**3. Data**

To simulate acceleration time histories of the Tecomán earthquake, we used two sources of data. Firstly, records of the 13 August 2006 earthquake. These records were obtained from previous temporal campaign in that area and from the support of other institutions with permanent instrumentation in that zone. Its epicenter, focal mechanism, and seismic moment were obtained from Centroid Moment Tensor Project [20]. The location of instruments that recorded this event (figure 1) is next described. The instruments were from permanent seismic networks: 15 Etna episensor wideband accelerographs from d.c. to 200 Hz at 200 samples per second from the national accelerations network of Instituto de Ingeniería (IINGEN) of Universidad Nacional Autonoma de Mexico (UNAM); two Guralp CMG40T-DM24 flat response wideband velocity type seismographs from 0.5 to 100 Hz at 100 samples per second from the network Red Sismica del Estado de Colima (RESCO). Secondly, data from temporal networks installed in the region as part of this project as follow: (i) four Altus Etna wideband accelerographs from d.c. to 100 Hz at 100 samples per second, four (ii) Geosig strong-motion recorder model 18 with analogue-digital converter, wideband accelerometers from d.c. to 100 Hz recording at 100 samples per second. Because 2 of the 25 records used in this study were velocity records, it was necessary to transform them to acceleration. Also, it was necessary to remove the instrumental response of each of the different instruments.

### **4. Method**

provides an efficient way to work when a limited number of parameters to be considered in

Finally from both estimations; it is said the PGAs, and the curves obtained with the two GMPE here used: (Ordaz [16], and Young's [17]), an trial and error iterative process of residuals minimization was conducted to identify the result that in the statistical sense better matched

The main contribution of this method is that it reflects a model that considers the source, the path, and the site effects. Another important contribution of the method is that reliable estimations about the energy distribution can be achieved in the high frequency band (between 0.1- and up to 10-Hz). This frequency range is of engineering interest because of the following reasons: (i) Many structures, including tall buildings and long bridges have their natural frequencies in the above frequency range, and (ii) 8 of the 10 major cities of this state are located in the sedimentary basins of the Colima graben and could amplify the ground motions in the frequency range of 0.1 to 10 Hz. It is therefore important to investigate how ground motions up to 10 Hz are generated from great subduction-zone earthquakes. This kind of investigations play a vital role in the effort to propose an scenario of strong ground motions from future large subduction earthquakes in the area in study and to evaluate the performance of structures

The Colima state is located in Mexico's Pacific coast. The tectonic of the region is complex, in which the Rivera, the Cocos, and the North American plates converge. In addition to the above, the existence of a microplate has also been proposed by DeMets and Stein [18], and Bandy [19]. There are significant changes in the parameters of the subduction process along the subduction zone on the Pacific coast of Mexico, which has been divided in four sections by Pardo and Suárez [8]. Although the dip of the interplate contact geometry is constant to a depth of 30 km, lateral changes in the dip of the subducted plate are observed once it is decoupled from the overriding plate. In front of the Jalisco block, the Rivera plate has a dip of 45° and its subduction rate below the North American Plate is estimated to be from 2 to 5 cm/yr. The Cocos plate below Colima shows a similar dip to that of the Rivera but the subduction rate below the North American Plate is estimated to be from 4 to 6 cm/yr. To the south, the dip of the Cocos plate decreases gradually and is almost sub-horizontal at Guerrero (where it subducts with a velocity from 6 to 7 cm/yr) before increasing again farther south to the large values observed in Central America. Pardo and Suárez [8] explained the observed no parallelism between the

To simulate acceleration time histories of the Tecomán earthquake, we used two sources of data. Firstly, records of the 13 August 2006 earthquake. These records were obtained from

volcanic belt and the subduction zone by these large lateral variations.

numerical simulations is available.

38 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

with the two GMPE here used.

subject to ground motions.

**2. Tectonic**

**3. Data**

The method used to model the target event requires a small magnitude event (earthquake of 13 August 2006) called element event, with hypocenter in close proximity to the earthquake that we want to simulate. For this particular case, the magnitude, location, focal mechanism and source parameters of the element event was reported by Harvard CMT (Mw 5.3, 18.45°N latitude and -103.63°W longitude, depth 23.5 km, strike 38°, dip 23°, and slip 96°, seismic moment 1.12e24 dyne-cm). For the simulated event (target event) and taking in consideration that the area in study is the region between the limits of the rupture areas of the Tecoman (2003) and the 1973 earthquakes, the hipocentral location was proposed just inside of the area in study and near to element event (18.45°N latitude and -103.75°W longitude). Considering the rupture area of 1973 earthquake and area of remainder gap of Tecoman earthquake we proposed 70 km along strike of fault area. Along the dip, we propose 80 km considering an intermediate value of dip length of neighbors earthquakes. Based on the above considerations the proposed effective rupture area is of 5600 km2 . Using equation (1), Somervile [6] we estimate a seismic moment of 1.1091e27 dine-cm.

$$\mathbf{A} = \mathbf{5.2}^{\cdot 15} \mathbf{\*} \mathbf{M} \mathbf{o}^{2/3} \tag{1}$$

Where *A* is the rupture area and Mo is the seismic moment.

