**1. Introduction**

According to the Andersonian faulting theory, the relative magnitude of the principle stresses can be simply related to the faulting style currently active in region. Information on the state of stress in the lithosphere comes from a variety of sources: earthquake focal mechanisms, young geologic data on fault slip and volcanic alignments, *in situ* stress measurements, and tensile fractures. The most simple and straightforward information about the state of stress is obtainable from focal mechanisms. However, a fundamental ambiguity of the most general point-source representation of an earthquake, the centroid moment tensor (CMT), is that it does not

specify which of the two nodal planes is the actual fault plane [1]. There are many approaches that give the seismic moment tensor (e.g., [2–4]) but the fault plane cannot be identified among the two nodal planes. On the other hand, when surface ruptures are not observed, as in the case of too small events or blind faults, the fault plane may be undetermined. Then, the determination of focal mechanisms and the identification of the fault plane of earthquakes can be a critical contribution of seismology to regional tectonic studies and to the assessment of expected deformation and damage patterns. The research aims to take advantage of the Coulomb stress change to discriminate between the fault and auxiliary planes of earthquakes.

Stress in brittle upper crust builds up during the interseismic period until it ruptures seismically. An earthquake occurs when the volume close to a fault moves. Earthquakes, as a result of an instability in faulting, are so pervasive that on many faults most slip occurs during them. The seismicity is an extremely important resource to studies of both continental tectonics and seismic hazard assessment in deforming regions. Stress fields and optimally oriented active faults reveal seismic potential around the cities that improves future earthquake scenarios and are helpful for disaster mitigation (e.g., [5]). The Coulomb failure stress changes caused by mainshock rupture effectively explain the aftershock distributions for the earthquakes. Not only do aftershocks appear to be triggered by such stress changes but moderate events prior to the earthquake increased the potential for failure along most of the future rupture zone, perhaps controlling the location of the later rupture.

The Coulomb stress change is one of a number of models relating to the stress triggering in earthquakes [6]. Since the 1990s, the Coulomb stress change has been widely employed to probe the cause of triggering in several general types of studies: a) main shock-main shock triggering, b) main shock-aftershock triggering, and c) faults optimally oriented for failure. A large number of studies have investigated the Coulomb stress changes and earthquake interactions (e.g., [6–24]). There are many recent works that applied the Coulomb stress change on the causative fault parameter determined by the other approaches to investigate the stress distribution after the earthquake triggering the second mainshock or the aftershocks (the "a" and "b" categories).

Methods generally used to select the fault plane of earthquakes are based on the observation of directivity effects associated with finite ruptures (e.g., [25–27]). The method presented in this article includes Coulomb stress change and its interaction with the surrounding area. Coulomb stress changes induced by regional stress (before the earthquake) are implemented to determine the optimally oriented nodal plane for failure. Our research lays in the "c" category of Coulomb stress studies mentioned above. The correlation between the epicentral distribution of aftershocks and the increased Coulomb stress area promoting failure is investigated. Our motivation for this investigation is the recognition of seismic faults, in particular, when there are uncertainties in location and fault plane orientations, and the ambiguity of which nodal plane is the right one. It could advance out knowledge of the pattern and kinematics of active faulting, and understanding the regional active deformation. This research aims to improve our understanding of kinematics and has important implications for seismic hazard assessment.

### **2. Method**

The slip that occurs on faults during earthquakes (referred to as "source faults") deforms the surrounding area and changes the stress field. A measure of this change is *New Insights into Major Seismic Events by Coulomb Stress Change Pattern and Aftershock… DOI: http://dx.doi.org/10.5772/intechopen.110728*

the Coulomb static stress [15, 28]. The strain created by the displacement of a source fault results in the Coulomb stress changes. Therefore, the stress change can be resolved on an area or specified "receiver" fault planes. The stresses imparted by the source faults or tectonic regime affect faults with a specified strike, dip, and rake namely receiver faults. In other representation, the faults with an optimal orientation, concerning the regional (also called "tectonic") stress or the stress imparted by the source fault, and the assumed friction coefficient are suitable for sliding and could be as a receiver fault. The Coulomb failure stress change, Δ*CFS*, is defined as [10, 29, 30]:

