Scaling Relationships of Source Parameters of Mw 6.9 ... - CiteSeerX

Bulletin of the Seismological Society of America, Vol. 104, No. 2, pp. 840–854, April 2014, doi: 10.1785/0120130041

Ⓔ

Scaling Relationships of Source Parameters of M w 6.9–8.1 Earthquakes in the Cocos–Rivera–North American Subduction Zone by Alejandro Ramírez-Gaytán, Jorge Aguirre, Miguel A. Jaimes, and Víctor Huérfano

Abstract

Seven slip models currently available from kinematic inversions, derived from near-source strong-motion and teleseismic body waves in the 0–1.25 Hz frequency range from Mexico’s subduction zone, are used to estimate source-scaling relationships applicable to the region. Our results are compared with existing scaling relations for subduction environments. The relationships for the rupture area of our results are closer to those of Somerville et al. (2002) than to any other, but, like the others, they have smaller areas than predicted by Somerville et al. (2002). Concerning the combined area of asperities, Murotani et al. (2008) and our results predict smaller areas than those obtained by Somerville et al. (2002). Concerning the area of largest asperity, the relationships obtained in this study are slightly smaller than those described by Somerville et al. (2002); this is a consistent result with the relationships of total rupture area and combined area of asperities. In general, the error estimates for the constrained equations derived in this study in all cases are smaller than those relationships compared here. This might suggest that the expressions obtained in this study could be appropriate for the simulations of strong ground motion for a specific scenario of earthquake slip in the region. Also, these results could be an indication that the relationships vary depending on a specific subduction tectonic region. On the other hand, Aguirre and Irikura (2007) estimated the source area for 31 Mexican earthquakes using corner frequencies; these areas show close resemblance with those predicted by the relationships derived in this study. Based on these findings, an important implication is that two different methodologies to determine the total area of asperities based on either low- or high-frequency data generate similar results. Online Material: Figures of fault models.

Introduction Simulation of earthquake scenarios is a topic of relevance in countries with a high rate of seismic activity, such as Mexico. A standard procedure to evaluate seismic hazard is based on simulation of ground motions generated by active faults. It has been demonstrated that asperities within the rupture area control specific characteristics of ground motions (Miyake et al., 2004). Also, these relationships allow modelers to understand the seismic source and generate response spectra, both useful pieces of information in structural engineering. Therefore, quantitative estimation of the size and slip of the asperities is important in modeling the source for predicting ground motions. Several methods are used to simulate strong ground motions from potential seismic sources; one of them is the so-called source-scaling relationships. Recent studies related the features of an earthquake source via the scaling of slip distributions (e.g., Somerville et al., 1999; Mai and Beroza, 2000), slip complexity (e.g., Mai and Beroza, 2002; Lavallée

and Archuleta, 2003), in terms of rupture area to the seismic moment for plate-boundary earthquakes (Kanamori and Anderson, 1975), and in terms of rupture area to the moment magnitude (Wells and Coppersmith, 1994). The influence of slip heterogeneities in the prediction of strong ground motion within a subduction zone has been investigated by Somerville et al. (2002), using worldwide events, and recently by Murotani et al. (2008), who focused on Japanese events. Blaser et al. (2010) and Strasser et al. (2010) derive sourcescaling relations between rupture dimensions and moment magnitude for subduction-zone earthquakes. In general, these relationships establish equations useful in the generation of strong ground motions. Another method used to simulate strong ground motions from potential seismic sources is the empirical Green’s function method (EGFM). This is a good alternative methodology for simulating strong ground motion produced by largemagnitude earthquakes. This method requires a small840

Scaling Relationships of Source Parameters of Mw 6.9–8.1 Earthquakes magnitude earthquake (element event) with a hypocenter close to the main earthquake (target event) that will be simulated. The broadband modeling process developed and detailed by Irikura (1986) produces in the end a source model in which synthetic strong ground motions share the best resemblance with observed records of the main earthquake; it is from these final models that the source parameters are estimated. There are two important characteristics of the strong ground motions generated by EGFM. First, the information of crustal structure and site effects are included in the simulations. Because records of the element event used as a seed already include them, instrumentation and detailed studies to determine the crustal structure and site effects are not necessary. Second, EGFM modeling is possible in the 0.1–10 Hz frequency interval. This is relevant for civil engineering because it is in this frequency range that many buildings, bridges, and civil constructions have their dominant vibration frequency. Recently, some studies have been conducted in Mexico to simulate strong ground motions of important earthquakes using EGFM (e.g., Aguirre, 2005; Garduño, 2006; RamírezGaytán et al., 2010). In these studies, source parameters that were estimated, such as the combined area of asperities and area of largest asperities, are poorly matched with the relationships proposed by Somerville et al. (2002). In their comparison, two important facts arise: (1) EGFM is a method capable of modeling strong-motion generation areas (SMGA), which are defined as finite extent areas with relatively large slip velocity within the total rupture area, and (2) the waveform inversions capture the presence of asperities (characterized by heterogeneous slip distribution) based on low-frequency (< 1 Hz) ground motions. Based on these descriptions, the following questions arise: what do the two methods of studying the source in different frequency bands have in common, how much energy is radiated in the high-frequency band, and how can high frequencies be included in their approach. Miyake et al. (2003) showed that the SMGA generated from 0.2–10 Hz frequency ranges coincide with the areas of the asperities of heterogeneous slip distributions derived from low-frequency (< 1 Hz) waveform inversions for crustal earthquakes. In the same study, Miyake et al. (2003) showed that SMGA contain both low- and high-frequency information and that quantified SMGA have the ability to perform the broadband ground-motion simulation. Based on the preceding discussion, we have compared the scaling relationships between seismic moment and the source parameters estimated using EGFM (combined area of asperities, area of largest asperity) with those relationships proposed by Somerville et al. (2002) for the studies conducted on the important Mexican earthquakes mentioned here (Aguirre, 2005; Garduño, 2006; Ramírez-Gaytán et al., 2010). The results of this comparison show a poor fit. These results might suggest the need to develop specific source-scaling relationships for Mexican subduction earthquakes. In this study, we develop new scaling relationships for earthquakes occurring in the Cocos–Rivera–North American

