Bulletin of the Seismological Society of America, Vol. 77, No. 6, pp , December 1987

Transcription

1 Bulletin of the Seismological Society of America, Vol. 77, No. 6, pp , December 1987 CONDITIONAL PROBABILITIES FOR THE RECURRENCE OF LARGE AND GREAT INTERPLATE EARTHQUAKES ALONG THE MEXICAN SUBDUCTION ZONE BY S. P. NISHENKO AND S. K. SINGH ABSTRACT Time-dependent conditional probabilities for the recurrence of large and great interplate earthquakes along the Mexican subduction zone are presented for time intervals of 5, 10, and 20 yr duration (i.e., , , and ). At present, the central Oaxaca (97.3 to 97.7 W), Ometepec-San Marcos (98.2 to 99.5 W), and central Guerrero (100 to 101 W) segments stand out as having the highest probability for the recurrence of large and great earthquakes in the near future. Segmentation of the margin is delineated by the rupture zones of the most recent earthquakes occurring in each area. For segments of the Mexican margin with one or more known recurrence intervals, probability estimates are based on the observed average recurrence time for each segment and the Iognormal probability distribution function. Use of a generic distribution function (Nishenko and Buland, 1987) allows a more stable estimate of average recurrence times than are available from a few observations. A long-term prediction time window is also defined, based on the 90 per cent confidence interval for our estimates of the recurrence time. Use of a predetermined confidence interval conveys valuable additional information as to the precision and information content of the forecast. For those segments of the margin with only one prior event, and hence, no historically observed recurrence times, repeat times are estimated by extrapolating the observed recurrence time behavior in Oaxaca, subject to the assumptions that recurrence time scales only as a function of the ratio of seismic displacement and convergence rate and that all events are characterized as simple sources (i.e., involve the rupture of a single asperity). INTRODUCTION Numerous authors (Kelleher et al., 1973; Rikitake, 1976; McCann et al., 1979; Singh et al., 1981; McNally, 1981) have recognized that the relatively short recurrence times for large and great earthquakes along the Mexican subduction zone make this region an attractive natural laboratory for earthquake forecasting and prediction research. The short observed recurrence times along portions of this margin, 30 to 60 yr, compared to the 100- to 200-yr intervals observed along many other plate boundaries, allow for the evaluation of earthquake forecasts and predictions in a relatively short amount of time. This rapid "turn-around" time for scientific evaluations in turn can lead to increased understanding of processes occurring along other plate boundaries and to the development of disaster mitigation programs for specific areas within socially useful time frames. The three necessary parameters for a successful earthquake prediction or forecast along any simple plate boundary are the expected location, size, and time of occurrence of a future event. The seismic gap hypothesis, that historically active segments of transform or convergent plate boundaries that have not ruptured in a large or great earthquake during the past few decades are the most likely sites of large or great shocks in the near future, has been successful in forecasting the first two parameters (location and size) for many earthquakes that have occurred along 21)95

2 2096 S. P. NISHENK0 AND S. K. SINGH the simple plate boundaries of the circum-pacific during the last two decades (see reviews by McCann et al., 1979 and Nishenko and McCann, 1981). It is the last parameter, the expected time of occurrence, however, that has been the most elusive and that has the most scientific and social impact. During the early 1980's, the emphasis in earthquake prediction has shifted from deterministic estimates of the expected time of occurrence to probabilistic statements of earthquake hazards as a means of expressing the likelihood for future events (see Sykes and Nishenko, 1984; Nishenko, 1985). The historical and instrumental records of large and great earthquakes form the primary data base for evaluating seismic hazards and formulating probabilistic earthquake forecasts and predictions. Statistical analysis of characteristic earthquake interoccurrence times, either for specific gaps or larger segments of plate boundaries, allows for a quantitative description of the likelihood of an event as a function of the time elapsed since a previous gap-filling event. The documentation of a relatively stable distribution of recurrence times for characteristic earthquakes along many fault segments provides the primary motivation for the development of time-dependent earthquake hazard models. Characteristic events are defined as those earthquakes which repeatedly rupture the same fault segment and whose source dimensions define that fault segment. Such an event is the largest earthquake to occur in that fault segment and dominates the strain release in that fault segment. Time-dependent hazard models, which take into account both the recurrence time and the amount of time elapsed since a previous shock, are compatible with the seismic gap hypothesis which suggests that the potential for a future shock is small immediately following a characteristic earthquake and increases as a function of time since the previous event. This family of models are distinct from time-independent models (i.e., Poisson distributions) which only use information about recurrence intervals and do not take into account the amount of time elapsed since a prior event. The use of probability density functions or distributions,/(t), and their associated measures of variability (the standard deviation, ~, and the coefficient of variation, a/mean) define the degree of temporal resolution possible using these types of data. Once a distribution function is defined, earthquake recurrence time estimates can be presented in terms of a conditional probability, which describes the likelihood of failure within a given time interval, t + dr, provided the event has not occurred prior to time t. In this study, the time interval, dr, chosen for our forecast ranges from 5 to 20 yr. These long-term predictions or forecasts provide an estimate of the background probability level against which intermediate and short-term phenomena, such as precursory seismic quiescence, can be evaluated. Additionally, seismic hazard estimates for the next 5, 10, and 20 yr provide time frames for the development and implementation of hazard mitigation programs. These varying time intervals provide a means for distinguishing areas of high, short-term seismic hazard, which require immediate attention, from areas where the hazard is presently low but is expected to significantly increase within the next few decades. The Mexican subduction zone extends along western Mexico between 92 and 106 W, and defines the zone of interaction between the Cocos, Rivera, and North American plates. Earthquake focal mechanism solutions for shallow earthquakes are indicative of thrusting of the Rivera and Cocos plates beneath the North American plate (Molnar and Sykes, 1969; Chael and Stewart, 1982; LeFevre and McNally, 1985) with about a N30 E direction of convergence at a rate of 2 to 8 cm/ yr (McNally and Minster, 1981). Figure 1 provides an overview of the regional structure and convergence vectors. In general, the majority of strain accumulation along the interface zone is relieved by the occurrence of large and great earthquakes

