Most and Least Likely Locations of Large to Great Earthquakes Along the Pacific Coast of Mexico, Estimated from Local Recurrence Times Based on b-

Transcription

1 version June 2001 Most and Least Likely Locations of Large to Great Earthquakes Along the Pacific Coast of Mexico, Estimated from Local Recurrence Times Based on b-values by F. Ramón Zuñiga Unidad de Ciencias de la Tierra-Instituto de Geofísica, UNAM, Juriquilla, Querétaro, CP Mexico and Max Wyss Geophysical Institute, University of Alaska, Fairbanks, 903 Koyukuk Dr accepted version Bulletin of the Seismological Society of America Abbreviated title: Probable locations of large earthquakes along the coast of Mexico Key words: Mexico, large earthquakes, b-value, asperities, probabilistic estimates. SUMMARY We mapped TL and PL (local recurrence time and local probability density, respectively) for M max = 7.2 earthquakes along the plate margin of the Pacific coast of Mexico to test two hypotheses. The first is that minima in TL (or maxima in PL), extracted probabilistically from the frequency-magnitude distribution, map asperities. The second hypothesis is that recurrence times for characteristic events are estimated more correctly by local recurrence times than by the overall recurrence times of the zone. Comparing these results with observed recurrence times for events with M 7.0, we find good agreement. The coast of Guerrero between longitude and 101.5, and the segment off the coast of southern Chiapas show the shortest TL estimated as about 20 years; the location at longitude 98.5 (near the boundary of Guerrero with Oaxaca, the Ometepec segment) follows with estimates of about 30 years as the next shortest TL; along the coast of Guerrero, between 99 and longitude, T L is estimated as about 40 years; and finally in the segments off the Oaxacan coast near 95.7 and 97.7 longitude, T L ranges from 40 to 60 years. These volumes we define as asperities. Long local recurrence times are observed for the areas offshore from the isthmus of Tehuantepec, on the Pacific plate off the coast of Guerrero, on land along the coast of most of Oaxaca, and along the northern-most 40 km of the Guerrero coast. If our ideas are correct, then major moment release should emanate from the volumes we defined as asperities and relatively minor moment release should emanate from volumes identified by the relatively long local recurrence times. 1

2 INTRODUCTION Recently, Wiemer and Wyss (1997) proposed that asperities may be characterized by anomalously low b-values of the frequency vs. magnitude distribution (FMD), in contrast with high b-values along creeping segments of faults (Amelung and King, 1997). If this anomaly in the characteristics of the seismicity within asperities holds in general, then it would be incorrect to estimate recurrence time by the probabilistic method from the constants a and b in eq. (1), as derived from the entire fault segment that may break in a main shock. Henceforth, such a time will be referred to as bulk recurrence time, T RB. The generally accepted model of the role of asperities is that they alone resist faulting significantly. Stress is assumed to accumulate within an asperity, but less so along the fault surface around it, because there it is reduced by aseismic creep. When the asperity fails, a main shock rupture propagates to some distance into the less stressed fault segments near the asperity. Thus, in this model the tectonic processes within the asperity alone control the time of failure of main shocks. It follows that the recurrence time must be estimated from the a- and b-values within the asperity (hereafter referred to as local time), if it can be estimated from these parameters at all. Wiemer and Wyss (1997) found that the local recurrence time, T L, estimated from a- and b-values within volumes with radii of about 5 km were much shorter than the T RB estimated from the entire rupture area of the 1966 Parkfield and the 1984 Morgan Hill earthquakes. In these cases of M6 main shocks along the San Andreas fault system, the TL estimates agreed closely with the return times estimated from historical events, T H, whereas T RB overestimated the return times by a factor of 3, approximately. Thus, we can propose two hypotheses that need to be tested. (1) Minima in local recurrence times, estimated probabilistically from local a- and b-values, may map asperities. (2) Recurrence times are estimated more correctly by local recurrence times than by bulk recurrence times. The first of these hypotheses was tested successfully in Southern California along the San Jacinto-Elsinore fault system (Wyss at al., 2000). Out of six main shocks (5.6 M 6.8) that occurred between 1899 and 1968, five were associated with minima in TL, mapped using the seismicity catalog from 1981 to 1998, which contained no shock with M>4.9. However, the second hypothesis could not be tested well, because there are no historic repeated ruptures of the same fault segments in Southern California. All one could conclude from that study was that the estimates of T L=200 years along the San Jacinto fault approximately agreed with the estimates derived from geologically measured slip rates. Also, the fact that T L observed along the Elsinore fault was about twice that on the San Jacinto fault agreed with geological estimates. Given the above, the purposes of this paper are (1) to determine if b-values and TL for mainshocks of magnitude M 7.0 are as heterogeneous along the plate margin of the Mexican Pacific coast as they are in California, (2) to see whether asperities can be mapped in this region by minima in TL, and (3) to test how close estimates of T L for mainshocks of the order of M 7.0 approach the observed historical recurrence times, TH, of large subduction shocks in Mexico. 2

