issues;

As a result of the recent earthquakes, new building codes for earthquakes have to be introduced in the affected countries, including new seismic zoning of the whole country, with the purpose to improve the standards of building execution and maintenance. In addition, any dangerous structural changes implemented over the lifecycles of schools or other public buildings which can weaken the building strength have to be avoided. Therefore an increased activity of inspection should be undertaken regularly, according with the building code in force, in order to interdict any possibility for improvisation or structural changes, mainly for the public buildings. In areas prone to natural hazards, including earthquakes and tsunamis, it is necessary to constantly review and implement the proper building codes for constructions. In particular, the presence of adobe-built houses or improvised makeshift shelters can become disastrous;

unusual increased seismic activity since the 90's, which is in contradiction with the generally constant trend of the previous decade. Based on lessons-learning approach, the activity of implementation of an earthquake resilient activity worldwide at local, regional or national level in the areas prone to earthquakes have to be assured by taking into account valuable recommendations of the risk managers involved into decisional planning, as indicated in the

Decision makers begin to understand that to save lives, they have to adopt an integrated, comprehensive and multi-hazard strategy for disaster risk reduction, regardless the type of the disaster management procedure. This strategy includes prevention, mitigation, prepared‐ ness, response, recovery and rehabilitation, therefore the following lessons learnt can be

The latest tragedies highlighted the importance of the addressing of public buildings (such as: hospitals, schools, fire-fighter units, etc.) in the national earthquake protection policies;

A multi-hazard approach (earthquake plus tsunami) should be envisaged when response actions are planned. For example, access routes could have survived the earthquake but not the impact of the tsunami or some areas may remain flooded and therefore not able for rescue

The constructions located in earthquake prone areas, erected before the last building regulation was put into force, have to be inspected in case of not complying with the norms, then have to be retrofitted or rebuild. A special attention should be done for retrofitting the construction for the most vulnerable socio-economical activities, which in case of earth‐ quake could lead to severe loss of life, due to increased damages to the most vulnerable public areas (such as schools, fire-fighters units, hospitals, etc.), and interruption of public services (transportation, gas, electricity, water supply) by damaging the bridges, fall of power

The retrofitting works for all old buildings should take into account the new changing in the building resilience due to earthquake activity, taking into account the building codes for the specific earthquake area wherein the construction is located (for example, in Europe, the general rules for the assessment and strengthening of structures are available in the European Standard, Part 1-4 of Euro code 8, prEN 1998-3, and for other countries, the available guidelines in force). The designers and the constructors of the public units should pay more attention to

As a result of the recent earthquakes, new building codes for earthquakes have to be introduced in the affected countries, including new seismic zoning of the whole country, with the purpose to improve the standards of building execution and maintenance. In addition, any dangerous

research paper.

drawn:

operations;

**5. Method used**

26 Earthquake Research and Analysis - New Advances in Seismology

**5.1. Prevention measures**

lines, pipelines rupture, etc;

structural issues;

In the coastal areas prone to tsunamis, it is necessary to implement prevention measures such as structural ones: tsunamis walls, sea walls, beach-long protection wall, automatic and manual closing water gates, evacuation routes and signing, establishing safer distances between different land use categories and the coastal line, depending to their economical activity, for minimizing the impact of possible tsunamis, or inexpensive protective lines of trees and dense vegetation, by planting local resistant trees species (for example mangroves in the tropical regions, coconut trees, etc.);

In addition, non-structural measures involve elaboration of tsunami vulnerability and risk maps, implementation of building codes and land use planning in order to define safe areas, education of the population regarding the behaviour in case of a tsunami wave, implementa‐ tion of a seismic observation network system in relation to the possible detection of the tsunami generated by earthquakes, coupled with installation of alarming systems for the early warning of the population, studies for mapping the hazard vulnerability in the coastal areas character‐ ized by intense socio-economical activity;

Early disaster events could be further analysed having a look at underwater sedimentary deposits in order to get a full picture of the vulnerability (including the case of marine deltas where new settled sediments once loosing stability can trigger tsunamis waves on the nearby coastal areas);

Although relatively reduced vulnerability of Stromboli type island (prone to underground landslides due to volcano material flow during eruptions) could be high due to holiday seekers and volcano tourists. Therefore the continuous activities of the volcano should seriously be watched and appropriate vulnerability analyses be performed. The focus should be put on landslides and/or lava flows due to volcanic activities; in addition, a multi-hazard approach could be useful as small earthquakes and/or tremors together with landslides trigger local tsunamis whose potential of destruction should not be underestimated. In the case of Stromboli one could promote structural actions (enforcing parts of the shoreline) and non-structural actions (educating the local population and especially instructing non-residents like tourists of potential signs of tsunamis). In the particular case of Stromboli volcano, which is of small size and not flat, it would be more efficient to manage an easy but effective concept of earlywarning system (for ex., the use of loudspeakers, sirens) together with an evacuation system that allows moving the local population towards safer places in extremely short time;

The recurrence maximum time period, taken into consideration by nuclear engineers for a tremor in relation with a nuclear facility, that is the 10,000 years quake event, does not necessarily takes place after such a long period of time, and can occur anytime, even today or tomorrow, in the most earthquake prone areas all over the world, represented especially by the Pacific ring of fire, where the recent great earthquakes occurred;

for increasing the preparedness capacity. Population should be also involved in the training drills, in order to become aware of the basic rules of survival and for recovery actions, to assure a better cooperation with the local authorities involved in the disaster mitigation activities;

Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of…

http://dx.doi.org/10.5772/55713

29

The damage assessment scenarios for inhabited areas located in tsunami prone areas, on the coastal lines, will re-evaluate the mitigation capabilities in case of a real disaster and lead to a

Countries located in tsunamis vulnerable areas should set their own national tsunami warning system, capable to watch and warn in due time the local inhabitants about any danger of producing a catastrophic event occurring nearby the inhabited area. For maintaining the awareness and the response capability of an already implemented tsunami warning system, simulation exercises should be periodically organized. Different responsibilities and tasks of the emergency personal involved in monitoring activities are reviewed, assuring the commu‐ nication in real time of the emergency relief cruses about the probabilities of producing the

The existence of the emergency stock of materials and means of interventions, located in the vicinity of the prone areas of natural hazards, including tsunamis, allows an optimized relief activity after a disaster in the region, assuring a successful intervention activity and minimi‐ zation of loss of lives and damages to the properties. It is crucial to have sufficient stock (including tents, blankets, medicine) available in order to support people that have fled from

An efficient preparedness measure depends of timely early warnings issued by the authorities following an earthquake with high magnitude, which often constitute the triggering factor for

Area that had been affected by similar events in the past should create a disaster prevention platform; it could help in better identifying vulnerable areas and/or weaknesses in prepared‐

Evacuation routes should be generated on the basis of flood maps and availability of shelters. If no natural shelters (hills, mounds, berms) are available it is advisable to construct vertical

It should be clear that living in houses which are built 1 - 3m above sea levels, a high level of

Already established safety zones, implemented in the planning of the coastal areas, will lower the risk of the highly vulnerable areas, both by earthquakes tremors and tsunami waves, therefore a multi-hazard approach in emergency planning would be advantageous. Preceding disasters, like a heavy earthquake, could (partly) destroy evacuation routes and assembly places; therefore a multi-hazard approach (earthquake plus tsunami) should put particular emphasis on having such routes and places secured. Moreover, the emergency planning should take into account that subsequent disasters or inconveniences may happen and request alteration of early plans, i.e. heavy rainfalls which, in turn, produce landslides and mudflows.

better response of the emergency services;

disasters and assurance of warning the population;

preparedness is required in the case a tsunami hit;

the tsunami;

the tsunami;

ness activities;

shelters.

The usual location for nuclear power plants are nearby large water available resources, sufficiently enough for assuring the cooling of water generated by the reactors, including tsunami prone areas nearby oceanic coastal shores. Consequently a higher location have to be selected for the backup power sources, and other electrical equipment for water pumps used to cool down the nuclear reactors following the automatic shut down due to largest possible tremor event ever recorded in the region, that means generally above 8 or 9 magnitude. Therefore every nuclear plant designs should take into account the resulting effects of this kind of event, including larger tsunamis than before experienced on a specific location chosen for nuclear development;

Periodical reevaluation of the nuclear power plant safety standards, depending of construction principle type e.g. light water cooled reactor (LWR), graphite-moderated, water-cooled reactor (RBMK), known as the Chernobyl type, heavy water moderated reactor (CANDU or AHWR), advanced gas cooled reactor (AGCR), liquid metal cooled reactor (LMF) or type of the nuclear fuel (uranium 253 and 258 or the most risky plutonium 239); NATECH scenarios (Natural Accidents that might trigger technical disasters) are to be considered, depending of natural hazards in the earthquake prone areas (e.g. landslides which may affect the land stability, storms or tsunamis which can flood the power generators, associated severe draught which may result in a water shortage in case of a water pipelines damage leading to nuclear fuel overheating), in order to avoid the worst case scenarios at a nuclear power plant, a nuclear leak due to melting down of the nuclear core, following failing of the cooling down of the exposed nuclear fuel rods.

#### **5.2. Preparedness measures**

The continuously monitoring of the areas prone to natural hazards, including earthquakes could lead to a better knowledge of the risk evolution of facing a possible disaster, also taking into account other vulnerability factors which can increase the probability of a disaster occurrence. Being known that many inhabited clusters could be closely located to an active tectonic area, and before some incipient earthquake activity will began, a detailed seismic analysis is necessary in order to detect the possible underground discontinuities. Generally speaking, even without having a historical evidence of earthquakes, worries can be raised regarding the overall seismic activity of a vulnerable area. In term of exposed population or industrial facilities, if an underneath fault is discovered, subsequent measures can be taken leading to a better preparedness activity for a possible earthquake;

The proper training of the personnel involved in emergency response and relief during natural disaster is essential for a better management of the emergency situations generated by an earthquake. Therefore constant simulation and drill exercises should be performed by the specialized personnel in order to be prepared in case of a major earthquake or for the possible forwarding aftershocks. An intense training program for the emergency personnel in the exposed areas should be performed using special trained sniff dogs and adequate equipment for increasing the preparedness capacity. Population should be also involved in the training drills, in order to become aware of the basic rules of survival and for recovery actions, to assure a better cooperation with the local authorities involved in the disaster mitigation activities;

necessarily takes place after such a long period of time, and can occur anytime, even today or tomorrow, in the most earthquake prone areas all over the world, represented especially by

The usual location for nuclear power plants are nearby large water available resources, sufficiently enough for assuring the cooling of water generated by the reactors, including tsunami prone areas nearby oceanic coastal shores. Consequently a higher location have to be selected for the backup power sources, and other electrical equipment for water pumps used to cool down the nuclear reactors following the automatic shut down due to largest possible tremor event ever recorded in the region, that means generally above 8 or 9 magnitude. Therefore every nuclear plant designs should take into account the resulting effects of this kind of event, including larger tsunamis than before experienced on a specific location chosen for

Periodical reevaluation of the nuclear power plant safety standards, depending of construction principle type e.g. light water cooled reactor (LWR), graphite-moderated, water-cooled reactor (RBMK), known as the Chernobyl type, heavy water moderated reactor (CANDU or AHWR), advanced gas cooled reactor (AGCR), liquid metal cooled reactor (LMF) or type of the nuclear fuel (uranium 253 and 258 or the most risky plutonium 239); NATECH scenarios (Natural Accidents that might trigger technical disasters) are to be considered, depending of natural hazards in the earthquake prone areas (e.g. landslides which may affect the land stability, storms or tsunamis which can flood the power generators, associated severe draught which may result in a water shortage in case of a water pipelines damage leading to nuclear fuel overheating), in order to avoid the worst case scenarios at a nuclear power plant, a nuclear leak due to melting down of the nuclear core, following failing of the cooling down of the

The continuously monitoring of the areas prone to natural hazards, including earthquakes could lead to a better knowledge of the risk evolution of facing a possible disaster, also taking into account other vulnerability factors which can increase the probability of a disaster occurrence. Being known that many inhabited clusters could be closely located to an active tectonic area, and before some incipient earthquake activity will began, a detailed seismic analysis is necessary in order to detect the possible underground discontinuities. Generally speaking, even without having a historical evidence of earthquakes, worries can be raised regarding the overall seismic activity of a vulnerable area. In term of exposed population or industrial facilities, if an underneath fault is discovered, subsequent measures can be taken

The proper training of the personnel involved in emergency response and relief during natural disaster is essential for a better management of the emergency situations generated by an earthquake. Therefore constant simulation and drill exercises should be performed by the specialized personnel in order to be prepared in case of a major earthquake or for the possible forwarding aftershocks. An intense training program for the emergency personnel in the exposed areas should be performed using special trained sniff dogs and adequate equipment

leading to a better preparedness activity for a possible earthquake;

the Pacific ring of fire, where the recent great earthquakes occurred;

28 Earthquake Research and Analysis - New Advances in Seismology

nuclear development;

exposed nuclear fuel rods.

**5.2. Preparedness measures**

The damage assessment scenarios for inhabited areas located in tsunami prone areas, on the coastal lines, will re-evaluate the mitigation capabilities in case of a real disaster and lead to a better response of the emergency services;

Countries located in tsunamis vulnerable areas should set their own national tsunami warning system, capable to watch and warn in due time the local inhabitants about any danger of producing a catastrophic event occurring nearby the inhabited area. For maintaining the awareness and the response capability of an already implemented tsunami warning system, simulation exercises should be periodically organized. Different responsibilities and tasks of the emergency personal involved in monitoring activities are reviewed, assuring the commu‐ nication in real time of the emergency relief cruses about the probabilities of producing the disasters and assurance of warning the population;

The existence of the emergency stock of materials and means of interventions, located in the vicinity of the prone areas of natural hazards, including tsunamis, allows an optimized relief activity after a disaster in the region, assuring a successful intervention activity and minimi‐ zation of loss of lives and damages to the properties. It is crucial to have sufficient stock (including tents, blankets, medicine) available in order to support people that have fled from the tsunami;

An efficient preparedness measure depends of timely early warnings issued by the authorities following an earthquake with high magnitude, which often constitute the triggering factor for the tsunami;

Area that had been affected by similar events in the past should create a disaster prevention platform; it could help in better identifying vulnerable areas and/or weaknesses in prepared‐ ness activities;

Evacuation routes should be generated on the basis of flood maps and availability of shelters. If no natural shelters (hills, mounds, berms) are available it is advisable to construct vertical shelters.

It should be clear that living in houses which are built 1 - 3m above sea levels, a high level of preparedness is required in the case a tsunami hit;

Already established safety zones, implemented in the planning of the coastal areas, will lower the risk of the highly vulnerable areas, both by earthquakes tremors and tsunami waves, therefore a multi-hazard approach in emergency planning would be advantageous. Preceding disasters, like a heavy earthquake, could (partly) destroy evacuation routes and assembly places; therefore a multi-hazard approach (earthquake plus tsunami) should put particular emphasis on having such routes and places secured. Moreover, the emergency planning should take into account that subsequent disasters or inconveniences may happen and request alteration of early plans, i.e. heavy rainfalls which, in turn, produce landslides and mudflows. Subsequently, people in emergency shelters had again to be redistributed in (different) safe locations;

and foreign aid organizations, in order to assure the economical income for a normal social life. Anyway it couldn't cover always integrally the loss, in the absence of a national-wide

Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of…

http://dx.doi.org/10.5772/55713

31

In the hazard prone areas where a certain disaster is present, the recovery activities are difficult to undertake, for example in arid regions there is the possibility that water tubes are broken triggering major damages. Response teams must be ready to get water lines repaired in short

In the rehabilitation phase the focus should be put on economical recovery and social sustain‐ ability within the affected communities. Therefore long-term intervention development programs have to be set up in the affected areas, for the benefit of the most vulnerable

The multi-hazard feature of the inhabited areas and population vulnerability, as a result of the economical developing, could worsen the condition of the affected population in case of a natural disaster, superposing the effect of more hazards. A prime task of the international assistance in the affected regions is the strengthening of the capacity to respond to future disasters in the area, because some regions could have been already suffering from the effects of other hazards before the earthquake, or to withstand to the associated hazards of the main event (such as aftershocks, tsunamis, fires due to broken gas pipelines or from the damaged reservoirs of the affected boats or cars carried by the waves into the houses walls, liquefaction

A prompt response activity in case of a natural disaster, including tsunami, is related to the existence of an already implemented, "Plan of emergency and intervention", at the level of local and central public authorities. It clearly stipulates the competencies and the activities during each phase of the emergency intervention for rehabilitation and clearance of the disaster effect. The plan should be constantly revised in order to assure the updating of the information with the changes in land planning activities at the level of the community, or modifications intervened in the structure of the emergency staff personal in charge with the response

Rescue operators have to count with a lot of destruction and uninhabitable houses thus having

The response capability in coastal areas, in the case of a tsunami event, should rely on the effectiveness of the early warning system for tsunami, which allows an efficient preparedness measure. In some vulnerable coastal areas the travel time for tsunami to reach the coastal area is very short (for example the Mediterranean region), generally in less than 10 min after start, due to relatively shallow and low step offshore bottom morphology. Consequently the period of time until the tsunami alert is initiated should be very short, in relation to an existing efficient

Automatic unmanned (anti-radiation proof for humans) crane coupled with long range powerful water pumps near a water source for spraying at distance large volume of waters, should be available for all nuclear facilities located in the earthquake prone areas, including

communities, mainly focusing on income generating projects;

to maintain a huge number of refugees over a long period;

alarm capability of the population and the emergency relief crews;

efficient insurance system;

and landslides, mudflows, etc.);

time;

activities;

In the particular case of Stromboli type volcanic island, due to the continuous activities of the volcano, constant preparedness is absolutely required, that is availability of responsible persons issuing the alarms, instruction non-residents, keeping free the evacuation routes;

On small islands telecommunication back-up system should be kept operating in order to start rescue operations;

The nuclear facilities located in the earthquake prone areas should have drilled in advance holes for vent up hydrogen released from the water cooling down reactor. The holes should be positioned at the top of the main building covering the nuclear reactor and containment vessel. This means preventing the hydrogen build up and risk of deflagration which might cause radioactive emissions, in case of core overheating due to breakdown of the cooling system. These hydrogen releases due to radiolysis may take place also because of the nuclear rods exposure in case of lowering down the water level in the cooling water pools with nuclear depleted material found inside the main buildings of the nuclear power plant;

Every nuclear power plant should take into consideration the availability of a pool of human resources to be used as a supplementary intervention in catastrophic event. In addition, a cleanup facility building located a few kilometers away from the main reactor facilities, including shelters large enough to host the emergency shifts for extended intervention in case of a nuclear incident. Such an action is recommended when the number of the normal available working shift personnel can not assure a proper emergency intervention in case of power failure and reestablishing the cooling down capabilities of a possible crippled nuclear reactor due to the twin action of a large scale tremor and subsequent tsunami event.

#### **5.3. Response measures**

The endowment of the rescue teams with special equipments and means of intervention in case of emergency situations is essential for an efficient response, increasing the chance for saving lives and reducing the economical impact of the natural disasters, including earth‐ quakes. In the aftermath of the disaster, many persons can be rescued beneath the rubble thanks to the sniffer dogs and hi-tech ultrasound equipment both from the national level or foreign emergency teams;

The existence of the communication routes through all remote communities within a prone area for natural disaster, including tsunami, is an essential factor for undertaken an efficient response activity in case of a disaster event;

For minimizing the pressure of the local community in case of disasters, the existence of an insurance system for the houses and goods against the natural disasters, including earthquakes is very efficient. This is due to the indemnity of the affected people, automatically covered by the insurance companies. The financial coverage of the response action will not be affected, in case of producing some damages. Commonly, in the aftermath of an earthquake, the only compensation of the homeless people in the affected areas are the subvention from the state and foreign aid organizations, in order to assure the economical income for a normal social life. Anyway it couldn't cover always integrally the loss, in the absence of a national-wide efficient insurance system;

Subsequently, people in emergency shelters had again to be redistributed in (different) safe

In the particular case of Stromboli type volcanic island, due to the continuous activities of the volcano, constant preparedness is absolutely required, that is availability of responsible persons issuing the alarms, instruction non-residents, keeping free the evacuation routes;

On small islands telecommunication back-up system should be kept operating in order to start

The nuclear facilities located in the earthquake prone areas should have drilled in advance holes for vent up hydrogen released from the water cooling down reactor. The holes should be positioned at the top of the main building covering the nuclear reactor and containment vessel. This means preventing the hydrogen build up and risk of deflagration which might cause radioactive emissions, in case of core overheating due to breakdown of the cooling system. These hydrogen releases due to radiolysis may take place also because of the nuclear rods exposure in case of lowering down the water level in the cooling water pools with nuclear

Every nuclear power plant should take into consideration the availability of a pool of human resources to be used as a supplementary intervention in catastrophic event. In addition, a cleanup facility building located a few kilometers away from the main reactor facilities, including shelters large enough to host the emergency shifts for extended intervention in case of a nuclear incident. Such an action is recommended when the number of the normal available working shift personnel can not assure a proper emergency intervention in case of power failure and reestablishing the cooling down capabilities of a possible crippled nuclear reactor due to the

The endowment of the rescue teams with special equipments and means of intervention in case of emergency situations is essential for an efficient response, increasing the chance for saving lives and reducing the economical impact of the natural disasters, including earth‐ quakes. In the aftermath of the disaster, many persons can be rescued beneath the rubble thanks to the sniffer dogs and hi-tech ultrasound equipment both from the national level or foreign

The existence of the communication routes through all remote communities within a prone area for natural disaster, including tsunami, is an essential factor for undertaken an efficient

For minimizing the pressure of the local community in case of disasters, the existence of an insurance system for the houses and goods against the natural disasters, including earthquakes is very efficient. This is due to the indemnity of the affected people, automatically covered by the insurance companies. The financial coverage of the response action will not be affected, in case of producing some damages. Commonly, in the aftermath of an earthquake, the only compensation of the homeless people in the affected areas are the subvention from the state

depleted material found inside the main buildings of the nuclear power plant;

twin action of a large scale tremor and subsequent tsunami event.

locations;

rescue operations;

30 Earthquake Research and Analysis - New Advances in Seismology

**5.3. Response measures**

emergency teams;

response activity in case of a disaster event;

In the hazard prone areas where a certain disaster is present, the recovery activities are difficult to undertake, for example in arid regions there is the possibility that water tubes are broken triggering major damages. Response teams must be ready to get water lines repaired in short time;

In the rehabilitation phase the focus should be put on economical recovery and social sustain‐ ability within the affected communities. Therefore long-term intervention development programs have to be set up in the affected areas, for the benefit of the most vulnerable communities, mainly focusing on income generating projects;

The multi-hazard feature of the inhabited areas and population vulnerability, as a result of the economical developing, could worsen the condition of the affected population in case of a natural disaster, superposing the effect of more hazards. A prime task of the international assistance in the affected regions is the strengthening of the capacity to respond to future disasters in the area, because some regions could have been already suffering from the effects of other hazards before the earthquake, or to withstand to the associated hazards of the main event (such as aftershocks, tsunamis, fires due to broken gas pipelines or from the damaged reservoirs of the affected boats or cars carried by the waves into the houses walls, liquefaction and landslides, mudflows, etc.);

A prompt response activity in case of a natural disaster, including tsunami, is related to the existence of an already implemented, "Plan of emergency and intervention", at the level of local and central public authorities. It clearly stipulates the competencies and the activities during each phase of the emergency intervention for rehabilitation and clearance of the disaster effect. The plan should be constantly revised in order to assure the updating of the information with the changes in land planning activities at the level of the community, or modifications intervened in the structure of the emergency staff personal in charge with the response activities;

Rescue operators have to count with a lot of destruction and uninhabitable houses thus having to maintain a huge number of refugees over a long period;

The response capability in coastal areas, in the case of a tsunami event, should rely on the effectiveness of the early warning system for tsunami, which allows an efficient preparedness measure. In some vulnerable coastal areas the travel time for tsunami to reach the coastal area is very short (for example the Mediterranean region), generally in less than 10 min after start, due to relatively shallow and low step offshore bottom morphology. Consequently the period of time until the tsunami alert is initiated should be very short, in relation to an existing efficient alarm capability of the population and the emergency relief crews;

Automatic unmanned (anti-radiation proof for humans) crane coupled with long range powerful water pumps near a water source for spraying at distance large volume of waters, should be available for all nuclear facilities located in the earthquake prone areas, including tsunamis. These special intervention equipments, including remote surveying robots with dosimeters, should be used in the event of a nuclear cooling down operation failure, following larger tsunamis that might drawdown the back up pumps used for emergency intervention. In addition, a longer enough power cable to be switched on at an existing nuclear facility from an outside existing power source, generally a mile longer, should be available to connect by emergency the main nuclear unit of reactors in case of power failure due to earthquake tremor or subsequent tsunamis. Large barge should be available nearby for transporting freshwater in case of a nuclear accident at a plant located at the sea shore, in order to cool down the reactors, because the marine salt water damages irrevocably the nuclear facility.