3 CONDITIONAL PROBABILITIES FOR RECURRENCE OF EARTHQUAKES " N 20' N 18" N 92" W - ~.%!~.~,,~\ ~ /\ ~ \ ~ ~ \ ~NOAM \ \" \ \ ~ \ % ' /~F Mexico City ~ - t f " // ~ "g / x " ~ - -" ), L.-,.'... ', r,f" L " ~ ~ ~ JALISCO 1 MICHOACAN ~1 -. ~ i -!) OAXACA ~ ~! ) GUERRERO ~,% \~ / If Colima! ij Puerto Ansel ~/ ~2 ~ ~ j. ~ ~ ~ r 1 ~ 4 "., /" y N r. 7.7 ~ - ~ 94" W 12 N 108" W 108" W 104 W 102" W 100" W 98 W 98 W ~ O x g o ~ 1988 I~ , i... -''''' OO (4 Events) "... O, = O.. ~? 1872 " ?~1,0 1820? ~--0-~? 1806? ~ I I- '~1 I I I I I I I I I " " FIG. 1. (Top) Location map of Mexican states, cities, and major bathymetric features discussed in the text. Bathymetry from Chase et al. (1970), and contour interval is 1000 m. Solid arrows indicate the direction and relative rates of convergence between the North American (NOAM) and Cocos (COCOS) or Rivera (RIV) plates [convergence vectors after McNally and Minster (1981) and Eissler and McNally {1984)]. (Bottom) Space-time diagram of historic and recent earthquakes along the Mexican subduction zone (from Table 1). Large circles represent events with Ms >= 7.7. Dashed horizontal lines with question marks represent uncertain locations for events prior to Horizontal lines indicate the lateral extent of rupture zones since 1928, based on aftershock studies and are dashed where less well-determined. at fairly regular intervals. The goal of this study is to define those recurrence intervals and use that data to estimate the time of occurrence of future large and great shocks. DATA AND ANALYSIS TECHNIQUES The basic data set used for the recurrence estimates in this study is presented in Table 1 and in the space-time diagram at the bottom of Figure 1. The catalog of

4 2098 S. P. NISHENKO AND S. K. SINGH TABLE 1 CATALOG OF LARGE AND GREAT MEXICAN EARTHQUAKES Region Date* Ms? Mo$ Character Repeat Time T~ Notesl 2. East Oaxaca, (6/5/1897(?)) W 3/22/ S 31(?) 8/23/ S Central Oaxaca, /11/ W 6/17/ S 58 11/29/ S Central Oaxaca, /27/1872(?) W 10/9/ S 56(?) (56) 5. West Oaxaca, /5/ W 11/2/ /4/ S 34 8/2/ S Ometepec, W 12/2/ /15/ (C) 12/23/ S (30-47) (12/14/1950) C (6/7/1982) 6.9, C 7. San Marcos, /4/1820(?) W 4/7/1845(?) 7.9 4/15/ (C) /28/ C (5/11,19/1962) 7.2, , 0.8 S, C 8. C. Guerrero, 100-4/7/1845(?) W# 12/24/ (?) (54) 3/26/ (3/27/1908) /30/ (S) (7/31/1909) /16/ Petatlan, W 2/22/ C 3/14/ C * Dates in parentheses not used in Ta~ determination. Dates with question marks are events with less certain locations. t Ms values revised from Abe and Noguchi (1983), Ms and Singh et al. (1984a). :~ Mo values from: Reichle et al. (1979); Espindola et al. (1981); Chael and Stewart (1982); Wang et al. (1982); Astiz and Kanamori (1984); Singh et al. (1984b); and Singh (1985, unpublished data). M0 values are in units of 1027 dyne-cm. S = simple source-time function from body-wave modeling; C = complex, multiple source-time function [from Chael and Stewart (1982) and Singh et al. (1984b)]. Letters in parentheses are based on visual inspection of seismograms. a = 1897 event possibly located in Tehuantepec, Ms may have been less than 7.4. b = complex rupture history; see text and Nishenko and Singh (1987); Tare based on either or c = Taw based on either or , and d = Gutenburg and Richter location (17 N, 98 W) poorly constrained; more likely location is west of Acapulco; see Singh et al. (1981). e = Gutenburg and Richter give a depth of 80 km, M = 7.8 and mb 7.7; record at Uppsala indicates a shallow shock with Ms 7.8. f = aftershock. # No well-determined recurrence history.

