**5. Results and discussion**

We applied the EGFM to generate a lot of models using the Somerville [6] relations to charac‐ terize the parameters of the source. The total rupture area was 5,571.90 km2 with an average slip of 3.2 m and a combined area of asperities of 1,269.11 km2 , in which the area of largest asperity was of 812.33 km2 . The hipocentral distance to the center of the closest asperity was estimate at 18 km. It should be pointed out that the Somerville [6] relationships do not define an azimuth to specify the location of asperity, this mean the largest asperity can be located within an azimuth of between 0o to 360o . Then in the modeled process the position of largest asperity was varied from 0 to 360 o.

The main goal of this study was in the context of obtaining the most probable scenario of the ground response in the major cities of region upon the occurrence of a MW 7.3 earthquake generated in the area in study. In this work, all the simulations were carried out to obtain a statistical sample that may represent the most probable scenarios of the ground response at the studied sites. For that purpose, the fault parameters and rupture process (i.e., (i) the azimuth of the closest asperity to hypocenter, (ii) the rise time, (iii) the rupture velocity, and (iv) the location of SMGA within the fault plane) were varied in an iterative process in order to generate a statistical sample of the most probable ground response scenario.

According to Somerville [6] an earthquake with a moment magnitude of 7.3 should have around 2.4 asperities. Based on the above, our procedure was divided in two stages. In the first stage, we used 2 SMGA and 3 SMGA in the second stage. These SMGA were positioned inside of different points into the dislocation area adopting the Somerville [6] criteria. In order to evaluate which scenario is the most probable we compare the PGA obtained from each scenario to those predicted by two GMPE, from Ordaz [16] and from Young´s [17].

It should be pointed out that both GMPE were obtained considering earthquake data from subduction tectonic environments as follows: (i) Ordaz [16] used subduction earthquakes from the Mexican pacific coast, and (ii) Young's [17] subduction earthquakes from around the world. The process of finding the best fit of the simulated PGA with respect to Ordaz [16], and Young's [17], GMPEs was based on the smallest residual criteria between the simulated PGA and the estimated GMPEs. The above, allowed us to identify 2 different source models that provided PGA values that better matched with the used GMPE as follows: (i) the first one with 2 SMGA, and (ii) the second one with 3 SMGA.

In order to find a best residual in each interaction, we varied the position of SMGA, the rupture velocity, rise time, radiation pattern, and the size of SMGA changes in the strike or dip directions, according to the azimuth of the station or stations that had poor adjustment with GMPE. In the process of modeling we found little sensitivity of the synthetics to the rise time variations. On the other hand, we found high sensitivity of the synthetics to the rupture velocity variation, the size of the SMGA and its location inside of fault plane. The parameters with major weight in the modeled are the number, the size and the location of SMGA. The optimal model is a combination of all these parameters. The best model for each stage was determined by minimizing the residual between synthetic and observed PGA.

After the above steps were completed, we proceeded to generate and compare the mean value of the residual between the PGAs and each one of the GMPEs by applying the definition of mean residuals as the weighted sum of the residuals of the logarithmic values between observed and estimated. The above step was applied to identify, in the statistical sense trough

We applied the EGFM to generate a lot of models using the Somerville [6] relations to charac‐ terize the parameters of the source. The total rupture area was 5,571.90 km2 with an average

estimate at 18 km. It should be pointed out that the Somerville [6] relationships do not define an azimuth to specify the location of asperity, this mean the largest asperity can be located

The main goal of this study was in the context of obtaining the most probable scenario of the ground response in the major cities of region upon the occurrence of a MW 7.3 earthquake generated in the area in study. In this work, all the simulations were carried out to obtain a statistical sample that may represent the most probable scenarios of the ground response at the studied sites. For that purpose, the fault parameters and rupture process (i.e., (i) the azimuth of the closest asperity to hypocenter, (ii) the rise time, (iii) the rupture velocity, and (iv) the location of SMGA within the fault plane) were varied in an iterative process in order