841

subduction zone in Mexico. However, the accuracy of source-scaling relationships depends strongly on the number of kinematic inversions considered in the study. Somerville et al. (1999) used 15 kinematic models from crustal earthquakes, and Somerville et al. (2002) used 10 kinematic models from interplate subduction-zone earthquakes. Asano and Iwata (2011) used five kinematic models from inland crustal earthquakes in Japan. In our study, despite the fact that in Mexico kinematic inversions are scarce, we utilized the data provided for seven earthquakes in the Mexican subduction environment whose kinematic inversion is currently available. With these data and as a product of this work, we generate new source-scaling relationships to simulate strong ground motion applicable to Mexican subduction-zone megathrust earthquakes between the Cocos–Rivera and North American plates. As a secondary task, we compare our results with the scaling relationships for subduction earthquakes first proposed by Somerville et al. (2002) and with the other important recently developed scaling relations for subduction environments: Murotani et al. (2008), Blaser et al. (2010), and Strasser et al. (2010). Murotani et al. (2008) characterized source rupture models with heterogeneous slip of plate boundary earthquakes in the Japan region. The slip models used are based on 26 estimates of 11 plate boundary earthquakes constructed by waveform inversions of strong ground motions, teleseismic, geodetic, or tsunami data. The source-scaling relationships that specifically relate seismic moment to rupture area, average slip, and combined area of asperities derived by Murotani et al. (2008) will be compared subsequently with our results. Strasser et al. (2010) derived source-scaling relations between rupture dimensions and moment magnitude for subduction-zone earthquakes, distinguishing interface events from intraslab events. They use a database that includes 139 models corresponding to 95 interface events and 21 models corresponding to 20 intraslab events. The relationship that involves the rupture area versus moment magnitude for interface events derived from Strasser et al. (2010) will be compared with the equivalent relationship derived in this study. Blaser et al. (2010) compiled a large database of source parameter estimates of 283 earthquakes for which all focal mechanisms are represented, and specifically the focus is on subduction-zone events. The product of rupture length and width for subduction-zone earthquakes and continental thrust events derived by Blaser et al. (2010) will be compared with the rupture area estimates in our study.

Data In this study, we have taken results of seven kinematic inversions available from earthquakes in the Cocos–Rivera and North American plates’ subduction environment in Mexico (Table 1 and Fig. 1). These inversions consider results of thrust-faulting earthquakes with moment magnitudes from 6.9 to 8.1 that occurred within the last 26 years (1979–2003). These results are composed of six kinematic inversions,

Petatlán Playa Azul Michoacán Zihuatanejo San Marcos Manzanillo Tecomán

1 2 3 4 5 6 7

1979/03/14 1981/10/25 1985/09/19 1985/09/21 1989/04/25 1995/10/09 2003/01/22

Date (yyyy/mm/dd)‡

−101.46; −102.24; −102.57; −101.82; −99.12; −104.58; −104.13; 17.46 17.74 18.18 17.6 16.83‡ 18.86 18.71

Longitude; Latitude (°)†

1:37 × 1020 8:49 × 1019 1:15 × 1021 1:53 × 1020 2:4 × 1019 ‡ 9:67 × 1020 2:30 × 1020

M 0 (N·m)†

7.39 7.25 8.01 7.42 6.90‡ 7.96 7.50

Mw †

15.00 15.00 17.00 20.00 17.30‖ 16.55 20.00

Depth (km)†

10 2700 25020 3500 2520‖ 17000 5950

S (km2 )§

293; 14; 90 300; 14; 90 300; 14; 72 300; 14; 100 276; 10; 66‡ 309; 14; 92 300; 22; 93

Strike; Dip; Rake (°)†

3.3 2.6 2.6 2.6 – 2.8 3.5

Vr (km=s)†

3800 400 5004 1250 324§ 3400 1075

Sc (km=s)§

0.288 0.746 1.390 1.028 1.265§ 1.355 0.607

Average Slip (m)§

3600 400 3127.5 1250 324§ 2100 700

Sl (km2 )§

120 60 180 90 60‖ 200 70

Le (km)†

120 70 139 90 42‖ 100 85

We (km)†

M 0 , seismic moment for slip subduction models; M w , moment magnitude; S, dimension of rupture area; V r , rupture velocity; Sc , estimated combined area of asperities; Sl , estimated area of largest asperity; W e and Le , estimated effective width and length fault dimensions. *1, Mendoza (1995); 2 and 4, Mendoza (1993); 3, Mendoza and Hartzell (1989); 5, Singh et al. (1989); 6, Mendoza and Hartzell (1999); 7, Yagi et al. (2004). † Information is from SRCMOD, Martin Mai’s Database of Finite-Source Rupture Models (see Data and Resources). ‡ Information is from the Global Centroid Moment Tensor (CMT) project catalog (1976–2013). §The source parameters determined in this study. ‖ Information is from Singh et al. (1989).

Event Name†

Reference*

Table 1 Fault Parameters from the Heterogeneous Slip Models

842 A. Ramírez-Gaytán, J. Aguirre, M. A. Jaimes, and V. Huérfano

Scaling Relationships of Source Parameters of Mw 6.9–8.1 Earthquakes

843

tember 1999 (Castro and Ruiz-Cruz, 2005). However, these studies were excluded from the analysis because the events are not thrust-faulting but normal-faulting earthquakes. In order to conduct an adequate comparison with relationships proposed by Somerville et al. (2002) in this study, we take only the seven reverse-slip subduction earthquakes available at this time.

Methodology

Figure 1. Distribution of Mexican earthquakes for which slip models were available as of the present study. Events 1–7 are the events used in this study. Events 8 and 9 represent the events excluded from the present analysis. The color version of this figure is available only in the electronic edition. compiled primarily based on the SRCMOD database from Martin Mai and coworkers (see Data and Resources), from which subduction events have been extracted. Further, we added the study that describes the rupture process of the 25 April 1989 M w 6.9 San Marcos event (Singh et al., 1989). Table 2 presents the frequency range and type of data used on the kinematic inversion of earthquakes involved in this study. With the exception of the study of the San Marcos earthquake (which used only strong ground motion records), slip models were constructed by waveform inversions primarily from teleseismic data; there are 117 components from teleseismic data that represent 77.48% of data and 34 components from strong-motion data that represent 22.52% of data (Table 2). In this study, we compare our results with those obtained by Somerville et al. (2002). Table 3 presents the frequency range and type of data used for Somerville et al.’s kinematic inversion of earthquakes. As shown in Table 3, we found that from the 10 slip models used by Somerville et al. (2002), and similarly to the tendency of data used in our study, these were constructed primarily from teleseismic data. There are 201 components from teleseismic data that represent 84.10% of data and 38 components from strong-motion data that represent 15.90% of data. The comparison between the percentages of teleseismic and strong ground motion data used in both studies do not show significant differences. In general in both studies, the quantity of teleseismic data is larger than strong-motion data. Also, Tables 2 and 3 show that, in both studies (with the exception of the study of the San Marcos earthquake), the inversions are derived from grounddisplacement waveforms in the 0–1.25 Hz frequency range. In addition to the seven studies shown in Table 1, there are two other studies available from Mexico: the kinematic inversions of the Michoacán earthquake of 11 January 1997 (Santoyo et al., 2005) and the Oaxaca earthquake of 30 Sep-