The information of the public about subsequent effects of a technological disaster (oil terminals and refineries, mostly located in the tsunamis prone coastal areas) or natural hazards in travel or inhabited area, including tsunamis, and about the presence of other possible accompanied triggered disasters, following an earthquake, such as landslides or rock falls, by all available means (police agents, local broadcasting, tv news, papers, warning panels, etc.), lead to avoid

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http://dx.doi.org/10.5772/55713

33

The case of Stromboli type islands, visited by numerous foreign tourists, requires permanent, effective and multi-lingual instruction of residents and non-residents, i.e. leaflets let to those arriving, pictograms let in hotel rooms, warning signs put on beaches and nearby paths;

Populations should be kept informed by local authorities on the possible restriction zone, generally following an accident at a nuclear reactor due to the impact of a twin event of tremor and the subsequent tsunami wave. The restriction zone is declared generally as an exclusion zone for population, excepting the nuclear plant emergency personnel and fire fighter units, and is particularly coffined at a specific distance radius to the crippled nuclear reactor,

Radiation self-detection equipment (dosimeters) for personal use should be available for the population individuals located nearby nuclear facilities, or the persons travelling nearby, for auto monitoring of the radiation doses (e.g. the hourly radiation dose is 0.1 micro Sievers µSv/hour). In case of exceeding the normal dose, depending on instructions from the emer‐ gency supervising personnel, a decontamination procedure is required (e.g. shower with water and soap washing); Food (milk and fresh harvested vegetables) and water nearby a crippled nuclear facility can be immediately affected by a nuclear leakage due to a catastrophic failure of the cooling down the nuclear reactor, or incidents at the nuclear rods being exposed, due to

Main radioactive isotopes (e.g. Iodine 131, Xenon-133, Krypton-85 and Caesium 137), pro‐ duced during a nuclear accident due to subsequent tsunami of an earthquake event, can immediately affect the health on long term, due to the carcinogenic effect. Special medication for radiation prevention should be used only on the certified medical surveillance, because the main antidote, for Iodine 131, the iodine salts (e.g. potassium iodine) is available just for a time window of 4 days, when the results are affective (e.g. for avoiding the accumulation in thyroid gland by aerial way), and the self medication with other similar inhibitors (for example iodine salt), can shift the effective period before the radioactive cloud is atmospherically drifting on

Contemporaneous seismic activity as well as complementary volcanicity are genetically linked to Cenozoic plate kinematics, involving interacting plates and/or intra-plate rifting steaming from triple junctions. Upper mantle heterogenic seismic structures are intimately related to

the wind dispersion (e.g. as far as 100 km radius far to the radioactive source);

the risk and limits the consequences in the aftermath of a natural disaster;

commonly of value of tens of miles around the radiation source;

a certain vulnerable inhabited zone.

plate breaking and motion.

**7. Status**

#### **6. Information to the public**

In the areas prone to natural disasters, including earthquakes, at the level of the regional or local administration, hazard vulnerability and risk maps should be available for all decisional factors involved in the management of this type of disaster but also for dissemination to the general public in order to be informed about the dangers nearby the inhabited areas;

The proper information of the population from the vulnerable areas to the earthquakes about the risk reduction issues and the possibility to reduce the vulnerability of their houses by applying correct building codes, is highly necessary. The using of the new building materials, such as iron or iron coated concrete beams, together with the traditional ones such as clay bricks, without respect to any elementary building code, sometimes worsened the strength of a construction, and put an increased risk of the inhabitants. For example, the use of the iron beam for strengthening and to allow the extra-store constructions, together with traditional materials (clay bricks), could increase the vulnerability in case of a possible earthquake, as well as in the case of recently affected areas by earthquakes, where multi-store buildings collapsed and produced more casualties than in a possible destruction of a one store house;

It is necessary to create a knowledge platform to disseminate information at the local level, to educate people about the risk reduction issues in case of an earthquake. For example, the existence of some water and food supplies, also some vital medicines in case of chronic diseases, available in case of trapping inside a house can increase the life expectancy in case of earthquake, which could produce the collapse of the inhabited house;

The adequate information regarding the situation nearby an affected area by a recent earth‐ quake lead to a more donor support from the surrounding communities and countries. An information booklet and a Website describing the earthquake effects during the relief opera‐ tions can bring more donor support and can contribute together with the information press for a humanitarian appeal from the international community;

The ongoing information of the public regarding the actions to avoid a tsunami wave (such as: the clear indication of the escape routes, the avoidance of the exposed coastal areas during the tsunami, urgent deployment to higher places, etc.) will lead to an adequate behaviour of the population in case of a real disaster, limiting the number of affected individuals;

The information of the public about subsequent effects of a technological disaster (oil terminals and refineries, mostly located in the tsunamis prone coastal areas) or natural hazards in travel or inhabited area, including tsunamis, and about the presence of other possible accompanied triggered disasters, following an earthquake, such as landslides or rock falls, by all available means (police agents, local broadcasting, tv news, papers, warning panels, etc.), lead to avoid the risk and limits the consequences in the aftermath of a natural disaster;

The case of Stromboli type islands, visited by numerous foreign tourists, requires permanent, effective and multi-lingual instruction of residents and non-residents, i.e. leaflets let to those arriving, pictograms let in hotel rooms, warning signs put on beaches and nearby paths;

Populations should be kept informed by local authorities on the possible restriction zone, generally following an accident at a nuclear reactor due to the impact of a twin event of tremor and the subsequent tsunami wave. The restriction zone is declared generally as an exclusion zone for population, excepting the nuclear plant emergency personnel and fire fighter units, and is particularly coffined at a specific distance radius to the crippled nuclear reactor, commonly of value of tens of miles around the radiation source;

Radiation self-detection equipment (dosimeters) for personal use should be available for the population individuals located nearby nuclear facilities, or the persons travelling nearby, for auto monitoring of the radiation doses (e.g. the hourly radiation dose is 0.1 micro Sievers µSv/hour). In case of exceeding the normal dose, depending on instructions from the emer‐ gency supervising personnel, a decontamination procedure is required (e.g. shower with water and soap washing); Food (milk and fresh harvested vegetables) and water nearby a crippled nuclear facility can be immediately affected by a nuclear leakage due to a catastrophic failure of the cooling down the nuclear reactor, or incidents at the nuclear rods being exposed, due to the wind dispersion (e.g. as far as 100 km radius far to the radioactive source);

Main radioactive isotopes (e.g. Iodine 131, Xenon-133, Krypton-85 and Caesium 137), pro‐ duced during a nuclear accident due to subsequent tsunami of an earthquake event, can immediately affect the health on long term, due to the carcinogenic effect. Special medication for radiation prevention should be used only on the certified medical surveillance, because the main antidote, for Iodine 131, the iodine salts (e.g. potassium iodine) is available just for a time window of 4 days, when the results are affective (e.g. for avoiding the accumulation in thyroid gland by aerial way), and the self medication with other similar inhibitors (for example iodine salt), can shift the effective period before the radioactive cloud is atmospherically drifting on a certain vulnerable inhabited zone.

#### **7. Status**

tsunamis. These special intervention equipments, including remote surveying robots with dosimeters, should be used in the event of a nuclear cooling down operation failure, following larger tsunamis that might drawdown the back up pumps used for emergency intervention. In addition, a longer enough power cable to be switched on at an existing nuclear facility from an outside existing power source, generally a mile longer, should be available to connect by emergency the main nuclear unit of reactors in case of power failure due to earthquake tremor or subsequent tsunamis. Large barge should be available nearby for transporting freshwater in case of a nuclear accident at a plant located at the sea shore, in order to cool down the reactors,

In the areas prone to natural disasters, including earthquakes, at the level of the regional or local administration, hazard vulnerability and risk maps should be available for all decisional factors involved in the management of this type of disaster but also for dissemination to the

The proper information of the population from the vulnerable areas to the earthquakes about the risk reduction issues and the possibility to reduce the vulnerability of their houses by applying correct building codes, is highly necessary. The using of the new building materials, such as iron or iron coated concrete beams, together with the traditional ones such as clay bricks, without respect to any elementary building code, sometimes worsened the strength of a construction, and put an increased risk of the inhabitants. For example, the use of the iron beam for strengthening and to allow the extra-store constructions, together with traditional materials (clay bricks), could increase the vulnerability in case of a possible earthquake, as well as in the case of recently affected areas by earthquakes, where multi-store buildings collapsed

It is necessary to create a knowledge platform to disseminate information at the local level, to educate people about the risk reduction issues in case of an earthquake. For example, the existence of some water and food supplies, also some vital medicines in case of chronic diseases, available in case of trapping inside a house can increase the life expectancy in case

The adequate information regarding the situation nearby an affected area by a recent earth‐ quake lead to a more donor support from the surrounding communities and countries. An information booklet and a Website describing the earthquake effects during the relief opera‐ tions can bring more donor support and can contribute together with the information press

The ongoing information of the public regarding the actions to avoid a tsunami wave (such as: the clear indication of the escape routes, the avoidance of the exposed coastal areas during the tsunami, urgent deployment to higher places, etc.) will lead to an adequate behaviour of

the population in case of a real disaster, limiting the number of affected individuals;

general public in order to be informed about the dangers nearby the inhabited areas;

and produced more casualties than in a possible destruction of a one store house;

of earthquake, which could produce the collapse of the inhabited house;

for a humanitarian appeal from the international community;

because the marine salt water damages irrevocably the nuclear facility.

**6. Information to the public**

32 Earthquake Research and Analysis - New Advances in Seismology

Contemporaneous seismic activity as well as complementary volcanicity are genetically linked to Cenozoic plate kinematics, involving interacting plates and/or intra-plate rifting steaming from triple junctions. Upper mantle heterogenic seismic structures are intimately related to plate breaking and motion.

A series of natural facts are to be taken into consideration in order to approach the causes of such unusual trend of increasing major earthquake frequency after 1990 which led to destruc‐ tive earthquakes in "classic" areas but also in areas not specifically known as prone area.

nental area covered by the ice is reducing due to the increased global temperature), can induce serious consequences over the tectonic stability of the earth, respectively the frequency and magnitude of the related phenomena, such as subsequent volcanoes activity which can be

Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of…

http://dx.doi.org/10.5772/55713

35

According to specific environmental evaluations that claim that the actual trend of global warming is continuing, in the next hundreds of years the continental ice will disappear. The rapid defrosting of the continental ice could lead also to some secondary tectonic effects due to the release of the equivalent pressure of the ice load. If the assumption of the paleoclimatologists is correct, a similar phenomenon, an increased warming episode, like the actual global trend, could lead to an unexpected increased tectonic activity, with unpredicted impact over the humans and surrounding environment. Therefore the actual increased trend of the earthquakes frequency could be a global indicator of the tectonic stress due to rapid defrosting

Furthermore the general lessons have to be implemented urgently by the risk managers involved in the activities of updating and implementing the building codes, seismic risk zoning and regulation, in order to avoid in the future any other misjudges of the earthquakes hazard,

Analysing the possible increased tendency of earthquake activity (Table no. 1), in order to clarify the cause of the unusual increased trend of the earthquakes frequency in certain periods of times after the 90's, a common fact was that all these recently past events surprised the local population as well as local and national level risk managers, because the hit areas were not considered before specific historically earthquake prone zone, so the building codes were not updated for a real seismic zone (including major cities as Kobe or Islamabad). The paradoxical issue of increased trend of earthquakes just after '90 was never been tackled seriously before. Generally it is considered that just 10% of the total energy from tectonic plates movement are transformed in earthquakes, and remain 90% converted in other forms of energy due to rock displacement and heating up processes [5]. A constant increasing trend of the Earth's earth‐ quake energy, revealed by our analysis over the last 30 years seismic records worldwide, could indicate a shifting of the remain 90% of the tectonic energy, normally dissipated in plates interactions, towards earthquakes. For the the first time in modern history, were recorded in the same day two great earthquakes more than magnitude 8 on Richter Scale, in the same area (off the west coast of Northern Sumatra, during 2012), instead of a smaller aftershock of the same tremor, usually not exceeding a lower range magnitude (the aftershock shouldn't exceed a magnitude 7 on the Richter scale). That's mean we will witness a future increasing in the

for minimizing the loss of human lives and material damages.

induced by the plates movements and evolution, and generating earthquakes.

of the continental ice sheet.

**9. Further research**

**10. Conclusions**

A cause of increasing trend of seismic activity may be induced by internal factors related to global tectonics. It is marked by intracrustal-subcrustal structural, sedimentologic and magmatic processes creating shallow or deep areas for large magnitude earthquakes., e.g. coupling convergence rate, age of subduction, lithosphere type, trench sediment thickness and so on.

Reality or mere coincidence, concurrent supracrustal processes at global scale may affect the Earth's structure and related sensitive tectono-seismic spots. Of them the global warming is considered by a large part of the academic world as major process with implications at atmospheric, hydrospheric, biospheric and lithospheric levels that represents the so-called Critical Zone of the Earth. So far Cenozoic eco-climate change was taken into consideration in order to explain seismic differences of orogenic regions based on sediment thickness, i.e. effect of coupling between tectonic and erosion.

The need for detailed analyses of the effects of the global warming and the assessment of all the aspects of the environmental factors, are due to the necessity to control the natural hazards at the level of the planet Earth, involving the approach of a global analysis. Therefore, to study the interrelation between global warming and the earthquakes can be made just analysing the involved phenomena (earthquakes, global warming, tectonic evolution) at the world scale level, taking into account all relevant aspects of the involved hazards, making reference to the historical evidence and data records.

Useful information can be provided by conclusions of the experts involved in the analyses of the core samples from the ice drillings 3000 m deep in Greenland, performed in early '90s. The unusual enriched content of sulphate found in the ice cores at a certain depth proved an episode of unusual intense volcanic activity, which took place at 7000 BC, induced by the tectonic instability due to the rapid defrosting of the continental ice sheet, because of a warmer climatic episode. The paleo-environmental reconstruction of the last major volcano activity occurred on earth, at 7000 BC, was a result of the analyses conducted on the ice drilling samples from glaciers by a research program performed in Greenland, through the European Science Foundation [6].

#### **8. Results**

The analyses of the earthquakes frequency trend all over the globe, in the recent years, correlated with the actual tendency of defrosting the ice from the polar regions [7], allow the study of presumable recurrences in future, of a similar event of volcano increasing activity and subsequently tectonic disturbance, as a result of the defrosting evolution of the actual glaciers due to global warming. The possible correlation between the analysed earthquake data and the actual ice sheet evolution, which covers actually 10% of the total crust (where the conti‐ nental area covered by the ice is reducing due to the increased global temperature), can induce serious consequences over the tectonic stability of the earth, respectively the frequency and magnitude of the related phenomena, such as subsequent volcanoes activity which can be induced by the plates movements and evolution, and generating earthquakes.

According to specific environmental evaluations that claim that the actual trend of global warming is continuing, in the next hundreds of years the continental ice will disappear. The rapid defrosting of the continental ice could lead also to some secondary tectonic effects due to the release of the equivalent pressure of the ice load. If the assumption of the paleoclimatologists is correct, a similar phenomenon, an increased warming episode, like the actual global trend, could lead to an unexpected increased tectonic activity, with unpredicted impact over the humans and surrounding environment. Therefore the actual increased trend of the earthquakes frequency could be a global indicator of the tectonic stress due to rapid defrosting of the continental ice sheet.

#### **9. Further research**

A series of natural facts are to be taken into consideration in order to approach the causes of such unusual trend of increasing major earthquake frequency after 1990 which led to destruc‐ tive earthquakes in "classic" areas but also in areas not specifically known as prone area.

A cause of increasing trend of seismic activity may be induced by internal factors related to global tectonics. It is marked by intracrustal-subcrustal structural, sedimentologic and magmatic processes creating shallow or deep areas for large magnitude earthquakes., e.g. coupling convergence rate, age of subduction, lithosphere type, trench sediment thickness and

Reality or mere coincidence, concurrent supracrustal processes at global scale may affect the Earth's structure and related sensitive tectono-seismic spots. Of them the global warming is considered by a large part of the academic world as major process with implications at atmospheric, hydrospheric, biospheric and lithospheric levels that represents the so-called Critical Zone of the Earth. So far Cenozoic eco-climate change was taken into consideration in order to explain seismic differences of orogenic regions based on sediment thickness, i.e. effect

The need for detailed analyses of the effects of the global warming and the assessment of all the aspects of the environmental factors, are due to the necessity to control the natural hazards at the level of the planet Earth, involving the approach of a global analysis. Therefore, to study the interrelation between global warming and the earthquakes can be made just analysing the involved phenomena (earthquakes, global warming, tectonic evolution) at the world scale level, taking into account all relevant aspects of the involved hazards, making reference to the

Useful information can be provided by conclusions of the experts involved in the analyses of the core samples from the ice drillings 3000 m deep in Greenland, performed in early '90s. The unusual enriched content of sulphate found in the ice cores at a certain depth proved an episode of unusual intense volcanic activity, which took place at 7000 BC, induced by the tectonic instability due to the rapid defrosting of the continental ice sheet, because of a warmer climatic episode. The paleo-environmental reconstruction of the last major volcano activity occurred on earth, at 7000 BC, was a result of the analyses conducted on the ice drilling samples from glaciers by a research program performed in Greenland, through the European Science

The analyses of the earthquakes frequency trend all over the globe, in the recent years, correlated with the actual tendency of defrosting the ice from the polar regions [7], allow the study of presumable recurrences in future, of a similar event of volcano increasing activity and subsequently tectonic disturbance, as a result of the defrosting evolution of the actual glaciers due to global warming. The possible correlation between the analysed earthquake data and the actual ice sheet evolution, which covers actually 10% of the total crust (where the conti‐

so on.

of coupling between tectonic and erosion.

34 Earthquake Research and Analysis - New Advances in Seismology

historical evidence and data records.

Foundation [6].

**8. Results**

Furthermore the general lessons have to be implemented urgently by the risk managers involved in the activities of updating and implementing the building codes, seismic risk zoning and regulation, in order to avoid in the future any other misjudges of the earthquakes hazard, for minimizing the loss of human lives and material damages.

#### **10. Conclusions**

Analysing the possible increased tendency of earthquake activity (Table no. 1), in order to clarify the cause of the unusual increased trend of the earthquakes frequency in certain periods of times after the 90's, a common fact was that all these recently past events surprised the local population as well as local and national level risk managers, because the hit areas were not considered before specific historically earthquake prone zone, so the building codes were not updated for a real seismic zone (including major cities as Kobe or Islamabad). The paradoxical issue of increased trend of earthquakes just after '90 was never been tackled seriously before. Generally it is considered that just 10% of the total energy from tectonic plates movement are transformed in earthquakes, and remain 90% converted in other forms of energy due to rock displacement and heating up processes [5]. A constant increasing trend of the Earth's earth‐ quake energy, revealed by our analysis over the last 30 years seismic records worldwide, could indicate a shifting of the remain 90% of the tectonic energy, normally dissipated in plates interactions, towards earthquakes. For the the first time in modern history, were recorded in the same day two great earthquakes more than magnitude 8 on Richter Scale, in the same area (off the west coast of Northern Sumatra, during 2012), instead of a smaller aftershock of the same tremor, usually not exceeding a lower range magnitude (the aftershock shouldn't exceed a magnitude 7 on the Richter scale). That's mean we will witness a future increasing in the


earthquake pattern trend, which may have profound implications at a global scale, in our understanding of Earth dynamics.

over crustal/sub-crustal settings. Consequently, discerning mere speculation from evidence is

Global Climatic Changes, a Possible Cause of the Recent Increasing Trend of…

http://dx.doi.org/10.5772/55713

37

The needs for increasing the resilience of the communities all over the world lead to more detailed studies on both small and large scale in order to try to explain the connection among factors which interact naturally on the Earth. The lessons learning activity based on the analysis of the recent tremors data all over the world can improve the preventive, preparedness and

intervention means of the earthquake vulnerable areas.

\*Address all correspondence to: maraseptimius@yahoo.com

CSMpp1\_History.pdf,accessed 24 March (2012).

underwater\_earthquakes.htm,accessed 15 April (2012).

1 Ministry of Environment and Forests, Romania, Bucharest, Romania

2 Faculty of Ecology and Environmental Protection, The Ecological University, Romania

[1] Airinei, Ş. (1972). Geophysics (in Romanian), Ministry of Education and Science, Bu‐

[2] Georgescu, E. S. B*ucureştiul şi seismele* (in Romanian), Editura Fundatiei culturale Li‐

[3] Lazarescu, V. (1980). Physical Geology (in Romanian), Technical publisher, Bucharest [4] Peter, M. Shearer, "Introduction To Seismology", Cambridge University Press, 1999http://earthquake.usgs.gov/hazards/about/workshops/thailand/downloads/

[5] U.S. Geological Survey, National Earthquake Information Center*- Earthquake list* http://earthquake.usgs.gov/earthquakes/eqarchives/year/eqstats.php, updated on

[6] Science daily: Underwater Earthquakes Geophysicists Discover Slippery Secret Of Weaker Underwater Earthquakes (2007)http://www.sciencedaily.com/videos/2007/

[7] Zielinski, G. A, Mayewski, P. A, Meeker, L. D, Whitlow, S, Twickler, M. S, Morrison, M, Meese, D. A, Gow, A. J, & Alley, R. B. *US Global Change Research Information Office-Increased Volcanism Linked To Climatic Cooling During The Period From 5000 To 7000 B.C. reference:* Record of Volcanism Since 7000 B.C. from the GISP2 Greenland Ice

Septimius Mara1\* and Serban-Nicolae Vlad2

still a priority.