5 CONDITIONAL PROBABILITIES FOR RECURRENCE OF EARTHQUAKES 2099 TABLE 1--Continued CATALOG OF LARGE AND GREAT MEXICAN EARTHQUAKES Region Date* Ms? Mo$ Character Repeat Time T~ Notesl] 10. Michoacan, W Colima, W Jalisco, W# 6/7/ (10/25/1981) /19/ C 74(?) (74) 4/15/ C 1/30/ C /25/1806(?) 7.5 5/31/1818(?) 7.7 1/20/ (?) 8/16/ /3/ C (?) ( ) 6/18/ C large and great earthquakes along the Mexican subduction zone primarily comes from Singh et al. (1981, 1984a) and is thought to be complete for events of Ms > 7.5 since The grouping of these events into separate subregions or source zones is based on a comparison of rupture zones determined from intensity and isoseismal maps compiled by Figueroa (1970) and Singh (unpublished data, 1985) for older events, and for more recent earthquakes, aftershock locations, and relocations by Kelleher et al. (1973), Tajima and McNally (1983), Singh et al. (1985), Quintanar and Ponce (personal communication, 1985), UNAM Seismology Group (1986), and Nishenko and Singh (1987). In general, the segmentation used in this study is delineated by the rupture zones of the most recent earthquakes occurring in each area. Detailed discussion of individual events and the data used to constrain locations and source zones is deferred to a later section. At this point, it is appropriate to note that while the short recurrence times observed along the Mexican subduction zone make this region an attractive natural laboratory for prediction research, the smaller magnitudes associated with many of these events result in diminished spatial resolution of rupture zones, especially for pre-1950 events. This problem is compounded in the 19th century, even for larger events. Note that in Figure 1, the majority of well-constrained locations for events prior to 1890 tend to be clustered within the states of Oaxaca and eastern Guerrero, between 95 and 100 W. The spatial inhomogeneity in the completeness of the catalog for this earlier time period reflects, in part, variations in population density along the entire coast. In addition, areas with shorter recurrence times tend to have more catalog entries than areas with longer recurrence times. The recurrence time and conditional probability estimates presented here will be the most reliable for the Oaxaca-eastern Guerrero region (95 to 100 W), where the observation time has been the longest and the historic record the most complete. Within the Oaxacaeastern Guerrero region, both the 19th and 20th century data are in reasonably good agreement as to the geographic location of characteristic segments or rupture zones. Hence, while the segmentaton defined in this study is based on the rupture zones of the most recent shocks, the historic record for Oaxaca and eastern Guerrero provides information with which to estimate an average recurrence time for each segment. Elsewhere along the margin, the historic record does not allow for a comparison of a number of repeated ruptures within the same segment, or for the determination of an average recurrence time. While the segmentation in these areas is still based on the location of the most recent events, another method must be

6 2100 S. P. NISHENKO AND S. K. SINGH used to estimate recurrence times. As discussed later in this section, we use the seismic moment of the most recent earthquake, subject to a few simple assumptions, to estimate recurrence times for those areas with an incomplete history. One of the basic problems that confronts the application of a probabilistic approach to a specific fault segment is the relatively small number of data from which the recurrence interval distribution and, hence, the forecast probability can be estimated. In this study, we use the results of Nishenko and Buland (1987), who examined recurrence intervals for characteristic earthquakes along a number of simple plate boundaries using a normalizing function, TITans. Taw is the average recurrence interval observed for a specific fault segment, and T is an individual recurrence interval. Based on a global data set, Nishenko and Buland (1987) found that the lognormal distribution provides a significantly better fit to the recurrence time data than either the Gauss or the Weibull distribution (see Rikitake, 1976; Lindh, 1983; Sykes and Nishenko, 1984; and Nishenko, 1985 for a discussion of these techniques). An additional result of Nishenko and Buland's analysis is that the standard deviation appears to be a fixed fraction of the recurrence interval. In other words, the coefficient of variation, a/mean, is approximately constant over a wide range of recurrence times and seismic moments in a variety of tectonic environments. Hence, the use of this distribution as a generic description of earthquake recurrence permits relatively high precision probability statements in areas of sparse data. The probability density function, f(t/t), defined in Nishenko and Buland (1987) and used in this study is /(T/T) - T e(_(l.(t/~.)_.l))2/2~2 (1) T~f~-~ where In T = ln(tave) + ~D; ~D, the mean = , and ad, the standard deviation = The expected recurrence time, Texp, based on the number of observations of T for a specific fault segment is given as: T~xp = Te ~'~+~0~/2. (2) Following the suggested terminology of Wallace et al. (1984), the above recurrence time estimate can also be presented in terms of a forecast or prediction time window. The window used in this study is defined as the time interval [Tpred- '7, Tpred + 7], where Tpred = to -}- Texp. Tpred is the expected date of the next characteristic event obtained from the date of the last characteristic earthquake, to, plus the expected recurrence time, T~xp, given by equation (2).,1 represents the 90 per cent confidence interval for the estimate of TCxp, where ~ = 1.645(var[Texp]) '/2 and vat[tempi = (52/T2 + ad 2 )T~xp. 2 For historic earthquakes, values of Taw, T, and 5 are estimated from observations of T. 5 describes how well the average recurrence time is known and depends on the number of observations of T available for each fault segment. ad describes the intrinsic variability of recurrence intervals, based on the global analysis of Nishenko and Buland (1987). For those regions along the Mexican subduction zone with histories of one or more repeats (i.e., two or more earthquakes of similar size occurring along the same segment of the margin), we have calculated Tpred and the associated conditional probability for time intervals of 5, 10, and 20 yr duration (i.e., , 1986-

