Strong ground-motion relations for Mexican interplate earthquakes

Transcription

1 J Seismol (2010) 14: DOI /s Author's personal copy ORIGINAL ARTICLE Strong ground-motion relations for Mexican interplate earthquakes Danny Arroyo Daniel García Mario Ordaz Mauricio Alexander Mora Shri Krishna Singh Received: 26 May 2009 / Accepted: 13 June 2010 / Published online: 2 July 2010 Springer Science+Business Media B.V Abstract We derive strong ground-motion relations for horizontal components of pseudoacceleration response spectra from Mexican interplate earthquakes at rock sites (NEHRP B class) in the forearc region. The functional form is obtained from the analytical solution of a circular finite-source model. For the regression analysis we use a recently proposed multivariate Bayesian technique. The resulting model has similar accuracy as those models derived from regional and worldwide subduction-zone databases. However, there are significant differences in the estimations computed from our model and other models. First, our results reveal that attenuation in Mexico tends to be stronger than that of worldwide relations, especially for large events. Second, our model predicts ground motions for large earthquakes at close distances to the source that are considerably larger than the estimations of global models. Lack of data in this range makes D. Arroyo (B) Departamento de Materiales, Universidad Autónoma Metropolitana, Azcapotzalco, Mexico DF, Mexico aresda@correo.azc.uam.mx D. García S. K. Singh Instituto de Geofísica, UNAM, Mexico DF, Mexico M. Ordaz M. A. Mora Instituto de Ingeniería, UNAM, Mexico DF, Mexico it difficult to identify the most appropriate model for this scenario. Nevertheless, according to the available data at the city of Acapulco, our model seems to estimate seismic hazard more adequately than the other models. These new relations may be useful in computing seismic hazard for the Mexican forearc region, where no similar equations had been yet proposed. Keywords Ground motion model SA spectra Subduction-zone interplate earthquakes 1 Introduction Earthquake engineering in Mexico has been traditionally focused on estimating ground motion at the Valley of Mexico, located in the volcanic belt, caused by subduction-zone interplate earthquakes (e.g., Singh et al. 1987; Castroetal.1988; Rosenblueth et al. 1989; Ordaz et al. 1994). This interest is motivated by the large population density on this area, and its particular propagation and site effects. Unfortunately, these effects make the referred relations of no use for sites outside the volcanic belt. In contrast, in the forearc region only a few relations for peak ground acceleration (PGA) and Modified Mercalli Intensity have been proposed (Anderson and Quaas 1988; Chávez and Castro 1988; Ordaz et al. 1989; Anderson and Lei 1994;

2 770 J Seismol (2010) 14: Anderson 1997). These models are only valid for the state of Guerrero. Due to the proximity of moderate to large (M w ) earthquake foci along the Pacific coast, there is an urgent need of ground-motion models in the forearc region. These models are crucial to estimate accurately seismic hazard at coastal areas, where much of the population in the region concentrates. In the last decade there has been a considerable improvement in the seismic networks in Mexico. Here we take advantage of the larger database currently available to develop pseudoacceleration (SA) strong ground-motion relations for rock sites in the Mexican forearc region. To achieve this goal we use a function based on the solution of a circular finite-source combined with a recently proposed Bayesian regression technique. We compare our results with previous PGA models for Guerrero and with other SA relations based on worldwide subduction-zone datasets. Table 1 Interplate earthquakes used in this study a Number of threecomponent records used Event no. Date (yymmdd) Lat N Lon W H(km) M w Records a