**Author details**

**References**

charest University

bra, Bucuresti, (2007).

2012 (accessed 03 March 2012)

**Table 1.** Evolution of the Earthquakes frequency (no/magnitude/year) during 1980-2012

All around the globe, in the earthquake prone areas, scientists monitor carefully earthquake activity, because many agglomeration centres, including large areas like Tokyo and Bucharest (later the capital of Romania, considered the most prone capital with a similar earthquake activity as Mexico City, in the opinion of the most celebre seismologist, Charles F. Richter) are expecting a devastating event, according to the statistics (Tokyo is expecting "the big one" earthquake following the last major event in 1923, so called "Kanto earthquake", and in Romania the same Vrancea source earthquake, with the last major event in 1977, with more than 2 billion US dollars in damage and 1500 fatalities).

Another explanation is that, following the global climatic changes, a large part of ice Polls sheet started melting (unprecedently during the summer of 2012, for the first time the Greenland ice sheet was partially melted at the surface, far exceeding with 100 years the climatologists previsions), so large volume of water were released into the ocean triggering potential changes in the global plate tectonic equilibrium. Taking into account that Antarctica (Southern Pole continent) is covered with snow and ice of almost 2000 m height, equivalent in weight of a real continent, whose melting can destabilise the established continental plates equilibrium. These sudden melting (which in terms of geological ages has never been experienced so fast until now in the whole Earth's geological history), might influence the global earthquake trend, a possible precursor of changes in the pattern of global plate tectonic movement. What is however certain is the fact that earthquakes are geological hazards of endogenous origin, and what is uncertain is the global warming itself and the potential influence of exogenous factors over crustal/sub-crustal settings. Consequently, discerning mere speculation from evidence is still a priority.

The needs for increasing the resilience of the communities all over the world lead to more detailed studies on both small and large scale in order to try to explain the connection among factors which interact naturally on the Earth. The lessons learning activity based on the analysis of the recent tremors data all over the world can improve the preventive, preparedness and intervention means of the earthquake vulnerable areas.

#### **Author details**

earthquake pattern trend, which may have profound implications at a global scale, in our

**1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990**

**1991 1992 1993 1994 1995 1996 1997 1998 1999 2000**

0 0 0 2 2 1 0 1 0 1 16 13 12 11 18 14 16 11 18 14 96 166 137 146 183 149 120 117 116 158

8.0 to 8.9 1 0 0 0 0 1 1 0 0 1 0 7.0 to 7.9 13 13 10 14 8 13 5 11 8 6 18 6.0 to 6.9 105 90 85 126 91 110 89 112 93 79 109

**2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012**

All around the globe, in the earthquake prone areas, scientists monitor carefully earthquake activity, because many agglomeration centres, including large areas like Tokyo and Bucharest (later the capital of Romania, considered the most prone capital with a similar earthquake activity as Mexico City, in the opinion of the most celebre seismologist, Charles F. Richter) are expecting a devastating event, according to the statistics (Tokyo is expecting "the big one" earthquake following the last major event in 1923, so called "Kanto earthquake", and in Romania the same Vrancea source earthquake, with the last major event in 1977, with more

Another explanation is that, following the global climatic changes, a large part of ice Polls sheet started melting (unprecedently during the summer of 2012, for the first time the Greenland ice sheet was partially melted at the surface, far exceeding with 100 years the climatologists previsions), so large volume of water were released into the ocean triggering potential changes in the global plate tectonic equilibrium. Taking into account that Antarctica (Southern Pole continent) is covered with snow and ice of almost 2000 m height, equivalent in weight of a real continent, whose melting can destabilise the established continental plates equilibrium. These sudden melting (which in terms of geological ages has never been experienced so fast until now in the whole Earth's geological history), might influence the global earthquake trend, a possible precursor of changes in the pattern of global plate tectonic movement. What is however certain is the fact that earthquakes are geological hazards of endogenous origin, and what is uncertain is the global warming itself and the potential influence of exogenous factors

**Table 1.** Evolution of the Earthquakes frequency (no/magnitude/year) during 1980-2012

than 2 billion US dollars in damage and 1500 fatalities).

1 0 1 2 1 1 4 0 1 1 1 2 15 13 14 14 10 10 14 12 16 21 15 12 126 130 140 141 148 148 178 168 144 151 134 108

understanding of Earth dynamics.

36 Earthquake Research and Analysis - New Advances in Seismology

**Magnitude/ year**

Septimius Mara1\* and Serban-Nicolae Vlad2

\*Address all correspondence to: maraseptimius@yahoo.com

1 Ministry of Environment and Forests, Romania, Bucharest, Romania

2 Faculty of Ecology and Environmental Protection, The Ecological University, Romania

#### **References**


Core and Implications for the Volcano-Climate System, Science, *http://www.science‐ mag.org/content/264/5161/948.short),*accessed 2 May (2012). , 264, 948-952.

**Chapter 3**

**Scaling Properties of Aftershock Sequences in Algeria-**

This chapiter is dedicated to the analysis of some aftershock sequences occurred in Algeria-Morocco region, namely Al Hoceima earthquakes of May 26, 1994 (Mw6.0) and February 24, 2004 (Mw6.1) which occurred in northern Morocco, the October 10, 1980 El Asnam earthquake (Mw7.3), the May 21, 2003 Zemouri earthquake (Mw6.9) and March 26 2006 Laalam earthquake

Aftershock sequence is usually attributed to the strain energy not released by the mainshock. Statistical properties of aftershocks have been extensively studied for long time. Most of them dealt with the distribution of aftershock in time, space and magnitude domain. Several authors have noted the importnace of systematic investigation of aftershock sequences to earthquake prediction and a number of statistical models have been proposed to describe seismicity characters in time, space and magnitude (Utsu, 1961; Utsu et al., 1995; Guo and Ogata, 1997; Ogata, 1999). It is also well known that aftershock sequence offer a rich source of information about Earth's crust and can provide and understanding of the mechanism of earthquakes, because tens of thousands of earthquakes can occur over a short period in small area. The tectonic setting and the mode of faulting are factors others than fault surface properties that might control the behavior of the sequence (Kisslinger and Jones, 1991; Tahir et al., 2012). It is widely accepted that aftershock sequence presents unique opportunity to study the physics of earthquakes. In the same time importnat questions concern the fundamental origin of some widely applicable scaling laws, as the Gutenberg-Richter frequency-magnitude relationship, the modified Omori law or the Omori-Utsu law for aftershock decay and Bath's law for the

difference between the magnitude of the largest aftershock and mainshock.

The frequency-magnitude distribution (Gutenberg and Richter, 1944), firstly examinated, describes the relation between the frequency of occurence and magnitude of earthquake

> © 2013 Hamdache et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Hamdache et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Morocco Region**

http://dx.doi.org/10.5772/54888

(Mw5.2) in northern Algeria.

**1. Introduction**

M. Hamdache, J.A. Pelàez and A. Talbi

Additional information is available at the end of the chapter

[8] National snow and ice data center (NSIDC) Sea Ice Decline Intensifies- (report on 28 September 2005); http://weathertrends.blogspot.com/2005/09/sea-ice-decline-intensi‐ fies.html,accessed 15 June (2012).

## **Scaling Properties of Aftershock Sequences in Algeria-Morocco Region**

M. Hamdache, J.A. Pelàez and A. Talbi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54888

#### **1. Introduction**

Core and Implications for the Volcano-Climate System, Science, *http://www.science‐*

[8] National snow and ice data center (NSIDC) Sea Ice Decline Intensifies- (report on 28 September 2005); http://weathertrends.blogspot.com/2005/09/sea-ice-decline-intensi‐

*mag.org/content/264/5161/948.short),*accessed 2 May (2012). , 264, 948-952.

fies.html,accessed 15 June (2012).

38 Earthquake Research and Analysis - New Advances in Seismology

This chapiter is dedicated to the analysis of some aftershock sequences occurred in Algeria-Morocco region, namely Al Hoceima earthquakes of May 26, 1994 (Mw6.0) and February 24, 2004 (Mw6.1) which occurred in northern Morocco, the October 10, 1980 El Asnam earthquake (Mw7.3), the May 21, 2003 Zemouri earthquake (Mw6.9) and March 26 2006 Laalam earthquake (Mw5.2) in northern Algeria.

Aftershock sequence is usually attributed to the strain energy not released by the mainshock. Statistical properties of aftershocks have been extensively studied for long time. Most of them dealt with the distribution of aftershock in time, space and magnitude domain. Several authors have noted the importnace of systematic investigation of aftershock sequences to earthquake prediction and a number of statistical models have been proposed to describe seismicity characters in time, space and magnitude (Utsu, 1961; Utsu et al., 1995; Guo and Ogata, 1997; Ogata, 1999). It is also well known that aftershock sequence offer a rich source of information about Earth's crust and can provide and understanding of the mechanism of earthquakes, because tens of thousands of earthquakes can occur over a short period in small area. The tectonic setting and the mode of faulting are factors others than fault surface properties that might control the behavior of the sequence (Kisslinger and Jones, 1991; Tahir et al., 2012). It is widely accepted that aftershock sequence presents unique opportunity to study the physics of earthquakes. In the same time importnat questions concern the fundamental origin of some widely applicable scaling laws, as the Gutenberg-Richter frequency-magnitude relationship, the modified Omori law or the Omori-Utsu law for aftershock decay and Bath's law for the difference between the magnitude of the largest aftershock and mainshock.

The frequency-magnitude distribution (Gutenberg and Richter, 1944), firstly examinated, describes the relation between the frequency of occurence and magnitude of earthquake

© 2013 Hamdache et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Hamdache et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

$$\log\_{10} \text{N}(m) = a - bm \tag{1}$$

The fractal dimension *D*2 deduced from the correlation integral is used to carry out the spatial analysis of the studied sequences. The inter-event distances analysis is performed for the different aftershock sequences and the density of probability of the inter-event distances are derived using non-parametric approach, especially using the kernel density estimation

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

http://dx.doi.org/10.5772/54888

41

In this section we give a large overview of the tectonic skech and the seismicity of the studied region (Pelaéz et al., 2012). The Morocco-Algeria region, namely the Maghrebian region (Fig. 1) occupies the NW part of the African (Nubia) Plate in what is referred to its continental crust. Its oceanic crust continues till the area of the Azores Islands. To the North it is immediately situated the Eurasian Plate, although between the Gibraltar Arc and the South of Italy an intermediate complex domain is intercalated. This domain is formed by some oceanic basins, as is the Algero-Provençal Basin and the Thyrrehnian Basin, and by a former region, presently disintegrated and now forming the Betic-Rifean Internal Zone, the Kabylias (in Algeria), the Peloritani Mountains (Sicily) and the Calabrian area in Italy (AlKaPeCa domain). This area underwent from the early Miocene a northwards subduction of Africa, then opening the small

oceanic basins quoted, accompanied by the disintegration of the AlKaPeCa domain.

**Figure 1.** Tectonic sketch showing the main tectonic domains in the studied region.

Presently, the convergence between the Nubia Plate and Iberia has an approximate NNW-SSE direction, with values of the order of 3 to 5 cm/year, according the places. This compression is accompanied, at least in the area of the Gibraltar Arc (in the Alboran Sea) by a noticeable ENE-WSW tension, in some cases even more important than the compression. For this reason, in the Alboran area, some extensional movements can be important The Maghrebian region is also a complex area in which the Saharan Shield affected by the Pan-African Orogeny (Pre‐ cambrian to early Cambrian) is in contact with the Atlasic Mountains of mainly Alpine age

technics (Silverma, 1986).

**2. Tectonic sketch and seismicity overview**

where, *N* (*m*) is the cumulative number of events with magnitude larger than or equal to *m a* and *b* are constants. The parameter *a* showing the activity level of seismicity exhibits significant variation from region to region becauses it depends on the period of observations and area of investigation. The parameter *b* describes the size distribution of events and is related to tectonic characteristics of the region under investigation. It is shown that the estimated coefficient *b* varies mostly from 0.6 to 1.4 (Weimer and Katsumata, 1999). Many factors can cause pertur‐ bations of the *b* value. For example it is established that the least square procedure introduce systematic biais in the estimation of the *b* parameter (Marzocchi and Sandri, 2003; Sandri and Marzocchi, 2005). The *b* value of a region not only reflects the relative proportion of the number of large and small earthquakes in the region, but is also related to the stress condition over the region. The physical implication of the *b* value, however, is not as obvious, is still under investigation.

The temporal decay of aftershocks is important task because it contains information about seismogenic process and physical condition in the source region. It is well known that the occurrence rate of aftershock sequences in time is empirically well described by the Omori-Utsu law as proposed by Utsu (Utsu, 1969). The power law decay represented by the Omori-Utsu relation is an example of temporal self-similarity of the earthquake source process. The variability of the parameter *p*-value is related to the structural heterogeneity, stress and temperature in the crust (Mogi, 1962; Kisslinger and Jones, 1991). The importance to derive reliable *p*-value, is due to the fact that it contains information about the mechanism of stress relaxation and friction law in seismogenic zones (Mikumo and Miyatake, 1979), but this information cannot be derived without a precise characterization of the empirical relations that best fit the data. In this study we examine the temporal patterns of aftershock distribution of earthquakes occurred in Algeria-Morocco region. The parameters of Omori-Utsu law are estimated by the maximum likelihood method, assuming that the seismicity follow a nonstationary Poisson process. Two statistical models, a first stage Omori-Utsu model, model without secondary aftershock and a two stage Omori-Utsu model including the existence of secondary aftershock activity, are tested for goodness of fit to aftershock data. We adopt the Akaike Information Criterion denoted *AIC*, (Akaike, 1974) as a measure for selecting the best among competing models, using fixed data.

A model describing the temporal behavior of cumulative moment release in aftershock sequences is analyzed as alternative approach with respect to the Omori-Utsu law. In this model the static fatigue is assumed to be the principal explanation of the aftershock temporal behavior. Following Marcellini (1997), the different aftershock sequences are analyzed using this model. The most important result shows that globally the model explain and fit correctly the data.

Modified Bath's law is analyzed for each aftershock sequence, it allows us to derive some important properties related to the energy partionning. This approach is used to derive the energy dropped during the mainshock.

The fractal dimension *D*2 deduced from the correlation integral is used to carry out the spatial analysis of the studied sequences. The inter-event distances analysis is performed for the different aftershock sequences and the density of probability of the inter-event distances are derived using non-parametric approach, especially using the kernel density estimation technics (Silverma, 1986).

#### **2. Tectonic sketch and seismicity overview**

<sup>10</sup> log *N m a bm* ( ) = - (1)

where, *N* (*m*) is the cumulative number of events with magnitude larger than or equal to *m a* and *b* are constants. The parameter *a* showing the activity level of seismicity exhibits significant variation from region to region becauses it depends on the period of observations and area of investigation. The parameter *b* describes the size distribution of events and is related to tectonic characteristics of the region under investigation. It is shown that the estimated coefficient *b* varies mostly from 0.6 to 1.4 (Weimer and Katsumata, 1999). Many factors can cause pertur‐ bations of the *b* value. For example it is established that the least square procedure introduce systematic biais in the estimation of the *b* parameter (Marzocchi and Sandri, 2003; Sandri and Marzocchi, 2005). The *b* value of a region not only reflects the relative proportion of the number of large and small earthquakes in the region, but is also related to the stress condition over the region. The physical implication of the *b* value, however, is not as obvious, is still under

The temporal decay of aftershocks is important task because it contains information about seismogenic process and physical condition in the source region. It is well known that the occurrence rate of aftershock sequences in time is empirically well described by the Omori-Utsu law as proposed by Utsu (Utsu, 1969). The power law decay represented by the Omori-Utsu relation is an example of temporal self-similarity of the earthquake source process. The variability of the parameter *p*-value is related to the structural heterogeneity, stress and temperature in the crust (Mogi, 1962; Kisslinger and Jones, 1991). The importance to derive reliable *p*-value, is due to the fact that it contains information about the mechanism of stress relaxation and friction law in seismogenic zones (Mikumo and Miyatake, 1979), but this information cannot be derived without a precise characterization of the empirical relations that best fit the data. In this study we examine the temporal patterns of aftershock distribution of earthquakes occurred in Algeria-Morocco region. The parameters of Omori-Utsu law are estimated by the maximum likelihood method, assuming that the seismicity follow a nonstationary Poisson process. Two statistical models, a first stage Omori-Utsu model, model without secondary aftershock and a two stage Omori-Utsu model including the existence of secondary aftershock activity, are tested for goodness of fit to aftershock data. We adopt the Akaike Information Criterion denoted *AIC*, (Akaike, 1974) as a measure for selecting the best

A model describing the temporal behavior of cumulative moment release in aftershock sequences is analyzed as alternative approach with respect to the Omori-Utsu law. In this model the static fatigue is assumed to be the principal explanation of the aftershock temporal behavior. Following Marcellini (1997), the different aftershock sequences are analyzed using this model. The most important result shows that globally the model explain and fit correctly

Modified Bath's law is analyzed for each aftershock sequence, it allows us to derive some important properties related to the energy partionning. This approach is used to derive the

investigation.

the data.

among competing models, using fixed data.

40 Earthquake Research and Analysis - New Advances in Seismology

energy dropped during the mainshock.

In this section we give a large overview of the tectonic skech and the seismicity of the studied region (Pelaéz et al., 2012). The Morocco-Algeria region, namely the Maghrebian region (Fig. 1) occupies the NW part of the African (Nubia) Plate in what is referred to its continental crust. Its oceanic crust continues till the area of the Azores Islands. To the North it is immediately situated the Eurasian Plate, although between the Gibraltar Arc and the South of Italy an intermediate complex domain is intercalated. This domain is formed by some oceanic basins, as is the Algero-Provençal Basin and the Thyrrehnian Basin, and by a former region, presently disintegrated and now forming the Betic-Rifean Internal Zone, the Kabylias (in Algeria), the Peloritani Mountains (Sicily) and the Calabrian area in Italy (AlKaPeCa domain). This area underwent from the early Miocene a northwards subduction of Africa, then opening the small oceanic basins quoted, accompanied by the disintegration of the AlKaPeCa domain.

**Figure 1.** Tectonic sketch showing the main tectonic domains in the studied region.

Presently, the convergence between the Nubia Plate and Iberia has an approximate NNW-SSE direction, with values of the order of 3 to 5 cm/year, according the places. This compression is accompanied, at least in the area of the Gibraltar Arc (in the Alboran Sea) by a noticeable ENE-WSW tension, in some cases even more important than the compression. For this reason, in the Alboran area, some extensional movements can be important The Maghrebian region is also a complex area in which the Saharan Shield affected by the Pan-African Orogeny (Pre‐ cambrian to early Cambrian) is in contact with the Atlasic Mountains of mainly Alpine age (Fig. 1). To the North of the Atlas is situated the Moroccan Meseta, to the West, and the High Plateaus in Algeria, which to the North contact with the Rif and Tell mountains, typically Alpine chains. The Saharan Shield forms part of the Precambrian areas of Africa, clearly cratonized and generally not affected by later important deformations. In fact, in the Magh‐ rebian area it corresponds to a clearly stable area. In Morocco, the so called Antiatlas, corre‐ sponds to a Precambrian and, mainly, Paleozoic area, making a tectonic transition between the shield and the Atlas. The Atlasic Mountains correspond to an intracontinental chain. To the West, in Morocco, the High Atlas reach the coast in the Agadir area and continues to the Northeast and East, passing, although with lesser heights, to the Saharan Atlas, which cross Algeria and reach the central part of Tunis. They can be considered as aulacogens bordering the northern part of the Saharan shield. To the North, the Middle Atlas in Morocco has a different direction, NE-SW, separating the Moroccan Meseta and the High Plateaus, both forming by Paleozoic rocks, although with a Mesozoic and Tertiary cover, well developed in some areas. On the whole, the Atlasic Mountains has been tectonically unstable from the Triassic times, and along the Alpine orogeny suffered important deformations and, more recently, also important volcanism, reaching the Quaternary. The Rif and Tell thrust south‐ wards the Moroccan Meseta and the High Plateaus, and even in some places part of the Atlasic Mountains. They are formed by sedimentary External zones (only slightly affected by meta‐ morphism in some Moroccan places) and by Internal zones. Mostly Internal zones (divided in several tectonic complexes) are affected by alpine metamorphism, moreover the existence of previous Paleozoic and even older deformations. In any case, their present structure has being formed during the Alpine Orogeny. They appear mainly to the E of Tetuan, in Morocco, and in the Kabylias, in Algeria. These Alpine chains have being structured from the Cretaceous to the Oligocene-early Miocene. Later, were formed numerous Neogene basins, clearly cutting in many cases previous structures. In this time, particularly from the late Miocene to the present, a near N-S compression provoked the existence of strike-slip faults (NE-SW, sinistral, and NW-SE, dextral), moreover reverse fault, many of which has N70ºE to E-W direction. In many cases, the cited strike-slip faults moved mainly as normal faults, releasing by this way the regional tension, practically perpendicular to the compression.

from the Spanish National Geographical Institut (IGN) earthquake catalog. For the sequences triggered by the May 21, 2003 Zemouri earthquake and by March 20, 2006 Laalam event, we used the data recorded by portable seismological stations network monitored by CRAAG. It is well known that the process to identify aftershock is related to the seismicity declustering process, a crucial step in separating an erthquake catalog into foreshock, aftershock and mainshock. This process is widely used in seismology, in particular for seismic hazard assessment and in earthquake prediction model. There are sevceral declustering algo‐ rithms that have been proposed. Up to now, most users have applied either the algo‐ rithm of Gardner and Knopoff (1974) or Reasenberg (1985). Gardner and Knopoff (1974) introduced a procedure for identifying aftershocks within seismicity catalog using interevent distances in time and space. They also provided specific space-time distances as a function of mainshock magnitude to identify aftershocks. This method is known as a window method and is one of the most used. Reasenberg's algorithm (1985) allows tolink up aftershock triggering within an earthquake cluster: if A is the mainshock of B, and B is the mainshock of C, then all A, B and C are considered to belong to one common cluster. When defining a cluster, only the largest earthquake is finaly kept to be the cluster's mainshock. In this study we have used the single-link cluster algorithm (Frohlich and Davis, 1990). We first identify large magnitude within the database. Earthquakes occurring within a certain distance *d* in km and periode *T* in days after these potentialmainshock were extrated from the database. Aftershocks were then selected from this subset of events using single-link cluster algorithm (Frohlich and Davis, 1990). A space-time metric *D* is used to

define the proximity of events relative to one another. The metric is defined as

*t*

events and *B* is a constant relating time to distance. Afteshpocks are then defined as events within a *Dc*- size (critical size) cluster containing the mainshock. The single-link cluster analysis has been used with the parameters defined by Frohlich and Davis (1990), it is natural choice for aftershock selection because it avoids subjective decision-making with regard to the spatial distribution and duration of the sequence, it requires no assumption as the efficiency of event triggering, as is necessary when applying other clustering algorithms

The May 26, 1994 Al Hoceima earthquake (Mw 6.0) took place at 12 km depth, the focal mechanism indicates the presence of a main set of sinistral fault with a N-S trend, which may involve several parallel surface (Calvert et al., 1997). Analysis of the aftershock sequence highlighted the presence of NNE-SSW distribution of the seismicity (El Alami et al., 1998). The sequence used covers a period of about one year from the mainshock, including 318 events with magnitude ranged from 2.0 to 6.0. The February 24, 2004 Al Hoceima earthquake (Mw 6.1) took place at a depth of 10 to 14 km. The focal mechanism suggests that the active nodal plane corresponds to a sinistral strike-slip fault oriented N11 N and dipping 70 toward the E

where *d* is the distance between two epicenters *Δ*

(e.g. Reasenberg, 1985).