7 CONDITIONAL PROBABILITIES FOR RECURRENCE OF EARTHQUAKES , and ). These results are shown in Table 2 along with the associated 90 per cent confidence limits. Note that the 90 per cent confidence intervals are all greater than 10 yr. Hence, the time windows defined in this study can best be categorized as long-term earthquake predictions according to the terminology of Wallace et al. (1984}. Inspection of these values in Table 2 also illustrates how the use of a predetermined confidence limit can provide additional information as to the precision of the forecast for each segment. Both knowledge of Texp and the length of the time interval, dt, influence the usefulness or information content of 9. I TABLE 2 LOGNORMAL RECURRENCE TIME AND CONDITIONAL PROBABILITY ESTIMATES Region to* T~# ~t _ Conditional Probability East Oaxaca, 95.2" % (0-53%) 21% (1-85%) 70% (19-99%) 96.4"W 3. Central Oaxaca, % 0% 0% (0-5%) 96.4"- 97.3"W 4. Central Oaxaca, % (10-65%) 59% (23-88%) 86% (51-99%) 97.3"-97.7"W [1973]# [29] [53% (18-86%)] [79% (37-98%)] [96% (68-100%)] 5. West Oaxaca, % (0-10%) 9% (1-38%) 52% (21-87%) 98.2 W 6. Ometepec, 98.2" "* 19 56% (30-81%) 83% (55-96%) 98% {85-100%) 99.5 W [1981]# [23] [48% (10-88%)] [75% (24-99%)] [95% {55-100%)] 7. San Marc.s, 99.5" t 25 1% (0-14%) 5% (0-36%) 29% (6-77%) 100"W 20248~ 29 0% (0-4%) 1% (0-14%) 9% (1-50%) 8. Guerrero, 100" [1960]# [39] [45% (17-100%)] [70% (33-100%)] [92% (60-100%)] 101 W 1908 [1976]# [44] [34% (7-74%)] [58% (15-94%)] [85% (35-100%)] 1909 [1959]# [32] [54% (25-100%)] [79% (46-100%)] [96% (74-100%)] 1911 [1979]# [44] [32% (6-74%)] [56% (13-94%)] [83% (31-99%)] Petatlan, 101" % 0% (0-8%) 10% (0-77%) I01.8 W Michoacan, % 0% 0% I03 W Colima, I03 -I03.7 W % (0-26%) 7% (0-70%) 57% (11-99%) Jalisco, 104.3" % (0-6%) 0% (0-16%) 1% (0-40%) I05.7"W % (0-65%) 16% (0-89%) 41% (1-99%) * to = date of last shock. t Tpred = to "~- Texp, where Te~, is from equation (2). :~ is the 90% confidence interval for Tew. Conditional probability calculated from , 10-, and 20-yr intervals represent , , and , respectively. Values in parentheses are conditional probabilities at 90% confidence intervals of T~. Values in brackets are extrapolated values based on Mo-repeat time calibration. Based on interval. # Based on Mo-repeat time calibration from Oaxaca. ** Based on average of and intervals. tt Based on and intervals. $:~ Based on and intervals. Based on average of and intervals. Based on average displacement from long-period Mo and rupture area estimates of 1932 shocks (Singh et al., 1985).