3 The history of main shocks in south-central Mexico with 7< M< 8.2 goes back to the mid-19th century and the TH are among the shortest in the world. Thus, this data set may be well suited for testing the hypothesis that T L estimates TH better than TRB does. Most of these main shocks belong to the subduction regime shown in Fig. 1. Furthermore, recent advances in network coverage by the Mexican Seismological Survey (Servicio Sismológico Nacional or SSN) have greatly improved the quality of epicenter locations, as well as the minimum reporting magnitude, therefore making this study feasible. DATA Our source of data is the catalog of seismicity compiled by the SSN, for the years 1988 to We do not include earlier data because there are large fluctuations in magnitude of completeness and variations in the record that can be attributed to changes in operational procedures and network coverage (Zuñiga, et al., 2000). We have not used other sources, like the PDE or ISC catalogs, because the resolution of our approach (b-value mapping) depends on the minimum magnitude of completeness, as well as on the number of events catalogued in a consistent fashion. In the case of the teleseismic catalogs, the minimum magnitude in this region is approximately 4.3, a value significantly larger than the one found for SSN data, as shown later. We restricted the analysis to shallow (h < 60 km) events since we are focusing on subduction thrust and shallow continental stress regimes, and also because those are the most active regimes in Mexico. Fig. 1a shows the spatial distribution of seismicity in southern Mexico. Fig. 1b shows the extent of the latest and largest ruptures that occurred during this century, as well as the most distinctive tectonic features in the area of study. METHOD We measure the a- and b-values, which are constants in the FMD equation Log N = a bm (1) where N is the cumulative number of earthquakes with magnitude larger or equal to M. Then we estimate how many years it would take to accumulate earthquakes according to (1), until one main shock of magnitude M max is expected to occur by T L(M max) = T/10 (a-bmmax) (2) where, T is the time span of the catalog. Alternatively we can estimate the local probability density, P L, for a main shock with magnitude M to occur by PL(Mmax) = 1 / (TL(Mmax) A) (3) where A is the area in kilometer, from which a and b were derived. Thus, P L has units of probability per year and km 2. The parameters b, TL(M) and PL(M) are all mapped by the gridding technique introduced by Wiemer (1996) and coded in the computer program ZMAP (Wiemer 3

4 2001). The procedure, in short, is as follows: 1) the region is divided into a predefined number of evenly spaced grid points or nodes; 2) all events larger than the minimum magnitude of completeness, which lie within a fixed radius from the node, are selected as representative of the seismicity around each node; 3) b- values and other parameters are calculated for each one of the node sets, 4) results are color-coded in order to display their spatial distribution. During the analysis, individual b-values at different nodes can be inspected interactively and anomalies tested by direct comparison with adjacent volumes. The maximum likelihood approach (Aki, 1965) was employed for the calculation of b-values. However, we also produced maps using the weighted least squares method (Shi and Bolt, 1982) to make sure that results did not depend on the choice of method to calculate b. In the case of the Mexican data set, the nodes of the grids were separated by 5 km, and the constant radius within which a and b were calculated was r =40 km. The density of data does not support smaller sampling volumes. Radii of 30 and 50 km were also used, to verify that the results did not depend on the exact size of the radius selected. Since our hypothesis assumes that the TL in asperities is the critical parameter, we should map T L with dense grids in volumes with radii equal to the dimensions of the asperities. In the case of the Parkfield asperity, we determined the optimal radius as that which yielded the shortest TL estimate in the asperity volume, and then mapped T L for the 150 km segment of the San Andreas fault near Parkfield using that value (r =4.5 km). Along the Pacific coast of Mexico, we don t know the size of the asperities, and they may also vary along the plate boundary. Thus, we have to expect that the choice of r may not equal the existing asperity dimensions along the entire plate margin. In this case our results will possibly be degraded, but not rendered useless. If r were smaller than the dimensions of the existing asperities, then our method would faithfully map the extent of the existing anomalies. If r is larger than the existing asperities (probably our case), then the samples will mix data from within an asperity with data from outside it, thus reducing the amplitude of the b- and T L-anomalies. Therefore, we use the smallest r, which samples enough earthquakes to allow a statistically meaningful estimate of b, and which, at the same time, yields results for most of the plate boundary. The main shocks in the study area are mostly of the M7.5±0.5 class, with ruptures ranging from about 100 to 200 km length. The events considered are all interplate events. The size of asperities and their relationship to the size of the main shocks is poorly known. For Californian examples, we found the dimensions of asperities tended to be about 1/4 to 1/3 the size of the main ruptures (Wyss et al., 2000). From a preliminary survey of published asperity dimensions of subduction ruptures, we estimate the ratio may be approximately the same. Therefore, we expect that asperities along the Mexican subduction zone may have radii of approximately 25 ± 15 km. Thus, we cannot expect to resolve the smaller asperities, those likely to be associated with M7 ruptures, but we can expect to at least resolve the asperities associated with larger earthquakes. In an ideal setup of the experiment, there would be no main shocks in the data set, as in the study of Southern California (Wyss et al., 2000), because the presence of main- and aftershocks could locally alter the b-value. In this study we removed the main- and aftershocks as follows. We declustered the catalog, using 4