3 J Seismol (2010) 14: Data and processing We used a subset of the Mexican interplate earthquakes database by García et al. (2009). These authors compiled all the interplate, thrust-faulting events with M w 5.0 occurred between 1985 and 2004 in the Pacific coast between the states of Colima and Oaxaca, only excluding those neartrench events whose high-frequency radiation is anomalously low (Shapiro et al. 1998; Iglesias et al. 2003). The dataset contains free-field, hardrock (NEHRP B class; BSSC 2004) recordings available from permanent networks. Any station with known, significant site amplification (Castro et al. 1990; Humphrey and Anderson 1992; Castro and Ruiz-Cruz 2005), as well as those located in the volcanic belt, was excluded. In addition, García et al. (2009) applied the H/V spectral ratio technique (Lermo and Chávez 1993) to verify that all stations included in their dataset satisfied the criteria of a generic rock station. For a more detailed description of the database the reader is referred to García et al. (2009). This study is focused on the magnitude distance range of most engineering interest (M w 6.5 and R < km). In order to increase the influence of this data range, we excluded those small events (M w 5.5) with few records and only collected at distant stations (R > 100 km). For events with magnitude M w 6.0, we estimated the minimum distance from the station to the fault plane; for the smaller events we took the hypocentral distance. We limited the distance range to 400 km. This upper limit takes into account the slow decay of the ground motion toward the continent reported by several authors (e.g., Singh et al. 1988; Cárdenas et al. 1998; Cárdenas and Chávez 2003; García et al. 2009), which forces us to consider larger distances than usual. To reduce the potential variability of the data, for any event recorded at two or more stations less than 5 km apart we selected only one of them, based on visual inspection of the traces. The resulting subset consists of 418 records from 40 interplate earthquakes obtained at 56 stations located at distances between 20 and 400 km (Table 1; Fig. 1). The selected data were recorded at 80 to 250 sps by bit digital accelerographs (66% of the data), which present a flat response for acceleration down to less than 0.1 Hz, and 24- bit broadband seismographs (34%), with a flat response for velocities between 0.01 and 30 Hz. Both the instrumental responses and the sampling rates ensure that reliable information can be retrieved from the records for frequencies up to nearly 30 Hz. Figure 2 shows the magnitude distance distribution of the data. Note that roughly 45% of the data come from km distance. The wave paths are shown in Fig. 3. Though the majority of records come from Guerrero, a noticeable amount Fig. 1 Map of central Mexico showing epicenters (circles) and stations (triangles) usedin this study. Filled symbols represent strong-motion stations (accelerographs) and open symbols represent broadband stations. The grey square represents ACAP station (see text). MVB Mexican Volcanic Belt (shaded grey). MAT Middle American Trench. States mentioned in the text are labeled

4 772 J Seismol (2010) 14: point-source model, the far-field approximation of the Fourier acceleration spectral amplitude of the most intense part of the ground motion, A( f ), assuming an ω 2 source model (Brune 1970), is defined by Eqs. 1 to 3: M 0 f 2 A ( f ) = CF ( f ) 1 + ( f / ) 2 e π fr β Q( f ) e πκf /R (1) f c C = (2π)2 R P F 1 P 4πρβ 3 (2) Fig. 2 Magnitude versus distance plot summarizing the data used in this study. Symbols indicate the type of data available. Circles accelerograms, open diamonds broadband velocity data of data also comes from other regions, especially Oaxaca. From the acceleration records, we read at the horizontal components PGA values and computed 5% damped SA spectra at 56 periods between 0.04 and 5 s ( Hz). 3 Functional form We chose a functional form based on the solution of a circular finite-source. According to the ( σ f c = β M 0 ) 1 3 (3) where f is frequency, F( f ) is a factor that corrects for the amplification of S waves as they propagate upwards through material of progressively lower velocity and it is roughly 2 for f 1 Hz (Boore 1986), M 0 is the seismic moment (in dyne cm), f c is the corner frequency, R is a measure of distance to the source (see below), β = 3.2 km/s is the shear-wave velocity, Q = Q 0 f (Q 0 = 100 s) is the quality factor that accounts for anelastic attenuation for the Pacific coast (Singh et al. 1989), κ is a parameter that corrects for the site effect (Singh et al. 1982; Anderson and Hough 1984), R P = 0.6 is the average radiation pattern (Boore and Boatwright 1984), F 1 = 2 is a factor that accounts for the free-surface amplification, P = is a factor that takes into account the equal partitioning of energy in the two horizontal components, ρ = 2.8 g/cm 3 is the density in the focal region, and σ is the Brune stress drop (in bars). Combining Eq. 1 and a high frequency approximation, Singh et al. (1989) derived, through random vibration theory, expressions for the Fourier spectral amplitude (Eq. 4a) and the root mean squared ground acceleration (Eq. 4b) foracircular finite-source model: Fig. 3 Epicenters of the earthquakes (circles), stations (triangles), and ray paths used in this study. Symbols are the same as in Fig. 1 A( f ) 2 = 2C 2 F ( f ) 2 ( M 0 fc 2 ) 2 e 2πκf E 1 (αr) E 1 (α R 2 + r0 2 r 2 0 ) (4a)