$$
\Delta \sigma\_f(\Delta \text{CFS}) = \Delta \tau\_s + \mu^\prime \Delta \sigma\_{n'} \tag{1}
$$

where Δ*τ<sup>s</sup>* is the change in shear stress on the receiver fault (positive in the direction of fault slip), Δ*σ<sup>n</sup>*´ is the change in normal stress acting on the target fault (positive for unclamping), and *μ*´ is the effective coefficient of friction [31, 32]. The shear stress change is dependent on the position, geometry, and slip of the source fault and the position, geometry, and rake of the receiver fault. The normal stress increase or decrease is independent of the receiver fault rake. The parameter *μ*´ is often called the apparent coefficient of friction and includes the effects of pore pressure changes and the material properties of the fault zone [10]. Fault friction *μ*´ is often inferred to be 0.4–0.8 for faults with little cumulative slip, which tend to be rough, and 0–0.4 for faults with great cumulative slip, which tend to be smooth [33]. This parameter is typically found to be around 0.4 for strike-slip faults or faults with unknown orientation [34, 35].

The positive Δ*CFS* represents that the desired fault is likely closer to failure; the negative Δ*CFS* indicates that the desired fault is away from failure. Both increased shear and unclamping of faults promote failure [36–40]. The Coulomb stress change depends on the geometry and slip of the earthquake, the geometry and sense of slip of the fault, and the effective coefficient of friction [20].

There are two principal considerations of the Coulomb stress changes on receiver faults: stress changes on the specified receiver fault and stress changes on an optimally oriented receiver fault. The specified receiver faults rely on resolving stress changes on faults with known geometry [20, 33, 41]. The optimally oriented receiver faults are determined by assuming that the earthquakes will be triggered only on those planes with maximum total Coulomb stress [7, 12, 13, 42].

The Coulomb static stress has been commonly used to determine the distribution of stress induced by an event. However, for the first time, it is applied to realize the distribution of regional stress triggering an event on appropriate fault. Determination of the principal regional stress directions and a measure of relative stress magnitudes are possible by a variety of different focal mechanisms within a region of uniform stress [43]. Theoretically, the earthquakes will be triggered only on the fault planes with maximum total Coulomb stress. It means that the earthquake-triggering faults might have an optimal orientation with maximum Coulomb stress imparted by the regional stress (e.g., [44]). Therefore, the earthquake causative faults can be determined from nodal planes by resolving Coulomb stress on them with respect to the regional stress and selecting those on which the imparted Coulomb stress is maximum.

### **3. Results**

The Sefidsang earthquake occurred on April 5th, 2017 Mw 6.15 at a depth of about 11.5 km. Its epicenter was about 35.776 degrees of latitude and 60.436 degrees of

longitude, southeast of Mashhad and east-northeast of Fariman, NE Iran (**Figure 1**). The maximum acceleration of this earthquake recorded by the Iranian Strong Motion Network was about 120 cm/s at the station 38 km from the epicenter. Based on the GSI field observations, the most destructive effects of the earthquake were observed near one of the Kashafrud fault segments. The Kashafrud reverse fault closely parallels the boundary between the Binalud and the Kopeh Dagh mountains. East of Mashad, the Kashafrud fault system runs to the Binalud mountains south of the Cimmerian arcrelated Fariman complex (**Figure 2**).

According to the focal mechanism solutions presented by some global seismological centers, the mechanism of the Sefidsang earthquake is reversed with a minor strike slip on northwest-southeast oriented nodal planes. The characteristic of the two nodal planes and the event are presented in **Table 1**.

Although historical seismicity in the northeast of Iran is mostly associated with the Baghan, Quchan, and Neyshabur faults [45–48], the Sefidsang earthquake occurred in a region that has faced almost no historic or recent seismicity and has been characterized by low deformation rate concerning Eurasia [49].