5 Reasenberg s (1985) algorithm with the parameters suggested in the original paper, and, in addition, we removed all the main shocks (equivalent cluster events) with M>6.7. Thus, the largest earthquake remaining in the catalog was M=6.6. We believe that in this way the locations of recent main shocks will not be highlighted by anomalous b-values due to these main shocks themselves. If these locations are highlighted, the signal must stem from the background seismicity alone. In the recent attempts to map asperities (Wiemer and Wyss, 1997; Wyss et al., 2000), as in this paper, the critical parameter which is evaluated through the b-value is the mean magnitude, since M is proportional to the mean crack length l activated in a rupture. What we are discovering is that M varies strongly along fault zones and that it is significantly larger in asperity segments and significantly lower in creeping segments, than in other parts of faults. Thus, we propose that the conditions of rupture are different in segments with different M, most likely with high and low stresses in asperities and creeping segments, respectively. To measure b-values is equivalent to measuring M because these parameters are inversely proportional (e.g. Aki, 1965) ( M ) b = 2.3/ M, (4) We express our results in b-values, although we are interested in M and the physics that changes it. This is because b-values can be compared directly to those from other areas, whereas the specific value of M depends on Mmin. By calculating the b-values using the maximum likelihood method (equation 4), our results are independent of fitting a straight line to the FMD. In a second step of the analysis, we use the information contained in the a- value of equation (1), in addition to the b-value, to map asperities. We do this because it helps to separate the anomalous fault segments from the normal ones more clearly. Also, it is common practice to calculate the recurrence time from a and b using equation (2). We accept the assumption that this is a valid approach for some tectonic areas, but do not wish to defend its general applicability. Whether or not the calculated recurrence times are coming close to estimating the observed historic ones is the second step in our investigation. The point of prime importance is that we propose that locally larger mean magnitudes (expressed by low b-values), coupled with local high seismicity (a-value) may help define asperities along faults. Thus, for our primary hypothesis of mapping asperities, it does not matter whether or not the FMD can be reliably extended to large magnitudes. However, if our calculations of local recurrence times agree with the historically observed ones, we will take this as an indication that the assumption was justified and that local recurrence times are more accurate than bulk recurrence times. min MAGNITUDE SCALE The b-value is widely observed to equal 1 (e.g. Frohlich and Davis, 1993) and Kagan (1999) argues for the universality of b =1. However, the b-value depends on the definition of the magnitude scale. In Southern California, the location of 5

6 the original definition of the magnitude scale by Gutenberg and Richter (1944), b=0.9 on average. For example, in the seismograph network in the Mudurnu Valley along the North Anatolian fault zone on average b=2.5 (Westerhaus et al., 2001). Because there is no indication that this region is tectonically unlike any other (on the contrary it is similar to the San Andreas system), these authors interpreted this observation as due to a compressed magnitude scale. In addition, there is clear evidence that magnitude scales change sometimes when new instrumentation or analysis procedures are introduced. Examples of this phenomenon have been documented by Zuñiga and Wyss (1995) and Zuñiga and Wiemer (1999). Thus, magnitude scales are not only not identical to the original one defined in California, but they also change with time. In many seismograph networks, local to world-wide, operators have struggled to design their procedure of estimating magnitude in such a way that the magnitudes they report correspond as closely as possible to the original magnitude scale. This is not an easy task, because local attenuation properties are different, station separations are different, and seismographs are not of the original type. So it is often hard to know how close a given magnitude scale is to the original one. Therefore, we believe that the absolute value of b depends on the magnitude scale used, but the estimation of TL for a certain Mmax measured on that scale can still be attained regardless of the meaning of the b-slope. In our paper, one of the two hypotheses to be tested is not affected by this problem, the other is. Mapping asperities by minima in TL depends only on differences in local b-values, not on their absolute level. However, the question of whether or not the estimate of TL comes close to TH, depends critically on the nature of the magnitude scale. The SSN routinely reports M d (magnitudes based on duration) for most of the events in the catalog (only the largest are assigned a magnitude value derived from amplitude data). This magnitude was calibrated to match mb as determined from the US Geological Survey, for the range 4.0 mb,d 6.0 (Zuñiga, et al. 2000). However, we employed a conversion into MS for the reasons stated below. We used the method given in Zuñiga and Wyss (1995) to find the relation between Md from SSN and MS reported by the USGS. The method rests on finding the relation which would result in a FMD for converted M d values which best fits the FMD obtained from MS. It has the advantage that one can use all data available and not only earthquakes which have estimates for both magnitudes. Another advantage is that it does not depend on the reliable magnitude overlap range for both scales as is the case for a simple linear regression. As provided by the method, the relation between both magnitudes solely depend on the a and b values of both original FMD. The resulting equation for conversion is: M s = 1.7 M d 3.38 (5) which is basically the same relation found for converting m b from PDE to M S for the Mexican subduction events. 6