5 J Seismol (2010) 14: a rms = 2 2CM 0 fc 3 πκfc E 1 (αr) E 1 (α R 2 + r0 2 r 2 0 ) 1 2 (4b) In accordance with Eq. 7, we set the functional form of the ground-motion relations at each period, T,as SA(T) = α 1 (T) + α 2 (T) M w + α 3 (T) ln ) E 1 (α 4 (T) R) E 1 (α 4 (T) R 2 +r0 2 r 2 0 where α =2π/βQ 0, E 1 (x) is the well-known exponential integral function that is defined in Eq. 5 and r 0 is the radius of a circular fault based on the Brune s model, given by Eq. 6: E 1 (x) = e t x t dt (5) r 0 = 2.34β 2π f c (6) In practice, the exponential integral function can be computed using numerical methods (see, for example, Abramowitz and Stegun (1972) forfurther details). Equations 4a and 4b were obtained considering that the source intensity, (M 0 f 2 c )2,is uniformly distributed over the rupture area. Inserting Eqs. 2 and 3 in Eq. 4b, usingtherelationship between moment magnitude, M w,and M 0 (Kanamori 1977), and taking the natural logarithm of Eq. 4b results in ln a rms = α 1 + α 2 M w + α 3 ln ( ) E 1 (α 4 R) E 1 α 4 R 2 + r0 2 r 2 0 (7) In the case of PGA, for example, the coefficients would be α 2 = 0.576, α 3 = 0.5, and α 4 = α. However, these values should be viewed as approximations, since there are several assumptions involved in Eq. 4b. (8a) where α i (T) are the coefficients determined through regression analysis, R is the closest distance to fault surface (according to the circular finite-source model), and r 0 is given by r 2 0 = e M w (8b) Equation 8b was obtained from Eq. 6 using a stress drop equal to 100 bars. In theory, the coefficients of Eq. 8b should be also obtained through regression. However, in order to keep the functional form as simple as possible we decided to fix the coefficients of Eq. 8b. As it will be shown later, the resulting function yields satisfactory results, thus regression coefficients α i (T) adequately correct the error introduced by the assumption of a stress drop of 100 bars. The third term in Eq. 8a accounts simultaneously for geometrical spreading, anelastic attenuation and near-source saturation. As R approaches to infinity this term approaches e to α 4 (T)R, thus the geometrical spreading 2R 2 and anelastic attenuation of SA are given by ( [α 3 (T) α 4 (T) R + 2α 3 (T) ln (R)]). When R becomes comparable to r 0 the nearsource effect is controlled by the coefficient α 4. As α 4 increases, saturation of SA increases; on the other hand, as α 4 becomes zero, saturation vanishes. We note that the proposed function allows for oversaturation (i.e., the value of SA starts to decrease when M w exceeds a certain threshold). Although the existence of this effect is questionable, we proceeded with this functional form, since saturation level will be finally determined in the regression by the available data. Finally, we note that, although the function is undefined for R = 0 km, this is not a problem for Mexican interplate earthquakes, since their rupture areas never reach the surface (e.g., Singh et al. 1989).

6 774 J Seismol (2010) 14: Regression model We performed the regression analysis through a Bayesian scheme recently developed by Arroyo and Ordaz (2010a, b). The model is able to include, in the framework of Bayesian analysis, the correlation between: (1) observations for a given earthquake (intra-event correlation), (2) the coefficients of the model, and (3) ordinates of different periods. This level of generality, however, is only achieved if the function is linear. Although the function defined in Eq. 8a is nonlinear, it becomes linear once α 4 (T) is set to a certain value. For this reason, we performed the regression analysis as follows: for a given period and a given value of α 4 for that period, we compute the coefficients α 1, α 2,andα 3 through Bayesian analysis (i.e., considering them as random variables with prior and posterior probability density functions). Repeating iteratively this step we set the value of α 4 for that period as the one which yields the best fit to data. This implies that the regression analysis in not fully Bayesian, since coefficient α 4 is not considered as a random variable. The same procedure is repeated for each period independently, thus disregarding correlation between ordinates. In order to stabilize the regression and avoid physically unacceptable values of the coefficients, the Bayesian method requires prior information about the coefficients. For a given combination of period and α 4 this information was defined through random vibration theory and the Fourier amplitude spectrum defined in Eq. 4a by way of computing SA values for several combinations of M w and R. Following Singh et al. (1989), we used σ = 100 bars, κ = s 1,andQ 0 = 100 s. Then, we applied the least squares method to compute the prior value of α 1, α 2,andα 3.This implies that a priori we believe that the behavior of SA could be properly characterized by the finite-source model defined in Eq. 4a. The prior covariance of α 1, α 2,andα 3, the prior expected value of the covariance of the residuals (σ 2 ;where residuals are defined as the logarithmic difference between observations and estimations), and the prior expected value of the inter-event correlation (γ e ) were set following previous studies. Further details can be found in Ordaz et al. (1994) and Arroyo and Ordaz (2010a, b). In order to obtain the posterior expected values of α 1 (T), α 2 (T), α 3 (T), σ 2,andγ e, the joint posterior density of the regression coefficients was numerically marginalized using the Gibbs sampling method with a number of terms of 150, for which convergence was achieved (see Arroyo and Ordaz (2010a) for further details). Although Eqs. 4a and 4b hold only in the short period range due to the high frequency approximation used, we decided to use these equations to define the prior mean value of the regression coefficients for all periods, since prior information will be modified with the information contained in the database. 5 Near-source saturation term: results for the α 4 coefficient The coefficient α 4 controls the near-source saturation effect. It might be viewed as an empirical modification of α = 2π/βQ 0 (Eq. 4b) totakeinto account the variation of the quality factor Q 0 with frequency. In the first stage of the regression analysis, we studied the variation of the standard deviation of the residuals (random variability, σ ) at each period: performing the Bayesian analysis for each value of α 4, we obtained the resultant values of α 1, α 2, α 3,andσ. Figure 4a shows random variability at four representative periods. For long periods (T 1s)σ increases monotonically with α 4, due to the absence of near-source saturation for SA in that range (the peak displacement of a long-period oscillator should be equal to the peak ground displacement). On the other hand, for short periods (T < 1 s) minimum random variability is attained at a certain value of α 4,which depends on period. The shorter the period, the larger value of α 4 for which the minimum is found. In other words, near-source saturation effect is more pronounced at short periods, as expected. For certain periods it is not clear which value of α 4 corresponds to the minimum σ ; in those cases, we selected the value of α 4 which resulted in the minimum mean value of residuals (bias, b). InFig.4bwe plot the value of coefficient α 4