According to Somerville [6] an earthquake with a moment magnitude of 7.3 should have around 2.4 asperities. Based on the above, our procedure was divided in two stages. In the first stage, we used 2 SMGA and 3 SMGA in the second stage. These SMGA were positioned inside of different points into the dislocation area adopting the Somerville [6] criteria. In order to evaluate which scenario is the most probable we compare the PGA obtained from each scenario

It should be pointed out that both GMPE were obtained considering earthquake data from subduction tectonic environments as follows: (i) Ordaz [16] used subduction earthquakes from the Mexican pacific coast, and (ii) Young's [17] subduction earthquakes from around the world. The process of finding the best fit of the simulated PGA with respect to Ordaz [16], and Young's [17], GMPEs was based on the smallest residual criteria between the simulated PGA and the estimated GMPEs. The above, allowed us to identify 2 different source models that provided PGA values that better matched with the used GMPE as follows: (i) the first one with 2 SMGA,

In order to find a best residual in each interaction, we varied the position of SMGA, the rupture velocity, rise time, radiation pattern, and the size of SMGA changes in the strike or dip

. The hipocentral distance to the center of the closest asperity was

. Then in the modeled process the position of largest

, in which the area of largest

the estimation of the residuals, how realistic our PGA estimations are.

42 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

slip of 3.2 m and a combined area of asperities of 1,269.11 km2

to 360o

to generate a statistical sample of the most probable ground response scenario.

to those predicted by two GMPE, from Ordaz [16] and from Young´s [17].

**5. Results and discussion**

asperity was of 812.33 km2

within an azimuth of between 0o

asperity was varied from 0 to 360 o.

and (ii) the second one with 3 SMGA.

Figures 2a and 2b show the comparison between both GMPE versus our results for the lowest residual case of the source models (two SMGA). Figure 2a shows the Young's [17] GMPE curves for rock and soil.


**Table 2.** Shows that the mean residual for the 25 stations decrease when using source models with 2 SMGA instead of when using source models with 3 SMGA. Table 2 shows the comparison of residuals between the theoretical values of each GMPE and the PGAs for all 25 stations.

Our data showed three clusters that according to their hypocentral distances are distributed as follows: (i) The first group was distributed within the distance from 35 to 60 km, in this group 5 of the simulated PGA were located nearby of both curves; (ii) The second group is defined for distances range from 60 to 120 km, on this case the PGA are distributed almost evenly below the GMPE curves; (iii) Finally, the third group is defined for distances range from 120 to 500 km, on this particular situation the PGA values are over-estimated by the GMPE and show a clear tendency to attenuate faster than the pattern showed on the GMPE. Figure 2b shows the Ordaz [16] GMPE, the author uses thrust subduction earthquakes from Mexico (such as event simulated in this study). In general the comparison shows that 90% our results are located above this curve.

For the GMPE of Ordaz [16], we compare only the 19 stations seated on rock. For the GMPE of Young's [17] we compare the 19 stations seated on rock, and 6 stations seated on soil sites (table 3), each of these groups with the respective curves for sites on rock and for sites on soil. From the modeling process of the target event, when three SMGA were used the lowest residuals we obtained between the PGA and the GMPE were: (i) 0.011 for Young's [17] GMPE Width (km)

Area (km2 )

3 14.25 14.25 203.05 2.4

Young's *et al.* (1997) and Ordaz *et al*. (1989).

(km)

SMGA SMGA Length

Numbers of

Table 2. Location, and area of SMGA´s for the 2 models generated, with two and three SMGA respectively, where Vr is the rupture velocity. Column 9, 10 and 11 show the mean residual between simulated PGA and GMPE of

> Total area

1281.76

Vr Km/s

2 17.81 10.69 190.36 2.5 0.011 0.101 0.252

Residual with Young's GMPE (Rock)

Residual with Young's GMPE (Soil)

Residual with Ordaz GMPE (Rock)