8 2102 S. P. NISHENKO AND S. K. SINGH the forecast. In some cases where there is only one recurrence interval available, the range of forecast probabilities described by the 90 per cent confidence interval can be so large as to be uninformative. The range of forecast probabilities can be reduced to a certain extent by improving our estimate of T~x, (i.e., by increasing the number of recurrence intervals used in calculating T~=~). Lacking additional recurrence information, however, the range of probabilities described by the 90 per cent confidence limits can also be reduced by choosing a shorter time interval for the conditional probability estimates (see Nishenko and Buland, 1987). For the majority of recurrence times observed in Mexico, the optimal time interval appears to be in the range of 5 to 10 yr. Figures 2 and 3 present in histogram and map view formats, respectively, the results of our analysis for a 10-yr interval ( ). For those segments of the Mexican margin that do not have a well-known history of prior events, we have attempted to extrapolate the recurrence behavior observed in segments with well-known repeats (i.e., Oaxaca, 95 to 98 W} using the concept of characteristic earthquakes. Singh et al. (1981, 1983, 1984a) noted that the frequency of occurrence of large earthquakes along some segments of the Mexican margin during the time period was peaked at Ms 7.7 and deviated significantly from the expected log frequency-magnitude relationship in the 6.4 _-< C Tehuantepec >, e5 o 12. t-.o_ "10 e'- O 100% 80% - Q :;:;:;::::::::::!:!:!:!:i:i:i:!: 60% - ii~i!ili!i!i!i!i ii~ili!i~!iiiiii,...,... 4o% - i!i!i!iii!i!i!ii...,...,..., 20% - i!i!i!?i~i~!iiii -- ::::::::::::;::: HH....,.,.,.,,,... 0% I I!:!:!:;:;:!:i::: 106 W 104 W o C. Guerrero Gap Ometepec Gap C. Oaxaca GaD 102 w 100 W 98 o W o o_ Y Q G < o o a_...,...,.,.,.,...,... :.:.:.:.:.:.:.:.:.:.:.:.:. :::::::::::::::::::::::::: :!:!:!:!:!:!:i:!:~:~:!:~:! ::::::::::::::::::::::::::......,..,,.,.,...,.,.., ,...,.,.,,.,......,......,.,...,::.,....,..,...,...,.,....,,,..,.,,.,,,,,.,,...,..,..,.,...,...,.,,,...,... ::::::::::::::::::::::::::...,,..,.,.,...,...,....,.,...,...,...,..,.,...,...,.,.,.,...,,. :::::::::::::::::::::::::: :::::::::::::::::::::::::: ::::::::::::::::::::::::::...,......,.,,.,.,. :.:.:.:.:.:.:.:.:.:.:.:.: !!! ::::::::::::::::::::::::::.:.:.:.:.:.:.:.:.:.:.:,:.: i!i!i!i!i!i!i!i!i!i!!i!i!i :::::::::::::::::::::::::: 96 W g E = F_ I? (b? I 94 W 100% 80% - 60% - 40% - 20% o% ~ Direct ~ MoRatio ~ Historic FIg. 2. Histogram of conditional probability estimates for the occurrence of large and great earthquakes along the Mexican subduction zone: Encircled numbers refer to segments as discussed in the text. For each segment, the height of the box represents the conditional probability at the 90 per cent confidence limits of Te~ (the estimated recurrence time of the next characteristic earthquake), and the horizontal bar is the preferred value for each model. Probability estimates based on historic data are shown as stippled boxes. Estimates based on the extrapolation of M0-recurrence time behavior from Oaxaca are shown as cross-hatched boxes. Note, for the central Guerrero gap (8), the thick dark band between 56 and 79 per cent represents the range of preferred values for the four earthquakes that occurred in this gap from For the Jalisco segment (13), the diagonally lined box indicates probability estimates based on the seismic moment and rupture area of the 1932 shock. Dates at the top of the figure indicate the time and lateral extent of the last large or great shock in each segment. C.G. is the Colima gap. Question marks indicate those segments where there are insufficient data for analysis. The locations of principal cities and towns are shown at the bottom of the figure.

9 CONDITIONAL PROBABILITIES FOR RECURRENCE OF EARTHQUAKES 2103 I I I I X I I k ) Conditional Probability A X " ~ Q (0-16%, _ 2 X ~ (~ 7% Mexico City ~L ~ a~anillo n ; : a n i~ l l o ~ 0% "~'-'k _...-..~ - (56-79%) - ~ Q 75-83% C~ 0% 5 0 ~ ~ -~Tehuantepec 20N W FIG. 3. Map view of the conditional probability estimates along the Mexican subduction zone for the time interval Probabilities are based on our estimates of the expected recurrence time using either historically observed data or recurrence behavior extrapolated from other segments of the margin. Encircled numbers refer to segments as discussed in the text. Percentages in parentheses represent values which, in our opinion, are less well-constrained. Segmentation of the margin into separate source zones is based on the lateral extent of the last large or great earthquake in each segment. Question marks denote segments with insufficient data for analysis. Ms --< 7.5 range. The observed peak at Ms 7.7 is suggested to indicate the existence of a characteristic size or magnitude for gap-filling earthquakes in this region. Astiz and Kanamori (1984) have proposed a simple relationship between average recurrence times and seismic moment, log T = ½ log Mo, suggesting a simple physical model where the length scale of asperities influences rupture dimensions and hence, recurrence times. While this relationship correctly accounted for recurrence times in Oaxaca and parts of Guerrero, Astiz and Kanamori (1984) noted that recurrence times in western Guerrero and Colima were systemically underestimated. Inspection of Table 1 indicates that earthquake sources in Oaxaca are characterized as being simple (i.e., long-period body waveforms can be modeled as point sources with a single trapezoidal source-time function), while sources in Michoacan, Colima, and Jalisco are characterized as being complex (i.e., long-period body waveform modeling requires multiple point sources and source-time functions). The contrast between simple and complex ruptures is suggested to indicate the amount of heterogeneity on the fault surface and the degree of interaction between adjacent asperities. Simple events reflect a relatively homogeneous distribution of asperities, such that failure of one does not trigger rupture in adjacent asperities. Note, that while this behavior is observed at long periods, it does not indicate similar behavior at shorter periods (Tajima, 1984). Complex events, however, indicate a more heterogeneous distribution of strength on the fault surface and instances where the failure of a single asperity usually triggers the failure of adjacent asperities. The availability of a number of nucleation points on the fault surface may result in a greater variability in both the sizes and recurrence times of earthquakes from cycle to cycle. In other words, the log T/log M0 recurrence model of Astiz and Kanamori (1984) may only be applicable for those earthquakes which involve the rupture of a single asperity,