7 J Seismol (2010) 14: Fig. 4 a Effect of coefficient α 4 on random variability, σ for different periods. Black circles T = 0s(PGA), white circles T = 0.5 s, black squares T = 1s,andwhite triangles T = 5s.b Coefficient α 4 obtained at the first stage of the analysis (minimum σ ; dashed curve) versus period, and smoothed function used in the second stage of the analysis (continuous curve) selected for each period. For the next stage of the analysis these values were smoothed over period (continuous curve). 6 Regression coefficients Once the smoothed values of α 4 were fixed, we generated prior information according to the considerations stated before and performed the Bayesian regression analysis to compute the final values for the rest of the regression coefficients. The results (in natural logarithm units) are summarized in Table 2 and Fig. 5. We have included in Table 2 the bias (b), the inter-even variability (σ e ), and the intra-event variability (σ r ).These last two values were computed from γ e and σ. Figure 5 includes a comparison between the mean prior values and the mean marginal posterior values obtained from the Bayesian analysis. The effect of the information in the dataset can be clearly observed: final regression coefficients are not over-constrained to their mean prior values. In addition, we noted that usually the prior values are closer to the posterior values in the short period range due to the high frequency approximation implicit in the prior information. Figure 5f also shows that the proposed model systematically tends to overestimate the observed values in the whole period range. However, since the largest bias is nearly 5% (T = 4.5 and 5 s), we consider this trend acceptable. Plots of residuals for the same periods as in Fig. 4 as a function of magnitude, distance, and depth are shown in Figs. 6, 7, and8, respectively. There is no significant trend in the residuals, and similar results are obtained for the rest of periods. Despite not including focal depth (H) as a parameter in the regression, residuals do not exhibit significant dependence on it (only a slight trend can be observed at 5 s). 7 Comparisons with other subduction-zone models In the past some ground-motion models to compute PGA for subduction-zone earthquakes in the state of Guerrero have been developed (Anderson and Quaas 1988; Ordaz et al. 1989; Anderson and Lei 1994; Anderson 1997). Also, in the last decades several authors have proposed ground-motion models for subduction-zone earthquakes using worldwide data (e.g., Crouse et al. 1988; Crouse 1991; Youngs et al. 1997; Atkinson and Boore 2003; Kanno et al. 2006; Zhaoetal. 2006). In this section we compare the estimations from our model with those from regional and worldwide studies, with special emphasis on large earthquakes at close distances. Among the regional models we considered the non-parametric model proposed by Anderson (1997) and the model proposed by Ordaz et al. (1989) [hereinafter referred to as A97 and O89, respectively]. For the case of the worldwide models, we chose the relations for interplate earthquakes at generic rock sites (NEHRP B) proposed by Youngs et al. (1997), Atkinson and Boore (2003),and Zhao et al.(2006) [hereinafter referred to as Y97, AB03, and Z06, respectively].

8 776 J Seismol (2010) 14: Table 2 Regression parameters of the proposed strong ground-motion model T (s) α 1 (T) α 2 (T) α 3 (T) α 4 (T) γ e b σ σ e σ r PGA Though the database of AB03 comprises the whole dataset of Y97 and many more records, we selected both formulations since they use different approaches to model near-source saturation. Both datasets contain several Mexican earthquakes, but only a small fraction of them are included in our

9 J Seismol (2010) 14: Table 2 (continued) T (s) α 1 (T) α 2 (T) α 3 (T) α 4 (T) γ e b σ σ e σ r database. The reason is twofold: (1) some of the Mexican events classified as interplate in Y97 and AB03 sets are actually reverse-faulting inslab events (H km) mislocated by global catalogues, thus having considerably higher stressdrops than interplate events and (2) some of the records used by those authors do not satisfy our quality criteria. On the other hand, the database Fig. 5 Prior values (white dots) and final values obtained from Bayesian regression analysis (black dots)ofa coefficient α 1, b coefficient α 2, c coefficient α 3, d random variability, σ ; e parameter γ e,andf bias, b,forthe proposed model versus period. All values are in natural logarithmic units (Eq. 8a)