2 22 *D dB <sup>t</sup>* = +D (2)

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

http://dx.doi.org/10.5772/54888

43

is the temporal separation between two

In this study, we analyze the aftershock sequences triggered by some important and damaging earthquakes which occurred in the Morocco-Algeria region. The seismic activity in this region is mainly characterized by moderate to destructive magnitude events. It has been the site of numereous historical earthquakes, and was therefore subject to extensive damage and several thousands of casualties in the past. Among the largest recorded earthquake in Morocco, the February 29, 1960 Agadir (Morocco) earthquake (Ms6.0), the May 26, 1994 and February 24, 2004 Al Hoceima earthquakes with Mw6.0 and Mw6.1 respectively (Pelàez et al., 2007). In northern Algeria, earthquakes up to magnitude Ms 7.3 have been recorded, namely the October 10, 1980 El Asnam earthquake (Ms 7.3) (Ouyed et al.,1981) and May 21, 2003 Zemouri earthquake (Mw6.9) earthquake, (Hamdache et al., 2004). It is important to point out that these two events were the most damaging events occurred in northern Algeria and, the region of EL Asnam experienced in the past damaging earthquake on 09 September 1954 (Hamdache et al., 2010). The original epicentral data‐ base and the arrival time readings of the different aftershock sequences used, were obtained

from the Spanish National Geographical Institut (IGN) earthquake catalog. For the sequences triggered by the May 21, 2003 Zemouri earthquake and by March 20, 2006 Laalam event, we used the data recorded by portable seismological stations network monitored by CRAAG. It is well known that the process to identify aftershock is related to the seismicity declustering process, a crucial step in separating an erthquake catalog into foreshock, aftershock and mainshock. This process is widely used in seismology, in particular for seismic hazard assessment and in earthquake prediction model. There are sevceral declustering algo‐ rithms that have been proposed. Up to now, most users have applied either the algo‐ rithm of Gardner and Knopoff (1974) or Reasenberg (1985). Gardner and Knopoff (1974) introduced a procedure for identifying aftershocks within seismicity catalog using interevent distances in time and space. They also provided specific space-time distances as a function of mainshock magnitude to identify aftershocks. This method is known as a window method and is one of the most used. Reasenberg's algorithm (1985) allows tolink up aftershock triggering within an earthquake cluster: if A is the mainshock of B, and B is the mainshock of C, then all A, B and C are considered to belong to one common cluster. When defining a cluster, only the largest earthquake is finaly kept to be the cluster's mainshock. In this study we have used the single-link cluster algorithm (Frohlich and Davis, 1990). We first identify large magnitude within the database. Earthquakes occurring within a certain distance *d* in km and periode *T* in days after these potentialmainshock were extrated from the database. Aftershocks were then selected from this subset of events using single-link cluster algorithm (Frohlich and Davis, 1990). A space-time metric *D* is used to define the proximity of events relative to one another. The metric is defined as

(Fig. 1). To the North of the Atlas is situated the Moroccan Meseta, to the West, and the High Plateaus in Algeria, which to the North contact with the Rif and Tell mountains, typically Alpine chains. The Saharan Shield forms part of the Precambrian areas of Africa, clearly cratonized and generally not affected by later important deformations. In fact, in the Magh‐ rebian area it corresponds to a clearly stable area. In Morocco, the so called Antiatlas, corre‐ sponds to a Precambrian and, mainly, Paleozoic area, making a tectonic transition between the shield and the Atlas. The Atlasic Mountains correspond to an intracontinental chain. To the West, in Morocco, the High Atlas reach the coast in the Agadir area and continues to the Northeast and East, passing, although with lesser heights, to the Saharan Atlas, which cross Algeria and reach the central part of Tunis. They can be considered as aulacogens bordering the northern part of the Saharan shield. To the North, the Middle Atlas in Morocco has a different direction, NE-SW, separating the Moroccan Meseta and the High Plateaus, both forming by Paleozoic rocks, although with a Mesozoic and Tertiary cover, well developed in some areas. On the whole, the Atlasic Mountains has been tectonically unstable from the Triassic times, and along the Alpine orogeny suffered important deformations and, more recently, also important volcanism, reaching the Quaternary. The Rif and Tell thrust south‐ wards the Moroccan Meseta and the High Plateaus, and even in some places part of the Atlasic Mountains. They are formed by sedimentary External zones (only slightly affected by meta‐ morphism in some Moroccan places) and by Internal zones. Mostly Internal zones (divided in several tectonic complexes) are affected by alpine metamorphism, moreover the existence of previous Paleozoic and even older deformations. In any case, their present structure has being formed during the Alpine Orogeny. They appear mainly to the E of Tetuan, in Morocco, and in the Kabylias, in Algeria. These Alpine chains have being structured from the Cretaceous to the Oligocene-early Miocene. Later, were formed numerous Neogene basins, clearly cutting in many cases previous structures. In this time, particularly from the late Miocene to the present, a near N-S compression provoked the existence of strike-slip faults (NE-SW, sinistral, and NW-SE, dextral), moreover reverse fault, many of which has N70ºE to E-W direction. In many cases, the cited strike-slip faults moved mainly as normal faults, releasing by this way

42 Earthquake Research and Analysis - New Advances in Seismology

the regional tension, practically perpendicular to the compression.

In this study, we analyze the aftershock sequences triggered by some important and damaging earthquakes which occurred in the Morocco-Algeria region. The seismic activity in this region is mainly characterized by moderate to destructive magnitude events. It has been the site of numereous historical earthquakes, and was therefore subject to extensive damage and several thousands of casualties in the past. Among the largest recorded earthquake in Morocco, the February 29, 1960 Agadir (Morocco) earthquake (Ms6.0), the May 26, 1994 and February 24, 2004 Al Hoceima earthquakes with Mw6.0 and Mw6.1 respectively (Pelàez et al., 2007). In northern Algeria, earthquakes up to magnitude Ms 7.3 have been recorded, namely the October 10, 1980 El Asnam earthquake (Ms 7.3) (Ouyed et al.,1981) and May 21, 2003 Zemouri earthquake (Mw6.9) earthquake, (Hamdache et al., 2004). It is important to point out that these two events were the most damaging events occurred in northern Algeria and, the region of EL Asnam experienced in the past damaging earthquake on 09 September 1954 (Hamdache et al., 2010). The original epicentral data‐ base and the arrival time readings of the different aftershock sequences used, were obtained

$$D = \sqrt{d^2 + B^2 \Lambda\_t^2} \tag{2}$$

where *d* is the distance between two epicenters *Δ t* is the temporal separation between two events and *B* is a constant relating time to distance. Afteshpocks are then defined as events within a *Dc*- size (critical size) cluster containing the mainshock. The single-link cluster analysis has been used with the parameters defined by Frohlich and Davis (1990), it is natural choice for aftershock selection because it avoids subjective decision-making with regard to the spatial distribution and duration of the sequence, it requires no assumption as the efficiency of event triggering, as is necessary when applying other clustering algorithms (e.g. Reasenberg, 1985).

The May 26, 1994 Al Hoceima earthquake (Mw 6.0) took place at 12 km depth, the focal mechanism indicates the presence of a main set of sinistral fault with a N-S trend, which may involve several parallel surface (Calvert et al., 1997). Analysis of the aftershock sequence highlighted the presence of NNE-SSW distribution of the seismicity (El Alami et al., 1998). The sequence used covers a period of about one year from the mainshock, including 318 events with magnitude ranged from 2.0 to 6.0. The February 24, 2004 Al Hoceima earthquake (Mw 6.1) took place at a depth of 10 to 14 km. The focal mechanism suggests that the active nodal plane corresponds to a sinistral strike-slip fault oriented N11 N and dipping 70 toward the E (Stich et al., 2005). The aftershocks were aligned preferently in NNE-SSW, in the same way as one of the nodal planes of the focal mechanism. As pointed by Galindo-Zaldivar et al., (2009) the main stresses for the two aftershock sequences trigged by the May 26, 1994 and February 24, 2004 events have a trend with NW-SE compression (P-axis) and orthogonal NE-SW extension (T-axis) compatible with the present convergence of the Africa and Eurasia plate. The aftershock sequence includes 1233 events with magnitude ranged between 0.6 to 6.1. The time span of the sequence is about 1 year.

Many factors can bias the *b* value estimation. It is established for example that the least square procedure introduce systematic error in the estimation of the *b* parameters (Marzocchi and Sandri, 2003; Sandri and Marzocchi, 2005). Locally, the *b* value not only reflects the relative proportion of the number of large and small earthquakes in the region, but it is also related to the stress condition over the region (Mogi, 1962). The physical meaning of the *b* value is,

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

http://dx.doi.org/10.5772/54888

45

The first step in the analysis of the Gutenberg-Richter law, is the determination of the threshold magnitude of completness. It is defined as the lowest magnitude for which all the events are reliably detected (Rydelek and Sacks, 1989). There are many approaches to the estimation of

The maximum curvature (MAXC) method (Weimer and Wyss, 2000) defines the completeness magnitude as the magnitude for which the first derivative of the frequency magnitude curve is maximum (being the maximum of the non-cumulative frequency-magnitude distribution). The goodness of fit (GFT) method (Weimer and Wyss, 2000) compares the observed frequencymagnitude distribution with a synthetic distribution, and the goodness of fit is calculated as the absolute difference of the number of earthquake in each magnitude bins between the observed and synthetic distribution. The synthetic distribution is calculated using *a* and *b*values estimated from the observed dataset by increasing the cutoff magnitude. The complet‐ ness magnitude, is given by the magnitude for which 90% of the data are fitted by a straight line. The entire magnitude range (EMR) method was developed by Ogata and Katsura (1993) and modified later by Woessner and Weimer (2005). The maximum likelihood estimation method is used to estimate the power law G-R law parameters *a* and *b*. The same method is applied to estimate the mean and standard deviation of the Normal distribution considered for the incomplete part of the frequency-magnitude distribution. *μ* and *σ* are the magnitude at which 50*%* of the earthquakes are detected and the standard deviation describing the width

The frequency-magnitude distribution as shown previously is defined as,(Gutenberg and

where, *N* (≥*m*) is the cumlulative number of earthquakes with magnitudes greater than or equal to magnitude *m*, and *a* and *b* are constants. This relationship holds for global earthquake catalogs and is applicable to aftershock sequences as well. The estimation of the *b*- value has been the subject of considerable research, and various methods exist. The most statistically appealing of these is the maximum likelihood method first used independently by Aki (1965)

> 10 min

log *<sup>e</sup> <sup>b</sup> m m* <sup>=</sup> -

<sup>10</sup> *Log N m a bm* ( ) ³=- (4)

\$ (5)

of the range where earthquakes are partially detected, respectively.

and Utsu (1965), which gives the estimate of the *b*- value as

however not clear and still under investigation.

*mc*, the most popular are;

Richter, 1954)

The October 10, 1980 El Asnam earthquake (Mw 7.3) is one of the most important and most damaging event occurred in northern Algeria. This event has taken place on the Oued-Fodda reversse fault. The later is segmented into three segments, ruptured along 26 km. This fault is located in the Cheliff high seismogenic Quaternary bassin, considered as very active. It is important to point out that almost all the seismicity in northern Algeria is located around the Plio-Quaternary intermountains active bassins (Meghraoui et al., 1996). The aftershock sequence used include the 130 most important magnitude events, ranged between 2.4 and 7.3. In the same way, the May 21, 2003 earthquake (Mw 6.9) has been located in the NE continuation of the south reversse fault system of the Quaternary Mitidja bassin (Maouche et al., 2011). The aftershock sequence we used include 1555 magnitude events, ranged between 0.9 to 6.9 and recorded during the first 40 days from the main shock (Hamdache et al., 2004). The March 20, 2006 Laalam earthquake (Mw 5.2), was located in the Babor chain, in the 'Petite Kabylie' south of Bejaia city. This chain belongs to the Tell Atlas, which is a portion of the Alpine belt in northern Africa. As pointed out by Beldjoudi et al., (2009) the region is affected by several faults. The regional seismicity analysis shows that the Babors chain seems to belongs to a "transition zone" between a large belt of reverse faulting along the western and central part of northern Algeria and a more distributed zone where deformation is mainly accomodated through strike-slip faulting (Beldjoudi et al., 2009). The aftershock sequence include 111 of the best recorded events with more than 54 with *RMS* < 0.3*s*, *ERH* < 3*km* and *ERZ* < 3*km*. The event magnitude varies between 1.3 and 5.2.

#### **3. Magnitude-frequency relationship**

The frequency-size distribution (Gutenberg and Richter, 1944) describes the relation between the frequency of occurrence and the magnitude of earthquake

$$-\log\_{10} N(m) = a - bm \quad ; \quad m\_c \le m \tag{3}$$

the statistic *N* (*m*) is the cumulative number of events with magnitude larger than or equal to *m*, whereas *a* and *b* are positive constant. The parameter *a* which exhibits significant variations in space measures the activity level of seismicity. This parameter is sensitive to the input period of observation and area of investigation. The parameters *b* describes the size distribution of events and is related to tectonic characteristics of the region under investigation. It is shown that the estimated coefficient *b* varies mostly from 0.6 to 1.4 (Weimer and Katsumata, 1999). Many factors can bias the *b* value estimation. It is established for example that the least square procedure introduce systematic error in the estimation of the *b* parameters (Marzocchi and Sandri, 2003; Sandri and Marzocchi, 2005). Locally, the *b* value not only reflects the relative proportion of the number of large and small earthquakes in the region, but it is also related to the stress condition over the region (Mogi, 1962). The physical meaning of the *b* value is, however not clear and still under investigation.

(Stich et al., 2005). The aftershocks were aligned preferently in NNE-SSW, in the same way as one of the nodal planes of the focal mechanism. As pointed by Galindo-Zaldivar et al., (2009) the main stresses for the two aftershock sequences trigged by the May 26, 1994 and February 24, 2004 events have a trend with NW-SE compression (P-axis) and orthogonal NE-SW extension (T-axis) compatible with the present convergence of the Africa and Eurasia plate. The aftershock sequence includes 1233 events with magnitude ranged between 0.6 to 6.1. The

The October 10, 1980 El Asnam earthquake (Mw 7.3) is one of the most important and most damaging event occurred in northern Algeria. This event has taken place on the Oued-Fodda reversse fault. The later is segmented into three segments, ruptured along 26 km. This fault is located in the Cheliff high seismogenic Quaternary bassin, considered as very active. It is important to point out that almost all the seismicity in northern Algeria is located around the Plio-Quaternary intermountains active bassins (Meghraoui et al., 1996). The aftershock sequence used include the 130 most important magnitude events, ranged between 2.4 and 7.3. In the same way, the May 21, 2003 earthquake (Mw 6.9) has been located in the NE continuation of the south reversse fault system of the Quaternary Mitidja bassin (Maouche et al., 2011). The aftershock sequence we used include 1555 magnitude events, ranged between 0.9 to 6.9 and recorded during the first 40 days from the main shock (Hamdache et al., 2004). The March 20, 2006 Laalam earthquake (Mw 5.2), was located in the Babor chain, in the 'Petite Kabylie' south of Bejaia city. This chain belongs to the Tell Atlas, which is a portion of the Alpine belt in northern Africa. As pointed out by Beldjoudi et al., (2009) the region is affected by several faults. The regional seismicity analysis shows that the Babors chain seems to belongs to a "transition zone" between a large belt of reverse faulting along the western and central part of northern Algeria and a more distributed zone where deformation is mainly accomodated through strike-slip faulting (Beldjoudi et al., 2009). The aftershock sequence include 111 of the best recorded events with more than 54 with *RMS* < 0.3*s*, *ERH* < 3*km* and *ERZ* < 3*km*. The

The frequency-size distribution (Gutenberg and Richter, 1944) describes the relation between

the statistic *N* (*m*) is the cumulative number of events with magnitude larger than or equal to *m*, whereas *a* and *b* are positive constant. The parameter *a* which exhibits significant variations in space measures the activity level of seismicity. This parameter is sensitive to the input period of observation and area of investigation. The parameters *b* describes the size distribution of events and is related to tectonic characteristics of the region under investigation. It is shown that the estimated coefficient *b* varies mostly from 0.6 to 1.4 (Weimer and Katsumata, 1999).

<sup>10</sup> log () ; *N m a bm m* =- £ *mc* (3)

time span of the sequence is about 1 year.

44 Earthquake Research and Analysis - New Advances in Seismology

event magnitude varies between 1.3 and 5.2.

**3. Magnitude-frequency relationship**

the frequency of occurrence and the magnitude of earthquake

The first step in the analysis of the Gutenberg-Richter law, is the determination of the threshold magnitude of completness. It is defined as the lowest magnitude for which all the events are reliably detected (Rydelek and Sacks, 1989). There are many approaches to the estimation of *mc*, the most popular are;

The maximum curvature (MAXC) method (Weimer and Wyss, 2000) defines the completeness magnitude as the magnitude for which the first derivative of the frequency magnitude curve is maximum (being the maximum of the non-cumulative frequency-magnitude distribution). The goodness of fit (GFT) method (Weimer and Wyss, 2000) compares the observed frequencymagnitude distribution with a synthetic distribution, and the goodness of fit is calculated as the absolute difference of the number of earthquake in each magnitude bins between the observed and synthetic distribution. The synthetic distribution is calculated using *a* and *b*values estimated from the observed dataset by increasing the cutoff magnitude. The complet‐ ness magnitude, is given by the magnitude for which 90% of the data are fitted by a straight line. The entire magnitude range (EMR) method was developed by Ogata and Katsura (1993) and modified later by Woessner and Weimer (2005). The maximum likelihood estimation method is used to estimate the power law G-R law parameters *a* and *b*. The same method is applied to estimate the mean and standard deviation of the Normal distribution considered for the incomplete part of the frequency-magnitude distribution. *μ* and *σ* are the magnitude at which 50*%* of the earthquakes are detected and the standard deviation describing the width of the range where earthquakes are partially detected, respectively.

The frequency-magnitude distribution as shown previously is defined as,(Gutenberg and Richter, 1954)

$$\text{Log}\_{10}\text{N}\{\geq m\} = a \quad - \quad bm \tag{4}$$

where, *N* (≥*m*) is the cumlulative number of earthquakes with magnitudes greater than or equal to magnitude *m*, and *a* and *b* are constants. This relationship holds for global earthquake catalogs and is applicable to aftershock sequences as well. The estimation of the *b*- value has been the subject of considerable research, and various methods exist. The most statistically appealing of these is the maximum likelihood method first used independently by Aki (1965) and Utsu (1965), which gives the estimate of the *b*- value as

$$
\hat{b} = \frac{\log\_{10} e}{m - m\_{\text{min}}} \tag{5}
$$

where *m*min is the minimum magnitude up to which the Gutenberg-Richter law can accurately represent the cumuluative number of earthquakes larger than or equal to a given magnotude, and *<sup>m</sup>*¯ is the average magnitude. The definition of *m*min origionates from the definition of the probability density function for magnitudes, *f* (*m*), consistent with the mathematical form of the Gutenberg-Richter law. This is given as (Bender, 1983)

$$f(m) = \frac{\lambda \exp\left[-\lambda \left(m - m\_{\rm min}\right)\right]}{1 - \exp\left[-\lambda \left(m\_{\rm max} - m\_{\rm min}\right)\right]}\tag{6}$$

It is straightforward to see that for *n* → *∞*, equation (6) gives (Tinti et al.,1987; Gutorp et al.,

*m m m*

(Tinti and Mulargia, 1987; Gutorp and Hopkins, 1986). It has been observed, however, that for

For the two aftershock sequences triggered by the mainshocks occurred around Al Hocei‐ ma city in Morocco on 1994 and 2004, the threshold magnitude *mc* has been examined in details, using the different procedures introduced previously, especially the maximum curvature procedure MAXC (Weimer and Wyss, 2000) and the changing point procedure introduced by Amores, (2007). The results obtained for these two aftershock sequences, are

(a) (b)

**Figure 2.** Graphs showing the non cumulative number of events, the threshold magnitide and the adjustment of the cumulative number by straight line with equation *Log*10*N* (≥*m*) = *a* − *bm* for *m*≥*Mc*. (a) For Al Hoceima 1994 afe‐

In Fig.2, the frequency-magnitude relation for the 1994 and 2004 aftershocks series of Al Hoceima (Morocco) are displayed. Based on maximum curvature procedure (MAXC), the magnitude of completeness was taken equal to 2.8 for the 1994 aftershock seqiuence and 3.4 for the 2004 sequence. It is important to point out that the changing point procedure (Amores, 2007) gives the same results. Using these threshold magnitudes, we derive the *b*-value of the Gutenberg-Richter relationship and its standard deviation using the maximum likelihood procedure. The *b*-value is estimated equal to 0.92 ± 0.02 for the 1994 aftershock sequence and 1.073 ± 0.003 for the 2004 series. For both sequences the *b*-value obtained is close to 1.0, the typical value for aftershock sequence. The obtained parameter *a* is equal to 4.689 ± 0.058 for the 1994 aftershock series and equal to 6.305 ± 0.014 for the 2004 aftershock sequence. The results obtained for the aftershock sequences triggered by the events occurred in northern

*c*

\$ (8)

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

^ obtained from

http://dx.doi.org/10.5772/54888

47

^ obtained from equation (7) (Bender,

d

æ ö

<sup>10</sup> 1

= + ç ÷ - è ø

*Log e <sup>m</sup> <sup>b</sup> Ln*

d

a difference of about 3.0 in magnitude between *m*min and *m*max, the value of *b*

equation (6) agrees closely with the asymptotic value of *b*

shock sequence and (b) for Al Hoceima 2004 aftershock sequence.

1986).