> Ramirez-Gaytán [23] simulate PGA and acceleration time histories for Tecoman earthquake located in the adjacent area at the event here simulated. The particularity and importance of this study is that the authors used observed strong motion records as a comparison reference to adjust the synthetics and found that from the comparison between PGA synthetics with respect to Young's [17] GMPE for rock and soil curves, and the Ordaz [16] GMPE curve (Figures 2e and 2f) behave very similar to the description previously provided for the same ranges of

> > **Maximum acceleration (cm/s/s)**

T 1 T 2

http://dx.doi.org/10.5772/53274

T 3 45

T 0.5

**PGA EW**

T 0.1

 SJAL 34.54 Rock 457.66 819.32 1934.28 958.19 193.3 159.37 30.9 CEOR 40.07 Rock 125.38 218.08 265.65 328.99 178.02 273.65 57.36 BA5 51.22 Soil 157.32 230.26 402.48 428.66 150.87 325.69 54.23 COJU 54.02 Rock 201.97 248.95 484.43 190.27 65.25 39.12 8.63 MARU 68.11 Rock 194.29 419.83 559.86 627.33 261.75 180.06 29.4 TAPE 76.76 Rock 30 60.46 84.91 94.25 20.38 25.95 5.56 R15 76.78 Soil 27.33 45.06 47.41 51.59 16.83 7.49 2.14 MANZ 77.11 Rock 91.74 133.89 260.72 174.85 37.56 26.15 4.94 CAM 85.23 Soil 78.43 113.16 366.71 135.51 24.06 30.26 4.63 NAR 89.25 Soil 51.95 70.01 215.24 139.55 18.02 13.37 2.1 CEN 92.34 Rock 20.73 33.06 49.66 60.03 13.19 19.46 2.87 COMA 93.68 Rock 63.3 78.45 146.38 207.83 117.09 112.31 19.73 EZA 100.73 Soil 25.49 32.19 87.7 59.22 14.75 13.34 2.06 CIHU 108.51 Rock 42.84 47.23 91.04 213.08 26.49 12.49 2.56 EZ5 113.45 Rock 52.18 92.98 113.73 150.01 32.7 39.9 5.93 COLL 113.83 Rock 29.68 35 76.05 157.38 24.04 17.21 3.07 CALE 132.32 Soil 71.7 84.37 120.62 167.18 109.63 60.38 10.92 CDGU 140.21 Rock 50.83 57.72 177.79 172.63 43.18 15.1 3.34 VILE 188.48 Rock 31.74 32.76 44.1 98.98 60.66 48.56 8.31 NITA 199.77 Rock 68.46 75.31 188.1 193.54 120.04 80.13 13.41 CANA 203.51 Rock 31.33 43.4 85.63 77.88 60.92 46.25 8.62 URUA 217.28 Rock 20.51 21.37 34.56 69.81 38.08 56.54 9.33 GDLC 247.67 Rock 1.71 2.1 5.37 5.72 0.98 0.29 0.06 CUP 504.35 Rock 3.53 3.95 5.79 9.29 7.18 6.58 0.97 SCT 509.27 Soil 3.55 3.78 7.32 14.28 3.78 0.57 0.21

**Table 3.** Relation of 25 stations where acceleration time histories was simulated, soil type, PGA, spectral acceleration

We made an additional comparison, for Tecoman earthquake Singh [10] used records of stations located at distances larger than 50 km and comparing the PGA versus Ordaz [16]. In figure 2g it can be seen that the behavior is the same: observed PGAs lie above the curve. The

corresponding to structural period of 0.1, 0.2, 0.3, 1.0, 2.0 and 3.0 s, EW component.

T 0.3

The Use of Source Scaling Relationships in the Simulation of a Seismic Scenario in Mexico

distances obtained in this study.