The first step in processing the information was to estimate the total rupture area and the number of asperities. The rupture area dimensions of the inverted slip models are frequently overestimated in order to accommodate the entire fault rupture into a rectangular area. We reduced the dimensions of the rectangular slips models in order to consider just the area with significant slip contribution. We apply a standard criterion for trimming the edges, as proposed by Somerville et al. (1999). The trimmed fault is then defined as the total rupture area. In our study and throughout the present paper, we follow the criteria of Somerville et al. (1999) to define this and other source parameters: rupture area A, average slip D, combined area of asperities Aa , area of largest asperities AL , and hypocentral distance to the center of the closest asperitiy RA , among others. These were examined, quantified, and scaled with respect to seismic moment M0 , using a regression analysis method. Ⓔ The fault models for the earthquakes used in this study and identification of asperities on them are available in the electronic supplement to this article. Regression Analysis Method The empirical relationships of source parameters obtained by Somerville et al. (2002) are of the form Y α × Mβ0 ;

1

in which constants α and β are functions of the seismic moment M0 in newton meters. This form is adopted in the present paper, and constants α and β were determined by regression analysis of the obtained data (Table 4). For the purpose of the regression analyses, it is useful to recast equation (1) to the form y a β × x;

2

in which y lnY, a lnα, and x lnM 0 . The values of a and slope β in equation (2) were determined by minimizing the squared error between the available and computed seismic source parameters. Then α was back-calculated from the relationship a lnα. We use equation (3) to estimate the standard error: s Pn 2 i1 yi − a β xi ; se n − 2

3

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A. Ramírez-Gaytán, J. Aguirre, M. A. Jaimes, and V. Huérfano

Table 2 Frequency Range and Type of Data Used in the Kinematic Inversion of Earthquakes Involved in This Study Event Number

1 2 3 4 5 6 7

Name of Earthquake

Petatlán Playa Azul Michoacán Zihuatanejo San Marcos Manzanillo Tecomán

Date (yyyy/mm/dd)

References

SGM*

TS†

Fmin (Hz)

Fmax (Hz)

1979/03/14 1981/10/25 1985/09/19 1985/09/21 1989/04/25 1995/10/09 2003/01/22

Mendoza (1995) Mendoza (1993) Mendoza and Hartzell (1989) Mendoza (1993) Singh et al. (1989) Mendoza and Hartzell (1999) Yagi et al. (2004) Total

0 0 4 0 12 0 18 34

15 15 13 24 0 38 12 117

0.01 0.00 0.00 0.00 0.05 0.02 0.01 –

0.2 0.2 0.5 0.5 1.25 0.5 0.5 –

All data, except that of the San Marcos earthquake (event 5) are provided from Martin Mai’s SRCMOD Database of Finite-Source Rupture Models (see Data and Resources). Data for the San Marcos earthquake are from Singh et al. (1989). *Number of strong ground motion component data used in the inversion. †Number of teleseismic component data used in the inversion.

Table 3 Frequency Range and Type of Data Used for Kinematic Inversion of Earthquakes Described in Somerville et al. (2002) Event Number

Name

Date (yyyy/mm/dd)

References

SGM*

TS†

Fmin (Hz)

Fmax (Hz)

1‡

Kanto Tonankai Peru Peru Petatlán Playa Azul Valparaiso Michoacán Ziuathanejo Hokkaido

1923/09/01 1944/12/07 1974/10/03 1974/10/09 1979/03/14 1981/10/25 1985/03/03 1985/09/19 1985/09/21 1993/07/12

Wald and Somerville (1995) Ichinose et al. (2003) Hartzell and Langer (1993) Hartzell and Langer (1993) Mendoza (1995) Mendoza (1993) Mendoza et al. (1994) Mendoza and Hartzell (1989) Mendoza (1993) Mendoza and Fukuyama (1996) Total

0 13 0 0 0 0 12 4 0 9 38

6 10 32 38 15 15 16 13 24 32 201

0.00 0.00 0.00 – 0.01 0.00 0.1 0.00 0.00 0.05 –

0.1 0.5 0.2 – 0.2 0.2 0.5 0.5 0.5 0.5 –

2§ 3‡,‖ 4‖ 5‡ 6‡ 7‡ 8‡ 9‡ 10‡

*Number of strong ground motion component data used in the inversion. Number of teleseismic component data used in the inversion. ‡ Information for events 1, 3, and 5–10 is provided from Martin Mai’s SRCMOD Database of Finite-Source Rupture Models (see Data and Resources). § Information for event 2 (1944, Tonankai earthquake, Ms 8.01) is taken directly from Ichinose et al. (2003). ‖ Information for event 3 (3 October 1974, Mw 8.0, Peru earthquake), is from Martin Mai’s SRCMOD Database of Finite-Source Rupture Models (see Data and Resources). However, because information for its largest aftershock, event 4 (9 November 1974, M s 7.1) does not appear in the database, the information is taken directly from Hartzell and Langer (1993) †

in which yi lnY i is the observed value (with Y i as the available data); a βxi lnα β lnM oi is the computed value of the ith data point; and n is the total number of data points. This procedure leads to values of α and β for equation (1) to represent the best fit, in the least-squared sense, of the available data. Thereby, we generated new sourcescaling relationships. After completing this process, the new relationships were compared with the worldwide largemagnitude (Mw 7.1–8.1) subduction earthquakes obtained by Somerville et al. (2002) and other published relationships. In kinematic inversions, the area of asperities depends on rupture velocity. The rupture velocities of the earthquakes used here are listed in Table 1. These values show a narrow range from 2.6 to 3:5 km=s, with an average value of 2:9 km=s. However, there is no evidence of the rupture velocity’s dependence on seismic moment. On the other hand, asperities of large earthquakes may be estimated within the first few days of aftershocks. The definition of aftershocks

does not vary as a function of rupture velocity. It will be interesting to conduct future studies to compare aftershocks and asperities defined by kinematic models for Mexican earthquakes. For the seven earthquakes studied here, it is difficult to estimate the area of the aftershock region because there is not enough information available that indicates their locations. At minimum, this comparison will require accurate location of aftershocks—information that, for some of the earthquakes studied here, is not available.

Results By analyzing the properties of individual asperities, we concluded that the number of asperities in the slip models ranges from 1 to 4. A total of 13 asperities of the seven earthquakes were used here, with an average of 2.04 asperities. The sum of the area for all asperities is only 19.57% of the overall rupture area. The largest asperity covers approximately 13.9% of the overall rupture area.