10 778 J Seismol (2010) 14: Fig. 6 Residuals (in natural logarithmic units) for the model as a function of distance, R, for periods: a 0s(PGA), b 0.5 s, c 1s,andd 5s. Continuous line shows linear regression of residuals Author's personal copy of Z06 is mainly comprised of Japanese strongground-motion records. Although the Z06 database contains a small number of near-source (R < 40 km) records of worldwide earthquakes from shallow crustal active regions, its authors did not include records of Mexican earthquakes because of the differences in the subduction characteristics between Mexico and Japan (Kanamori 1986). Fig. 7 Residuals (in natural logarithmic units) for the model as a function of magnitude, M w, for periods: a 0s (PGA); b 0.5 s; c 1s,and d 5s.Continuous line shows linear regression of residuals

11 J Seismol (2010) 14: Fig. 8 Residuals (in natural logarithmic units) for the model as a function of depth, H,for periods: a 0s(PGA), b 0.5 s, c 1s,andd 5s. Continuous line shows linear regression of residuals Author's personal copy In Fig. 9 we compare the scaling of SA with magnitude in the near-source region from our model and those by Y97, AB03, and Z06. For PGA we include the curve derived from a finitesource model (Eq. 4a). Also plotted are all our data at distances shorter than 25 km. Note that Fig. 9 Scaling of SA with M w for distances close to 20 km. Curves correspond to our proposed model for Mexico (continuous), models for Guerrero (only for PGA) by A97 (dashed and dotted)and O89 (medium dotted), Japanese model by Z06 (line and double dotted), and worldwide models by Y97 (dotted)andab03 (short dashed). Open circles Mexican data at distances shorter than 25 km (R km; average of 20.8 km). For PGA (frame a) large dashed curve represents the estimation from a finite-source model with σ = 100 bars, κ = 0.023, and Q 0 = 100 s (Eq. 4b)

12 780 J Seismol (2010) 14: only 16 records are available at this range, and only five of them correspond to large earthquakes (three events of M w > 7.0). Thus, any anomalous characteristic on these large earthquakes may strongly influence the regression results. There are significant differences between the models. In particular, for large magnitudes our model predicts considerably larger motions than those estimated by A97, Y97, and AB03. For example, for an M w 8.0 event at 20 km the estimated Fig. 10 Observed (open circles) and estimated SA (curves; same symbols as in Fig. 9) as a function of distance for the same periods as in Fig. 9 and magnitudes M w 6.0 and 8.0

13 J Seismol (2010) 14: PGA values are roughly 1.5 and three times larger than those by Y97 and AB03, respectively. We note that AB03 model is in closer agreement with the observed values during the 1985 Michoacan M w 8.0 earthquake than the other models and with the non-parametric A97 model. Therefore, according to AB03 and A97 models Michoacan values are representative of the average values of SA for M w 8.0. However, this assumption is questionable, since there is a consensus on the anomalously low SA values observed during that earthquake (e.g., Cohee et al. 1991; Crouse 1991). Moreover, the PGA values predicted by the A97 model start to decrease for M w larger than 6. Also, we note that the O89 model yields larger values of PGA than the other models especially for M w larger than 7. Interestingly, our model is similar to the Z06 model, even more similar than the regional models for Guerrero, despite the Z06 model was developed with a completely different database and regression technique. For this distance range the maximum differences between our model and the Z06 model for PGA and SA at 0.1 s, 1 s, and 3 s are roughly 10%, 20%, 15%, and 35%, respectively. Figure 10 compares the decay of SA with distance for M w 6.0 and 8.0. The adopted functional form is based on the theory for far-field body waves, so the question if the ground motion model is able to properly describe the decay of ground motion for long distances naturally arises for distances where the influence of surface waves might be important. However, Fig. 10 suggests that, on average, the proposed model seems to reproduce the attenuation of Mexican data better than other models. Differences in attenuation are more pronounced for large earthquakes, where our model tends to predict a faster decay, especially for short periods. Furthermore, the decay of ground motion with distance for our model is similar to the decay proposed by Z06, despite the shorter distance range considered in the latter model. However, our model clearly departs from the data for M w 8.0 at 3 s of period, where it predicts larger values of SA than the observed ones. In the case of the regional models for Guerrero, we note that the attenuation of our model is comparable to the observed in the O89 model and it decays faster than the A97 model. Nevertheless, the A97 model seems physically unacceptable since in some cases the predicted values increase with distance. 8 Discussion The differences observed in the previous section may be due to differences in the datasets, the regression technique, and the adopted functional form. Although there are few coincidences in the data used by each model, for the most interesting range (large magnitudes at close distances) all databases are nearly equal, except for the Z06 model, mainly derived from Japanese data. However, it is precisely at this range where our model significantly differs from the Y97 and AB03 models, and where the Z06 model and the proposed model are more similar. Closer inspection of random variability and residuals of the models does not reveal any noticeable difference between them. Therefore, from a statistical point of view, we cannot determine which model fits data better. Certainly, more data than currently available are needed to define statistically the mean value of SA in the near-field of large Mexican interplate earthquakes. In spite of this limitation, to gain further insight into this question we examined the scaling of PGA with M w at close distances in a broader range of magnitudes than that used by the studies considered. For this purpose we included 115 PGA values obtained from Mexican interplate events with M w recorded at hypocentral distances between 16 and 37 km (Gaite 2005). All PGA values were reduced to a common distance of 16 km by correcting them with the factor (Singh et al. 1989): f R = ( ) R e π (R 16) β Q 0 (9) 16 where the values of β and Q 0 have been previously defined. The reduced PGA values and the estimations from the considered models are shown in Fig. 11. For magnitudes where enough data are available, there is a large scatter in the data, spanning from more than an order of magnitude. Therefore, statistical significance of the scarce data from large