**distance Soil type**

**No Station Hipocentral**

Figure 2. Comparison of synthetics PGA versus PGA from GMPE. In first row comparison of PGA from our simulated acceleration time histories using 2 SMGA versus PGA predicted using the following GMPE: (a) Young's [17], (b) Ordaz [16]. In second row comparison of PGA from our simulated acceleration time histories using 3 SMGA versus PGA predicted using the following GMPE: (c) Young's [17], (d) Ordaz [16]. In third row comparison of simulated PGA of Tecoman earthquake from Ramirez-Gaytán [23] versus PGA predicted using the following **Figure 2.** Comparison of synthetics PGA versus PGA from GMPE. In first row comparison of PGA from our simulated acceleration time histories using 2 SMGA versus PGA predicted using the following GMPE: (a) Young's [17], (b) Ordaz [16]. In second row comparison of PGA from our simulated acceleration time histories using 3 SMGA versus PGA pre‐ dicted using the following GMPE: (c) Young's [17], (d) Ordaz [16]. In third row comparison of simulated PGA of Teco‐ man earthquake from Ramirez-Gaytán [23] versus PGA predicted using the following GMPE: (e) Young's [17], (f) Ordaz [16]. In (e) comparison of real PGA of the Tecoman earthquake using records of stations with distances larger than 50 km versus GMPE of Ordaz [16] from Singh [10].

(Rock), (ii) 0.101 Young's [17] GMPE (Soil), and (iii) 0.252 for Ordaz [16] GMPE for the sites shown in Figure 2c and 2d. The best fit between the estimated values of PGA and GMPE, estimated by means of the lowest residual, was obtained for the source model with two SMGA. The respective estimated residuals were: (i) 0.009 for Young's [17]GMPE (Rock), (ii) 0.024 for Young's [17] GMPE (Soil) and (iii) 0.245 for Ordaz [16]. 8 stations with distances larger than 50 km versus GMPE of Ordaz [16] from Singh [10].

GMPE: (e) Young's [17], (f) Ordaz [16]. In (e) comparison of real PGA of the Tecoman earthquake using records of

Ramirez-Gaytán [23] simulate PGA and acceleration time histories for Tecoman earthquake located in the adjacent area at the event here simulated. The particularity and importance of this study is that the authors used observed strong motion records as a comparison reference to adjust the synthetics and found that from the comparison between PGA synthetics with respect to Young's [17] GMPE for rock and soil curves, and the Ordaz [16] GMPE curve (Figures 2e and 2f) behave very similar to the description previously provided for the same ranges of distances obtained in this study.


**Table 3.** Relation of 25 stations where acceleration time histories was simulated, soil type, PGA, spectral acceleration corresponding to structural period of 0.1, 0.2, 0.3, 1.0, 2.0 and 3.0 s, EW component.

(Rock), (ii) 0.101 Young's [17] GMPE (Soil), and (iii) 0.252 for Ordaz [16] GMPE for the sites shown in Figure 2c and 2d. The best fit between the estimated values of PGA and GMPE, estimated by means of the lowest residual, was obtained for the source model with two SMGA. The respective estimated residuals were: (i) 0.009 for Young's [17]GMPE (Rock), (ii) 0.024 for

Figure 2. Comparison of synthetics PGA versus PGA from GMPE. In first row comparison of PGA from our simulated acceleration time histories using 2 SMGA versus PGA predicted using the following GMPE: (a) Young's [17], (b) Ordaz [16]. In second row comparison of PGA from our simulated acceleration time histories using 3 SMGA versus PGA predicted using the following GMPE: (c) Young's [17], (d) Ordaz [16]. In third row comparison of simulated PGA of Tecoman earthquake from Ramirez-Gaytán [23] versus PGA predicted using the following GMPE: (e) Young's [17], (f) Ordaz [16]. In (e) comparison of real PGA of the Tecoman earthquake using records of

**Figure 2.** Comparison of synthetics PGA versus PGA from GMPE. In first row comparison of PGA from our simulated acceleration time histories using 2 SMGA versus PGA predicted using the following GMPE: (a) Young's [17], (b) Ordaz [16]. In second row comparison of PGA from our simulated acceleration time histories using 3 SMGA versus PGA pre‐ dicted using the following GMPE: (c) Young's [17], (d) Ordaz [16]. In third row comparison of simulated PGA of Teco‐ man earthquake from Ramirez-Gaytán [23] versus PGA predicted using the following GMPE: (e) Young's [17], (f) Ordaz [16]. In (e) comparison of real PGA of the Tecoman earthquake using records of stations with distances larger