7 If duration magnitudes are used, b=1.5, on average. However, if we use the converted MS values, b = Following the procedure outlined in Wiemer and Wyss (2000) we also obtained the minimum magnitude of completeness for the corrected MS magnitudes giving a value of 4.3. We concluded that in our case the use of MS is best, because for this scale b 0.9, a value found in California and in other areas, and because we wish to estimate TL for main shocks with magnitudes measured by MS. MAPPING b- VALUES AND LOCAL RECURRENCE TIME The b-value and TL maps, resulting from the procedure outlined above for the Pacific coast of Mexico, are shown in Figs. 2a and 2b. One can see that, for most of the area mapped, b=1, but locally the values range from 0.5 to 1.5.TL ranges from 15 years to larger than 100 years. The distribution of b-and T L- values can be seen in the histograms of Fig. 3. Clearly, a strong heterogeneity of b-values and T L exists along the Pacific plate boundary of Mexico. This stands against the null hypothesis of b = constant. In order to help identify anomalous segments of faults by b-values, we estimate the significance level of the difference between two b-value distributions by the test of Utsu (1992): where da P = exp( 2 2) (6) n 2( ) ln 2 ln 2 b 1 n ln 1 b da = n + n (n + n ) + n ( + n ) + n ( 2 b + n 2 ) 2 2 b 1 This test assumes that two samples are selected at random. The greater the difference between the two b-values (mean magnitudes) and the larger the numbers of events in the two samples, the greater the confidence that the two samples are indeed drawn from different populations. Instead of estimating the uncertainty in each of the two estimates of b, which is not of direct interest in this study, the test estimates the significance level of the difference between samples, the observation we are interested in. To verify that the algorithm estimates b correctly, and that Fig. 2a is a meaningful presentation of facts, we verified the FMDs at numerous places using the interactive features of ZMAP. A few examples of contrasting anomalously high and low b-values are shown in Fig. 4. In these figures, we also give the probability, estimated by Utsu s (1992) test, that the two samples in each frame come from the same population. Furthermore, in order to objectively identify anomalously high or low b-values, we carried out the following test. Magnitudes were randomly permuted, preserving hypocenter locations, and a second b-value map was obtained. The difference between both sets was calculated together with the probability, based on equation (6), that this difference was significant. Fig. 5 shows the differential b-values found and those which stand out as having the largest significance of being different. After some additional random 7

8 trials, it was apparent that the main features in Fig. 5 remained basically unaltered. It can be observed that the main features of the original b value distribution of Fig. 2 are still seen in the differential map. From these results we concluded that some areas have b-values which significantly stand out from their neighbors. In Fig. 5b, we want to draw particular attention to those regions having probabilities higher than 98% significance. Looking at the values shown in Fig. 5b we can see that regions, which are significantly different, include both positive (red) and negative (blue) differences (i.e. high and low b-values). On the basis of this test, we are confident that the heterogeneity in b is highly significant. The dimensions of the regions of coherent b-values range from about 30 km in Oaxaca, to 150 km in Guerrero (Fig. 2a). The lower limit of this resolution is dictated by the fact that we are forced to base the analysis on sampling volumes with 80 km diameter. Nevertheless, strong regional differences of b- values are mapped as observed in other regions (Ogata and Katsura, 1993; Wiemer and Wyss, 1997; Wiemer and Katsumata, 1999; Wyss et al., 2000). Considering the results shown in Figures 2 and 5, regions of significantly anomalously high b-values are: (1) the Northwestern coast of Guerrero, near longitude and offshore at the megathrust, near longitude 99.5 ; (2) Two subsections along the coast of Oaxaca near 95.5 and 97.5 longitude; (3) Near the isthmus of Tehuantepec; (4) Moderate high b-values exist off the coast of southern Chiapas, at the megathrust. Anomalously low b-values are seen (1) along the deeper part of the subducted slab in western Guerrero (especially between longitudes 100 and 101 ); (2) near the boundary of Guerrero with Oaxaca, west of the Ometepec segment; (3) off the Oaxacan coast (on the megathrust, near 97 longitude); and (4) off the coast of southern Chiapas, toward the deeper end of the subducted slab. The map of local recurrence time (Fig. 2b) was calculated by eq. (2) for M max=7.2, with r=40 km and using the b-values of Fig. 2a, together with the corresponding a-values, which can be gauged from Fig. 1a. This map shows similar patterns as the b-value map, but it sharpens the contrasts. (1) The shortest TL are estimated as about 20 years for the coast of Guerrero between longitude and 101.5, and (2) off the coast of southern Chiapas. (3) The location at longitude 98.5 (near the boundary of Guerrero with Oaxaca, the Ometepec segment) follows with estimates of about 30 years as the next shortest TL. (4) Along the coast of Guerrero, between 99 and longitude, TL is estimated as about 40 years. (5) In the segments off the Oaxacan coast near 95.7 and 97.7 longitude, TL ranges from 40 to 60 years. Long local recurrence times are observed in the following locations. (1) Off shore from the isthmus of Tehuantepec, (2) on the Pacific plate off the coast of Guerrero, (3) on land along the coast of most of Oaxaca, (4) along the northernmost 40 km of the Guerrero coast. The probability density map (Fig. 2c) was calculated by eq. (3) for M max=7.2. The patterns on this map mirror closely those of the TL map (Fig. 2b), because PL is essentially the inverse of T L, except that it is normalized for the sampling area used. Again, two spots stand out with the highest probability for M7.2 earthquakes. These are the Guerrero coast near longitude and the plate 8