14 782 J Seismol (2010) 14: Fig. 11 Near-source PGA data (open circles) from Mexican interplate earthquakes reduced to a distance of 16 km (see text for details) as a function of M w. The different curves (same symbols as in Fig. 9) represent the estimations from O89, A97, Y97, AB03, and Z06 models, and this study events is very low. However, the following observations can be drawn: A97 and AB03 models tend to systematically underestimate Mexican near-source PGA, even for the magnitude range considered by the models (M w ). For M w < 5 our model is closer to the mean value of the data than O89, Y97, and Z06 models, though those data were not included in the regression. For M w > 5 it is difficult to discern if O89, Y97, Z06, or our model gives more rational estimates of near-source PGA. The final goal of deriving strong ground-motion relations is the computation of seismic hazard for specific sites. It is interesting to explore how differences between models are translated into probabilistic-hazard estimates for the city of Acapulco. Acapulco is a medium-sized (ca. 1 million people) Pacific coastal city located in the middle of a seismic gap where an M w earthquake is expected in the near future (e.g., Singh et al. 1981). Station ACAP, placed on rock in Acapulco (Fig. 1), hasbeencontinuouslyrecordingfor nearly 40 years. Following Ordaz and Reyes (1999), we computed empirical seismic hazard curves for ACAP station by counting the number of times that a certain value of SA was exceeded per unit of time from the available data due to interplate earthquakes. We compare the resulting empirical curves with hazard curves obtained through probabilistic seismic hazard analysis (PSHA) based on seismicity information of interplate-subduction sources located in the Pacific coast of Mexico. These hazard curves were computed separately for the Y97, AB03, and Z06 models, as well as for the proposed model. For PSHA the seismicity of the Pacific coast of Mexico was divided into two groups. The first, which is responsible for events with M w < 7, has magnitude exceedance rates that follow the modified Gutenberg-Richter model. For the second group, responsible for events with M w > 7, we used a Gaussian distribution of magnitudes to take into account the characteristic earthquake behavior observed by Singh et al. (1983) for the Mexican subduction zone. The first group was subdivided into four sources, while the second group was divided into 14 sources. For each source the parameters of the seismicity models were obtained from the earthquake catalog of Mexican earthquakes prepared by Zúñiga and Guzmán (1994), with the use of the Bayesian approach described in Rosenblueth and Ordaz (1987). The geometry of the seismic sources and their parameters can be found in Ordaz and Reyes (1999). In addition, we assume that the conditional probability density function of SA given M and R is a lognormal density function with median value and standard deviation of the natural logarithm of SA given by the mean value and random variability of the considered ground motion model. It is important to underline that the purpose of this analysis is to assess the impact of the observed differences between ground-motion models in the framework of PSHA. Figure 12 summarizes the results of this comparison. The analytical curve derived from this study and the curve based on the Z06 model constitute better approximations to the empirical curve than those obtained from Y97 and AB03 models. However, these results should be viewed with caution, since for the observation time of

15 J Seismol (2010) 14: Fig. 12 Seismic hazard curves for ACAP site in Acapulco computed from different strong-motion relations (same symbols as in Fig. 9). Open circles are empirical data computed from records at ACAP Author's personal copy ACAP ( 40 years) the smaller exceedance rate that could be reasonably estimated with the empirical data is 0.25 year 1 (Beauval et al. 2008). Nevertheless, for small exceedance rates the hazard curves obtained with the proposed model and Y97 model become similar. The trends presented in Fig. 12 are only valid for ACAP station, and may not be necessarily appropriate for other rock sites in the forearc region. Unfortunately, there are no more available stations in the area with such a long time window of data to compute other empirical hazard curves. From the results presented in this section we consider that the proposed model is more suitable for Mexican interplate earthquakes than other models based on regional and worldwide data. On the other hand, the use of this model in other subduction-zones may not be adequate, especially for interplate events deeper than 30 km. 9 Conclusions We have developed SA strong ground-motion relations for Mexican interplate earthquakes