GMPE Simulation rock Simulation soil

10 100 1000

Table 2. Location, and area of SMGA´s for the 2 models generated, with two and three SMGA respectively, where Vr is the rupture velocity. Column 9, 10 and 11 show the mean residual between simulated PGA and GMPE of

> Total area

1281.76

<sup>2</sup> 1 24.94 32.06 799.51 1256.38 3.0 0.009 0.024 0.245 2 21.37 21.37 456.86 2.9

10 100 1000

Hypocentral Distance (km)

10 100 1000

Hypocentral Distance (km)

GMPE (Ordaz) rock Simulation rock

GMPE (Ordaz) rock Simulation rock

Vr Km/s

2.3 2 17.81 10.69 190.36 2.5 0.011 0.101 0.252

Residual with Young's GMPE (Rock)

Residual with Young's GMPE (Soil)

2 SMGA

3SMGA

g

Residual with Ordaz GMPE (Rock)

Young's *et al.* (1997) and Ordaz *et al*. (1989).

(km)

<sup>3</sup> 1 35.62 24.94 888.35

10 100 100

10 100 1000

Simulation soil Simulation rock GMPE(Youngs) soil GMPE(Youngs) rock

Hypocentral Distance (km)

10 100 1000

than 50 km versus GMPE of Ordaz [16] from Singh [10].

Simulation soil 0

GMPE rock Simulation rock GMPE soil

Simulation soil Simulation rock GMPE(Youngs) soil GMPE(Youngs) rock

Hypocentral Distance (km)

Width (km)

44 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

Area (km2 )

3 14.25 14.25 203.05 2.4

PGA (cm/s2)

a b

c d

PGA (cm/s2)

e f

1

10

100

1000

SMGA SMGA Length

1

1

0

1

10

100

1000

10

100

PGA (cm/s2)

1000

10

100

PGA (cm/s2)

1000

Numbers of

8

Young's [17] GMPE (Soil) and (iii) 0.245 for Ordaz [16].

stations with distances larger than 50 km versus GMPE of Ordaz [16] from Singh [10].

We made an additional comparison, for Tecoman earthquake Singh [10] used records of stations located at distances larger than 50 km and comparing the PGA versus Ordaz [16]. In figure 2g it can be seen that the behavior is the same: observed PGAs lie above the curve. The comparison made are important because in the first case Ramirez-Gaytán [23] generate PGA based in a previous model Ramirez-Gaytán [24] when using observed records to compare with synthetics. In the second case Singh [10] use real data, in both cases the results are very similar with the obtained in this study. All mentioned studies correspond at the same tectonic environment. Figure 2g show than for Singh [10] major PGA locate at distances above 120 km this explained because he use data from regional stations. In the case of Ramirez-Gaytan [23] major PGA are located at distances from 10 to 100 km this explain why authors only use data from local networks.

In this study, we compare our PGA's with those obtained by the GMPE of Ordaz [16] and because they used data from Mexico. However, all of these studies considered all of the data available at the time of their analyses. This means that the data used were essentially strong motion data from the southern part of the country Tejeda- Jácome and Chávez-García [25]. None of these studies included data from western Mexico, along the northern section of the subduction zone. It is uncertain that ground-motion prediction equations developed for Guerrero in a very different tectonic setting can be applied to Colima Tejeda-Jácome and Chávez-García [25]. For this reason, it is important to compare our results with GMPE of other parts of the world, such as the GMPE of Young's [17]. They used some similar parameters to those of the event simulated in this study (tectonic environment or hypocentral distance magnitude, etc.). This seems to be justified when we observed that the minor residual is reached when compared with the GMPE of Young's [17] with minor residual (0.009) than Ordaz [16] with residual of 0.245 for the model with best adjust (model with two SMGA). However, we expect that any of the two GMPEs compared in this paper satisfy the detailed similarities with the event simulated in this study for the Colima region. For this reason, our intention is to use local and world parameters in order to validate our results and to give a degree of confidence when applying this methodology to future earthquakes for determination of acceleration time histories and PGA.