Though in such a moderate earthquake that the causative fault is not exposed at the surface, theoretically, each nodal plane has the same possibility for failure, however, following the rules of focal mechanism inversion [50], one of them must be selected for each earthquake. The seismic fault is determined by assuming that the earthquake will be triggered on the plane with maximum total Coulomb stress. In other words, the earthquake-triggering fault should have maximum Coulomb stress with respect to

#### **Figure 1.**

*The epicenter and focal mechanism solutions processed by international seismological centers of the Sefidsang earthquake (2017.04.05) plotted over the SRTM 30 m DEM. The red star presents the mainshock of the Sefidsang earthquake. The epicenters of historical earthquakes with magnitude above 6 from 1500 to 1965, modified after Refs. [45, 46], are shown as violet circles. Abbreviations for active faults are ASFS: Ashkabad fault system, NKFS: North Kopeh Dagh fault system, AFS: Atrak fault system, BF: Bijvard fault, BQFS: Baghan-Quchan fault system, CHF: Chakaneh fault, DBF: Dasht-e-Bayaz fault, DFS: Doruneh fault system, HF: Herat fault, KFS: Kashafrud fault system, JF: Jangal fault, KHF: Khaf fault, SHF: Shandiz fault, and NYFS: Neyshabur fault system.*

*New Insights into Major Seismic Events by Coulomb Stress Change Pattern and Aftershock… DOI: http://dx.doi.org/10.5772/intechopen.110728*

#### **Figure 2.**

*Simplified geological map of the area. The Sefidsang earthquake sequence is represented by circles (the greater earthquakes, the greater circles). The location of the Sefidsang mainshock is marked by the yellow star.*


#### **Table 1.**

*The geometry of the Sefidsang earthquake nodal planes taken from GCMT and ISC.*

regional stress. The best-fitting regional stress tensor compatible with the majority of ISC collected earthquake focal mechanisms over the period of years was defined by the Win-Tensor program (**Table 2**). Then, we should select the nodal plane on which imparted Coulomb stress is maximum.

The stress change calculations were performed using the software Coulomb 3.3 [44]. For all the calculations of the Coulomb stress change, the shear modulus (G), <sup>32</sup> <sup>10</sup><sup>5</sup> bar, Poisson ratio (ν) 0.25, Young modulus (E) 8 <sup>10</sup><sup>5</sup> bar, and effective coefficient of friction (μ´ ) 0.6 were used. The nodal plane located in the red region on


**Table 2.** *Principle stress direction.*

**Figure 3.**

*The regional Coulomb stress change has been calculated for two nodal planes of the Sefidsang earthquake. The maximum Coulomb stress region is shown in red. White rectangles show the nodal plane geometry. Green lines represent the assumptive fault traces on the ground. The yellow star represents the epicenter of the Sefidsang earthquake.*

the Coulomb map has the most consistency with the inferred Coulomb stress field and should be selected as the earthquake-triggering fault. However, the result represents both nodal planes, more or less, are situated in the positive ΔCFS area (**Figure 3**). The calculated positive ΔCFS area has exactly placed the bend of the Kashafrud fault proximity in the Fariman complex.

The aftershocks preferentially occur in the calculated stress increase and are less likely in the calculated stress decrease areas [51]. Therefore, the aftershock distributions control which nodal plane results in more matching with high Coulomb stress. The epicentral distribution of aftershocks by MN≥2 and ≥3 is mostly situated in the maximum (most positive) Coulomb stress area (**Figure 4**) and is more consistent with the first nodal plane in **Table 1**. The general pattern of aftershocks brings up that the geometry of the Sefidsang earthquake sequence causative faults is in listric form.

Factors such as unknown stress concentration before the mainshock, crustal heterogeneity, and the existence of small faults with different orientations [15, 52, 53] may play a role in perturbing the stress field and thus it is not surprising that all of the aftershocks have not been completely matched with regions of increased Coulomb stress.