1983).

shown in Fig. 2

where *m*max is the maximum magnitude up to which *f* (*m*) describes the distribution of magnitudes and *λ* = *bLn*(10). There are two problems with equation (4) when applied to real earthquake catalogs. Firstly, it considers reported earthquake magnitudes as a continuous variable, which is not accurate as most earthquake catalogs report magnitudes up to a precision of one decimal place for each event. Therefore, magnitude should be considered as a grouped or binned variable with a finite non zero bin length *δm*, which generally and in our case it is taken equal to 0.1, *δm* = 0.1. This means that instead of observing *m*min physically in the catalog,

we observe a different minimum magnitude *mc* = *m*min + *δm* <sup>2</sup> , which is the aforementioned completeness magnitude. This is the smallest observed magnitude in the catalog above which the cumulative number of earthquakes, above a given magnitude, are accurately described by the Gutenberg-Richter law. It is very important to note that the minimum magnitude of completeness *mc*, physically observed in the catalog, is not present in the equation (4), and hence we need to express *m*min in terms of *mc* to be able to use the formula for real catalog. Assuming that *m*min = *mc* would lead to a bias in the estimate. The other source of inaccuray in equation (4) is the fact that it considers the maximum magnitude value for the dataset to be infinite, which is never the case. in fact, for aftershock sequences, the maximum magnitude in the sequence can be pretty small. This too introduces a bias in the estimate of the *b*- value obtained using the equation (4) (Bender, 1983; Tinti and Mulargia, 1987; Guttorp and Hopkins, 1986). This problem was considered by Bender (1983), and she gave a method for obtaining the *b*- value of grouped and finite maximum magnitude data as a function of the root of the following equation

$$\frac{q}{1-q} + \frac{nq^n}{1-q^n} = \frac{\overline{m} - m\_{\text{min}} - \frac{1}{2}\delta m}{\delta m} \tag{7}$$

where *q* = exp − *Ln*(10).*b* ^ .*δm* and *<sup>n</sup>* <sup>=</sup> (*m*max <sup>−</sup> *<sup>m</sup>*min) *<sup>δ</sup>m*. It is straightforward to see that for *n* → *∞*, equation (6) gives (Tinti et al.,1987; Gutorp et al., 1986).

where *m*min is the minimum magnitude up to which the Gutenberg-Richter law can accurately represent the cumuluative number of earthquakes larger than or equal to a given magnotude, and *<sup>m</sup>*¯ is the average magnitude. The definition of *m*min origionates from the definition of the probability density function for magnitudes, *f* (*m*), consistent with the mathematical form of

> ( ) ( ) min max min

(6)

(7)

*m m*

ë û

*δm*

<sup>2</sup> , which is the aforementioned

*m m*

 l

é ù - - ë û <sup>=</sup> -- - é ù

where *m*max is the maximum magnitude up to which *f* (*m*) describes the distribution of magnitudes and *λ* = *bLn*(10). There are two problems with equation (4) when applied to real earthquake catalogs. Firstly, it considers reported earthquake magnitudes as a continuous variable, which is not accurate as most earthquake catalogs report magnitudes up to a precision of one decimal place for each event. Therefore, magnitude should be considered as a grouped or binned variable with a finite non zero bin length *δm*, which generally and in our case it is taken equal to 0.1, *δm* = 0.1. This means that instead of observing *m*min physically in the catalog,

completeness magnitude. This is the smallest observed magnitude in the catalog above which the cumulative number of earthquakes, above a given magnitude, are accurately described by the Gutenberg-Richter law. It is very important to note that the minimum magnitude of completeness *mc*, physically observed in the catalog, is not present in the equation (4), and hence we need to express *m*min in terms of *mc* to be able to use the formula for real catalog. Assuming that *m*min = *mc* would lead to a bias in the estimate. The other source of inaccuray in equation (4) is the fact that it considers the maximum magnitude value for the dataset to be infinite, which is never the case. in fact, for aftershock sequences, the maximum magnitude in the sequence can be pretty small. This too introduces a bias in the estimate of the *b*- value obtained using the equation (4) (Bender, 1983; Tinti and Mulargia, 1987; Guttorp and Hopkins, 1986). This problem was considered by Bender (1983), and she gave a method for obtaining the *b*- value of grouped and finite maximum magnitude data as a function of the root of the

min


d

*mm m*

*<sup>δ</sup>m*.

1 2

d

l

the Gutenberg-Richter law. This is given as (Bender, 1983)

46 Earthquake Research and Analysis - New Advances in Seismology

*f m*

we observe a different minimum magnitude *mc* = *m*min +

1 1

*q nq*

+ = - -

*n n*

^ .*δm* and *<sup>n</sup>* <sup>=</sup> (*m*max <sup>−</sup> *<sup>m</sup>*min)

*q m q*

following equation

where *q* = exp − *Ln*(10).*b*

exp ( ) 1 exp

l

$$\hat{b}^{\quad} = \frac{\text{Log}\_{10}e}{\delta m} \text{Ln} \left( 1 + \frac{\delta m}{m - m\_c} \right) \tag{8}$$

(Tinti and Mulargia, 1987; Gutorp and Hopkins, 1986). It has been observed, however, that for a difference of about 3.0 in magnitude between *m*min and *m*max, the value of *b* ^ obtained from

equation (6) agrees closely with the asymptotic value of *b* ^ obtained from equation (7) (Bender, 1983).

For the two aftershock sequences triggered by the mainshocks occurred around Al Hocei‐ ma city in Morocco on 1994 and 2004, the threshold magnitude *mc* has been examined in details, using the different procedures introduced previously, especially the maximum curvature procedure MAXC (Weimer and Wyss, 2000) and the changing point procedure introduced by Amores, (2007). The results obtained for these two aftershock sequences, are shown in Fig. 2

**Figure 2.** Graphs showing the non cumulative number of events, the threshold magnitide and the adjustment of the cumulative number by straight line with equation *Log*10*N* (≥*m*) = *a* − *bm* for *m*≥*Mc*. (a) For Al Hoceima 1994 afe‐ shock sequence and (b) for Al Hoceima 2004 aftershock sequence.

In Fig.2, the frequency-magnitude relation for the 1994 and 2004 aftershocks series of Al Hoceima (Morocco) are displayed. Based on maximum curvature procedure (MAXC), the magnitude of completeness was taken equal to 2.8 for the 1994 aftershock seqiuence and 3.4 for the 2004 sequence. It is important to point out that the changing point procedure (Amores, 2007) gives the same results. Using these threshold magnitudes, we derive the *b*-value of the Gutenberg-Richter relationship and its standard deviation using the maximum likelihood procedure. The *b*-value is estimated equal to 0.92 ± 0.02 for the 1994 aftershock sequence and 1.073 ± 0.003 for the 2004 series. For both sequences the *b*-value obtained is close to 1.0, the typical value for aftershock sequence. The obtained parameter *a* is equal to 4.689 ± 0.058 for the 1994 aftershock series and equal to 6.305 ± 0.014 for the 2004 aftershock sequence. The results obtained for the aftershock sequences triggered by the events occurred in northern Algeria, namely the October 10, 1980 El Asnam earthquake (Mw 7.3), the May 21, 2003 Zemouri earthquake (Mw 6.9) and March 20, 2006 Laalam earthquake (Mw 5.2) are displayed in the following Fig. 3.

( ) ( ) *<sup>p</sup> <sup>k</sup> <sup>t</sup> t c*

+

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

*λ*(*t*) is the rate of occurrence of aftershocks per unit time, at time *t* after the mainshock (*t* = 0). The parameters *k*, *c* and *p* are positive constants. *k* depends on the total number of events in the sequence, *c* on the rate of activity in the earliest part of the sequence and *p* is related to the power law decay of aftershocks. It is generally accepted that the number of aftershocks cannot be counted completely in the beginning of the sequence when small shock are often obscured by large ones due to overlaping, thus an overly large value of the parameter *c* is obtained. After Utsu, (1971), the parameter *c* must be zero if all shocks could be counted. Two opinions constitue the nowdays debate around the *c* value: one is that *c* value is essentially zero and all reported positive *c* value results from incompletness in the early stage of an aftershock sequence; the second point of view is that *c* value do exist (Enescu and Ito, 2002; Kagan, 2004; Shcherbakov et al. 2004a, b; 2005, 2006; Enescu et al. 2009). The constant *c* is a controversial quantity (Utsu et al. 1995; Enescu et al. 2009) and is mainly influenced by the incomplete detection of small aftershocks in the early stage of the sequence (Kisslinger and Jones, 1991). According to Olsson (1999), *p* values generally vary in the interval 0.5 to 1.8 and this index has shown by Utsu et al. (1995), differs from sequence to sequence and vary according to the tectonic condition of the region, however it is not clear which factor is the most significant in controlling *p* value. Although more attention in the estimation of the *p* value have been done to take into account the recommandation by Nyffenegger and Frolich (1998, 2000), we have use the standard use the standard deviation obtained by maximum likelihood which could be over or underestimating (Nyffenegger and Frolich, 1998; 2000).

In this study aftershock sequences are modeled using point process defined by the following

*t c*

+

with, ℑ*<sup>t</sup>* is the history of observation until time *t*, e.g the *σ*- algebra generated by the events occurred before the time *t*, thus, following Daley and Vere-Jones (2005), the family (ℑ*<sup>t</sup>* , *<sup>t</sup>* <sup>∈</sup> ℝ+) is called the natural filtration of the point process or the internal history. The conditional intensity in equation 4, is independent of the internal history and depends only on the current time *t*, like *λ*(*<sup>t</sup>* <sup>|</sup>ℑ*<sup>t</sup>* ). It defines a non-stationary (nonhomogeneous) Poisson process. We assume the occurrence time's of the aftershock sequence, namely {*t*<sup>1</sup> , *t*<sup>2</sup> , ............., *tn*} <sup>⊆</sup> *Ts* , *Te* are distributed according to a non-stationary Poisson process with conditional intensity function defined by equation 4. The parameters *k* , *p* and *c* are

( ) ( )*<sup>t</sup> <sup>p</sup> <sup>k</sup> <sup>t</sup>*

lÁ =

estimated by maximizing the following likelihood function

conditional intensity,

(9)

49

http://dx.doi.org/10.5772/54888

(10)

l=

**Figure 3.** Graph displaying the non cumulative number of event in blue circle and the adjustment of the cumulative number (red circles) by straight line, representing the Gutenberg-Richter relation for the aftershock sequence trig‐ gered by (a) October 10, 1980 El Asnam earthquake (b) by May 21, 2003 Zemouri earthquake and (c) by March 20, 2006 Laalam earthquake.

For the sequence of October 10,1980 El Asnam earthquake and March 20, 2006 Laalam earthque, we have used the maximum curvature procedure to derive the threshold magnitude, we obtained *mc* = 3.9 *mbLg* for the El Asnam 1980 aftershock sequence and *mc* = 2.1 *mbLg* for Laalam 2006 sequence. The higher value obtained for El Asnam series reflect the quality of the data include in the El Asnam series, it seems that the file doesn't include all the events. It is till now one of the "best" file including the mainshock and almost all the aftershock occurred just after the mainshock. The *b*-value obtained for these two series, 0.82 ± 0.10 for El Asnam series and 0.99 ± 0.10 for Laalam aftershock series are close to 1.0, a typical value for the aftershock sequences. For the Zemouri aftershock sequence we have used the best combination between *mc* obtained for 95*%* and 90% confidence and the maximum curvature procedure (Weimer and Wyss, 2000), which gives a threshold magnitude equal to *mc* = 3.5 *mbLg*. To improve the *b*-value analysis for this sequence, we obtained a threshold magnitude *mc* = 3.7 *mbLg*, using the proce‐ dure based on the stabilisation of the *b*-value and its uncertainty derived by Shi and Bolt (1982), as implemented by Weimer and Zuniga, (1994) in the software Zmap under Matlab. We obtained *b* = 1.10 ± 0.04 for the first procedure and *b* = 1.30 ± 0.06 for the second proce‐ dure, the difference between the two values is of the order of 0.20.

#### **4. Decay rate of aftershock activity — Omori-Utsu law**

The third studied scaling law is related to the decay rate of aftershock activity. It is well know that the decay rate of aftershock activity with time is governed by the modified Omori law or Omori-Utsu law (Utsu et al. 1995),

#### Scaling Properties of Aftershock Sequences in Algeria-Morocco Region http://dx.doi.org/10.5772/54888 49

$$\mathcal{A}(t) = \frac{k}{\binom{t+c}{t+c}^p} \tag{9}$$

*λ*(*t*) is the rate of occurrence of aftershocks per unit time, at time *t* after the mainshock (*t* = 0). The parameters *k*, *c* and *p* are positive constants. *k* depends on the total number of events in the sequence, *c* on the rate of activity in the earliest part of the sequence and *p* is related to the power law decay of aftershocks. It is generally accepted that the number of aftershocks cannot be counted completely in the beginning of the sequence when small shock are often obscured by large ones due to overlaping, thus an overly large value of the parameter *c* is obtained. After Utsu, (1971), the parameter *c* must be zero if all shocks could be counted. Two opinions constitue the nowdays debate around the *c* value: one is that *c* value is essentially zero and all reported positive *c* value results from incompletness in the early stage of an aftershock sequence; the second point of view is that *c* value do exist (Enescu and Ito, 2002; Kagan, 2004; Shcherbakov et al. 2004a, b; 2005, 2006; Enescu et al. 2009). The constant *c* is a controversial quantity (Utsu et al. 1995; Enescu et al. 2009) and is mainly influenced by the incomplete detection of small aftershocks in the early stage of the sequence (Kisslinger and Jones, 1991). According to Olsson (1999), *p* values generally vary in the interval 0.5 to 1.8 and this index has shown by Utsu et al. (1995), differs from sequence to sequence and vary according to the tectonic condition of the region, however it is not clear which factor is the most significant in controlling *p* value. Although more attention in the estimation of the *p* value have been done to take into account the recommandation by Nyffenegger and Frolich (1998, 2000), we have use the standard use the standard deviation obtained by maximum likelihood which could be over or underestimating (Nyffenegger and Frolich, 1998; 2000).

Algeria, namely the October 10, 1980 El Asnam earthquake (Mw 7.3), the May 21, 2003 Zemouri earthquake (Mw 6.9) and March 20, 2006 Laalam earthquake (Mw 5.2) are displayed in the

(a) (b) (c)

**Figure 3.** Graph displaying the non cumulative number of event in blue circle and the adjustment of the cumulative number (red circles) by straight line, representing the Gutenberg-Richter relation for the aftershock sequence trig‐ gered by (a) October 10, 1980 El Asnam earthquake (b) by May 21, 2003 Zemouri earthquake and (c) by March 20,

For the sequence of October 10,1980 El Asnam earthquake and March 20, 2006 Laalam earthque, we have used the maximum curvature procedure to derive the threshold magnitude, we obtained *mc* = 3.9 *mbLg* for the El Asnam 1980 aftershock sequence and *mc* = 2.1 *mbLg* for Laalam 2006 sequence. The higher value obtained for El Asnam series reflect the quality of the data include in the El Asnam series, it seems that the file doesn't include all the events. It is till now one of the "best" file including the mainshock and almost all the aftershock occurred just after the mainshock. The *b*-value obtained for these two series, 0.82 ± 0.10 for El Asnam series and 0.99 ± 0.10 for Laalam aftershock series are close to 1.0, a typical value for the aftershock sequences. For the Zemouri aftershock sequence we have used the best combination between *mc* obtained for 95*%* and 90% confidence and the maximum curvature procedure (Weimer and Wyss, 2000), which gives a threshold magnitude equal to *mc* = 3.5 *mbLg*. To improve the *b*-value analysis for this sequence, we obtained a threshold magnitude *mc* = 3.7 *mbLg*, using the proce‐ dure based on the stabilisation of the *b*-value and its uncertainty derived by Shi and Bolt (1982), as implemented by Weimer and Zuniga, (1994) in the software Zmap under Matlab. We obtained *b* = 1.10 ± 0.04 for the first procedure and *b* = 1.30 ± 0.06 for the second proce‐

dure, the difference between the two values is of the order of 0.20.

**4. Decay rate of aftershock activity — Omori-Utsu law**

Omori-Utsu law (Utsu et al. 1995),

The third studied scaling law is related to the decay rate of aftershock activity. It is well know that the decay rate of aftershock activity with time is governed by the modified Omori law or

following Fig. 3.

48 Earthquake Research and Analysis - New Advances in Seismology

2006 Laalam earthquake.

In this study aftershock sequences are modeled using point process defined by the following conditional intensity,

$$\mathcal{N}(t \Big| \mathfrak{I}\_t) = \frac{k}{\binom{t+c}{t+c}^p} \tag{10}$$

with, ℑ*<sup>t</sup>* is the history of observation until time *t*, e.g the *σ*- algebra generated by the events occurred before the time *t*, thus, following Daley and Vere-Jones (2005), the family (ℑ*<sup>t</sup>* , *<sup>t</sup>* <sup>∈</sup> ℝ+) is called the natural filtration of the point process or the internal history. The conditional intensity in equation 4, is independent of the internal history and depends only on the current time *t*, like *λ*(*<sup>t</sup>* <sup>|</sup>ℑ*<sup>t</sup>* ). It defines a non-stationary (nonhomogeneous) Poisson process. We assume the occurrence time's of the aftershock sequence, namely {*t*<sup>1</sup> , *t*<sup>2</sup> , ............., *tn*} <sup>⊆</sup> *Ts* , *Te* are distributed according to a non-stationary Poisson process with conditional intensity function defined by equation 4. The parameters *k* , *p* and *c* are estimated by maximizing the following likelihood function

$$L\left(\theta \middle| T\_{s\wedge} T\_{\epsilon}\right) = \left\{ \prod\_{i=1}^{i=n} \mathbb{A}\left(t\_{t\wedge} \theta \middle| \mathfrak{F}\_{t\_{i}}\right) \right\} \exp\left\{ - \int\_{-\cdot}^{T\_{\epsilon}} \mathbb{A}\left(t\_{\bullet} \theta \middle| \mathfrak{F}\_{t}\right) dt \right\} \tag{11}$$

It is often observed that a sequence of aftershocks contains secondary aftershocks, which are aftershocks of a major aftershock (Utsu, 1970). Secondary aftershock are typically detected as changing-point in the activity rate of the sequence using Akaike information criteria (AIC) (Akaike, 1974). In this study, the changing-point in the activity rate of the sequence is detected by using the plot of cumulative number of events vs time from the mainshock. Assuming one secondary aftershock occurred at time *τ*0, we test four different hypothesis, H1 : no secondary aftershock, H2: a secondary aftershock series does exist with the same *p*-value and *c*- value as the original series, H3; secondary aftershock series does exist with same *c*- value as the original series and H4: a secondary aftershock series does exist with Omori law parameters different from the original series. Four point process models are tested. Respectively, the conditional

intensity and the cumulative function of such point process are given by;

<sup>ï</sup> <sup>+</sup> <sup>ï</sup>

( ) ( )

1

*p*

( ) ( ) ( ) ( )

1 2

*p p*

1 1

similar to the given observations, and is defined by

1

( )

and the cumulative function is given by;

( )

*N t*

*t*

l

*t*

Á = í

ï

( )

1

*<sup>p</sup> <sup>t</sup> <sup>c</sup>*

1

1

<sup>ì</sup> £ < <sup>ï</sup>

*<sup>k</sup> for t <sup>T</sup>*

*k k for t <sup>T</sup>*

0

t

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

http://dx.doi.org/10.5772/54888

*e*

*s*

t

*e*

(17)

t

(16)

51

0

1 1 0

t

*s*

1 2

<sup>ï</sup> <sup>+</sup> £ £ <sup>ï</sup> + -+ <sup>î</sup>

1 1


<sup>ì</sup> é ù <sup>ï</sup> <sup>+</sup> - £ < ê ú <sup>ï</sup> - ë û <sup>ï</sup> <sup>=</sup> <sup>í</sup>


<sup>ï</sup> é ùé ù <sup>ï</sup> + + - + - - £ £ ê úê ú <sup>ï</sup> - - ë ûë û <sup>î</sup>

*Ts* <sup>=</sup> 0 is the occurrence time of the main shock, and *Te* is the occurrence time of the last event. All the occurrence time are counted as the number of days elapsed from the mainshock. For all the model relative to the hypothesis H1, H2, H3 and H4, the model with the lowest AIC is selected as the best model. The AIC is used as a measure to select which model fits the observations better. This is a measure of which model most frequently reproduces features

a model with smaller value of *AIC* is considered to be better fit to the observations. The fit of the data by the Omori-Utsu law is obtained for both the minimlum magnitude *m*min in the

1 1 2 2

*k k <sup>p</sup> p p <sup>p</sup> t t c c c c for t <sup>T</sup>*

1 2 1 2 0 0

t

*AIC Max Lnlikelihood number of used parameters* = ( 2) ( - +) 2( ) (18)

*<sup>k</sup> <sup>p</sup> <sup>p</sup> <sup>t</sup> <sup>c</sup> <sup>c</sup> for t <sup>T</sup>*

t

( ) ( )

<sup>1</sup> <sup>1</sup> <sup>1</sup>

<sup>1</sup> 1 1 <sup>1</sup> 1 2

1 02

1 2

*p p t t c c*

where, *θ* = (*k* , *p* , *c*) are the model parameters.

The log likelihood is then given by;

$$Ln\,L\left(\theta \middle| T\_{s\prime}, T\_{\epsilon}\right) = nLn\left(k\right) - p\sum\_{i=1}^{i=n}Ln\left(t\_{i} + c\right) - k\Psi\left(\theta \middle| T\_{s\prime}, T\_{\epsilon}\right) \tag{12}$$

with

$$\Psi\left(\theta \middle| T\_s, T\_t\right) = \begin{cases} \frac{\left(T\_\epsilon + c\right)^{1-p} - \left(T\_s + c\right)^{1-p}}{1-p} & \text{for} \quad p \neq 1 \\\\ \Lambda n \binom{T\_\epsilon + c}{T\_\epsilon + c} - \Lambda n \binom{T\_s + c}{T\_s + c} & \text{for} \quad p = 1 \\\\ \end{cases} \tag{13}$$

it follows that the maximum likelihood estimate MLE *θ*˜ = (*k* ˜ , ˜ *p* , *c*˜) of the parameter *θ* is solution of the following equation

$$\frac{\partial}{\partial \theta} \mathcal{L} \ln \mathcal{L} \left( \theta \middle| T\_{s \prime} T\_e \right) = 0 \tag{14}$$

Following, Ogata (1983), the maximum estimation of the parameters are obtained by using the Davidon-Fletcher-Powell optimization algorithm (Press et al. 1986, pages 277, 308) applied to equation 14. The standard deviation of the estimated parameters through the maximum likelihood procedure are derived using the inverse of the Fisher information matrix *J*(*θ*˜)−<sup>1</sup> . In our case, Fisher information matrix is given by

$$J(\boldsymbol{\theta}) = \int\_{\boldsymbol{T}\_{\boldsymbol{s}}}^{\boldsymbol{T}\_{\boldsymbol{s}}} \frac{1}{\lambda \left(\boldsymbol{t}\_{\boldsymbol{s}}, \boldsymbol{\theta} \Big| \mathfrak{T}\_{\boldsymbol{t}}\right)} \frac{\partial}{\partial \boldsymbol{\theta}} \mathcal{A}\Big(\boldsymbol{t}\_{\boldsymbol{s}}, \boldsymbol{\theta} \Big| \mathfrak{T}\_{\boldsymbol{t}}\Big) \frac{\partial}{\partial \boldsymbol{\theta}} \mathcal{A}\Big(\boldsymbol{t}\_{\boldsymbol{s}}, \boldsymbol{\theta} \Big| \mathfrak{T}\_{\boldsymbol{t}}\Big) dt \tag{15}$$

the results obtained using this procedure for the aftershock sequences are shown on Fig. 4.