9 boundary off the southern coast of Chiapas, near longitude 93. The next most likely spot for M7.2 events is located near the boundary of Guerrero and Oaxaca and to the west of it. DISCUSSION The heterogeneity of the b-value distribution found in the San Andreas fault system (Wiemer and Wyss, 1997; Wyss et al. 2000), beneath volcanoes (Wiemer and McNutt, 1997; Wyss et al., 1997; Power et al., 1998; Wiemer et al., 1998) and in subducting slabs (Wiemer and Benoit, 1996) is confirmed by the data for the plate boundary along the Pacific coast of Mexico. According to our study, b-values range from 0.5 to more than 1.5 (Figs 2a, 3a). Although the bulk value of the whole data set, as well as the peak in the distribution of the local b- value (Fig. 3a), average b=0.85, approximately 50% of the b-values are significantly different from the average (Fig. 3a). The errors in b-values are ± 0.06 in the average, and errors larger than 0.1 are found only for an area seaward of the trench. Thus, errors can not cause the heterogeneity found, nor should they affect significantly the T L results. The physical cause of these perturbations of the b-values is most likely a difference in stress level. Laboratory experiments (Scholz, 1968), correlation with pore pressure (Wyss, 1973) and measurements in underground mines (Urbancic et al., 1992) all showed that in high stress environment b-values are lower than average. That is, at high ambient stress levels, the probability for any rupture that initiates to grow into a relatively large earthquake is increased. Therefore, we interpret crustal volumes with elevated average magnitude (low b-value) as locations of increased stress level. This interpretation fits the model of asperities, which are defined as the strongest locations along faults, where stress accumulates. Alternatively, variations in heterogeneity of the medium can also perturb the average b-value (Mogi. 1962). However, that would require strong heterogeneity, for example, along the creeping segment of the San Andreas fault and low heterogeneity in the Parkfield asperity, an interpretation which does not seem reasonable (Wiemer and Wyss, 1997). Therefore, we interpret volumes with significantly low b-value and anomalously short local recurrence times along the Mexican Pacific coast as volumes with relatively high stress regimes, that is, as asperities. The resolution afforded by the data is not entirely satisfactory. The minimum size of volumes we can analyze, and yet cover most of the Pacific coast of Mexico, is dictated as r=40 km by the data density. This dimension may approximately equal the dimensions of asperities of M8 earthquakes, the largest main shocks in this area. For these events our mapping has an adequate resolution. Asperities rupturing in M7.2 main shocks are likely smaller; perhaps they have radii about half the radii we used to map b-values. Therefore, we must expect that in segments of the plate boundary we mapped that are dominated by M7.2 shocks the asperities may be poorly resolved, and we may be mostly looking a bulk b-values, rather than local b-values. The sensitivity of the results to the free parameters is low. We varied the radii of sampling volumes between 40 and 60 km, and the minimum number of events per volume between 30 and 50 which lead to the same patterns of low and 9

10 high b-values (i.e. short and long T L) as previously observed. The absolute value of TL, of course, depends on the volume size. Based on our hypothesis the correct volume size is equal to the volume of the largest asperity in each main shock. Since we analyze a 1000 km long plate boundary with somewhat varying segmentation length, we violate this requirement for many segments. Therefore, the absolute values of T L we present should be taken as approximations only. Our radii of sampling are larger than the hypocenter errors (± 10 km), so we might miss some events that should be inside an anomalous zone, but currently fall outside, and a few in the opposite sense. This makes no difference, unless the location error is M-dependent. The M-dependence in our case would have to generate errors larger than 40 km (radius-=40km) in order to create the anomalies we see. This we do not consider plausible. The linear extrapolation of the frequency-magnitude relation from small and medium size events to the largest magnitudes is a debated issue. Some studies have pointed out that the curve may flatten out at larger magnitudes (characteristic earthquake model) while others have shown a limiting size. Wiemer and Wyss (1997) advanced the hypothesis that the observation of a characteristic event type distribution may be due to incorrectly including in the earthquake distribution relation parts of the fault that do not participate actively in the rupture process. Thus, by employing the mapping procedure discussed here and in Wiemer and Wyss (1977) we avoid uncertainties produced by characteristic event type distributions. Even though large uncertainties in the mean recurrence time are still bound to be obtained from the extrapolation, our results are valid because regions with a minimum TL show good correlation with locations of known ruptures and reported recurrence intervals for subduction events. The magnitude scale one uses for mapping contrasts in b-value, or minima in local recurrence time, does not matter. The same volumes are anomalous using M d or M s scales. However, it matters what magnitude scale is used, if one wants to compare estimates of recurrence times from other studies. The Md scale (with b=1.5 on average) is not suitable for this purpose, but the Ms scale (with b = 0.85 on average) is, because we wish to estimate the recurrence time for shocks commonly measured on the Ms scale. The differences in local recurrence times, as imperfectly mapped by samples from volumes with r = 40 km, are enormous along the Pacific coast of Mexico (Fig. 2b). The differences between volumes is so large that we must use a logarithmic scale to present the histogram of the T L distribution (Fig. 3b). We propose that these differences, together with the differences of the b-values (Fig. 2a), show that the crustal properties vary strongly. Since minima in T L correlate with minima in b, we hypothesize that minima in TL are locations of high stress, i.e. asperities. Based on this hypothesis, we propose the distribution of asperities along the Pacific coast of Mexico as shown in Table 1. It may be a little bold to propose the specific list of major asperities as in Table 1. However, this is not done as an assertion. We propose this table as part of the test of our hypothesis. Future earthquakes may provide the test. If our hypothesis is correct, then major moment release should emanate from the volumes we defined as asperities in Table 1, and relatively minor moment release should emanate from volumes identified in Table 2. 10