845

Table 4 Scaling Relationships Derived in This Study When Assuming Self-Similarity Parameter

Unit 2

Rupture area (A)

km

Average slip (D)

m

Results Analysis Type

A 1:87 × A 1:99 × A 2:41 ×

Murotani et al. (2008) Strasser et al. (2010) Blaser et al. (2010)

A 1:48 × log10 A −3:476 0:952 × Mw log L −2:69 0:64 × Mw ‡ log W −1:12 0:33 × M w ‡ D 8:45 × 10−3 M0:099 0 D 1:43 × 10−7 M1=3 0 D 1:14 × 10−7 M1=3 0

km

Aa 1:74 × 10−11 M0:684 0

Unconstrained Self-similar scaling with β 2=3 Somerville et al. (2002)

Area of largest asperity (AL )

km

Unconstrained Self-similar scaling with β 2=3

km

Overall slip duration (T s )

km

s

0.568 0.587 0.630 †

0.684 0.758 1.233 0.606 0.704 0.751 0.706 0.669 0.667 0.839 0.708 0.652 0.676 0.732

Unconstrained

RA 2:74 × 10−3 M 0:177 0

0.870

Self-similar scaling with β 1=3

RA 1:81 × 10−6 M 1=3 0

0.902

RA 3:79 × 10−6 M 1=3 0

Somerville et al. (2002) Hypocentral distance to center of largest asperity (Ra )

AL 7:78 × 10−9 M 0:550 0 AL 3:25 × 10−11 M 2=3 0 AL 4:12 × 10−11 M 2=3 0

Somerville et al. (2002) Hypocentral distance to center of closest asperity (RA )

Aa 3:99 × 10−11 M2=3 0 Aa 5:62 × 10−11 M2=3 0 Aa 2:89 × 10−11 M2=3 0

Murotani et al. (2008) 2

10 M0:570 0 10−10 M 2=3 0 10−10 M 2=3 0 10−10 M 2=3 0

D 1:48 × 10−7 M1=3 0

Murotani et al. (2008) Combined area of asperities (Aa )

−8


Unconstrained Self-similar scaling with β 1=3 Somerville et al. (2002) 2

se *

Best-Fit

1.257

Unconstrained

Ra 2:41 × 10−5 M0:280 0

1.081

Self-similar scaling with β 1=3

Ra 2:00 × 10−6 M1=3 0

1.085

T S 1:52 × 10−6 M0:309 0


T S 4:80 × 10−7 M1=3 0 T S 7:80 × 10−7 M1=3 0

1.161 1.162 1.296

*The standard error estimate for each regression, M 0 in newton meters. The relationship in terms of moment magnitude obtained by assuming self-similar scaling. M w is an independent variable we have converted to seismic moment by M w 2=3 log10 M 0 − 6:033 (M 0 is in newton meters; Hanks and Kanamori, 1979). Coefficient b is forced to 1 to reflect direct proportionality between seismic moment and rupture area by assuming self-similar scaling (Strasser et al., 2010). ‡Because Blaser et al. (2010) did not derive relationships for rupture area directly from the data, we simply multiply rupture length L and width W, derived by them. †

Figure 2 and Table 4 show the relationships between seismic moment and each seismic source parameter obtained in this study. For each parameter, the unconstrained equation (Fig. 2, black continuous lines) is shown first, followed by the equation that imposes self-similarity (Fig. 2, gray continuous lines). The scaling self-similarity forces the coefficient β in equation (1) to reflect direct proportionality between seismic moment and source parameters as described after equation (6). The scalar seismic moment is defined as the product of the fault surface area, average displacement on the fault, and the rigidity of the rock. The assumption of constant stress drop leads to the static similarity condition, constant fault aspect ratio, and constant strain (equations 4 and 5): W k1 ; L

4

and D k2 : L

5

So in equation (6), we rewrite the scalar seismic moment as × W × L μ × k 1 × k 2 × L3 : M0 μ × D

6

From this, M 0 ∝ L3 (Lay and Wallace, 1995), and, therefore, is proportional to M 1=3 M01=3 ∝ L, as D 0 and the surface area that includes two dimensions is proportional to M 02=3 . This condition is also known as the self-similar source model. The self-similar model is convenient to use because it provides a reasonably good description of the phenomena (Somerville et al., 1999). In this analysis of large-magnitude Mexican subduction earthquakes, we found that scaling the fault parameters with the seismic moment fits reasonably well with a self-similar scaling model. For the case of the

846

A. Ramírez-Gaytán, J. Aguirre, M. A. Jaimes, and V. Huérfano 100000

10

(b) Average Slip (m)

Rupture Area (km2)

(a)

10000

(g)

1000

100

1000

100

100

(f)

10

1 100

Overall Slip Duration (s)

10000

Area of Largest Asperity (km2)

(d)

Hypocentral Distance to Center of Largest Asperities (km)

(e)

0.1

10000

Hypocentral Distance to Center of Closest Asperities (km)

(c)

Combined Area of Asperities (km2)

1000

1

1000

100

10

1 1×1019

1×1020 1×1021 Seismic Moment (N •m)

1×1022

10

1

0.1 1×1019


1×1022

Figure 2.

Regression results of the source-scaling relations of this study. In all cases (a–g), we show the relation between seismic moment versus the following: (a) rupture area, (b) average slip, (c) combined area of asperities, (d) area of largest asperity, (e) hypocentral distance to center of closest asperity, (f) hypocentral distance to center of largest asperity, and (g) overall slip duration. In all cases, filled circles indicate the events, black continuous lines are the results of this study (unconstrained), gray lines are the fit when self-similar scaling is assumed, and dashed lines are the 95% confidence intervals for the mean when self-similar scaling is assumed.

relationship of average slip versus seismic moment, the unconstrained relationship suggests a non-self-similar scaling. For this case, the physical interpretation suggests the absence of a scale factor in the average slip of Mexican subduction earthquakes. However, as can be appreciated from Figure 2b, the data are dispersed and do not show a clear tendency. Note that the standard deviation (Table 4) is smaller than that of Somerville et al. (2002), even for the self-similar assumption. The results shown in Table 4 follow the regression analysis given by equation (1) for:

1. unconstrained regression analysis to estimate α and β; 2. self-similar scaling regressions to estimate α while the value of β is forced to be 2=3 (for rupture area, combined area of asperities, and area of largest asperity) or 1=3 (for average slip, hypocentral distance to the center of the closest asperity, hypocentral distance to the center of the largest asperity, and overall slip duration); 3. self-similar scaling regression with values of α and β that were fixed according to Somerville et al. (2002) to determine the standard error se (values of α and β from

Scaling Relationships of Source Parameters of Mw 6.9–8.1 Earthquakes Somerville et al. were computed to be compatible with units used in this work); and 4. standard errors were estimated for comparison with other publications of source scaling for subduction zone earthquakes (Murotani et al., 2008; Blaser et al., 2010; Strasser et al., 2010). se was determined by computing the mean square error between the available data and computed values from the relationships. Relationships expressed in terms of moment magnitude, as the independent variable, have been converted to seismic moment by Mw 2=3 log10 M 0 − 6:033 (M 0 is in newton meters; Hanks and Kanamori, 1979). These regression analyses, which use the data from all earthquakes (Table 1), lead to the equations and data provided in Table 4. Figure 2 provides a visual representation for each equation obtained from each regression analysis: a dark continuous line shows the unconstrained relationship, gray lines are the fit when self-similar scaling is assumed together with the available data (filled circles), and dashed lines correspond to the 95% confidence intervals for the mean when self-similar scaling is assumed for each seismic source parameter. As stated previously, Figure 2 provides a graphical view of data scattering of the seismic source parameters relative to curves from regression analyses. As expected, self-similar scaling regression generally implies large error of estimated se (Table 4), showing larger scatter of the data about the best-fit curve.