It is often observed that a sequence of aftershocks contains secondary aftershocks, which are aftershocks of a major aftershock (Utsu, 1970). Secondary aftershock are typically detected as changing-point in the activity rate of the sequence using Akaike information criteria (AIC) (Akaike, 1974). In this study, the changing-point in the activity rate of the sequence is detected by using the plot of cumulative number of events vs time from the mainshock. Assuming one secondary aftershock occurred at time *τ*0, we test four different hypothesis, H1 : no secondary aftershock, H2: a secondary aftershock series does exist with the same *p*-value and *c*- value as the original series, H3; secondary aftershock series does exist with same *c*- value as the original series and H4: a secondary aftershock series does exist with Omori law parameters different from the original series. Four point process models are tested. Respectively, the conditional intensity and the cumulative function of such point process are given by;

$$\mathcal{A}(t \mid \mathfrak{T}\_t) \quad = \begin{cases} \frac{k\_1}{\left(t + c\_1\right)^{p\_1}} & \text{for } \quad T\_s \le t \le\_{\tau\_0} \\\\ \frac{k\_1}{\left(t + c\_1\right)^{p\_1}} + \frac{k\_2}{\left(t - \tau\_0 + c\_2\right)^{p\_2}} & \text{for } \quad \tau\_0 \le t \le T\_e \end{cases} \tag{16}$$

and the cumulative function is given by;

( ) ( ) ( )

*<sup>L</sup> dt T T t t t t*

*i*

( ) ( ) ( ) ( ) 1 , , *i n s e i s e i*

=

( ) ( )

*T T c c*

*e s*

1


( ) ( )

*T Ts e* , 0 )

Following, Ogata (1983), the maximum estimation of the parameters are obtained by using the Davidon-Fletcher-Powell optimization algorithm (Press et al. 1986, pages 277, 308) applied to equation 14. The standard deviation of the estimated parameters through the maximum likelihood procedure are derived using the inverse of the Fisher information matrix *J*(*θ*˜)−<sup>1</sup>

( ) ) ( ) <sup>1</sup> , ,

the results obtained using this procedure for the aftershock sequences are shown on Fig. 4.

 lq

¶ ¶ <sup>æ</sup> <sup>=</sup> ¢ <sup>ç</sup> Á Á ¶ ¶ ¢ <sup>Á</sup> <sup>è</sup> <sup>ò</sup> (15)

 q

*<sup>J</sup> dt t t t t*

l q

q

*p*

*e s*

1 1

*p p*

*Ln c Ln c for p T T*

<sup>ï</sup> +- + = <sup>ï</sup>

 *T T nLn k p Ln c k t T T* =

*e*

 l q

î þ Õ ò (11)

> q

*for p*

= - + -Y å (12)

1

1

˜ , ˜

¶ <sup>=</sup> ¶ (14)

*p* , *c*˜) of the parameter *θ* is

(13)

.

*T*

ì ü ì ü ï ïï <sup>ï</sup> <sup>=</sup> í ýí Á Á - <sup>ý</sup> ï ï î þ ï ï

*T*

*s*

, , exp ,

1

=

 lq

*i n s e i i*

=

q

The log likelihood is then given by;

*LnL* q

with

where, *θ* = (*k* , *p* , *c*) are the model parameters.

50 Earthquake Research and Analysis - New Advances in Seismology

( )

In our case, Fisher information matrix is given by

*e*

*T*

*s*

l q

,

*T t t*

( )

q q

solution of the following equation

*T T*

,

*s e*

ï î

it follows that the maximum likelihood estimate MLE *θ*˜ = (*k*

*LnL*(q

q

$$N(t) \quad = \begin{cases} \frac{k\_1}{\left(1 - p\_1\right)} \left[ \left(t + c\_1\right)^{1 - p\_1} - c\_1^{1 - p\_1} \right] & \text{for } \quad T\_s \le t <\_{70} \\\\ \frac{k\_1}{\left(1 - p\_1\right)} \left[ \left(t + c\_1\right)^{1 - p\_1} - c\_1^{1 - p\_1} \right] + \frac{k\_2}{\left(1 - p\_2\right)} \left[ \left(t - \tau\_0 + c\_2\right)^{1 - p\_2} - c\_2^{1 - p\_2} \right] & \text{for } \quad \tau\_0 \le t \le T\_e \end{cases} \tag{17}$$

*Ts* <sup>=</sup> 0 is the occurrence time of the main shock, and *Te* is the occurrence time of the last event. All the occurrence time are counted as the number of days elapsed from the mainshock. For all the model relative to the hypothesis H1, H2, H3 and H4, the model with the lowest AIC is selected as the best model. The AIC is used as a measure to select which model fits the observations better. This is a measure of which model most frequently reproduces features similar to the given observations, and is defined by

$$AIC \quad = \text{ (--2)} \text{Max(Lulikellihod)} + \text{2(number of used parameters)} \tag{18}$$

a model with smaller value of *AIC* is considered to be better fit to the observations. The fit of the data by the Omori-Utsu law is obtained for both the minimlum magnitude *m*min in the

**Figure 4.** Fit of the number of events pêr day by the modified Omori law, for the studied aftershock sequence. The graphs display the fit for *<sup>m</sup>* <sup>≥</sup> *mc* in dashed line and in solid line for *m* ≥ *m*min.


denoting, *θ* = (*k*1, *p*1, *c*1, *k*2, *p*2, *c*2, *τ*0) and where *H* (*t*) is teh Heaviside unit step function. The occurrence of secondary aftershock is analyzed using the procedure of detecting the aftershock activity change point by *AIC*, procedure introduced by Ogata (1999), Ogata (2001) and Ogata et al., (2003). Using the changing point *AIC* procedure to the aftershock sequence

**Figure 5.** Graphs showing the cumulative number of aftershocks of Al Hoceima earthquake of 1994, with magnitude greater or equal to *mc*, fitted by a simple Modified Omori law – graph (*a*)- and two stage Modified Omori law, includ‐ ing secondary aftershock shown on the plot – graphs *b, c* and *d* – The parameters of each model and the AIC are given on the plot. (A) for AL Hoceima 1994 aftershock sequence and (B) for AL Hoceima 2004 afetsrhock sequence.

change. Fitting the data by two stage Omori-Utsu models, shows that the smaller *AIC* value, equal to -403.6618 is obtained for simple Omori-Utsu model. The results obtained are shown on Fig. 5. The results obtained for the two stage Omori-Utsu models are shown on Fig 5 (b),

The analysis of the aftershock sequence of Al Hoceima 2004, give us that a suspecious point

is obtauined for the simple Omori-Utsu model as shown on the following Fig. 6(B). The results obtained for the two stage Omori-Utsu models are displayed on Fig. 5 (b), (c) and (d), including the *AIC* values. The principal reason of this, seen from the comparaison of the predicted and real cumulative curves would be that the secondary aftershock triggered by large aftershocks are not frequent enough in relation to their magnitude. It is well established that the residual analysis of point process is a "good" tool to evaluate the goodness of fit of the selected model

^ = 8.0215 days is a suspecious point of activity

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

http://dx.doi.org/10.5772/54888

53

¯ = 2.402 days, the lower *AIC* equal to *AIC*= -3787.1548

Á (20)

of Al Hoceima 1994, it appears that the time *t*

of aftershock activity change is given by *t*

(c) and (d). The *AIC* values are include on the graphs.

to the data (Ogata, 1988; Ogata, 1999). The integral

( )

0

*t <sup>s</sup>* L = *t s ds* òl

( )

of non-negative conditional intensity function produces a 1-1 transformation of the time from *t* to *τ* = *Λ*(*t*), so that the occurrence times *t*1, *t*2,*t*3,*t*4, *t*5,.................., *tN* are transformed into

**Table 1.** Omori-Utsu Parameters *p*, *c*, *k* and their standard deviation obtained for each aftershock sequence with magnitude above the threshold magnitude, *m* ≥ *mc*

aftershock sequence and the threshold magnitude *mc* discussed and derived in the previous section. The results of the fit are shown on the following figure

The Omori-Utsu parameters obtained for each aftershock sequence for magnitude above the threshold magnitude, *m* ≥ *mc*, are given on the Table 1.

As pointed previously, it is often observed that a sequence of aftershocks contains secondary aftershocks, aftershocks of a major aftershock (Utsu, 1970). If a secondary aftershock equence starts at time *τ*0 then from the Eq. 15 and 16, the conditional intensity of the point process is given as

$$\lambda(t\Big|\mathfrak{z}\_t) \quad = \ & k\_1(t+c\_1)^{-p\_1} + H(t-\tau\_0)k\_2\left(t-\tau\_0+c\_2\right)^{-p\_2} \tag{19}$$

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region http://dx.doi.org/10.5772/54888 53

**Figure 5.** Graphs showing the cumulative number of aftershocks of Al Hoceima earthquake of 1994, with magnitude greater or equal to *mc*, fitted by a simple Modified Omori law – graph (*a*)- and two stage Modified Omori law, includ‐ ing secondary aftershock shown on the plot – graphs *b, c* and *d* – The parameters of each model and the AIC are given on the plot. (A) for AL Hoceima 1994 aftershock sequence and (B) for AL Hoceima 2004 afetsrhock sequence.

denoting, *θ* = (*k*1, *p*1, *c*1, *k*2, *p*2, *c*2, *τ*0) and where *H* (*t*) is teh Heaviside unit step function. The occurrence of secondary aftershock is analyzed using the procedure of detecting the aftershock activity change point by *AIC*, procedure introduced by Ogata (1999), Ogata (2001) and Ogata et al., (2003). Using the changing point *AIC* procedure to the aftershock sequence of Al Hoceima 1994, it appears that the time *t* ^ = 8.0215 days is a suspecious point of activity change. Fitting the data by two stage Omori-Utsu models, shows that the smaller *AIC* value, equal to -403.6618 is obtained for simple Omori-Utsu model. The results obtained are shown on Fig. 5. The results obtained for the two stage Omori-Utsu models are shown on Fig 5 (b), (c) and (d). The *AIC* values are include on the graphs.

The analysis of the aftershock sequence of Al Hoceima 2004, give us that a suspecious point of aftershock activity change is given by *t* ¯ = 2.402 days, the lower *AIC* equal to *AIC*= -3787.1548 is obtauined for the simple Omori-Utsu model as shown on the following Fig. 6(B). The results obtained for the two stage Omori-Utsu models are displayed on Fig. 5 (b), (c) and (d), including the *AIC* values. The principal reason of this, seen from the comparaison of the predicted and real cumulative curves would be that the secondary aftershock triggered by large aftershocks are not frequent enough in relation to their magnitude. It is well established that the residual analysis of point process is a "good" tool to evaluate the goodness of fit of the selected model to the data (Ogata, 1988; Ogata, 1999). The integral

aftershock sequence and the threshold magnitude *mc*

magnitude above the threshold magnitude, *m* ≥ *mc*

graphs display the fit for *<sup>m</sup>* <sup>≥</sup> *mc*

52 Earthquake Research and Analysis - New Advances in Seismology

threshold magnitude, *m* ≥ *mc*, are given on the Table 1.

*t* l

given as

section. The results of the fit are shown on the following figure

The Omori-Utsu parameters obtained for each aftershock sequence for magnitude above the

**Figure 4.** Fit of the number of events pêr day by the modified Omori law, for the studied aftershock sequence. The

Omori-Utsu parameters for *m* ≥ *mc p* ± σ*<sup>p</sup> c* ± σ*<sup>c</sup> k* ± σ*<sup>k</sup>*

in dashed line and in solid line for *m* ≥ *m*min.

Al Hoceima 1994 0.76 ± 0.03 0.0040 ± 0.0008 12.47 ± 1.51 Al Hoceima 2004 0.85 ± 0.02 0.034 ± 0.016 47.38 ± 3.81 El Asnam 1980 0.84 ± 0.06 0.025 ± 0.045 4.48 ± 3.81 Zemouri 2003 1.13 ± 0.06 0.311 ± 0.053 107.53 ± 15.83 Laalam 2006 0.69 ± 0.09 0.014 10.27 ± 1.47

**Table 1.** Omori-Utsu Parameters *p*, *c*, *k* and their standard deviation obtained for each aftershock sequence with

As pointed previously, it is often observed that a sequence of aftershocks contains secondary aftershocks, aftershocks of a major aftershock (Utsu, 1970). If a secondary aftershock equence starts at time *τ*0 then from the Eq. 15 and 16, the conditional intensity of the point process is

( ) ( ) ( ) 1 2

 - - Á = + + - -+ (19)

 t

t

1 1 02 0 2 ( ) *p p*

*t k t c Ht k t c*

discussed and derived in the previous

$$\Lambda\left(t\right) = \int\_0^t \lambda(s\left|\mathfrak{z}\_s\right)ds\tag{20}$$

of non-negative conditional intensity function produces a 1-1 transformation of the time from *t* to *τ* = *Λ*(*t*), so that the occurrence times *t*1, *t*2,*t*3,*t*4, *t*5,.................., *tN* are transformed into

Following figure 7.6 displays for El Asnam 1980, Zemouri 2003 and Laalam 2006 aftershock sequences the adjustment of the data with the appropriate model, as deduce from the Table2

(a) (b) (c)

**Figure 7.** Adjustment of the cumulative number of events by the appropriate Omori-Utsu model, first stage Omori-Utsu model for (a) EL Asnam 1980 aftershock sequence and (b) for Laalam aftershock sequence. Two stage Omori-

The temporal aftershock decay is also analyzed using the approach introduced by Marcellini (1997). This approach describes the temporal behavior of the cumulative seismic moment released in aftershock sequences. It is an alternative approach to the Omori-Utsu law, previ‐ ously analyzed. Static fatigue is assumed to be the principal explanation of the aftershock temporal behavior. Under the condition that the main shock causes a redistribution of stress, the initial stress condition of the afterhock sequence at main shock origin time *t*0 can be considered as the superposition of the stress before the main shock and the stress step *dσ* caused

by the dynamic rupture of the main shock. It has been shown Marcellini (1995) that

( ) ( ) *i i RT S d Ln t t* s

g

where *ti* is the time from the mainshock to the *ith* aftreshok, *T* the absolute temperature, *<sup>R</sup>* the universal gas constant, *γ* is a constant and *S*(*ti*) the cumulative stress drop. Since the seismic moment may be defined as *M*<sup>0</sup> <sup>=</sup> *Δσ <sup>V</sup>* , where *V* is the focal volume (Madariaga, 1979), the

*mj k*

*k k j*

*VV V*

=

*MM t a bLn*

; ;

*k*

g

= + (21)

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

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55

( )

0

= = =+ å (23)

1

*j*

*k*

+ =+ å (22)

Utsu model for Zemouri 2003 aftershock sequence

previous equation can be written as follow

where

0 0 1

*<sup>V</sup> RT ad b <sup>V</sup>* s

*j*

=

*k*

**Figure 6.** Residual analysis to derive the best fitting for the two Al Hoceima aftershocks.


**Table 2.** Akaike information criteria (AIC) of each model and for each aftershock sequence. Table gives in the last column the best model with the lower AIC.

*τ*1, *τ*2, *τ*3, *τ*4, *τ*5,.................., *τ<sup>N</sup>* . It is well known that *τ<sup>k</sup>* , k = 1,.....,N are distributed as a standard Poisson process. If *λ*(*<sup>t</sup>* <sup>|</sup>ℑ*t*) is the intensity function of the process actually generating the data, using the maximum likelihood conditional intensity *λθ* ^ (*<sup>t</sup>* <sup>|</sup>ℑ*t*), the corresponding *τ* ^ 1, *τ* ^ <sup>2</sup>, *τ* ^ <sup>3</sup>, *τ* ^ 4, *τ* ^ 5,.................., *τ* ^ *<sup>N</sup>* called residual process (Ogata, 1988; 1999), provides a measure of teh deviation of the data from the hypothezed model. The residual analysis performed for the two aftershock sequences, trigged respectively by Al Hoceima earthquakes of 1994 and 2004 is shown on Fig. 6. The graphs display the Omori-Utsu model fit and the residual process for Al Hoceima 1994 series and for Al Hoceima 2004 series.

from the graphs of the residual process we can deduce, as shown previously using the *AIC* criteria, a global agreement with the Omori-Utsu model. We proceded with the same technics for the others aftershock sequences, the *AIC* is used to select the most appropriate model fitting the data. Table 2, gives the obtained results.

Following figure 7.6 displays for El Asnam 1980, Zemouri 2003 and Laalam 2006 aftershock sequences the adjustment of the data with the appropriate model, as deduce from the Table2

**Figure 7.** Adjustment of the cumulative number of events by the appropriate Omori-Utsu model, first stage Omori-Utsu model for (a) EL Asnam 1980 aftershock sequence and (b) for Laalam aftershock sequence. Two stage Omori-Utsu model for Zemouri 2003 aftershock sequence

The temporal aftershock decay is also analyzed using the approach introduced by Marcellini (1997). This approach describes the temporal behavior of the cumulative seismic moment released in aftershock sequences. It is an alternative approach to the Omori-Utsu law, previ‐ ously analyzed. Static fatigue is assumed to be the principal explanation of the aftershock temporal behavior. Under the condition that the main shock causes a redistribution of stress, the initial stress condition of the afterhock sequence at main shock origin time *t*0 can be considered as the superposition of the stress before the main shock and the stress step *dσ* caused by the dynamic rupture of the main shock. It has been shown Marcellini (1995) that

$$S(\mathbf{f}\_{\mathbf{f}\_i}) = d\sigma \, + \, \frac{RT}{\gamma} L\boldsymbol{n}(\mathbf{f}\_i) \tag{21}$$

where *ti* is the time from the mainshock to the *ith* aftreshok, *T* the absolute temperature, *<sup>R</sup>* the universal gas constant, *γ* is a constant and *S*(*ti*) the cumulative stress drop. Since the seismic moment may be defined as *M*<sup>0</sup> <sup>=</sup> *Δσ <sup>V</sup>* , where *V* is the focal volume (Madariaga, 1979), the previous equation can be written as follow

$$M\_{0m} \quad + \sum\_{j=1}^{k} M\_{0j} \quad = \quad a \quad + \quad bLn(t\_k) \tag{22}$$

where

*τ*1, *τ*2, *τ*3, *τ*4, *τ*5,.................., *τ<sup>N</sup>* . It is well known that *τ<sup>k</sup>* , k = 1,.....,N are distributed as a standard Poisson process. If *λ*(*<sup>t</sup>* <sup>|</sup>ℑ*t*) is the intensity function of the process actually generating the

**Table 2.** Akaike information criteria (AIC) of each model and for each aftershock sequence. Table gives in the last

Al Hoceima 1994 -639.1429 -609.7559 -609.276 -633.7404 Model 1 AlHoceima 2004 -3616.8231 -36020.7106 -3609.2007 -3610.6351 Model 1 El Asnam 1980 -47.1127 -32.118 -31.2841 -42.9912 Model 1 Zemouri 2003 -8973.1703 -9244.9968 -9342.0748 -9353.1883 Model 4 Laalam 2006 -293.5383 -274.8197 -275.9812 -288.698 Model 1

of teh deviation of the data from the hypothezed model. The residual analysis performed for the two aftershock sequences, trigged respectively by Al Hoceima earthquakes of 1994 and 2004 is shown on Fig. 6. The graphs display the Omori-Utsu model fit and the residual process

from the graphs of the residual process we can deduce, as shown previously using the *AIC* criteria, a global agreement with the Omori-Utsu model. We proceded with the same technics for the others aftershock sequences, the *AIC* is used to select the most appropriate model fitting

*<sup>N</sup>* called residual process (Ogata, 1988; 1999), provides a measure

**Akaike Information Criteria Model 1 Model 2 Model 3 Model 4 B. Model**

^ (*<sup>t</sup>* <sup>|</sup>ℑ*t*), the corresponding

data, using the maximum likelihood conditional intensity *λθ*

**Figure 6.** Residual analysis to derive the best fitting for the two Al Hoceima aftershocks.

54 Earthquake Research and Analysis - New Advances in Seismology

^

for Al Hoceima 1994 series and for Al Hoceima 2004 series.

5,.................., *τ*

column the best model with the lower AIC.

the data. Table 2, gives the obtained results.

*τ* ^ <sup>1</sup>, *τ* ^ <sup>2</sup>, *τ* ^ 3, *τ* ^ <sup>4</sup>, *τ* ^

$$a = V\_k d\sigma \quad ; \quad b = \frac{V\_k RT}{\gamma} \quad ; \quad V\_k = V\_0 + \sum\_{j=1}^k V\_j \tag{23}$$

*Vk* is the cumulative focal volume, *V*<sup>0</sup> is the focal volume of the main shock, *V <sup>j</sup>* is the focal volume of the *j th* aftershock and *M*0*m* and *M*<sup>0</sup> *<sup>j</sup>* are the seismic moment of the main shock and the *j th* aftershock, respectively.

Following Marcellini (1997), we consider the aftershock zone as characterized by barriers that breaks after a given elapsed time proportional to the stress intensity factor *Ki* and therefore to the stress *σi*. Data fit of equation (22) characterizes the distribution, namely, the more our data explained by Eq. 22, the most likely the distribution of *σ* is close to the uniform distribu‐ tion. This property is partially influenced by the spatial variation of the stress change produced by the mainshock, given that in the present static fatigue model a barrier breaks at *σ<sup>i</sup>* , which is the superposition of the static stress before the mainshock and stress step induced by the mainshock In this study, as in Marcellini (1997), the seismic moment is evaluated using the Thatcher and Hanks (1973) relation, given by

$$\text{LogM}\_0 = \text{9.0 } + \text{ 1.5M} \tag{24}$$

**Figure 8.** Fit of aftershock sequence, the plot displays the 95% confidence limit of the regression, the parameters of the adjustment and the coefficient of the correlation are shown on the plot. For Al Hoceima series of 1994 and 2004 the results are shown on graph (a) and (b) respectively. The graph (c) displays the results of the El Asnam serie of 10

The other scaling law exalined in this study is the modified Bath law. In its original form, Bath law states that the difference *Δm* between a given mainshock with magnitude *mms* and its

Extensive studies about the statistical variability of *Δm* have been carried out by several authors e.g Vere-Jones (1969), Kisskinger and Jones (1991) and Console et al. (2003). However, the law remains an open problem nowadays (Vere-Jones, 1969; Vere-Jones et al. 2005). In this study, we use the modified Bath's law proposed by Shcherbakov and Turcote (2004a). It is based on an extrapolation of the Gutenberg-Richter relationship for aftershocks. Namely, the magnitude of the largest aftershock consistent with the Gutenberg-Richter relationship for aftershocks is obtained by formally putting *N* (≥*m* \*) = 1 which yields to *a* − *bm* \* = 0. If Bath

max is approximately constant, independently of the main‐

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

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57

max D= - *m m m ms as* (26)

and given on each graph, the

october 1980. Graphs (d) and (e) display the results for the series of Zemouri 2003 and Laalam 2006.

modele *y* = *a* + *b Log*(*t*) introduced by Marcellini (1997) fit very well our data.