### **4. Discussion**

The regional inferred Coulomb stress changes triggering the April 5th, 2017 Mw 6.15 Sefidsang earthquake (pre-event stress; **Table 2**) was resolved on two nodal planes. The status of ΔCFS distribution was investigated to identify which nodal plane has been more consistent with high Coulomb stress. The nodal plane has the most consistency with the regional inferred Coulomb stress field (situated in the red region *New Insights into Major Seismic Events by Coulomb Stress Change Pattern and Aftershock… DOI: http://dx.doi.org/10.5772/intechopen.110728*

#### **Figure 4.**

*The green dots represent the aftershock distribution. It is more compatible with the first geometry of nodal planes in Table 1. The epicentral distribution of aftershocks is limited to the area behind the assumptive fault trace (the green line on the coulomb map), suggesting a listric form of the causative fault. a) The magnitude of aftershocks is greater than 2. b) The magnitude of aftershocks is greater than 3. Most of the aftershocks have well matched with the maximum Coulomb stress area.*

#### **Figure 5.**

*Conceptual model with 3D topographic relief of SRTM 30m DEM on it represents the preexisting normal faults that were reactivated as reverse faults in current tectonic regime, viewed from S70°E. The Sefidsang earthquake sequence is shown by the red circles on the top. The structural pattern of the area illustrates thick-skin tectonics including crustal-penetrating low-angle faults reactivated in the current stress field coupled with mafic–ultramafic magmatism in the lower crust.*

on the Coulomb map), on one hand, and the epicentral distribution of aftershocks, on the other hand, is closer to failure and should be selected as the earthquake-triggering fault. Although the regional inferred Coulomb stress field is consistent with both

nodal planes, the epicentral distribution of aftershocks confirmed the nodal plane with 316° strike, 20° dip to the north, and 120° rake geometry as the earthquake-triggering fault (**Figure 4**). From the general pattern of aftershocks distribution, it is also obvious that the geometry of the Sefidsang earthquake sequence causative faults is in the form of listric. Considering the proximity of the Sefidsang sequence to the Fariman complex (**Figure 1**) as an arc-related basin formed by extensional faults with low initial dips [54] reveals that reversal slips occurred on preexisting normal faults. Therefore, it is very likely that the Sefidsang earthquake-triggering fault is the inverted arc-related structures reactivated in the recent tectonic regime. A kinematic model of fault planes reactivated during the Sefidsang earthquake has been represented in **Figure 5**.

### **5. Conclusion**

The most important question concerning earthquakes is about the geometry and kinematics of the causative faults. In other words, we like to know which nodal planes would be the causative fault plane accommodating the slip during seismic activation, especially in the case that there is no rupture evidence at the surface. The Coulomb static stress has been commonly used to determine the stress distribution induced by an event. However, for the first time in this research, the Coulomb regional stress was resolved on nodal planes to realize the optimally oriented one for failure. The seismic fault is determined by assuming that the earthquake will be triggered on the plane with maximum total Coulomb stress. In other words, the earthquake-triggering fault should have maximum Coulomb stress concerning regional stress. The method has been conducted for the April 5th, 2017 Sefidsang earthquake in NE Iran. The results reveal that the earthquake occurred on a northeast-dipping listric fault with dextral reverse movement. Recognition of the pattern and kinematics of active deformation in addition to paleo-structures can help us to shed light on structural aspects subjected to active deformation in the area. The results of this study have crucial implications for seismic hazard assessment of the region and potential future failure areas.

### **Acknowledgements**

I thank the Iranian Seismological Center (IRSC). I utilized Win-Tensor and Coulomb software. I am grateful to the International Seismological Centre (ISC), Global Centroid Moment Tensor (GCMT), and USGS for open access to their online Bulletin. I also used SRTM DEM derived from the USGS/NASA SRTM data.

The author has no relevant financial or nonfinancial interests to disclose.

*New Insights into Major Seismic Events by Coulomb Stress Change Pattern and Aftershock… DOI: http://dx.doi.org/10.5772/intechopen.110728*