Using equation (2) by Kanamori [21], the maximum estimated MW magnitude is 7.3.

$$\mathbf{M}\_{\rm w} = \begin{pmatrix} 1/1.5 \\ \end{pmatrix} \log \begin{pmatrix} \mathbf{M}\_{\rm o} \end{pmatrix} \text{ -10.73} \tag{2}$$

Where *Mw* is the moment magnitude and Mo is the seismic moment.

We use the relationships of Somerville [6] to characterize the source parameters as follows: (i) equation (3) to estimate the combined area of asperities (*A2)*, (ii) equation (4) to estimate area of largest asperity (*A1*), (iii) equation (5) to estimate the hipocentral distance to center of closest asperity (*CA*), and (iv) equation (6) to estimate the rise time (*Rt*) that is related to seismic moment of a small earthquake. For the S-wave propagation velocity we used 3.4 km/s.

$$A2 = 1.21e-15 \text{ } ^\ast Mo^{2/3} \tag{3}$$

1/3

where *Ā0* and *ā0* are the flat level of the acceleration Fourier spectrum of the target and element

Then the synthetic motion of the target event *A*(*t*), is given by the element event *a*(*t*) using the

*ij*

*n N n*

åå (10)

t

DUMMY TEXT, KOJI NIJE IME KNJIGE *A at at <sup>G</sup>* max| ( )| max| ( )| 1 2 *fort fort* 2 2

> max 2 *A A N E <sup>A</sup>*

DUMMY TEXT, KOJI NIJE IME KNJIGE *A at at <sup>G</sup>* max| ( )| max| ( )| 1 2 *fort fort* 2 2

max 2


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

( ) ( )\* ( )

( 1)


*k*

1 <sup>1</sup> ( 1) ( )( ) [ ] ( 1) *N n*

where *n'* is an appropriate value to eliminate spurious periodicity, *r* is the distance from the station to the element event hypocenter, *rij* is the distance from the station to the subfault (i, j), *tij* is the sum of the delay times due to the rupture propagation and the differences of distances between the location of the element event and the location of the target event

During the simulation process, we use the Somerville [6] relationships to assume and vary the inner and outer fault parameters in order to simulate acceleration records. Such parameters are: the rupture velocity, the rise time and the point where the rupture starts among others.

The PGAs were estimated for the three orthogonal components. On the other hand, earthquake magnitude, focal depth, hypocentral distance, and site characteristics (rock or soil) were the controlling parameters to estimate curves of ground motion by using the GMPE from Ordaz [16] and Young's [17] used in this study. To compare our results with respective GMPE the

**GMPE Horizontal components Equation**

*A A N E <sup>A</sup>* Ordaz *et al*. (1989) Cuadratic mean

=

 d

*<sup>r</sup> A t Ft t at r* = = æ ö <sup>=</sup> ç ÷ - ç ÷ è ø

(9)

41

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

, *A M <sup>N</sup>*

æ ö = = ç ÷ ç ÷ è ø

0 0 0 0

*a m*

1 1

*ij ij ij ij*

PGAs of two horizontal components was computed according with table 1.

Youngs *et al*. (1997) Geometric mean *\**

**Table 1.** Computation of two horizontal components in the two GMPEs.

d

*<sup>k</sup> Ft t t t t t*

*i j ij*

*Nx NW*

events respectively.

equations 10 and 11.

(*i,j*) at the observed site.

\*

Douglas (2003)

$$A1 = 8.87e-16 \, ^\ast Mo \text{ $^{2/3}$ } \tag{4}$$

$$
\mathbb{C}A = 1.76e-8 \, ^\ast M0^{1/3} \tag{5}
$$

$$Rt = 1.79e-9\*Mo^{1/3}\tag{6}$$

The fault plane was defined considering: an azimuth of 38°, a dip of 23° and a slip of 96°. These parameters were taken assuming that the mainshock will have the same focal mechanism as the element earthquake.

To estimate the number of sub-events, we applied the ω-2 spectral model, Aki [22], obtaining the number of sub-events necessary and estimate *N3* by using the relationship between seismic moments of the target event (*M0*), and the element event (*m0*) that is used as empirical Green's function. N3 is equal to the number of sub-faults in direction of the strike (*Nx*), the dip (*Nw*) and the time (*Nt*).

The above description clearly states that it is necessary to find the parameter *N,* which will be used to scale the fault area for the event to simulate. Since it is divided into *N* x *N* subfaults, *N3* is obtained using the equation (7), and the relationship between these parameters is stated through equations (7), (8), and (9).

$$N^3 = N\_x \ge N\_w \ge N\_p \tag{7}$$

$$\begin{aligned} \frac{\overline{\mathbf{U}\_0}}{\overline{\mathbf{u}\_0}} = \frac{\mathbf{M}\_0}{m\_0} = \mathbf{N}^3, \end{aligned} \tag{8}$$

where *Ū0* and *ū*0 is the flat level of the displacement Fourier spectrum for the target and element events respectively. On the other hand *Mo* and *mo* are the seismic moments of the target and element events respectively. The relationship for high frequency is given by:

The Use of Source Scaling Relationships in the Simulation of a Seismic Scenario in Mexico http://dx.doi.org/10.5772/53274 41

$$
\frac{\overline{A\_0}}{\overline{a\_0}} = \left(\frac{M\_0}{m\_0}\right)^{1/3} = N\_\prime \tag{9}
$$

where *Ā0* and *ā0* are the flat level of the acceleration Fourier spectrum of the target and element events respectively.