10 2104 S. P. NISHENKO AND S. K. SINGH and whose source zones exhibit consistent magnitudes and recurrence times from cycle to cycle. The log T/log Mo recurrence model may not be applicable to more complex sources which involve the rupture of a number of asperities and exhibit variable recurrence times and magnitudes from cycle to cycle. We have redetermined the relationship between average seismic moment and average recurrence time, using only those sources in Oaxaca which are demonstrated to be simple events (see Table 1). The resulting relationship is found to be log T = log M , with r (the coefficient of determination) = Extrapolation of recurrence time behavior is subject to two basic assumptions. First, earthquakes are all characterized as simple events (i.e., involve the rupture of a single asperity and presumably have well-behaved recurrence characteristics) and second, that differences in recurrence time scale only as a function of the convergence rate and the ratio of displacements. In other words, ; [Mo _ + ~2 Tm-+~3 V1 TR2 + ~4 LMol -- (3) where U01, TR1, and V1 are the averge seismic moment, average repeat time, and convergence rate for the calibration event. ~1 and c3 are the coefficients of variation of /01 and TRI. M02 -+ E2 and TR ~4 are the corresponding seismic moment and repeat time estimates for the earthquake in the region of interest. The exponent, n, describes the fraction of the seismic moment that is related to the displacement, and hence, contributes to the recurrence relationship. For circular ruptures, n = ½, and based on the above regression equation, we use a value of n The dominant sources of variability for the repeat time estimate (TR2) are associated with the calibration repeat time (e3) and the seismic moments (El and e2). Based on the analysis of Nishenko and Buland (1987), the observed coefficient of variation of TR1 for sources in Oaxaca is on the order of The coefficient of variation of M0 is estimated to be on the order of The total uncertainty in the repeat time estimate, e4, is given as, e4 = ~//e32 + (n ~4~12 + E22) 2. (4) For ~1,2 = 0.50 and e , {~4 = Substitution of TR2 for T and the use of E4 to compute the variance of Te~p, T = ~ + ad 2 = 0.33, allows conditional probabilities based on repeat time estimates from the M0-repeat time calibration to be calculated in the same manner as those based on historical observations. These values are listed in Table 2 for three segments which appear to meet our initial criteria: central Oaxaca; Ometepec, and central Guerrero. DISCUSSION OF INDIVIDUAL SOURCE ZONES The following sections discuss the basic data for the 13 segments along the Mexican subduction zone and are organized by state within the Republic of Mexico. Within each state, segments or source zones are identified by number, name, and longitudinal extent. Each section contains a description of the previous earthquake history and our estimates of Tare, Tpr~d, and the conditional probability for recurrence during the next 5, 10, and 20 yr. The values for Tare, Tpr~d, ~, and the conditional probability are summarized in Tables 1 and 2 and Figures 2 and 3.