11 Locations of anomalously high b-values are taken as fault segments not capable of generating very large earthquakes. We assume that these segments slip along relatively passively when a neighboring asperity ruptures. Thus, such volumes could form part of an aftershock area in a large earthquake, provided that a neighboring asperity has been mainly responsible for the rupture. Locations which produced significantly fewer medium to larger size earthquakes during the time covered by the catalog (anomalously high b-values, and very long T L) are given in Table 2. A special case is that of the coast of central Oaxaca, since in this area the b-values are mixed on a scale finer than we can resolve. Therefore, the recurrence times we calculate are not local enough. This observation is consistent with the fact that main shocks in this area are M7 rather than M8. In Guerrero, where M8 earthquakes have occurred historically, our method suggests high probabilities for M7.2 shocks. The fact that asperities seem to be smaller in Oaxaca than in Guerrero is also consistent with the observation that M max tends to be smaller in this area. A possible difference in tectonic coupling between the plates is suggested by the difference in asperity distribution in Guerrero and Oaxaca. In Guerrero the b-values are low (T L short) on the deeper part of the megathrust (below the land mass), whereas in Oaxaca we observe relatively high b-values (long TL) below the land mass, with small asperities on the upper part of the megathrust, offshore. We speculate that this may indicate a difference in the style of coupling between these two plate segments. It seems that this observation correlates with the fact that the size of the Mmax ruptures in Guerrero are somewhat larger than those in Oaxaca. We suggest that the deeper position and the larger size of asperities in Guerrero lead to stronger coupling of the plates than in Oaxaca. Others have also suggested that the coupling in the Guerrero segment is stronger than further west (e.g. Kostoglodov and Ponce, 1994; Singh and Mortera, 1991). It seems that the agreement of our interpretation with other reasoning supports our ideas that minima in T L (and minima in b-values) map locations of relative fault plane strength, i.e. asperities. A comparison of local recurrence times with historical recurrence times for the different regions, yields a very good correlation (Table 1). Singh et al. (1981) had proposed values of 34 to 56 years for the Oaxaca and Guerrero regions based on the registered occurrences of main shocks up to that time. The recent event of Copala of September 14, 1995 (Courboulex et al., 1997), which took place near the western boundary of the Ometepec segment, occurred in a location which had not experienced a large event since Previous large mainshocks had taken place there in 1909 and The TL for this area varies between 13 and 47 years. The region of western Guerrero is a place where events with M > 7.0 have recently occurred in 1943, 1979 and 1985 also in apparent agreement with our estimates of TL. The Seismic Hazard off Chiapas. A case which attracted our attention was that of the area off the coast of Chiapas, because it was there we found one of the shortest T L (about 20 years), yet the region has seldom been discussed in the literature. We reviewed the recent occurrence of large events in the area between longitudes 92 and 94, and 11

12 latitudes 14 to 15 and found two events which took place in April 29, 1970 (M s = 7.1) and in September 10, 1993 (Ms = 7.3) with nearly identical teleseismic aftershock areas (Fig. 1b). Searching for other past events listed in catalogs or local studies, we found that the same region experienced repeated ruptures on January 14, 1903 (M s= 7.7, Nishenko and Singh, 1987), December 10, 1925 (M s = 7.0, Miyamura, 1976) and also on June 28, 1944 (Ms = 7.1, Abe, 1984). Thus, an average recurrence time of 22.5 ± 3 years is calculated from four inter-event times. The regularity with which this pattern has occurred (Fig. 6), the apparent overlap of ruptures off the coast of Chiapas and the average TH is in remarkable agreement with our results for T L, which is based on the small and medium size event distribution. The event of 1903 is a case in point. It was relocated after it was noticed that the original location given by Gutenberg (1956) fell seaward of the trench and it did not match the macroseismic observations. Looking at the recurrence pattern, we can now state that Nishenko and Singh s (1987) epicenter (15 N 93 W) is very likely quite close to the precise location of the event. With these observations, we conclude that the area off the coast of Chiapas has a high potential for the occurrence of a large earthquake, although there is a high probability that it may not be expected to occur for quite some time, most likely not before we estimate this time because the last main shock occurred in 1993 and we take into account the standard deviation of the mean observed recurrence time. CONCLUSIONS We have shown that mapping the b- value, together with estimates of local recurrence time and local probability density, extracted from a and b values of contiguous regions along the Pacific coast of Mexico, provide an important clue for the identification of places which may be susceptible to future large ruptures. The analysis we performed, based on the occurrence of M = 7.2 shocks, provides locations which stand out as having the lowest local recurrence times, as well as anomalously low b-values. Among these we find the coast of Guerrero between longitude and 101.5, and off the coast of southern Chiapas which show the shortest T L estimated as about 20 years. To these we may add the location at longitude 98.5 (near the boundary of Guerrero with Oaxaca the Ometepec segment) which follows with estimates of about 30 years as the next shortest T L. Along the coast of Guerrero, between 99 and longitude, TL is estimated as about 40 years. In the segments off the Oaxacan coast near 95.7 and 97.7 longitude, TL ranges from 40 to 60 years. These volumes we define as asperities. The agreement between observed recurrence times with our results for TL supports the hypothesis that the b-value inside asperities is a better estimate of recurrence than that given by the bulk b-value of the region. The region off the coast of Chiapas is estimated as having a large potential for a future large (M 7) event with the most probable time for occurrence being after