Where *Mw* is the moment magnitude and Mo is the seismic moment.

40 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

the element earthquake.

function. N3

and the time (*Nt*).

through equations (7), (8), and (9).

the number of sub-events necessary and estimate *N3*

We use the relationships of Somerville [6] to characterize the source parameters as follows: (i) equation (3) to estimate the combined area of asperities (*A2)*, (ii) equation (4) to estimate area of largest asperity (*A1*), (iii) equation (5) to estimate the hipocentral distance to center of closest asperity (*CA*), and (iv) equation (6) to estimate the rise time (*Rt*) that is related to seismic moment of a small earthquake. For the S-wave propagation velocity we used 3.4 km/s.

The fault plane was defined considering: an azimuth of 38°, a dip of 23° and a slip of 96°. These parameters were taken assuming that the mainshock will have the same focal mechanism as

To estimate the number of sub-events, we applied the ω-2 spectral model, Aki [22], obtaining

moments of the target event (*M0*), and the element event (*m0*) that is used as empirical Green's

The above description clearly states that it is necessary to find the parameter *N,* which will be used to scale the fault area for the event to simulate. Since it is divided into *N* x *N* subfaults, *N3* is obtained using the equation (7), and the relationship between these parameters is stated

0 0 3

where *Ū0* and *ū*0 is the flat level of the displacement Fourier spectrum for the target and element events respectively. On the other hand *Mo* and *mo* are the seismic moments of the target and

0 0 , *U M <sup>N</sup>*

element events respectively. The relationship for high frequency is given by:

is equal to the number of sub-faults in direction of the strike (*Nx*), the dip (*Nw*)

2/3 *A e Mo* 2 1.21 15 \* = - (3)

2/3 *A e Mo* 1 8.87 16 \* = - (4)

1/3 *CA e M* = - 1.76 8 \* 0 (5)

1/3 *Rt e Mo* = - 1.79 9 \* (6)

3 *N N xN xN xwt* <sup>=</sup> (7)

*<sup>u</sup> <sup>m</sup>* = = (8)

by using the relationship between seismic

Then the synthetic motion of the target event *A*(*t*), is given by the element event *a*(*t*) using the equations 10 and 11.

$$A(t) = \sum\_{i=1}^{\text{Nx}} \sum\_{j=1}^{N\_{\text{N}}} \left( \frac{r}{r\_{ij}} \right) F(t - t\_{ij})^\* \ a(t) \tag{10}$$

$$F\_{ij}(t - t\_{ij}) = \delta(t - t\_{ij}) + \frac{1}{n} \sum\_{k=1}^{(N-1)n} \delta[t - t\_{ij} - \frac{(k-1)\tau}{(N-1)n}] \tag{11}$$

where *n'* is an appropriate value to eliminate spurious periodicity, *r* is the distance from the station to the element event hypocenter, *rij* is the distance from the station to the subfault (i, j), *tij* is the sum of the delay times due to the rupture propagation and the differences of distances between the location of the element event and the location of the target event (*i,j*) at the observed site.

During the simulation process, we use the Somerville [6] relationships to assume and vary the inner and outer fault parameters in order to simulate acceleration records. Such parameters are: the rupture velocity, the rise time and the point where the rupture starts among others.

The PGAs were estimated for the three orthogonal components. On the other hand, earthquake magnitude, focal depth, hypocentral distance, and site characteristics (rock or soil) were the controlling parameters to estimate curves of ground motion by using the GMPE from Ordaz [16] and Young's [17] used in this study. To compare our results with respective GMPE the PGAs of two horizontal components was computed according with table 1.


**Table 1.** Computation of two horizontal components in the two GMPEs.

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

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

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

> **Total area**

1256.38

1281.76

**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

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

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

2 17.81 10.69 190.36 2.5 0.011 0.101 0.252

**Vr Km/s**

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

3.0

2.3

**Residual with Young's GMPE (Rock)**

**Residual with Young's GMPE (Soil)**

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

43

0.009 0.024 0.245

**Residual with Ordaz GMPE (Rock)**

by minimizing the residual between synthetic and observed PGA.

**Width (km)**

1 24.94 32.06 799.51

1 35.62 24.94 888.35

**Area (km2)**

2 21.37 21.37 456.86 2.9

3 14.25 14.25 203.05 2.4

curves for rock and soil.

**SMGA Length (km)**

each GMPE and the PGAs for all 25 stations.

are located above this curve.

**Numbers of SMGA**

2

3