11 CONDITIONAL PROBABILITIES FOR RECURRENCE OF EARTHQUAKES 2105 OAXACA I. Tehuantepec gap: 94 to 95.2 W. The Tehuantepec gap is one of two segments along the Mexican margin that are presently distinguished as having no historic record of large or great earthquakes (Kelleher et al., 1973; Kelleher and McCann, 1976; Singh et al., 1981). This gap is coincident with the intersection of the Tehuantepec Ridge with the Middle America Trench, and is near the triple junction between the North American, Cocos and Caribbean plates. At present, there are no data with which to base a seismic hazard estimate for this segment, since the date of the last large or great earthquake in this segment is not known. One possible candidate for a prior event in this region is the 5 June 1897 Ms 7.4 shock, which had previously been associated with the eastern Oaxaca segment (Singh et al., 1981). The area of highest intensity for the 1897 event is located near Tehuantepec, and is significantly east of the high intensity zones associated with the 1928 and 1965 shocks (see next section). In addition, the behavior of the aftershocks was apparently quite different, being more associated with swarm-type activity (Singh, unpublished data, 1984). Based on the dimensions of the Tehuantepec gap (125 km length, 80 km width), this region may be capable of producing an event of Mw 8.0 (M s dyne-cm). This region should be regarded as having a poorly known seismic potential, and should be the target of future research to better constrain both the earthquake history and hazard level. 2. Eastern Oaxaca: 95.2 to 96.4 W. Previous large earthquakes that are known to have occurred within this segment include: 22 March 1928, Ms 7.7 and 23 August 1965, Ms 7.8. For the 1965 event, both the teleseismic main shock and aftershock locations of Kelleher et al. (1973) fall near or within the area of highest intensity. Aftershock relocations, using the 1978 central Oaxaca event as a calibration (Quintanar and Ponce, personal communication, 1985), indicate a smaller rupture zone for the 1965 event which is in better agreement with the distribution of isoseismals. In contrast, the teleseismic location of the 1928 event, given by Kelleher et al. (1973), is significantly east of the zone of highest intensity. Relocation of aftershocks associated with the 1928 event by Ponce et al. (1984) indicate a rupture seaward of the zone of highest intensities; however, a comparison of the intensity distributions of the 1928 and 1965 events, as given by Figueroa (1970), suggest similar rupture zones. Based on the one available recurrence time, or 37 yr, the observation of simple body waveforms (Chael and Stewart, 1982; Singh et al., 1984b), and the comparable magnitudes of both events, the next occurrence of a Ms 7.7 to 7.8 event may be expected in approximately 37 yr from 1965 or the year 2002 (see Table 2). Corresponding estimates of conditional probability for the next 5, 10, and 20 yr are 5, 21, and 70 per cent, respectively. Note in Table 2 that the large range of probability values for the 90 per cent confidence limits indicates the degree of resolution available with only one recurrence interval. 3. and 4. Central Oaxaca: 96.4 to 97.7 W. Previous large and great earthquakes that have occurred along this segmvnt of the margin include: 11 May 1870, Ms 7.9; 27 March 1872, Ms 7.4(?); 17 June 1928, Ms 8.0; 9 October 1928, Ms 7.8; and 29 November 1978, Ms 7.8. A comparison of epicenters and rupture zones based on aftershock data for these events is shown in Figure 1. Note that the Central Oaxaca region contains two segments or source zones, one between 96.4 and 97.3 W (zone 3) and a second between 97.3 and 97.7 W (zone 4). In general, there is good agreement between the earlier intensity and later instrumental data that the 1870,

12 2106 S. P. NISHENK0 AND S. K. SINGH 17 June 1928, and 1978 events reruptured the same segment of the plate boundary. Poor data for the 1872 event excludes any firm association with a particular rupture zone. The 9 October 1928 event appears to define a separate source zone within this region and will be discussed later in this section. For the segment between 96.4 and 97.3 W (zone 3), the data indicate a fairly consistent history of great earthquakes with relatively long (>50-yr) recurrence times. Analysis of long-period body waves for both the 17 June 1928 and 1978 events indicate simple pulse shapes consistent with the rupture of a single asperity (Chael and Stewart, 1982; Singh et al., 1984b). Comparison of the seismic moments of both events (see Table 1) suggest that while the 17 June 1928 event was larger, within the resolution capability of the data, both events are similar in size. Hence, the observed 54-yr average repeat time appears to represent a good recurrence estimate for this region. Based on these data, the next repeat of a Ms 7.8 to 8.0 earthquake may be expected in 2033, and the conditional probabilities for the next 5, 10, and 20 yr are negligible (see Table 2). In contrast, the adjacent segment (97.3 to 97.7 W) (zone 4), which last ruptured on 9 October 1928, has not had a repeat since that time and is presently considered to have a very high probability for recurrence based on the available data. Relocation of aftershocks associated with the 1968 and 1978 Oaxaca earthquakes (Tajima and McNally, 1983; Quintanar and Ponce, personal communication, 1985) indicate the existence of a distinct seismic gap between 97.3 and 97.7 W. Unfortunately, the historic record is not clear as to what event ruptured this segment prior to 1928, or whether this segment is capable of rupturing independently. Hence, well-constrained estimates similar to others discussed in this study are not possible at this time. Based on the size of this gap (~55 km in length and 80 km wide), the estimated seismic moment of an event which would fill this region is approximately 2 x 1027 dyne-cm (equivalent to Ms 7.7 or the size of the 9 October 1928 event). One possible candidate for the previous event is the 27 March 1872 earthquake. Comparison of available intensity data for the 1870 and 1872 events indicate a higher intensity in Mexico City for the latter event (MM V versus VI, respectively), which is consistent with a source slightly to the west of the 1870 event. Using the time interval , 56 yr, as a recurrence time estimate, the estimated date for the next shock is 1985, and the associated conditional probabilities are at the 34, 59, and 86 per cent level for the next 5, 10, and 20 yr, respectively. Body waveforms for the 9 October 1928 event indicate a simple mode of rupture (Singh et al., 1984b); hence, an additional constraint on a possible recurrence time is available by comparing the observed recurrence times and seismic moments for earthquakes that have occurred on either side of this segment (i.e., the central and western Oaxaca segments). These data indicate a shorter recurrence interval of about 44 yr. The corresponding probability levels based on the comparison of seismic moments are about 10 to 20 per cent higher than those based on the postulated recurrence interval discussed previously and are also presented in Table 2. While the absolute values are not well-constrained, all of these probability estimates are significantly higher than the estimates for adjacent segments of the margin in Oaxaca, and zone 4 should be regarded as having a high but less well-constrained hazard level. 5. Western Oaxaca: 97.7 to 98.2 W. Previous large earthquakes that have occurred in this segment include: 5 May 1854, Ms 7.7; 2 November 1894, Ms 7.4; 4 August 1928, Ms 7.6; and 2 August 1968, Ms 7.4. With the exception of the 1894 event, all of these earthquakes have zones of highest intensity which coincide spatially. For the 1968 event, the area of highest intensity is also in good agreement