13 ACKNOWLEDGMENTS The authors wish to thank comments by Carl Kisslinger, Masijiro Imoto, Cliff Frohlich and an anonymous referee which greatly improved the presentation of our ideas and observations. We also thank M. Guzmán-Speziale for his help in gathering large earthquakes information from Chiapas. This work was started while M. W. visited the Juriquilla campus as a visiting scholar supported by the Mexican Science and Technology Council (CONACYT) under project No. 0263PT, and UNAM s Academic Exchange Program (DGIA). The study was also supported in part by the Wadati foundation at the Geophysical Institute of the University of Alaska, Fairbanks. REFERENCES Abe, K., Complements to magnitudes of large shallow earthquakes from 1904 to 1980, Phys. Earth planet. Inter., 34, Aki, K., Maximum likelihood estimate of b in the formula log N = a bm and its confidence limits, Bull. Earthquake Res. Inst. Univ. Tokyo, 43, Amelung, F., and G. King, Earthquake scaling laws for creeping and noncreeping faults, Geophys. Res. Lett., 24, Courboulex, F., M.A. Santoyo, J.F. Pacheco and S.K. Singh, The 14 September 1995 (M = 7.3) Copala, Mexico, Earthquake: A source study using Teleseismic, Regional and Local Data,, Bull. seism. Soc. Am., 87, Frohlich, C., and S. Davis, Teleseismic b-values: Or, Much Ado about 1.0, J. geophys. Res., 98, Gutenberg, B. and C.F. Richter, Frequency of earthquakes in California, Bull. seism. Soc. Am., 34, Gutenberg, B., Great earthquakes , Trans. Am. Geophys. Union, 37, Kagan, Y.Y., Universality of the seismic moment-requency relation, Pure Appl. Geophys., 155, Kostoglodov, V. and L. Ponce, Relationship between subduction and seismicity in the Mexican part of the Middle America trench, J. geophys. Res., 99, Kostoglodov, V. and J. F. Pacheco, Cien Años de Sismicidad en México, Map, Instituto de Geofísica, UNAM, Mexico. Miyamura, S., Provisional magnitudes of middle American earhquakes not listed in the magnitude catalogue of Gutenberg-Richter, Bull. Int. Inst. Seismol. Earthquake Eng. Tokyo Univ., 14, Mogi, K., Magnitude-Frequency Relation for Elastic Shocks Accompanying Fractures of Various Materials and some Related Problems in Earthquakes, Bull. Earthq. Res. Inst., Univ. of Tokyo, 40, Nishenko, S.P. and S.K. Singh, Relocation of the Great Mexican earthquake of 14 January 1903, Bull. seism. Soc. Am., 77, Ogata, Y., and K. Katsura, Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues, Geophys. J. Int., 113,

14 Power, J.A., M. Wyss, and J.L. Latchman, Spatial variations in frequencymagnitude distribution of earthquakes at Soufriere Hills volcano, Montserrat, West Indies, Geophys. Res. Lett., 25, Reasenberg, P.A., Second-order moment of Central California Seismicity, J. geophys. Res., 90, Scholz, C.H., The Frequency-Magnitude Relation of Microfracturing in Rock and its Relation to Earthquakes, Bull. seism. Soc. Am., 58, Shi, Y. and B.A. Bolt, The standard error of the magnitude-frequency b- value, Bull. seism. Soc. Am., 72, Singh, S.K., L. Astiz and J. Havskov, Seismic gaps and recurrence periods of large earthquakes along the Mexican subduction zone: A reexamination, Bull. seism. Soc. Am., 71, Singh, S.K. and F. Mortera, Source time functions of large Mexican subduction earthquakes, morphology of the Benioff zone, age of the plate, and their tectonic implications, J. geophys. Res., 96, Urbancic, T.I., C.I. Trifu, J.M. Long, and R.P. Young, Space-time correlations of b-values with stress release, Pure Appl. Geophys., 139, Utsu, T., On seismicity, in Report of the Joint Research Institute for Statistical Mathematics, pp , Institute for Statistical Mathematics Tokyo. Westerhaus, M., Wyss, M., Yilmaz, R., Zschau, J., Correlating variations of b-values and crustal deformations during the 1990s may have pinpointed the rupture initiation of the Mw=7.4 Izmit earthquake of Aug. 17, 1999, Geophys. J. Int., in press. Wiemer, S., Analysis of seismicity: New techniques and case studies, PhD thesis, University of Alaska, Fairbanks, Alaska. Wiemer, S., and J. Benoit, Mapping the b-value anomaly at 100 km depth in the Alaska and New Zealand subduction zones, Geophys. Res. Lett., 23, Wiemer, S., and K. Katsumata, Spatial variability of seismicity parameters in aftershock zones, J. geophys. Res., 103, Wiemer, S., and S. McNutt, Variations in frequency-magnitude distribution with depth in two volcanic areas: Mount St. Helens, Washington, and Mt. Spurr, Alaska, Geophys. Res. Lett., 24, Wiemer, S., S.R. McNutt, and M. Wyss, Temporal and three-dimensional spatial analysis of the frequency-magnitude distribution near Long Valley caldera, California, Geophys. J. Int., 134, Wiemer, S., and M. Wyss, Mapping the frequency-magnitude distribution in asperities: An improved technique to calculate recurrence times?, J. Geophys. Res., 102, Wiemer, S., and M. Wyss, Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western US and Japan, Bull. Seism. Soc. Am., 90, Wiemer, S., A software package to analyze seismicity: ZMAP. Seismological Research Letters, 72, 3, Wyss, M., Towards a physical understanding of the earthquake frequency distribution, Geophys. J. R. Astron. Soc., 31,