11

47

Figure 3. Simulated synthetic acceleration time histories (intense period) with next distances from hypocenter: (a) 34 to 78 km, (b) 85 to 114 km, (c) 132 to 248

0

50

100

150

0

50

100

150

http://dx.doi.org/10.5772/53274

km, (d) major to 500 km. In left column type of soil and epicentral distance are denoted above and left of each trace. PGA and code of station is denoted above

and right of trace. In right column PGA is denote above and left of trace.

Rock 247.67

Rock 217.28

Rock 203.51

Rock 199.77

Rock 188.48

Rock 140.21

Soil 132.32

71.7 CALE

108.6

50.8 CDGU

20.9

31.7 VILE

26

68.5 NITA

30.7

31.3 CANA

45

Soil 509.27

3.5 SCT

3.9

20.5 URUA

11.4

1.7 GDLC

5.3

**Figure 3.** Simulated synthetic acceleration time histories (intense period) with next distances from hypocenter: (a) 34 to 78 km, (b) 85 to 114 km, (c) 132 to 248 km, (d) major to 500 km. In left column type of soil and epicentral distance are denoted above and left of each trace. PGA and code of station is denoted above and right of trace. In right column

c

EW Component cm/s/s

Rock 77.11

Soil 76.78

Rock 76.76

Rock 68.11

Rock 54.02

Soil 51.22

Rock 40.07

Rock 34.54

457.7 SJAL

169.7

125.4 CEOR

173.9

157.3 BA5

303.2

202 COJU

78.7

194.3 MARU

150.6

30 TAPE

55.5

27.3 R15

27.5

91.7 MANZ

30.1

0

Rock 113.83

Rock 113.45

Rock 108.51

Soil 100.73

Rock 93.68

Rock 92.34

Soil 89.25

Soil 85.23 29.7 COLL

13.9

52.2 EZ5

84.9

42.8 CIHU

55

25.5 EZA

58.8

63.3 COMA

29.5

20.7 CEN

37.7

51.9 NAR

72.6

78.4 CAM

77.2

d

EW Component cm/s/s

NS Component cm/s/s

Rock 504.35

3.5 CUP

3.6

The Use of Source Scaling Relationships in the Simulation of a Seismic Scenario in Mexico

NS Component cm/s/s

EW Component cm/s/s

a

PGA is denote above and left of trace.

NS Component cm/s/s

b

EW Component cm/s/s

NS Component cm/s/s

The main contribution of the process detailed above is not obtaining PGA, for this case is sufficient to consult GMPE. The purpose of this paper is to prepare acceleration time histories to be used by structural engineers on the analysis and design of structures. In modern seismic design approaches the quality of a structural solution frequently depends on the detailed knowledge that designers have on the characteristics of the seismic ground motion that the structure will suffer at a site if an earthquake of a given magnitude occur at a given location. Figures 3a-3d show the acceleration time histories for the model with minor residual after applying the process previously described. The largest acceleration was obtained in the nearto-source station SJAL (rock site) with 0.47 g. It is important to point out that stations CUP and SCT (figure 3c) located in Mexico City with hipocentral distances larger than 470 km still produced considerable values of peak accelerations (3.53 and 3.55 gal) similar of those of the GDLC station (with 1.71 and 5.3 gal) located to 273.48 km from the epicenter. This is due to the fact that seismic waves are enormously amplified at lake-bed sites respect to hill-zone sites in Mexico City, although it has been suggested that even hill-zone sites suffer amplification and Singh [26].