16 784 J Seismol (2010) 14: through a Bayesian regression technique in which the functional form has been obtained from the analytical solution of a circular finite-source model. These equations are valid for rock sites (NEHRP B) located in the forearc region. The resulting model shows that amplitudes from large earthquakes in Mexico decay faster in comparison with estimates from models based on worldwide datasets, especially at high frequencies. Our model also predicts ground motions for large earthquakes at close distances that are larger than those expected from worldwide studies. Due to the paucity of data in this range, it is difficult to elucidate which model represents the best choice for this scenario. However, near-source PGA scaling with magnitude and probabilistic seismic hazard analysis suggest that the model derived in this study is a more suitable approximation for the available Mexican near-field data. Acknowledgements We thank Miguel Herraiz and Beatriz Gaite for long and fruitful discussions. Figures 1 and 3 were created with the GMT free software (Wessel and Smith 1998). D. García was supported by Predoctoral Fellowships Program from Universidad Complutense de Madrid, Spain, and Postdoctoral Fellowships Program from DGAPA, UNAM. References Abramowitz M, Stegun IA (1972) Handbook of mathematical functions. Dover Publications, Inc., New York, pp Anderson JG (1997) Nonparametric description of peak acceleration above a subduction thrust. Seism Res Lett 68(1):86 93 Anderson JG, Hough SE (1984) A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencies. Bull Seism Soc Am 74(6): Anderson JG, Lei Y (1994) Nonparametric description of peak acceleration as a function of magnitude, distance, and site in Guerrero, Mexico. Bull Seism Soc Am 84(4): Anderson JG, Quaas R (1988) The Mexico earthquake of September 19, 1985 effect of magnitude on the character of strong ground motion: an example from the Guerrero, Mexico, strong motion network. Earthq Spectra 4(3): Arroyo D, Ordaz M (2010a) Multivariate Bayesian regression analysis applied to ground-motion prediction equations, Part 1: theory and synthetic example. Bull Seism Soc Am (in press) Arroyo D, Ordaz M (2010b) Multivariate Bayesian regression analysis applied to ground-motion prediction equations, Part 2: numerical example with actual data. Bull Seism Soc Am (in press) Atkinson G, Boore DM (2003) Empirical ground-motion relations for subduction-zone earthquakes and their application to Cascadia and other regions. Bull Seism Soc Am 93(4): Beauval C, Bard P-Y, Hainzl S, Guéguen P (2008) Can strong-motion observations be used to constrain probabilistic seismic-hazard estimates? Bull Seism Soc Am 98(2): Boore DM (1986) The effect of finite bandwidth on seismic scaling relationships. In: Das S, Boatwright J, Scholz C (eds) Earthquake source mechanics. American Geophysical Union Monograph 37: Boore DM, Boatwright J (1984) Average body-wave radiation coefficient. Bull Seism Soc Am 74(6): Brune JN (1970) Tectonic stress and the spectra of seismic shear waves from earthquakes. J Geophys Res 75(26): BSSC (2004) NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, 2003 Edition. Part 1 Provisions, Part 2 Commentary, Technical Report FEMA 450, Building Seismic Safety Council for the Federal Emergency Management Agency, Washington, DC Cárdenas M, Chávez FJ (2003) Regional path effects on seismic wave propagation in Central Mexico. Bull Seism Soc Am 93(3): Cárdenas M, Núñez-Cornú F, Lermo J, Córdoba D, González A (1998) Seismic energy attenuation in the region between the coast of Guerrero and Mexico City: differences between paths along and perpendicular to the coast. Phys Earth Pl Int 105(1):47 57 Castro RR, Ruiz-Cruz E (2005) Stochastic modeling of the 30 September 1999 M w 7.5 earthquake, Oaxaca, Mexico. Bull Seism Soc Am 95(7): Castro RR, Singh SK, Mena E (1988) An empirical model to predict Fourier amplitude spectra of horizontal ground motion. Earthq Spectra 4(4): Castro RR, Anderson JG, Singh SK (1990) Site response, attenuation and source spectra of S waves along the Guerrero, Mexico, subduction zone. Bull Seism Soc Am 80(7): Chávez M, Castro R (1988) Attenuation of Modified Mercalli Intensity with distance in Mexico. Bull Seism Soc Am 78(7): Cohee BP, Somerville P, Abrahamson NA (1991) Simulated ground motions for hypothesized M w = 8 subduction earthquakes in Washington and Oregon. Bull Seism Soc Am 81(1):28 56 Crouse CB (1991) Ground-motion attenuation equations for earthquakes on the Cascadia subduction zone. Earthq Spectra 7(2): Crouse CB, Vyas YK, Schell BA (1988) Ground motions from subduction-zone earthquakes. Bull Seism Soc Am 78(1):1 25 Gaite B (2005) Escalade movimientos fuertes en la zona de subducción de Guerrero (México). M. Sc. Thesis. Universidad Complutense de Madrid. 101 pp (In Spanish)