Taking into account the obtained coefficient of correlation *r* <sup>2</sup>

**5. Energy partitioning**

*Δm* is typically around 1.2.

largest aftershock magnitude *mas*

shock magnitude (Bath, 1965). That is,

to test if the static model fatigue holds as represented by equation (22), two conditions must be checked:

(a) The validity of equation 22, which is adjusted to different aftershock data and plotted on Figure 8. The same figure shows the estimates *a* and *b*, their respective standard deviation *σ<sup>a</sup>* and *σ<sup>b</sup>* and the determination coefficient *r* <sup>2</sup> of the linear adjustment on the semi-logarithmic scale. Solid curves are plots of the function *y* = *a* + *bx* where *x* = log(*t*). Dashed curves say (*Δ<sup>i</sup>* − ), *y* = *a* <sup>−</sup> + *b* <sup>−</sup> *<sup>x</sup>* and (*Δ<sup>i</sup>* + ), *y* = *a* <sup>+</sup> + *b* <sup>+</sup> *x*, correspond to the 95% confidence limits relative to the confidence intervals *I*(*a*) = *a* <sup>−</sup> , *a* + and *I*(*b*) = *b* <sup>−</sup> , *b* + of *a* and *b*, respectively. Namely, *b* <sup>+</sup> = *b* ^ <sup>+</sup> *tn*−<sup>2</sup> (*α*/2) *Sb* ^ , *b* <sup>−</sup> = *b* ^ <sup>−</sup> *tn*−<sup>2</sup> (*α*/2) *Sb* ^ ; where *tn*−<sup>2</sup> (*α*/2) is the *α* / 2-quantile of the Student distribution with *n* −2 degrees of freedom (*α* = 0.05 in our case) with

$$S\_{\hat{b}} = \sqrt{\frac{\sum\_{i=1}^{n} \hat{\sum}\_{i}^{2} \left(n - 2\right)}{\sum\_{i=1}^{n} \left(\chi\_{i} - \overline{\chi}\right)^{2}}}\tag{25}$$

*ε* ^ *<sup>i</sup>* <sup>=</sup> *yi* <sup>−</sup> *y* ^ *<sup>i</sup>* are the regression errors and *y* ^ *<sup>i</sup>* = *a* ^ + *b* ^ *xi* the predicted *yi* values. The confidence limite of *a* ^ are calculated from those of *b* ^ using the relation *a* ^ = *y*¯ − *b* ^ *x*¯.

(b) The validity of the definition of the constants *a* and *b* as expressed previously by the relation (23). The conditions (a) and (b) are analyzed first by the quality of the fit, shown on figure 8.

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region http://dx.doi.org/10.5772/54888 57

**Figure 8.** Fit of aftershock sequence, the plot displays the 95% confidence limit of the regression, the parameters of the adjustment and the coefficient of the correlation are shown on the plot. For Al Hoceima series of 1994 and 2004 the results are shown on graph (a) and (b) respectively. The graph (c) displays the results of the El Asnam serie of 10 october 1980. Graphs (d) and (e) display the results for the series of Zemouri 2003 and Laalam 2006.

Taking into account the obtained coefficient of correlation *r* <sup>2</sup> and given on each graph, the modele *y* = *a* + *b Log*(*t*) introduced by Marcellini (1997) fit very well our data.

#### **5. Energy partitioning**

*Vk* is the cumulative focal volume, *V*<sup>0</sup> is the focal volume of the main shock, *V <sup>j</sup>* is the focal volume of the *j th* aftershock and *M*0*m* and *M*<sup>0</sup> *<sup>j</sup>* are the seismic moment of the main shock

Following Marcellini (1997), we consider the aftershock zone as characterized by barriers that breaks after a given elapsed time proportional to the stress intensity factor *Ki* and therefore to the stress *σi*. Data fit of equation (22) characterizes the distribution, namely, the more our data explained by Eq. 22, the most likely the distribution of *σ* is close to the uniform distribu‐ tion. This property is partially influenced by the spatial variation of the stress change produced

is the superposition of the static stress before the mainshock and stress step induced by the mainshock In this study, as in Marcellini (1997), the seismic moment is evaluated using the

to test if the static model fatigue holds as represented by equation (22), two conditions must

(a) The validity of equation 22, which is adjusted to different aftershock data and plotted on Figure 8. The same figure shows the estimates *a* and *b*, their respective standard deviation *σ<sup>a</sup>* and *σ<sup>b</sup>* and the determination coefficient *r* <sup>2</sup> of the linear adjustment on the semi-logarithmic scale. Solid curves are plots of the function *y* = *a* + *bx* where *x* = log(*t*). Dashed curves say

to the confidence intervals *I*(*a*) = *a* <sup>−</sup> , *a* + and *I*(*b*) = *b* <sup>−</sup> , *b* + of *a* and *b*, respectively. Namely,

( )


*n*

2

2

( )

(b) The validity of the definition of the constants *a* and *b* as expressed previously by the relation (23). The conditions (a) and (b) are analyzed first by the quality of the fit, shown on figure 8.

*x x*


*i*

(*α*/2)

2 1

e

\$

1

^ *<sup>i</sup>* = *a* ^ + *b*

*i*

^ are calculated from those of *b*

=

å

<sup>0</sup> *LogM* = + 9.0 1.5*M* (24)

*x*, correspond to the 95% confidence limits relative

^ *xi* the predicted *yi* values.

^ = *y*¯ − *b*

^ *x*¯.

^ using the relation *a*

is the *α* / 2-quantile of the Student distribution

, which

(25)

by the mainshock, given that in the present static fatigue model a barrier breaks at *σ<sup>i</sup>*

and the *j th* aftershock, respectively.

56 Earthquake Research and Analysis - New Advances in Seismology

Thatcher and Hanks (1973) relation, given by

*<sup>x</sup>* and (*Δ<sup>i</sup>*

+

^ <sup>−</sup> *tn*−<sup>2</sup> (*α*/2) *Sb*

with *n* −2 degrees of freedom (*α* = 0.05 in our case) with

*<sup>i</sup>* are the regression errors and *y*

), *y* = *a* <sup>+</sup> + *b* <sup>+</sup>

*S*

\$

=

^ ; where *tn*−<sup>2</sup>

*n i i b n*

å

=

be checked:

), *y* = *a* <sup>−</sup> + *b* <sup>−</sup>

^ <sup>+</sup> *tn*−<sup>2</sup> (*α*/2) *Sb* ^ , *b* <sup>−</sup> = *b*

(*Δ<sup>i</sup>* −

*b* <sup>+</sup> = *b*

*ε* ^

*<sup>i</sup>* <sup>=</sup> *yi* <sup>−</sup> *y* ^

The confidence limite of *a*

The other scaling law exalined in this study is the modified Bath law. In its original form, Bath law states that the difference *Δm* between a given mainshock with magnitude *mms* and its largest aftershock magnitude *mas* max is approximately constant, independently of the main‐ shock magnitude (Bath, 1965). That is,

$$
\Delta m = \left. m\_{\rm rms} - \left. m\_{\rm as}^{\rm max} \right. \tag{26}
$$

*Δm* is typically around 1.2.

Extensive studies about the statistical variability of *Δm* have been carried out by several authors e.g Vere-Jones (1969), Kisskinger and Jones (1991) and Console et al. (2003). However, the law remains an open problem nowadays (Vere-Jones, 1969; Vere-Jones et al. 2005). In this study, we use the modified Bath's law proposed by Shcherbakov and Turcote (2004a). It is based on an extrapolation of the Gutenberg-Richter relationship for aftershocks. Namely, the magnitude of the largest aftershock consistent with the Gutenberg-Richter relationship for aftershocks is obtained by formally putting *N* (≥*m* \*) = 1 which yields to *a* − *bm* \* = 0. If Bath law is applicable to the inferres magnitude *m* \*, the Gutenberg-Richter relationship takes the following form;

$$\log\_{10} \text{N}(\ge m) = b \left( \mu\_{\text{Mms}} - \Delta m^\* - m \right) \tag{27}$$

aftershock magnitude unferred from the Gutenberg-Richter relationship and is denoted *m* \*. The total radiated energy in the aftershock sequence is obtained by integrating over the

*m* \* is the largest aftershock magnitude inferred from the Gutenberg-Richter law. Taking the

\* 10 10 ( )10 *ms m*

in addition, different version of the above equation, Eq 35 is obtained if we use the equation

( ) 10 10 <sup>0</sup> 10 <sup>2</sup> *ms*

( ) ( ) <sup>3</sup> \* 2 0

the ratio of the total radiated energy by the aftershocks *Eas* to the total energy radiated by the

( )

2 <sup>10</sup> 3 2 *as m*

*E b E b* -¥

\* 3


3 \* 2

*m*

*dN*

æ ö = -ç ÷ è ø <sup>ò</sup> (33)

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

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59

( ) ( \* ) 10 10 *ms dN b Ln b mm m dm* -D - = - (34)

<sup>=</sup> ò (35)

<sup>=</sup> ò (36)



\* ( )

( ) ( ) \*

*bm m bm as E b Ln E m dm* - D -

( ) ( ) \*

2

<sup>10</sup> 3 2 *m m ms as b E E <sup>b</sup>*

*bm m b m as E E b Ln dm* - D -

*E E m dm dm* -¥

*m*

*as*

by combining the former equations, Eq. 33 and 34, we obtain

giving *E*(*m*) as a function of *E*0 and *b* value, we get

taking into account the modified Bath's law, we obtain

*ms*

mainshock *Ems* is given by

distribution of aftershock as,

derivative of the modified Bath law,

where,

$$
\Delta m^\* = \prescript{}{m\_{\rm ms}}{}-\prescript{}{m\_{\rm as}}{}\tag{28}
$$

combining this last relation with the empirical relation of the energy dissipated

$$
\Box \text{LogE} = \begin{array}{c} \text{a} \ - \ \delta \text{m} \end{array} \tag{29}
$$

we derive the partionning of the energy, in the following way. It is wellestablished that the magnitude distribution of aftershocks clearly exhibits a near-universal scaling relative to the mainshock magnitude. To explore this relation for our aftershock sequences, we will determine the ratio of the total energy radiated by the afytershock sequence to the seismic energy radiated by the mainshock. The energy radiated during an earthquake is related empirically to its moment magnitude *m* by (Utsu, 2002)

$$
\log\_{10} E(m) \quad = \frac{3}{2}m + \log\_{10} E\_0 \tag{30}
$$

with,

$$E\_0 = \text{6.3} \times 10^4 \,\text{J} \,\text{Joules} \tag{31}$$

This relation is applied directly to describe the link between the energy radiated by the mainshock *Ems* and the moment magnitude of the mainshock *mms*,

$$E\_{ms} = -E\_0 \cdot 10 \text{\textquotedbl{}^{\text{\textquotedbl{}}}{}^{\text{\textquotedbl{}}}{}^{\text{\textquotedbl{}}}{}^{\text{\textquotedbl{}}}{}^{\text{\textquotedbl{}}} \tag{32}$$

following Shcherbakov et al.(2004a), the total energy radiated during the aftershock sequence *Eas* is obtained by integrating over the distribution of aftershock till the inferred largest magnitude as upper bound in the integration. The upper bound of the integration is the largest aftershock magnitude unferred from the Gutenberg-Richter relationship and is denoted *m* \*. The total radiated energy in the aftershock sequence is obtained by integrating over the distribution of aftershock as,

$$E\_{as} = \int\_{-\infty}^{m^\*} E(m) \left(-\frac{dN}{dm}\right) dm \tag{33}$$

*m* \* is the largest aftershock magnitude inferred from the Gutenberg-Richter law. Taking the derivative of the modified Bath law,

$$dN\_{\quad} = -b \left(Ln10\right)10^{b\left(m\_m - \Lambda m^\* - m\right)}dm\tag{34}$$

by combining the former equations, Eq. 33 and 34, we obtain

law is applicable to the inferres magnitude *m* \*, the Gutenberg-Richter relationship takes the

combining this last relation with the empirical relation of the energy dissipated

*LogE m* = a d

we derive the partionning of the energy, in the following way. It is wellestablished that the magnitude distribution of aftershocks clearly exhibits a near-universal scaling relative to the mainshock magnitude. To explore this relation for our aftershock sequences, we will determine the ratio of the total energy radiated by the afytershock sequence to the seismic energy radiated by the mainshock. The energy radiated during an earthquake is related empirically to its

> 10 10 0 <sup>3</sup> log ( ) log <sup>2</sup>

> > 4

This relation is applied directly to describe the link between the energy radiated by the

3

following Shcherbakov et al.(2004a), the total energy radiated during the aftershock sequence *Eas* is obtained by integrating over the distribution of aftershock till the inferred largest magnitude as upper bound in the integration. The upper bound of the integration is the largest

mainshock *Ems* and the moment magnitude of the mainshock *mms*,

( ) <sup>10</sup> *Log Nm b m m* () \* ³ = -D - *mms* (27)

\* D= - *m* \* *m m ms as* (28)

*Em m* = + *E* (30)

<sup>0</sup> *E* = ´ 6.3 10 *Joules* (31)

<sup>2</sup> 0.10 *ms ms E E* = *m* (32)

(29)

following form;

58 Earthquake Research and Analysis - New Advances in Seismology

moment magnitude *m* by (Utsu, 2002)

where,

with,

$$E\_{as} = -b \left(Ln10\right)10^{\left(m\_{ms} - \Delta m^{\circ}\right)^{m^{\circ}}} \int\_{-\infty}^{\cdot} E(m)10^{-bm} \, dm \tag{35}$$

in addition, different version of the above equation, Eq 35 is obtained if we use the equation giving *E*(*m*) as a function of *E*0 and *b* value, we get

$$E\_{as} = -b \left( Ln10 \right) 10^{b\left(m\_{ms} - \Delta m^\*\right)} E\_0 \int\_{-\infty}^{m^\*} 10^{\left(\frac{3}{2} - b\right)m} \, dm \tag{36}$$

taking into account the modified Bath's law, we obtain

$$E\_{as} = \frac{2b}{\left(3 - 2b\right)} E\_0 10^{\frac{3}{2}\left(m\_m - \Delta m^\*\right)}\tag{37}$$

the ratio of the total radiated energy by the aftershocks *Eas* to the total energy radiated by the mainshock *Ems* is given by

$$\frac{E\_{as}}{E\_{ms}} = \frac{2b}{\left(3 \quad - \quad 2b\right)} 10^{-\frac{3}{2}\Lambda m^\*} \tag{38}$$

assuming that all earthquakes have the same seismic efficiency, which means that the ratio of the radiated energy to the total drop is stored as elastic energy is also the ratio of the drop in the stored elastic energy due to the aftershocks to the drop in the stored elastic energy due to the mainshock. Finally, the following relation is derived

$$\frac{E\_{as}}{E\_{ms} + E\_{as}} = \left(1 + \frac{3 - 2b}{2b} 10^{3 \frac{l}{2 \cdot \Delta m^\circ}}\right)^{-1} \tag{39}$$

**6. Spatial aftershock distribution**

Procaccia, 1983)

given by

power of *D*2, i.e *C*(*r*) ≈ *r*

It is well known that seismicity is a classical example of a complex phenomenon that can be quantified using fractal theory (Turcotte, 1997). In particular, fault networks and epicenter distributions have fractal properties (Goltz, 1998). Thus, a natural way to analyze the spatial distribution of seismicity is to determine the fractal dimension *D*2. This *D*2 - value is an extension of the Euclidian dimension and measures the degree of clustering of earthquakes. In the two dimensional space, *D*2 can be a decimal number and ranges from 0 to 2.0. Therefore, the distributions characterized by different fractal dimensions defiine different clustering of events in space. In the two dimensional space, as *D*<sup>2</sup> approaches 1, the distribution of events approaches a line (Euclidean dimension equal to 1). The same occurs for the distribution of events along a fault. Alternatively, as *D*<sup>2</sup> approaches 2, the distribution of events tends to be uniform on the plane (Euclidean dimension equal to 2). When the *D*2-values approaches 0, the distribution is concentrated in a single point (Beauval et al. 2006; Spada et al. 2011). In this study, the fractal dimension is estimated using the correlation dimension (Grassberger and

> ( ) ( ) 10

® *Log r* <sup>=</sup> (40)

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

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61

<sup>=</sup> åå - - (41)

, where *D*2 is the correlation dimension equals the second generalized

; *i* = 1,...., *N* are the coordinates of

0 10 *r Log C r <sup>D</sup> Lim*

where *r* is the radius of the sphere considered in the study, and *C*(*r*) is the correlation integral

( ) <sup>2</sup> ( ) 1 1 1 *N N*

*C r Lim Hr x x* ®+¥ *<sup>N</sup>* = =

*i j <sup>N</sup> i j*

*H* (*x*) = 1 *for x* ≥0. The quantity *C*(*r*) is equivalent to the probability that two points will be separated by a distance less than *r*. The correlation integral is theoretically proportional to the

Renyi dilmension *d*<sup>2</sup> (Molchan and Kronod, 2009). To estimate *D*<sup>2</sup> from the correlation integral (Spada et al. 2011), we plot *C*(*r*) versus *r* on the log-log scale, Fig. 6., then we use the least square method to fit the data over the region where *C*(*r*) is linear, which corresponds to the

2

where *N* is the number of points in the analysis window, *xi*

*D*2

the epicenters, and *H* (.) the Heaviside step function, *H* (*x*) = 0 *for x* ≤0,

gradient of straight line of the resulting plot of log10*C*(*r*) against log10(*r*).

Using the Eq. 39 for the studied aftershock sequences, the results are shown on the following table.


**Table 3.** b-value, Bath law and energy partitionning derived for the different studied aftershock sequences.

From the obtained results shown on Table 3, we deduce the percentage of the total energy radiated during the mainshock. From this point of view, 95 % of the total energy has been radiated during the Al Hoceima 1994 mainshock and 65% during Al Hoceima 2004 mainshock. On the other side the El Asnam 1980 main shock radiated about 98% of the total energy, 2% has been radiated by the aftershock sequence, but we shouldpoint out that these results depend directly on the quality of data used and it is clear that whatever the sequence of aftershocks used, it is still incomplete, especially at the beginning just after the occurrence of the main shock. For the aftershock sequence triggered by the El Asnam earthquake of 1980, it seems that the sequence used is truncated due to the delay in the implementation of seismological network just after the main shock. Nevertheles, the results shown on Table 3, gives a large overview on the ratio of the total energy radiated by the main shock and by the aftershocks. Thus, 86 % of the total energy has been radiated during the main shock of Zemouri 2003 and 99% during Laalam 2006 mainshock.

#### **6. Spatial aftershock distribution**

assuming that all earthquakes have the same seismic efficiency, which means that the ratio of the radiated energy to the total drop is stored as elastic energy is also the ratio of the drop in the stored elastic energy due to the aftershocks to the drop in the stored elastic energy due to

> 3 2 3 2 <sup>1</sup> <sup>10</sup> <sup>2</sup> *as m*

Using the Eq. 39 for the studied aftershock sequences, the results are shown on the following

<sup>D</sup> æ ö - = + ç ÷ <sup>+</sup> è ø

*Al Hoceima 1994* 1.07 ± 0.07 1.10 0.05 *Al Hoceima 2004* 1.13 ± 0.05 0.50 0.35 *El Asnam 1980* 0.82 ± 0.10 1.20 0.02 *Zemouri 2003* 1.10 ± 0.04 0.82 0.14 *Laalam 2006* 0.99 ± 0.10 1.70 0.01

**Table 3.** b-value, Bath law and energy partitionning derived for the different studied aftershock sequences.

From the obtained results shown on Table 3, we deduce the percentage of the total energy radiated during the mainshock. From this point of view, 95 % of the total energy has been radiated during the Al Hoceima 1994 mainshock and 65% during Al Hoceima 2004 mainshock. On the other side the El Asnam 1980 main shock radiated about 98% of the total energy, 2% has been radiated by the aftershock sequence, but we shouldpoint out that these results depend directly on the quality of data used and it is clear that whatever the sequence of aftershocks used, it is still incomplete, especially at the beginning just after the occurrence of the main shock. For the aftershock sequence triggered by the El Asnam earthquake of 1980, it seems that the sequence used is truncated due to the delay in the implementation of seismological network just after the main shock. Nevertheles, the results shown on Table 3, gives a large overview on the ratio of the total energy radiated by the main shock and by the aftershocks. Thus, 86 % of the total energy has been radiated during the main shock of Zemouri 2003 and 99% during

*E b E E b*

\* 1

**Ratio of the elastic energy released**

*<sup>b</sup>* <sup>±</sup> <sup>σ</sup>*<sup>b</sup>* <sup>Δ</sup>*m*\* *Eas*


(39)

*Eas* + *Eas*

the mainshock. Finally, the following relation is derived

60 Earthquake Research and Analysis - New Advances in Seismology

*ms as*

table.

Laalam 2006 mainshock.

It is well known that seismicity is a classical example of a complex phenomenon that can be quantified using fractal theory (Turcotte, 1997). In particular, fault networks and epicenter distributions have fractal properties (Goltz, 1998). Thus, a natural way to analyze the spatial distribution of seismicity is to determine the fractal dimension *D*2. This *D*2 - value is an extension of the Euclidian dimension and measures the degree of clustering of earthquakes. In the two dimensional space, *D*2 can be a decimal number and ranges from 0 to 2.0. Therefore, the distributions characterized by different fractal dimensions defiine different clustering of events in space. In the two dimensional space, as *D*<sup>2</sup> approaches 1, the distribution of events approaches a line (Euclidean dimension equal to 1). The same occurs for the distribution of events along a fault. Alternatively, as *D*<sup>2</sup> approaches 2, the distribution of events tends to be uniform on the plane (Euclidean dimension equal to 2). When the *D*2-values approaches 0, the distribution is concentrated in a single point (Beauval et al. 2006; Spada et al. 2011). In this study, the fractal dimension is estimated using the correlation dimension (Grassberger and Procaccia, 1983)

$$D\_2 \quad = \lim\_{r \to 0} \frac{\text{Log}\_{10} \mathbb{C}\{r\}}{\text{Log}\_{10}\{r\}} \tag{40}$$

where *r* is the radius of the sphere considered in the study, and *C*(*r*) is the correlation integral given by

$$\mathcal{C}\{r\} \quad = \lim\_{N \to \!\!\rightarrow \!\!\infty} \frac{1}{N^2} \sum\_{i=1}^{N} \sum\_{j=1}^{N} H\{r - \left| \mathbf{x}\_i - \mathbf{x}\_j \right|\} \tag{41}$$

where *N* is the number of points in the analysis window, *xi* ; *i* = 1,...., *N* are the coordinates of the epicenters, and *H* (.) the Heaviside step function, *H* (*x*) = 0 *for x* ≤0,

*H* (*x*) = 1 *for x* ≥0. The quantity *C*(*r*) is equivalent to the probability that two points will be separated by a distance less than *r*. The correlation integral is theoretically proportional to the power of *D*2, i.e *C*(*r*) ≈ *r D*2 , where *D*2 is the correlation dimension equals the second generalized Renyi dilmension *d*<sup>2</sup> (Molchan and Kronod, 2009). To estimate *D*<sup>2</sup> from the correlation integral (Spada et al. 2011), we plot *C*(*r*) versus *r* on the log-log scale, Fig. 6., then we use the least square method to fit the data over the region where *C*(*r*) is linear, which corresponds to the gradient of straight line of the resulting plot of log10*C*(*r*) against log10(*r*).