comparison made are important because in the first case Ramirez-Gaytán [23] generate PGA based in a previous model Ramirez-Gaytán [24] when using observed records to compare with synthetics. In the second case Singh [10] use real data, in both cases the results are very similar with the obtained in this study. All mentioned studies correspond at the same tectonic environment. Figure 2g show than for Singh [10] major PGA locate at distances above 120 km this explained because he use data from regional stations. In the case of Ramirez-Gaytan [23] major PGA are located at distances from 10 to 100 km this explain why authors only use data

46 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

In this study, we compare our PGA's with those obtained by the GMPE of Ordaz [16] and because they used data from Mexico. However, all of these studies considered all of the data available at the time of their analyses. This means that the data used were essentially strong motion data from the southern part of the country Tejeda- Jácome and Chávez-García [25]. None of these studies included data from western Mexico, along the northern section of the subduction zone. It is uncertain that ground-motion prediction equations developed for Guerrero in a very different tectonic setting can be applied to Colima Tejeda-Jácome and Chávez-García [25]. For this reason, it is important to compare our results with GMPE of other parts of the world, such as the GMPE of Young's [17]. They used some similar parameters to those of the event simulated in this study (tectonic environment or hypocentral distance magnitude, etc.). This seems to be justified when we observed that the minor residual is reached when compared with the GMPE of Young's [17] with minor residual (0.009) than Ordaz [16] with residual of 0.245 for the model with best adjust (model with two SMGA). However, we expect that any of the two GMPEs compared in this paper satisfy the detailed similarities with the event simulated in this study for the Colima region. For this reason, our intention is to use local and world parameters in order to validate our results and to give a degree of confidence when applying this methodology to future earthquakes for determination

The main contribution of the process detailed above is not obtaining PGA, for this case is sufficient to consult GMPE. The purpose of this paper is to prepare acceleration time histories to be used by structural engineers on the analysis and design of structures. In modern seismic design approaches the quality of a structural solution frequently depends on the detailed knowledge that designers have on the characteristics of the seismic ground motion that the structure will suffer at a site if an earthquake of a given magnitude occur at a given location. Figures 3a-3d show the acceleration time histories for the model with minor residual after applying the process previously described. The largest acceleration was obtained in the nearto-source station SJAL (rock site) with 0.47 g. It is important to point out that stations CUP and SCT (figure 3c) located in Mexico City with hipocentral distances larger than 470 km still produced considerable values of peak accelerations (3.53 and 3.55 gal) similar of those of the GDLC station (with 1.71 and 5.3 gal) located to 273.48 km from the epicenter. This is due to the fact that seismic waves are enormously amplified at lake-bed sites respect to hill-zone sites in Mexico City, although it has been suggested that even hill-zone sites suffer amplification

from local networks.

of acceleration time histories and PGA.

and Singh [26].

**Figure 3.** Simulated synthetic acceleration time histories (intense period) with next distances from hypocenter: (a) 34 to 78 km, (b) 85 to 114 km, (c) 132 to 248 km, (d) major to 500 km. In left column type of soil and epicentral distance are denoted above and left of each trace. PGA and code of station is denoted above and right of trace. In right column PGA is denote above and left of trace.

c

a 11

Figure 3. Simulated synthetic acceleration time histories (intense period) with next distances from hypocenter: (a) 34 to 78 km, (b) 85 to 114 km, (c) 132 to 248

km, (d) major to 500 km. In left column type of soil and epicentral distance are denoted above and left of each trace. PGA and code of station is denoted above

and right of trace. In right column PGA is denote above and left of trace.

define the seismic coefficients for the plateaus of the elastic design spectra for standard

The Use of Source Scaling Relationships in the Simulation of a Seismic Scenario in Mexico

http://dx.doi.org/10.5772/53274

49

It can be also seen that only in 1 of 25 stations with distances comparable to the source dimensions the seismic ordinates are underestimated respect to the elastic design spectra. This station is SJAL located in rock site having seismic ordinate of 1.97 g in structural period of T= 0.3 sec. This is possibly because radiation patterns and source heterogeneity, which are taken into account in this work, causes spatial variations in ground motion around the fault Somer‐ ville [30]. These changes are very clear in the EGFM, but may be unnoticed in the GMPE. Therefore, obtaining future acceleration time histories and response spectra is a matter of essential interest for the present seismic design to achieve more efficient and safer structures.