15 Wyss, M., K. Shimazaki, and S. Wiemer, Mapping active magma chambers by b-value beneath the off-ito volcano, Japan, J. geophys. Res., 102, Wyss, M., D. Schorlemmer, and S. Wiemer, Mapping asperities by minima of local recurrence time: The San Jacinto-Elsinore fault zones, J. geophys. Res., 105, Zuñiga, F.R. and M. Wyss, Inadvertent changes in magnitude reported in earthquake catalogs: Influence on b-value estimates, Bull. seism. Soc. Am., 85, Zuñiga, F.R. and S. Wiemer, Seismicity patterns: Are they always related to natural causes?, Pure Appl. Geophys., 155, Zuñiga, F.R., M. Reyes and C. Valdés, A general overview of the catalog of recent seismicity compiled by the Mexican Seismological Survey, Geofís. Intern., 39,

16 FIGURE CAPTIONS Figure 1: (a) Epicenter map of the Mexican Pacific coast for earthquakes with M 3.5 reported by SSN between 1988 and 1998, the Mid-America Trench is shown as a dashed line. (b) Map of the approximate aftershock areas of latest main shocks with M 6.9 along the boundary between the Cocos and American plates in Mexico. Solid outlines indicate aftershock areas estimated from local data, dashed outlines are areas inferred from regional or teleseismic aftershock locations. The years of the earthquakes are given in or near the rupture areas. GG stands for Guerrero Gap segment, MAT - Mid-America Trench (Modified after Kostoglodov and Pacheco, 1999). Figure 2: (a) Map of local b-values along the Pacific coast of Mexico. The node spacing of the grid was 5 km, the radius for selecting earthquakes was 40 km. Grey circles indicate the location from where example FMD shown in Figure 4 were extracted. (b) Map of local recurrence times, T L estimated probabilistically for an M7.2 main shock, using the b-values from Figure 2a and the corresponding a-values (sampling radius = 40 km). (c) Map of local probability density, PL, for a magnitude M7.2 main shock. Figure 3: Histograms of (a) b-values observed at the nodes of the grid used to map b in Figure 2a, (b) local recurrence times, TL, estimated probabilistically for an M =7.2 main shock with radii of 40 km at the nodes in Figure 2b, and (c) local probability density, PL as estimated in Figure 2c. Figure 4: Examples of contrasting frequency-magnitude distributions. The probability P that the two samples are selected from the same distribution by chance is given in each frame. They compare samples from volumes interpreted as asperities (filled circles) to samples from nearby volumes with high b-values (filled squares). The locations of the volumes are shown in Figure 2, the regions after Figure 1. Figure 5. a) Difference between observed b-values and synthetic b-values generated by a random permutation of magnitudes. Epicenter locations are kept unchanged. b) Same as in frame (a) but showing only those values with a 98% or larger significance of difference based on Utsu s test. Figure 6. Magnitude vs. time histogram for large (M 7.0) events off the coast of Chiapas, which have taken place during this century. 16

17 TABLES Table 1: Proposed Asperities Along the Pacific Coast of Mexico No Location Longitudes T L (M7.2, r40) [Years] T H (M 7.0) 1 West Guerrero ± 21.2* 2 Off Southern Chiapas ± Ometepec ± 13.4 # 4 Acapulco-San Marcos ± 7.1** 5 Guerrero Gap > 90 6 Off Central Oaxaca ## 7 Off western Oaxaca ϒ Events regarded as rupturing the same segment of the Mexican subduction zone: * 1943/06/22,1979/03/14,1985/09/ /01/14,1925/12/10,1944/06/28,1970/04/29,1993/09/10 # 1937/12/23,1950/12/14,1982/06/07 **1909/07/30,1957/07/28,1995/09/14 last event 1911/12/16 ## 1928/03/22,1965/08/23 ϒ 1968/08/02, 1996/02/25 Table 2: Proposed Volumes Incapable of Generating Large to Great Earthquakes Along the Pacific Coast of Mexico No Location Coordinates 1 Off Guerrero, outer rise Off Isthmus of Tehuantepec Below land Oaxaca 96.7 &

18 18

19 19

20 20

21 21

22 22

23 23