Source Scaling The relationship between rupture area A (km2 ) and seismic moment M0 (N·m) determined without constraining the slope is (Fig. 2a) A 1:87 × 10−8 M0:570 : 0

7

By self-similar scaling of the slope to be 2=3, the relationship is A 1:99 ×

10−10 M 02=3 :

8

From the self-similar scaling equations (see Fig. 3a and Table 4) provided by Somerville et al. (2002), Murotani et al. (2008), Strasser et al. (2010), and Blaser et al. (2010), se values are 0.630, 0.684, 0.758, and 1.233, respectively. In all four cases, these values are greater than estimated by the self-similar scaling equation with respect to the estimated rupture area of large-magnitude Mexican subduction earthquakes (se 0:587). These results are examined in the Discussion section. The relationship between average slip D (m) and seismic moment M0 (N·m) determined without constraining the slope is (Fig. 2b) : D 8:45 × 10−1 M0:099 0

9

By self-similar scaling of the slope to be 1=3, the relationship is

847 D 1:43 × 10−5 M 1=3 0 :

10

From the self-similar scaling equations provided by Somerville et al. (2002) and Murotani et al. (2008), se is 0.751, and 0.706, respectively; these values are greater than those found by the constrained equation that estimates the average slip of large-magnitude Mexican subduction earthquakes (se 0:704). These results show a close resemblance between the relationship derived in this study and those proposed by Murotani et al. (2008). The scaling law of combined area of asperities Aa (km2 ) and seismic moment M0 (N·m) determined without constraining the slope is (Fig. 2c) : Aa 1:74 × 10−11 M 0:684 0

11

By self-similar scaling of the slope to be 2=3, the relationship is Aa 3:99 × 10−11 M2=3 0 :

12

As shown in Figure 2c, the self-similar scaling equation indicates that the estimated combined area of asperities of large-magnitude Mexican subduction-zone earthquakes shows a clear dependence on seismic moment. The relationships in equations (8), (10), and (12) provide smaller values than the self-similar scaling equation provided by Somerville et al. (2002). In this study, the area covered by asperities is 19.4% of the total rupture area, which is smaller than the 25% proposed by Somerville et al. (2002). Table 4 shows that, for the constrained equation provided by Somerville et al. (2002) and Murotani et al. (2008), the se values are 0.839 and 0.708, respectively. These results are larger than those found by the constrained equation that estimates the combined area of asperities of large-magnitude Mexican subduction earthquakes (se 0:667). The relationship between area of largest asperity AL (km2 ) and seismic moment M0 (N·m) determined without constraining the slope is (Fig. 2d) AL 7:78 × 10−9 M 0:55 0 :

13

By self-similar scaling of the slope to be 2=3, the relationship is AL 3:25 × 10−11 M 02=3 :

14

As shown in Figure 2d, the comparison of both constrained equations indicates that the estimated area of the largest asperity of large-magnitude Mexican subduction earthquakes is smaller than the constrained equation provided by Somerville et al. (2002). The area of the largest asperity for the two relationships compared in this study shows a clear dependence on seismic moment. The average value for the area of largest asperity is 13.79% of the total rupture area versus the 17.5% proposed by Somerville et al. (2002). Table 4 shows that, for the self-similar scaling equation provided by Somerville et al. (2002), the error estimate (se 0:732) is greater than that found by the self-similar

848


This study Somerville et al. (2002) Murotani et al. (2008) Strasser et al. (2010) Blaser et al. (2010)

1000

Combined Area of Asperities (km2)

10000

Hypocentral Distance to Center of Closest Asperities (km)

(e)

(g)

1000

This study Somerville et al. (2002) Murotani et al. (2008)

100 100

(f)

10

1

1

0.1

(d)

1000

Overall Slip Duration (s)

Average Slip (m)

10000

100

(c)

10

(b)

This study Somerville et al. (2002) Murotani et al. (2008)

10000

Area of Largest Asperity (km2)

Rupture Area (km2)

100000

Hypocentral Distance to Center of Largest Asperities (km)

(a)

1000

100 1000

100

10

1 1×1019


1×1022

100

10

1

0.1 1×1019


1×1022

Figure 3. Comparison of scaling relations of this study with existing relations. In all cases (a–g) we show the relation between seismic moments versus the following: (a) rupture area, (b) average slip, (c) combined area of asperities, (d) area of largest asperity, (e) hypocentral distance to center of closest asperity, (f) hypocentral distance to center of largest asperity, and (g) overall slip duration. In all cases, gray lines are the results of this study, dotted lines are from Somerville et al. (2002), dashed-dotted lines are from Murotani et al. (2008), and dotted lines are from Strasser et al. (2010).

scaling equation that estimates the area of largest asperities of large-magnitude Mexican subduction earthquakes (se 0:676). The scaling law that relates hypocentral distance to the center of the closest asperity RA (km) and seismic moment M 0 (N·m) determined without constraining the slope is (Fig. 2e) : RA 2:47 × 10−3 M 0:177 0

15

By self-similar scaling of the slope to be 1=3, the relationship is

RA 1:81 × 10−6 M 1=3 0 :

16

Table 4 shows that, for the self-similar scaling equation provided by Somerville et al. (2002), the error estimate (se 1:257) is greater than that found by the constrained equation that estimates the hypocentral distance to the center of the closest asperity for large-magnitude Mexican subduction earthquakes (se 0:902). This can also be observed in Figure 2e, in which the dashed lines corresponding to the


Relationships between Stress Drop and Depth Because the stress drop is a phenomenon related to the level of the seismic-wave radiation, which may vary as a function of depth, we estimated the average stress drop of individual asperities. For the seven earthquakes (kinematic studies) considered here, we estimate the average stress drop of each one of the 13 asperities within the rupture area, as well as the small stress drop of the surrounding area. The static stress drop of each asperity is estimated from equation (17), following Madariaga (1979), when a circular source fault can be assumed (Boatwright, 1988). 7 M × 2 0 ; Δσ a 16 r ×R

17

in which Δσ a is the static stress drop on asperity in MPa, r is the equivalent asperity radius in kilometers, R is the equivalent radius of the source faults in kilometers, and M 0 is in newton meters. The stress drop of the 13 asperities considered here (Table 5) ranged from 0.504 to 3.284 MPa. There is not a clear dependency of the stress drop of the asperities with the depth in our dataset.

Discussion Comparison with Recent Source-Scaling Relationships From analysis of Figure 3a–g, in which the results of this study are compared with four different source-scaling relationships for subduction events, it is apparent that our results involving rupture area (Fig. 3a) show a similar tendency to those obtained by Strasser et al. (2010), Blaser et al. (2010), and Murotani et al. (2008) in the sense that they generate smaller areas than predicted by Somerville et al. (2002).