17 J Seismol (2010) 14: García D, Singh SK, Herraiz M, Ordaz M, Pacheco JF, Cruz-Jiménez H (2009) Influence of subduction zone structure on coastal and inland attenuation in Mexico. Geophys J Int 179(1): Humphrey JR Jr, Anderson JG (1992) Shear-wave attenuation and site response in Guerrero, Mexico. Bull Seism Soc Am 82(4): Iglesias A, Singh SK, Pacheco JF, Alcántara L, Ortiz M, Ordaz M (2003) Near-trench Mexican earthquakes have anomalously low peak accelerations. Bull Seism Soc Am 93(2): Kanamori H (1977) The energy release in great earthquakes. J Geophys Res B 82(20): Kanamori H (1986) Rupture process of subduction-zone earthquakes. Ann Rev Earth Planet Sci 14: Kanno T, Narita A, Morikawa N, Fujiwara H, Fukushima Y (2006) A new attenuation relation for strong ground motion in Japan based on recorded data. Bull Seism Soc Am 96(3): Lermo J, Chávez FJ (1993) Site effect evaluation using spectral ratios with only one station. Bull Seism Soc Am 83(6): Ordaz M, Reyes C (1999) Earthquake hazard in Mexico City: observations versus computations. Bull Seism Soc Am 89(6): Ordaz M, Jara JM, Singh SK (1989) Riesgo sísmico y espectros de diseño en el estado de Guerrero, Report No 8782/9745, UNAM Instituto de Ingeniería (In Spanish) Ordaz M, Singh SK, Arciniega A (1994) Bayesian attenuation regressions: an application to Mexico City. Geophys J Int 117(2): Rosenblueth E, Ordaz M (1987) Use of seismic data from similar regions. Earthq Eng Struct Dyn 15: Rosenblueth E, Ordaz M, Sánchez-Sesma FJ, Singh SK (1989) The Mexico earthquake of September 19, 1985 design spectra for Mexico s Federal District. Earthq Spectra 5(1): Shapiro NM, Singh SK, Pacheco JF (1998) A fast and simple diagnostic method for identifying tsunamigenic earthquakes. Geophys Res Lett 25(20): Singh SK, Astiz L, Havskov J (1981) Seismic gaps and recurrence periods of large earthquakes along the Mexican subduction zone; a reexamination. Bull Seism Soc Am 71(3): Singh SK, Apsel R, Fried J, Brune JN (1982) Spectral attenuation of SH-wave along the Imperial fault. Bull Seism Soc Am 72(7): Singh SK, Rodríguez M, Esteva L (1983) Statistics of small earthquakes and frequency of occurrence of large earthquakes along the Mexican subduction zone. Bull Seism Soc Am 73(7): Singh SK, Mena E, Castro R, Carmona C (1987) Empirical prediction of ground motion in Mexico City from coastal earthquakes. Bull Seism Soc Am 87(6): Singh SK, Mena E, Castro RR (1988) Some aspects of source characteristics of the 19 September 1985 Michoacan earthquake and ground motion amplification in and near Mexico City from strong motion data. Bull Seism Soc Am 88(2): Singh SK, Ordaz M, Anderson JG, Rodriguez M, Quaas R, Mena E, Ottaviani M, Almora D (1989) Analysis of near-source strong-motion recordings along the Mexican subduction zone. Bull Seism Soc Am 79(7): Wessel P, Smith WHF (1998) New, improved version of generic mapping tools released. EOS 79(47):579 Youngs RR, Chiou SJ, Silva WJ, Humphrey JR (1997) Strong ground motion attenuation relationships for subduction zone earthquakes. Seism Res Lett 68(1): Zhao JX, Zhang J, Asano A, Ohno Y, Oouchi T, Takahashi T, Ogawa H, Irikura K, Thio HK, Somerville PG, Fukushima Y, Fukushima Y (2006) Attenuation relations of strong ground motion in Japan using site classification based on predominant period. Bull Seism Soc Am 96(3): Zúñiga R, Guzmán M (1994) Main seismogenic sources in Mexico, Tech. Rep., Seismic Hazard Project, Instituto Panamericano de Geografía e Historia (IPGH), Mexico 1-Mex 82