We use the 25 records of August 13 2006 earthquake Mw 5.3 as element event to simulate strong ground motions for an eventual earthquake Mw 7.3 in the studied area. To reach this objective we integrate the advantages of three methodologies (EGFM, Somerville [6] relations and GMPE) to estimate the possible PGA, acceleration time histories and response spectra for an eventual earthquake in the studied area. We apply the empirical Green's function method (EGFM) whose main contribution is to reflect a model that considers the source, the path, and the site effects. In Mexico this method has been used to simulate an event that already occurred. In this study we applied it to predict some probable earthquake which may be expected in the region. To overcome the absence of observed records we made use of Somerville [6] relations to be able to make more accurate predictions of strong motions and two GMPE adequate for region to compare our results. The process of finding the best adjustment generated 2 different models (2 and 3 SMGA). This process of minimizing the residual between synthetics and observed PGA clearly shows that the mean residual for 25 stations is obtained when comparing with GMPE of Young's [17] and modeled with 2 SMGA. Ramirez-Gaytan [23] simulate PGA for Tecoman earthquake, whit difference that in this case the earthquake had occurred and exist observed records to compare and adjust synthetics, results are similar to those obtain in this study. Singh [10] comparing real PGA for Tecoman earthquake versus GMPE of Ordaz [16], results are similar to those obtain in this study. The purpose of this paper is to rescue the acceleration time histories of simulated event prepared to be used by structural engineers to analyze and design structures. Response spectrum show that for 1 of 25 stations (this station is near the source or with distance comparable with the source dimensions) the seismic ordinates are underestimated with the design spectra of the MOC-2008 [27] due possibly to radiation patterns and source heterogeneity, which is still to be confirmed by future records. For any practical evaluation of the seismic hazard in terms of response spectra is possible to integrate the advantages of three methodologies aboard in this study to estimate the possible PGA, acceleration time histories and response spectra for an eventual future earthquake.

occupancy structures Tena-Colunga [29].

**6. Conclusions**

**Figure 4.** Comparison of the 25 response spectra ordered for hipocentral distance of the simulated event for east– west component (thin continuous line) and north–south component (discontinuous line) with the design spectra (dark continuous line). It can be observed that the response spectra obtained with EGFM is realistic.

On the other hand, with acceleration time histories it is possible to generate a response spectrum, which considers forces related to parameters of maximum response like spectral acceleration. Response spectra are essential for the seismic design, any effort to accurately predict these should be done. The synthetic acceleration response spectra for an equivalent viscous damping of 5 percent were calculated and compared with the elastic acceleration design spectra for structures of group B (standard occupancy) of the Manual of Civil Structures MOC-2008 [27], a model design code in Mexico and seismic provisions for current Mexico's Federal District Code NTCS-2004 [28], Sites CUP and SCT. In the MOC-2008 [27] code, seismic hazard in Mexico is defined as a continuum function where peak accelerations in rock are associated with return periods that were obtained using an optimization design criterion to define the seismic coefficients for the plateaus of the elastic design spectra for standard occupancy structures Tena-Colunga [29].

It can be also seen that only in 1 of 25 stations with distances comparable to the source dimensions the seismic ordinates are underestimated respect to the elastic design spectra. This station is SJAL located in rock site having seismic ordinate of 1.97 g in structural period of T= 0.3 sec. This is possibly because radiation patterns and source heterogeneity, which are taken into account in this work, causes spatial variations in ground motion around the fault Somer‐ ville [30]. These changes are very clear in the EGFM, but may be unnoticed in the GMPE. Therefore, obtaining future acceleration time histories and response spectra is a matter of essential interest for the present seismic design to achieve more efficient and safer structures.