10000

1000

Area (km2)

mean 95% confidence intervals when self-similar scaling is assumed. In this study, we compared the new relationships proposed in the present paper with the areas of 31 Mexican subduction earthquakes estimated by Aguirre and Irikura (2007). One item to note is that these areas are generated by a process that considered high frequencies, while our relationships that involve the rupture area, area of largest asperity, and combined area of asperities were determined primarily from sources that consider low-frequency data. Aguirre and Irikura (2007) used the flat level of acceleration spectra records for high frequencies from 31 earthquakes recorded by the Guerrero Mexico accelerographic array from 1985 to 1998. The 31 earthquakes belong to the subduction earthquakes (those occurring on the plate interface). From the corner frequency of the source spectra for the acceleration records, the authors estimated the corresponding source area and compare their results with the area of the largest asperity provided by Somerville et al. (2002). In Figure 4, we show our results for this comparison.

849 Source area estimated by Aguirre & Irikura (2007) Rupture area estimated by Somerville et al. (2002) This study: Rupture area This study: Area of largest asperity This study: Combined area of asperities

100

10

1

0.1 1×1015

1×1016

1×1017 1×1018 1×1019 Seismic Moment (N •m)

1×1020

1×1021

Figure 4. Relationships between seismic moment versus total rupture area, area of largest asperity, and combined area of asperities. The relationship between seismic moment and total rupture area generated by Somerville et al. (2002) is represented by the dotted line, the relationship between seismic moment and rupture area obtained in this study is represented by the continuous line, the relationship between seismic moment and the area of largest asperity obtained in this study is represented by the dashed-dotted line, the relationship between seismic moment and combined area of asperities obtained in this study is represented by the dashed line, and the areas estimated by the corner frequencies of source spectra of acceleration records estimated by Aguirre and Irikura (2007) are represented by gray circles. As mentioned in the Results section, for the relationship derived in this study, the error estimate (se 0:587) is smaller than those relationships compared here, which are 0.630 for Somerville et al. (2002), 0.684 for Murotani et al. (2008), 0.758 for Strasser et al. (2010), and 1.233 for Blaser et al. (2010). The results from this study show a close resemblance to the relationships proposed by Somerville et al. (2002) and Murotani et al. (2008). The closest resemblance with Somerville et al. (2002) could be explained because four of the source models, representing 40% of the data considered in the regression of Somerville et al. (2002), are derived from the Mexican subduction zone; those models are considered in our study and represent 57% of our data. Also, our results highlight that there is a clear offset of a factor of ∼2 in rupture area between our relationships and those obtained by Blaser et al. (2010). A similar offset is obtained by Blaser et al. (2010) when comparing their relationships that involve rupture area with the result derived by Murotani et al. (2008). The difference between the results of this study and those proposed by Blaser et al. (2010) could be due to two factors: (1) our study focuses only on Mexican events, whereas they used worldwide data, and (2) the method used in our study to estimate the rupture areas of the source is based only on slip distribution, unlike that of Strasser et al. (2010) and Blaser et al. (2010), who used earthquakes from different tectonic environments in the world and some rupture areas that are

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Table 5 Stress Drop of All Asperities from Earthquakes Used in This Study and Depth Measured at the Center of the Asperity Event Number

Name of Earthquake

Date (yyyy/mm/dd)

Number of Asperity

Depth (km)

Stress Drop (MPa)

1

Petatlán

1979/03/14

2 3

Playa Azul Michoacán

1981/10/25 1985/09/19

4 5 6

Zihuatanejo San Marcos Manzanillo

1985/09/21 1989/04/25 1995/10/09

7

Tecomán

2003/01/22

1 2 1 1 2 1 1 1 2 3 4 1 2

11.685 29.830 16.330 15.247 18.610 20.005 16.845 5.080 24.430 13.545 5.079 18.125 29.365

0.558 0.504 3.049 1.577 1.442 3.284 1.066 2.728 2.258 2.159 1.984 2.971 3.046

based in the aftershock distribution. As explained by Blaser et al. (2010), this evaluation could involve subjective judgment and other sources of uncertainties. The predicted areas generated by Murotani et al. (2008) that involve rupture area and combined area of asperities, like the corresponding relationships generated in this study, show the same tendency as our results in the sense that they generated smaller areas than those obtained by Somerville et al. (2002), as shown in Figure 3a,c. One reason for this behavior is that both relationships (Murotani et al., 2008; and the results of this study) are derived from a similar process (Somerville et al., 1999) to determine the area of asperities and rupture area, unlike the other relationships compared here (Blaser et al., 2010; Strasser et al., 2010). Despite the fact that Murotani et al. (2008) and our results show a similar tendency, the comparison highlights an important difference, because our results generated larger areas than those proposed by Murotani et al. (2008). There is not a clear explanation for this behavior; however, it is important to note that both relationships are derived exclusively from specific subduction regions (Japan and Mexico) and that one of the justifications of these types of studies is to know whether or not this relationship varies depending on a specific subduction tectonic region. Figure 3b shows that predicted average slip by Murotani et al. (2008) is very similar to our results because both lines are almost superimposed. Additionally, both lines show the same tendency in the sense that both generated higher values than those obtained by Somerville et al. (2002). Comparison with Somerville et al. (2002) As shown in Figure 3a–g from the source-scaling relationships determined in this study, for most source parameters studied here, our results present smaller values than those obtained by Somerville et al. (2002), with the only exception being the relationship that involves the average slip versus seismic moment. The se for each regression, summarized in Table 4, suggests that in general, for all source parameters studied here, the se from the self-similar scaling

equation of large-magnitude Mexican subduction earthquakes is smaller than the self-similar scaling equation provided by Somerville et al. (2002). This can also be observed in Figure 2a–g, with the dashed lines corresponding to the mean 95% confidence intervals when self-similar scaling is assumed. This result suggests that the expressions obtained in this study could be appropriate for simulation of strong ground motions only in the case of the Mexican subduction-zone environment, although it is necessary to take into account that the database used in this study is limited. Irikura and Miyake (2011) define the rupture area and seismic moment as outer fault parameters and the slip heterogeneities and combined area of asperities as inner fault parameters. Figure 2a–d show that the scaling laws that involve areas (inner and outer fault parameters) in general show a greater dependence with respect to seismic moment than other relationships studied here (Fig. 2b–e). In the case of average slip, this dependence is less. However, Figure 2b shows that, with the exception of Petatlán and San Marcos earthquakes, the average slip of the remaining five earthquakes shows a dependence on seismic moment. The basic difference between constrained and unconstrained relationships that relate the average slip versus seismic moment (equations 9 and 10; Fig. 2b) comes from the San Marcos earthquake event (25 April 1989). Interestingly, this event only shows a different tendency in the slip versus seismic moment, but not in the other relationships studied here. Particularly, relationships that relate the combined area of asperities versus seismic moment (with both constrained and unconstrained equations; equations 11 and 12) are very similar. Additionally in this case, the point that represents the San Marcos event shows the best agreement with both tendency lines (constrained and unconstrained). What can produce this behavior? Let us examine this in detail: (1) This event is the only one that has not been taken from Martin Mai’s SRCMOD Database of Finite-Source Rupture Models (see Data and Resources). (2) In contrast to the other kinematic inversions used in this study that mainly use teleseismic data,