**Figure 9.** Graph displaying the plot of the correlation integrale in log-log scale, with the 95% of confidence limit (in dashed lines), the graphs show also, the plot the slope, related to the first derivative of the correlation integral for Al Hoceima 1994 and 2004 aftershock sequences.

In practice, however, for large values of *r* the gradient is artificially low, whereas for small values of *r* the gradient is artificially high. These two cases have been called "saturation" and "depopulation" (Nerenberg and Essex, 1990). Whereas, it is common in the estimation of the fractal dimension to use fiting procedure to straight line than to a subjectivelly chosen straight part of the curve. Nerenberg and Essex (1990), give formulas for determining the distances of depopulation and saturation, *rd* and *rs* given by

$$r\_d = -2R\left(\frac{1}{N}\right)^{ld} \qquad and \qquad r\_s = -\frac{R}{d+1} \tag{42}$$

The results obtained are close to 2.0, which allow us to deduce that the spatial distribution of

The ratio of the slip on the primary fault to the total slip over the fault system is given by


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63

**Fractale dimension and ratio of the slip** *<sup>D</sup>***<sup>2</sup> <sup>±</sup> <sup>σ</sup>***D***<sup>2</sup> Range** *<sup>S</sup> <sup>p</sup>* **/** *<sup>S</sup>*

( ) <sup>2</sup> <sup>3</sup> 1 2 *<sup>p</sup> <sup>D</sup> <sup>S</sup>*

in each case the remainder of the slip is distributed over the secondary rupture.

*Al Hoceima 1994* 1.60 ± 0.05 1.79 - 12.56 0.62 *Al Hoceima 2004* 1.67 ± 0.04 2.16 - 17.27 0.60 *El Asnam 1980* 1.70 ± 0.09 12.90 - 31.35 0.59 *Zemouri 2003* 1.79 ± 0.02 1.60 - 10.00 0.57 *Laalam 2006* 2.13 ± 0.02 1.57 - 8.90 0.45

In this section we attempt to analysis the inter-event distance distribution of probability. We use a non-parametric approach to analysis the density of probability of the inter-event distances, especially the kernel density estimation, this methodlogy is clearly presented in Silverman (1986). We used it in the following way. Given a sample of *n* observations *x*<sup>1</sup> , *x*<sup>2</sup> ,........., *xn* with unknown probability distribution function *f* , the kernel density estimate

1

where *K*(.) is a positive function called kernel, a typical example is the Gaussian kernel defined

*i x x f xh K nh h* =

=

*i*

æ ö - <sup>=</sup> ç ÷ è ø <sup>å</sup> (44)

*i n*

**Table 4.** Fractale dimension *D*2 and ratio of the slip on the primary fault over the fault system.

<sup>µ</sup> ( )

<sup>1</sup> ,

where *Sp* is the slip over primary fault and *S* represents the total slip over the fault-system. The obtained results are shown on Table 3, we deduce that during Al Hoceima earthquake of 1994, 62% of the total slip accomodates the primary rupture, 60 % during Al Hoceima 2004 earthquake. During the El Asnam earthquake of 10 October 1980, 59% of the total slip accom‐ odates the primary fault segment, during Zemouri earthquake of 2003 this ratio has been estimate to 57% and 45% during Laalam earthqiuake of 2006. It is important to point out that

*S*

the epicenters tends to be uniform on the plane.

(Khattri, 1995)

of *f* is given by,

by;

where *d* is the dimensionality of the data cluster, and 2*R* is the approximate lenght of the side of the area containing data. As pointed by Eneva (1996), it is safe to start the scaling range at values of *r* as low as *rd* / 3, but in this study, we have use the slope method, which as explained previously consist in estimating the slope of the double logarithmic plot of the correlation integral versus distance. The stability of the scaling range is verified with the slope. It consists in calculating the first derivative between each two pints of the correlation integrale curve and plotting versus logarithmic distance. To eliminate the depopulation and saturation effects, the scaling range is defined within the region where the slope is most constant. Using this procedure and as for Al Hoceima 1994 and 2004 series, the results obtained are displayed in the following figure

**Figure 10.** Graph showing the correlation integral *Log*10*C*(*r*) *vs Log*10(*r*).

The results obtained are close to 2.0, which allow us to deduce that the spatial distribution of the epicenters tends to be uniform on the plane.

The ratio of the slip on the primary fault to the total slip over the fault system is given by (Khattri, 1995)

$$\frac{\mathcal{S}\_p}{\mathcal{S}\_p} = \begin{array}{ccccc} 1 & - & 2^{-\left(3-D\_2\right)} \end{array} \tag{43}$$

where *Sp* is the slip over primary fault and *S* represents the total slip over the fault-system.

**Figure 9.** Graph displaying the plot of the correlation integrale in log-log scale, with the 95% of confidence limit (in dashed lines), the graphs show also, the plot the slope, related to the first derivative of the correlation integral for Al

In practice, however, for large values of *r* the gradient is artificially low, whereas for small values of *r* the gradient is artificially high. These two cases have been called "saturation" and "depopulation" (Nerenberg and Essex, 1990). Whereas, it is common in the estimation of the fractal dimension to use fiting procedure to straight line than to a subjectivelly chosen straight part of the curve. Nerenberg and Essex (1990), give formulas for determining the distances of

*N d*

where *d* is the dimensionality of the data cluster, and 2*R* is the approximate lenght of the side of the area containing data. As pointed by Eneva (1996), it is safe to start the scaling range at values of *r* as low as *rd* / 3, but in this study, we have use the slope method, which as explained previously consist in estimating the slope of the double logarithmic plot of the correlation integral versus distance. The stability of the scaling range is verified with the slope. It consists in calculating the first derivative between each two pints of the correlation integrale curve and plotting versus logarithmic distance. To eliminate the depopulation and saturation effects, the scaling range is defined within the region where the slope is most constant. Using this procedure and as for Al Hoceima 1994 and 2004 series, the results obtained are displayed in

è ø +

1

(42)

Hoceima 1994 and 2004 aftershock sequences.

the following figure

depopulation and saturation, *rd* and *rs* given by

62 Earthquake Research and Analysis - New Advances in Seismology

<sup>1</sup> <sup>1</sup> <sup>2</sup>

**Figure 10.** Graph showing the correlation integral *Log*10*C*(*r*) *vs Log*10(*r*).

*d d s <sup>R</sup> r R and r*

æ ö = = ç ÷

The obtained results are shown on Table 3, we deduce that during Al Hoceima earthquake of 1994, 62% of the total slip accomodates the primary rupture, 60 % during Al Hoceima 2004 earthquake. During the El Asnam earthquake of 10 October 1980, 59% of the total slip accom‐ odates the primary fault segment, during Zemouri earthquake of 2003 this ratio has been estimate to 57% and 45% during Laalam earthqiuake of 2006. It is important to point out that in each case the remainder of the slip is distributed over the secondary rupture.


**Table 4.** Fractale dimension *D*2 and ratio of the slip on the primary fault over the fault system.

In this section we attempt to analysis the inter-event distance distribution of probability. We use a non-parametric approach to analysis the density of probability of the inter-event distances, especially the kernel density estimation, this methodlogy is clearly presented in Silverman (1986). We used it in the following way. Given a sample of *n* observations *x*<sup>1</sup> , *x*<sup>2</sup> ,........., *xn* with unknown probability distribution function *f* , the kernel density estimate of *f* is given by,

$$\hat{f}\left(\mathbf{x},h\right) \quad = \ \underbrace{1\ \mathbf{1}}\_{nh}\sum\_{i=1}^{i=n}\mathbf{K}\left(\frac{\mathbf{x}-\mathbf{x}\_{i}}{h}\right) \tag{44}$$

where *K*(.) is a positive function called kernel, a typical example is the Gaussian kernel defined by;

$$K(x) \quad = \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}x^2} \tag{45}$$

( ) ( ) ( ) ( ) <sup>2</sup> *K x K Kx d* x

consites to minimize the simplified score function defined as follow, we replace *M*<sup>0</sup>

( ) ( ) ( ) <sup>2</sup>

distribution with variance 2. In this case the simplified score function is written as follow

é ù ì üì ü - - ê ú ï ïï ï = -+ í ýí ý

*n h h h nh*

*i n j n i j <sup>i</sup>*

*x y x x M h <sup>K</sup> <sup>K</sup> <sup>K</sup>*

é ù æ ö - æ ö - <sup>=</sup> ê ú ç ÷ - + ç ÷ ç ÷ ê ú è ø è ø ë û

1 2 2 0

11 1 2 exp 2 exp <sup>2</sup> 4 2

ï ïï ï ë û î þî þ

the parameter *h* minimizing the simplified score function is then obtained as solution of the

<sup>1</sup> 1 exp <sup>2</sup> 1 20

å (54)

<sup>µ</sup> ( )

(. , *h* ) is the kernel density calculated from the sample

test the null hypothesis *H*<sup>0</sup>

1 max , *n*

*i h Arg f x h* -

= æ ö <sup>=</sup> ç ÷

*x*1,*x*2,...........,*xi*−1, *xi*+1, ........, *xn*. We use the Silverman multi-modal tests to estimate the number

é ù ì ü ì üì ü - -- ê ú ï ï ï ïï ï í ý í ýí ý - - - - -=

*i j i j*

+¥


assuming that the minimum of *M*<sup>0</sup>

−*∞*

1 1

we observe that in the case of the Gaussian kernel, the kernel *K* (2)

( ) ( ) ( ) 2 2 1 2 2 2 2

> ( ) ( ) ( ) 2 22 2 22

*x x xx xx*

*i j ij ij*

*h hh*

ï ï ï ïï ï ë û î þ î þî þ

the parameter *h* obtained using teh cross-validation method is then given by

*cv i i*

*x y x y M h*

*i j*

,j

*i*

2 2 4

p

= =

= =

1 2 2

*n h*

+*∞ f*

it is in the vicinity of *E*{ *∫*

(*h* ) given by

following equation

,j

*i*

where *f*

^ −*i*

of true bumps. This test is as follow *T* (*<sup>k</sup>* )

*M*<sup>1</sup>

 xx.

(*h* ) is in the vicinity of the minimum of *E M*<sup>0</sup>

^(*x*) <sup>−</sup> *<sup>f</sup>* (*x*) <sup>2</sup> *dx*}. Also, for n large, (*<sup>n</sup>* <sup>−</sup>1)≅*n*; finaly the problem

åå (52)

*h h nh*

å (53)

<sup>=</sup> - ò (51)

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

(*h* ) and then

http://dx.doi.org/10.5772/54888

(.) is a centered Gaussian

 p

*n*

è ø <sup>Õ</sup> (55)

*k*

: " *f* has *k* bumps " against

(*h* ) by

65

in Eq. 44, *h* is a parameter and its determination is crucial. There are differents method to estimate the parameter *h* , in the following lines we summarise the least-square cross-valida‐ tion introduced by Silverman (1986, pp 48). The kernel density estimate of *f* is given as shown previously by

$$\left(\widehat{f}\left(\mathbf{x},h\right)\right) = \frac{1}{nh}\sum\_{i=1}^{i=n} \mathbf{K}\left(\frac{\mathbf{x}-\mathbf{x}\_i}{h}\right) \tag{46}$$

considere a sample of *n* observations *x*<sup>1</sup> , *x*<sup>2</sup> ,........., *xn*; the quadratic uncertainty is then given by

$$\int\_{-\alpha}^{+\alpha} \left[\hat{f}\left(\mathbf{x}\right) - f\left(\mathbf{x}\right)\right]^2 d\mathbf{x} \quad = \int\_{-\alpha}^{+\alpha} \left[\hat{f}\left(\mathbf{x}\right)\right]^2 d\mathbf{x} - 2\int\_{-\alpha}^{+\alpha} \left[f\left(\mathbf{x}\right)\hat{f}\left(\mathbf{x}\right)\right] d\mathbf{x} + \int\_{-\alpha}^{+\alpha} \left[f\left(\mathbf{x}\right)\right]^2 d\mathbf{x} \tag{47}$$

The last term of the right member of the last equality is independnat of the parameter *h* , thus the optimal value of h is obtained by minimizing the two others terms. The problem then consists to find *h* minimizind the score function defined as follow

$$M\_0(h) = \int\_{-\infty}^{+\infty} \left[\hat{f}(\mathbf{x})\right]^2 d\mathbf{x} \quad - \frac{1}{2n} \sum\_{i=1}^n \hat{f}\_{-i}(\mathbf{x}\_i) \tag{48}$$

where,

$$
\hat{f}\_{-i}\left(\mathbf{x}\_{i}\right) = \frac{1}{(n-1)h} \sum\_{i \neq j} K\left(\frac{\mathbf{x} - \mathbf{x}\_{i}}{h}\right) \tag{49}
$$

futhermore, the score function could be written in the following form

$$M\_0\left(h\right) = \frac{1}{n^2h} \sum\_{i=1}^n \sum\_{j=1}^n K^{(2)}\left(\frac{\mathbf{x}\_i - \mathbf{x}\_j}{h}\right) - \frac{2}{n\left(n-1\right)h} \sum\_{i=1}^n \sum\_{j=1}^n K\left(\frac{\mathbf{x}\_i - \mathbf{x}\_j}{h}\right) \tag{50}$$

with,

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region http://dx.doi.org/10.5772/54888 65

$$K^{\binom{2}{2}}(\boldsymbol{x}) = \bigcap\_{-\infty}^{+\infty} K(\boldsymbol{\xi}).K(\boldsymbol{x} - \boldsymbol{\xi}^{\boldsymbol{\varepsilon}})d\boldsymbol{\xi} \tag{51}$$

assuming that the minimum of *M*<sup>0</sup> (*h* ) is in the vicinity of the minimum of *E M*<sup>0</sup> (*h* ) and then it is in the vicinity of *E*{ *∫* −*∞* +*∞ f* ^(*x*) <sup>−</sup> *<sup>f</sup>* (*x*) <sup>2</sup> *dx*}. Also, for n large, (*<sup>n</sup>* <sup>−</sup>1)≅*n*; finaly the problem consites to minimize the simplified score function defined as follow, we replace *M*<sup>0</sup> (*h* ) by *M*<sup>1</sup> (*h* ) given by

( )

64 Earthquake Research and Analysis - New Advances in Seismology

<sup>µ</sup> ( )

<sup>1</sup> ,

+¥ +¥ +¥ +¥


consists to find *h* minimizind the score function defined as follow

+¥

<sup>µ</sup> ( ) ( )

futhermore, the score function could be written in the following form

2

1 2

*M h K K*

*i i*

0

( ) ( )

0 2

previously by

by

where,

with,

*Kx e*

1 <sup>2</sup> <sup>2</sup> 1 2


p

in Eq. 44, *h* is a parameter and its determination is crucial. There are differents method to estimate the parameter *h* , in the following lines we summarise the least-square cross-valida‐ tion introduced by Silverman (1986, pp 48). The kernel density estimate of *f* is given as shown

1

considere a sample of *n* observations *x*<sup>1</sup> , *x*<sup>2</sup> ,........., *xn*; the quadratic uncertainty is then given

The last term of the right member of the last equality is independnat of the parameter *h* , thus the optimal value of h is obtained by minimizing the two others terms. The problem then

( ) <sup>µ</sup> ( ) <sup>µ</sup> ( ) <sup>2</sup>

*M h f x dx f x*

1 1

*x x f x <sup>K</sup> n h h* -

*i j*

¹

1 1 1 1

*n h h h nn h* = = = = æ ö - - æ ö <sup>=</sup> ç ÷ - ç ÷ ç ÷ - ç ÷ è ø è ø

*i j i j*


é ù éù é ù -= - + é ù ò òò ò ë û ëû ë û ë û (47)

1

*i*

( )

*n n n n i j i j*

1

*x x x x*

åå åå (50)

*i i*

<sup>=</sup> é ù - ò ë û å (48)

æ ö - <sup>=</sup> ç ÷ - è ø <sup>å</sup> (49)


*i*

*n*

1 2

*n*

*i x x f xh K nh h* =

<sup>µ</sup> ( ) ( ) <sup>µ</sup> ( ) ( ) <sup>µ</sup> ( ) ( ) 2 2 <sup>2</sup> *f x f x dx f x dx f x f x dx f x dx* 2

= æ ö - <sup>=</sup> ç ÷

*i*

*i n*

*x*

= (45)

è ø <sup>å</sup> (46)

$$M\_1(h) = \frac{1}{n^2h^2} \sum\_{i=1}^{i=n} \sum\_{j=1}^{i=n} \left[ K^{(2)}\left(\frac{\mathbf{x}\_i - \mathbf{y}\_j}{h}\right) - 2K\left(\frac{\mathbf{x} - \mathbf{x}\_i}{h}\right) \right] + \frac{2}{nh}K(0) \tag{52}$$

we observe that in the case of the Gaussian kernel, the kernel *K* (2) (.) is a centered Gaussian distribution with variance 2. In this case the simplified score function is written as follow

$$M\_1(h) = \frac{1}{n^2 h^2} \frac{1}{\sqrt{\pi}} \sum\_{i,j} \left[ \frac{1}{2} \exp\left[\frac{\left(\mathbf{x}\_i - \mathbf{y}\_j\right)^2}{4h^2}\right] - \sqrt{2} \exp\left[\frac{\left(\mathbf{x}\_i - \mathbf{y}\_j\right)^2}{2h^2}\right] \right] + \frac{\sqrt{2}}{nh\sqrt{\pi}}\tag{53}$$

the parameter *h* minimizing the simplified score function is then obtained as solution of the following equation

$$\sum\_{i,j} \left[ \frac{1}{\sqrt{2}} \left\{ \frac{\left(\mathbf{x}\_i - \mathbf{x}\_j\right)^2}{2h^2} - 1 \right\} \exp\left\{ -\frac{\left(\mathbf{x}\_i - \mathbf{x}\_j\right)^2}{4h^2} \right\} - 2\left[ \frac{\left(\mathbf{x}\_i - \mathbf{x}\_j\right)^2}{h^2} - 1 \right] \right] - 2n = 0\tag{54}$$

the parameter *h* obtained using teh cross-validation method is then given by

$$h\_{cv} = -\operatorname{Arg} \max \left( \prod\_{i=1}^{n} \hat{f}\_{-i}(\mathbf{x}\_i, h) \right) \tag{55}$$

where *f* ^ −*i* (. , *h* ) is the kernel density calculated from the sample *x*1,*x*2,...........,*xi*−1, *xi*+1, ........, *xn*. We use the Silverman multi-modal tests to estimate the number of true bumps. This test is as follow *T* (*<sup>k</sup>* ) test the null hypothesis *H*<sup>0</sup> *k* : " *f* has *k* bumps " against the alternative *H*<sup>1</sup> *k* : " *f* has more than *k* bumps". Under the hypothesis *H*<sup>0</sup> *k* , the smoothing parameter of the Gaussian kernel density estimate *f* ^(. , *<sup>h</sup>* ) is given by

$$h\_{crit}\left(k\right) = \text{Inf}\left\{h \in \mathbb{R} \mid \hat{f}\left(\Box h\right) \text{has k bumps or less}\right\}\tag{56}$$

(a) (b) (c)

Scaling Properties of Aftershock Sequences in Algeria-Morocco Region

http://dx.doi.org/10.5772/54888

67

**Figure 11.** Kernel density estimated for Al Hoceima 1994 aftershock sequence (a) using the rule of thumb (b)using

The Fig. 11(a) gives the estimated density obtained using the rule of thumb. The cross valida‐ tion optimal smoothing method gives a bandwidth parameter *h* = 1.2, the estimated density of probability obtained is shown on Fig. 11(b). The estimated density obtained with one mode critical bandwidth equal to *hcrit* = 6.4 is shown on Fig. 11(c). On the three Figures a concentra‐ tion of the inter-event distances around the value 8.9 km, which correspond to the mode of the estimated distribution of probability. The results obtained for the Al Hoceima 2004 aftershock sequence are shown on the Fig. 12. The estimated density using the rule of thumb shown on Fig 12(a) displays a concentration of the inter-event distances around the value 9.45 km, the estimated density using the cross validation optimal smoothing has been obtained using a bandwidth parameter *h* = 1.0. The density obtained displays a concentration of the inetr-event distances around the value 7.5 km. Although, the estimated density with one mode critical bandwidth obtained equal to *hcrit* = 11, shows a concentration of the inter-event distances

(a) (b) (c)

**Figure 12.** Kernel density estimated for Al Hoceima 2004 aftershock sequence (a) using the rule of thumb (b)using

For the aftershock sequence triggered by the 21 May 2003 Zemouri earthquake (Mw 6.9), the

cross validation smoothing and (c) Estimated density obtained with one mode critical bandwidth *hcrit* = 11

cross validation smoothing and (c) Estimated density obtained with one mode critical bandwidth *hcrit* = 6.4

around the value 14.14 km.

obtained results are shown on Fig. 13.

The test *T* (*<sup>k</sup>* ) is inspired from the fact that big values of parameter *hcrit* (*k*) reject the null hypothesis *H*<sup>0</sup> *k* . The following therorem by Silverman (1981) gives a characterisation

**Theorem** (Silverman, 1981)

The kernel density estimate *f* ^(. , *<sup>h</sup>* ) with Gaussian kernel, has more than *<sup>k</sup>* bumps if and only *h* < *hcrit* (*k*).

The test *T* (*<sup>k</sup>* ) is constructed by simulating *N* statistics *hcrit* (1) (*k*); *hcrit* (2) (*k*) ; *hcrit* (3) (*k*); .........; *hcrit* (*N* ) (*k*) from *N* smoothed bootstrap samples of size *n* obtained from *x*<sup>1</sup> , *x*<sup>2</sup> ,........., *xn*.

**Proof.** The proof of this theorem is given in details in Silverman (1981).

Under the null hypothesis, samples can be simulated from the kernel density estimate by using Efron formula,

$$y\_i = \overline{\mathbf{x}} + \left(\mathbf{1} + \frac{h^2}{\sigma^2}\right)^{-\frac{1}{2}} \left(\mathbf{x}\_{l(i)} - \overline{\mathbf{x}} + h\_{crit}(k)\varepsilon\_i\right) \tag{57}$$

where (*xI* (*i*); *i* =1 , n) is a bootstrap sample of size *n* simulated from the sample *x* \_ <sup>=</sup> (*x*<sup>1</sup> , *<sup>x</sup>*<sup>2</sup> ,........., *xn*); *x*¯ and *<sup>σ</sup>* <sup>2</sup> are the mean value and variance of the sample *x* \_ , and (*ε<sup>i</sup>* ; *i* =1,*n*) is a randomly simulated sample from the standard normal distribution.

if *hcrit* \* (*k*) is the parameter obtained from *x* \_ then the *p* value of this test is given by

$$P\_{value} = \frac{\#\left\{h\_{crit}^{(i)}\left(k\right) > h\_{crit}^{\star}\left(k\right)\right\}}{N} \tag{58}$$