Scaling Relationships of Source Parameters of Mw 6.9–8.1 Earthquakes this event has been inverted using only strong ground motion data (see Table 2). (3) The published article that studied the rupture process of the San Marcos earthquake (Singh et al., 1989) reports only the slip distribution with arrows of different sizes corresponding to the displacement in each subfault. Because the discretization slip values were obtained from measurements of the slip lines from the printed figures, this could produce some uncertainties in our slip distribution data. However, from Figure 2c, it is interesting to observe that the self-similarity assumption is almost the same as the unconstrained relation. One point that contributes to this behavior is the well-confined area of asperities from the San Marcos event. That means that even the absolute values of displacement assigned to each subfault could be inaccurate; the contrast between them allows us to determine the combined area of asperities appropriately. The scaling laws of seismic moment M0 versus total area of rupture and average slip, Figure 2a and 2b, respectively, hold a relationship in the sense that the concept of the fault rupture area reveals the zone of the fault that radiates seismic energy, and this necessarily implies that this relationship has a direct implication with average slip. Our results show that only the case of the average slip relationship obtained in this study (Fig. 2b) is larger than the relationship proposed by Somerville et al. (2002). The relationship between seismic moment versus total rupture area and seismic moment versus average slip for large-magnitude Mexican subduction zone earthquakes (Figs. 2a and 2b) might contribute to the explanation of small rupture areas obtained by Aguirre (2005), Garduño (2006), and Ramírez-Gaytán et al. (2010). If seismic moment is the result of the product of area, average slip, and rock shear modulus, then a decrease in the area of seismic source and combined area of asperities implies a necessary increase of average slip in order to maintain a similar seismic moment. In this study, the area covered by asperities is 19.4% of the total rupture area, which is smaller than the 25% proposed by Somerville et al. (2002). The average value for the area of the largest asperity is 13.79% of the total rupture area, which is smaller than the 17.5% proposed by Somerville et al. (2002). Both results are congruent with the two relationships described above in the sense that a reduction in area implies a larger slip in order to maintain a similar seismic moment. Additionally, the comparison of the combined area of asperities versus area of largest asperity suggests that the largest asperity is responsible for releasing a large amount of energy during an earthquake. By comparing both constrained equations (see Fig. 2e) of the estimated hypocentral distance with the closest asperity of large-magnitude Mexican subduction earthquakes, we observe that it is 50.23% smaller than the self-similar scaling equation provided by Somerville et al. (2002). During the process of simulating strong ground motions, we found that the location of an asperity, inside of a seismic source at large distance from the hypocenter, in most cases generates a poor fitting between the synthetic and the observed motions

851

(Ramírez-Gaytán et al., 2010). This fitting slowly improves when an asperity approaches the hypocenter. In this case, the location of the nearest asperity to the hypocenter is an important factor when dealing with strong ground motion simulations. In this study, our result is 50.23% smaller than that proposed by Somerville et al. (2002) and in this particular case may have a direct implication of bringing the asperity closer to the hypocenter. This suggests that the nucleation process of some earthquakes probably starts at the location of an asperity. Comparison with Mexican Subduction Earthquakes (High Frequencies) Aguirre and Irikura (2007) conducted a study to estimate the rupture areas of 31 earthquakes from the Mexican subduction zone. The process considers the corner frequencies of source spectra of acceleration records. In their study, they plot the source areas obtained with the process described above and note that these areas fit well with the relationship proposed by Somerville et al. (2002) between the seismic moment and the area of the largest asperity for subduction earthquakes. They conclude that the estimated areas were not the total rupture areas of earthquake. In Figure 4, we plot the same areas estimated by Aguirre and Irikura (2007) for the 31 Mexican subduction-zone earthquakes, but now compared with the results of the present study (rupture area, combined area of asperities, area of largest asperities) and with the rupture area determined by Somerville et al. (2002). The relationships between seismic moment and rupture area determined by Somerville et al. (2002) in Figure 4 are represented with a dotted line, and the same relationship obtained from the Mexican subduction earthquakes obtained in this study is represented with a solid line (equation 8). In both cases, relationships lie considerably above the estimated areas of 31 earthquakes, confirming the conclusion obtained by Aguirre and Irikura (2007) that the areas estimated for 31 earthquakes did not correspond to the total rupture areas. This could be explained because areas of high-frequency radiation mainly correspond to regions adjacent to the large slip velocity area (Miyake et al., 2003). This means that the determined source area of these 31 earthquakes mainly reflects the area of asperities. Then, while using the rectangular representation of the fault rupture from kinematic inversions and source-scaling relationships, the asperities represent only a fraction of the rupture area (asperities represent 22% of the source area in the case of Somerville et al. [1999]). The remaining 78% of the source area considered in this sourcescaling relationship is not reflected by the source areas estimated using acceleration spectra. The dashed-dotted line (equation 14) in Figure 4 represents the relationship of seismic moment versus area of largest asperity. This line gives a best-fit and is located inside a cloud of gray circles that represents the estimated areas of 31 earthquakes. However, 60% of these circles are located above the line. As mentioned previously, this can be explained

852


because the circles that represent the source areas of 31 earthquakes primarily reflect the area of asperities, meaning the total area of asperities. On the contrary, the trend line (dashed-dotted line) given here represents only the area of the largest asperity. This relationship excludes the area of small asperities that contributes to the generation of high frequencies. This could be the reason why the trend line (dashed-dotted line) is located slightly below the center of the clustered circles. The dashed line (equation 12) of Figure 4 represents the relationships of seismic moment versus combined area of asperities located near the center of the clustered circles, showing the best-fit of the four relationships compared here. As mentioned, this may explain why the circles representing the source areas of 31 earthquakes reflect the total area of asperities estimated through a process that considers high frequencies, and the trend line determined here in fact represents the combined area of asperities generated through a process that considers low frequencies. This result is in accordance with that stated by Irikura and Miyake (2011) in the sense that the flat level of the acceleration spectra was theoretically related to the combined asperity areas. Based on these considerations, an important implication is that two different methodologies to determine the source area provide similar results. Namely, these methodologies are (1) the source-scaling relationship to determine the combined area of asperities from kinematic inversions (based on low frequencies) and (2) the area of combined asperities estimated by the corner frequencies (based on high frequencies). Stress Drop Strong dependence of stress drop when depth increases may indicate that the asperity areas could take smaller values than predicted by scaling relationships; that is, when the areas are located at larger depths within the rupture area. We calculate the stress drop of the 13 asperities considered here and found that they ranged from 0.504 to 3.284 MPa (Table 5). There is not a clear dependence of the stress drop of those asperities with the depth in our dataset. Scholz (1982, 2002) stated that shear strength of the lithosphere increases with depth. So, we expected that the deeper asperities could have associated a larger stress drop. However, the dataset used here, shows a null dependence of stress drop with the depth. Moya et al. (2000) estimated the stress drop for the aftershocks of the Kobe earthquake and compared the stress drop with depth; their results show a similar trend with the one obtained in this study, that is, although a slight indication of dependency can be recognized, in general the dependence of stress drop with depth is very scattered.

Conclusions We obtain source-scaling relationships for Mexican subduction events. These relations were compared with those proposed by four different authors for subduction environ-

ments. Concerning the relationships for the rupture area, our results are closer to those of Somerville et al. (2002) than any other, but, like the others, they have smaller areas than predicted by Somerville et al. (2002). This resemblance could be because 40% of the source data models considered in Somerville et al. (2002) are derived from the Mexican subduction zone and represent 57% of our data. In contrast, one of the reasons for the difference with those relationships, proposed by Strasser et al. (2010) and Blaser et al. (2010), could be because our study focuses only on Mexican events, whereas they use worldwide data. Another reason could be because, for some earthquakes, the criteria to estimate the rupture area used in their studies are based on the aftershock distribution. That is different than our study, which is based only on slip distribution. The criteria based on aftershock distribution could involve subjective judgment and other sources of uncertainties (Blasser et al., 2010). Because rupture areas from Murotani et al. (2008) are derived from the same process applied in the present study (Somerville et al., 1999), their relationship also predicts larger values than Strasser et al. (2010) and Blaser et al. (2010), but smaller values than ours. There is not a clear explanation for this behavior; however, it is important to note that both relationships are derived exclusively from specific subduction regions (Japan and Mexico) and that one justification of this type of study is to know whether or not this relationship varies depending on a specific region. Concerning the combined area of asperities, both Murotani et al. (2008) and our results predict smaller areas than those obtained by Somerville et al. (2002). However, both relationships highlight an important difference, because our results generated larger areas than those proposed by Murotani et al. (2008), which, as mentioned could be related to the specific subduction regions (Japan and Mexico). Concerning the area of largest asperity, the relationships obtained in this study are slightly smaller than those described by Somerville et al. (2002), which is consistent with the relationships of total rupture area and combined area of asperities. This is important because they are involved in the source models used for strong ground motion simulation. In the case of the average slip, our relationship is slightly larger than Somerville et al. (2002). That is an expected result because a decrease in the area of the seismic source implies an increase of average slip in order to maintain the same seismic moment. The error estimates for the constrained equations derived in this study in all cases are smaller than those relationships compared here. This might suggest that the expressions obtained in this study could be appropriate for the simulations of strong ground motion for the specific scenario of earthquake slip on the Mexican subduction-zone megathrust between the Cocos–Rivera and the North American plates. An important implication of this result is that the source-scaling relationships vary depending on specific regions. However, the improvement of these relationships requires more information to become available.

Scaling Relationships of Source Parameters of Mw 6.9–8.1 Earthquakes For the case of relationships that involve the seismic moment versus combined area of asperities, the small difference between the results obtained by Somerville et al. (2002) and the result obtained in this study could only partially explain the result obtained by Aguirre (2005), Garduño (2006), and Ramírez-Gaytán et al. (2010). From the comparison between the source areas of 31 Mexican earthquakes estimated by Aguirre and Irikura (2007) and the relationships generated in this study, the following are observed. (1) The relationships between seismic moment and rupture area determined by Somerville et al. (2002) and the same relationship from Mexican subduction earthquakes obtained in this study lie considerably above the estimated areas of 31 earthquakes, confirming the conclusion obtained by Aguirre and Irikura (2007) in the sense that the areas estimated for 31 earthquakes were not corresponding to the total rupture areas. (2) The relationships of seismic moment versus combined area of asperities generated in this study located near the center of the clustered circles obtained by Aguirre and Irikura (2007) shows the best-fit of the four relationships compared here. This result is in accordance with what is stated by Irikura and Miyake (2011) in the sense that acceleration level was theoretically related to the combined asperity areas. Based on these results, an important implication is that two different methodologies to determine the total area of asperities show similar results. To reiterate, these methods are (1) the source-scaling relationship from kinematic inversions to determine the combined area of asperities (based on low-frequency data) and (2) the area of Mexican earthquakes estimated by corner frequencies (based on high-frequency data). Finally, the stress drop of asperities from our dataset does not show a clear dependence with the depth. Although the seven slip models considered in this study are the only available studies for the Mexican subduction zone at this time, in the future it will be important to incorporate new slip models in the simulation of strong ground motions. A strong dependence of stress drop on increasing depth could imply that the asperity areas could take smaller values than predicted by scaling relationships; that is, when the areas are located at larger depths within the rupture area. The relationships between the stress drop and the depth of the asperity could then be used in the prediction of strongmotion scenarios of future large magnitude earthquakes occurring in the Mexican subduction zone. The slip models considered in this study are the only available studies for the Mexican subduction zone at this time. In the near future, incorporation of new slip models in the simulation of strong ground motions will be an important contribution. Also, a future task will be to determine how the relationships vary for specific regions. Further work in developing these scaling relationships will make it possible to more accurately predict and simulate strong ground motions produced by large-magnitude earthquakes from specific seismogenic zones in close proximity to highly populated urban areas.

853

Data and Resources The slip models and slip distribution from the earthquakes used in this study are available from the SRCMOD —Database of Finite-Source Rupture Models (http://equake ‑rc.info/SRCMOD/searchmodels/allevents/; last accessed 30 July 2013). The Global Centroid Moment Tensor (CMT) project catalog (1976–2013) is available at www.globalcmt. org (last accessed 13 March 2010). The seven published slip models of earthquakes used in this study are listed in the references. The ten published slip models of earthquakes used for Somerville et al. (2002) are listed in the references. Maps were created using ArcGIS version 9.3. Graphics and plots were created using MATLAB version 7.0.

Acknowledgments The authors wish to thank Kojiro Irikura and one anonymous reviewer whose comments helped to significantly improve the original manuscript. We thank Associate Editor Heather DeShon for her important comments that have led to significant improvements to this manuscript. This study was considerably facilitated by the SRCMOD database compiled by Martin Mai and coworkers, who provided the finite fault-slip models from the Finite-Source Rupture Model Database, and by the willingness of Carlos Mendoza, the principal author of the models used in this study. We are grateful to Ramón Zúñiga of the Instituto de Geociencias of the Universidad Nacional Autónoma de México for providing additional data and Evan Hirakawa of University of California in San Diego/San Diego State University for valuable comments and review. This research was supported by the Consejo Nacional de Ciencia y Tecnología (CONACyT) under Grant Number 164501.

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Instituto de Ingeniería Universidad Nacional Autónoma de México Ciudad Universitaria Coyoacán 04510, México DF, México [email protected] [email protected] (J.A., M.A.J.)

Puerto Rico Seismic Network Department of Geology University of Puerto Rico Residencie 2ª Mayagüez R. 9000, 00680 [email protected] (V.H.) Manuscript received 9 February 2013; Published Online 25 March 2014