13 CONDITIONAL PROBABILITIES FOR RECURRENCE OF EARTHQUAKES 2107 with the aftershock area. As in the case of the central Oaxaca events, the 1968 earthquake is characterized as a simple event (Chael and Stewart, 1982; Singh et al., 1984b). The magnitude estimates for the previous events are essentially identical, and the observed recurrence times appear to be fairly constant (see Table 1). Based on the observed 38-yr average recurrence interval, the next Ms 7.4 to 7.6 event is expected in 2006, and the conditional probability estimates for the next 5, 10, and 20 yr are 1, 9, and 52 per cent, respectively. GUERRERO 6. Ometepec: 98.2 to 99.3 W. Previous large earthquakes that are known or suspected to have occurred in this segment include 2 December 1890, Ms 7.5; 15 April 1907, Ms 7.9; 23 December 1937, Ms 7.5; 14 December 1950, Ms 7.3; and 7 June 1982, Ms 6.9, 7.0. This segment has been classified as a seismic gap by Singh et al. (1981), on the basis of the amount of time elapsed since a previous large earthquake. During this century, the recurrence history along the Ometepec segment has been somewhat anomalous when compared to the adjoining segments in Oaxaca. As previously discussed, the gap-filling earthquakes in Oaxaca can be characterized as simple events with regular recurrence times and similar magnitudes from event to event. Earthquakes in Ometepec, however, exhibit both simple and complex modes of rupture with large differences in magnitude. Hence, it is more difficult to determine what is a characteristic earthquake for this segment. Although characterized as a simple event, the 1937 shock was followed by a complex event in While the aftershock zones of both events overlap, analysis by Nishenko and Singh (1987) suggest that the short time interval between these events does not constitute a recurrence interval, but rather a complicated mode of rupture which took 13 yr to complete. With regards to earlier events in this region, both the magnitude and distribution of felt intensities of the great 15 April 1907 earthquake suggest that it may have ruptured the Ometepec segment as well as the Acapulco-San Marcos segment (Nishenko and Singh, 1987). If the 1907 earthquake ruptured the entire Ometepec segment, the observed interal ( ) provides one estimate for a recurrence interval. Alternatively, if the 1907 shock did not rupture the entire Ometepec segment, the only other historically observed interval in our catalog is the period or 47 yr. The average of the above recurrence time candidates is 38.5 yr. Using this estimate, the expected recurrence date is 1976, and the conditional probabilities for the next 5, 10, and 20 yr are at the 56, 83, and 98 per cent levels, repsectively. We can also use the seismic moment of the 1937 event as an independent check on the above repeat time estimate. The Mo-repeat time relationship suggests a recurrence time of 43 yr for an event of Ms >= 7.5. The corresponding conditional probability estimates are at the 48, 75, and 95 per cent levels for the next 5, 10, and 20 yr, respectively, and are in good agreement with the above estimates despite the uncertainty as to when the previous gap-filling event occurred (i.e., 1890 or 1907). The region between 98.5 and 99.5 W is presently associated with a conspicuous seismic quiescence anomaly that began in January 1977 and has continued until at least mid-1985 (McNally, 1981 and personal communication, 1985). Whether this decrease in activity reflects an actual change in physical processes occurring within the earth or a coincidental decrease in the teleseismic reporting of smaller events during this time interval is not clear at present (Habermann, 1988). The 7 June 1982 Ometepec earthquake doublet (Astiz and Kanamori, 1984) ruptured the eastern

14 2108 S. P. NISHENKO AND S. K. SINGH portion of the Ometepec gap (98.2 to 98.5 W). Either the seismic quiescence or the 1982 doublet may be indicative that this segment is in the preparation stages for a large shock within the next two decades. 7. Acapulco-San Marcos: 99.3 to IO0 W. Previous large and great earthquakes that are associated with this segment include: 4 May 1820(?), Ms 7.6; 7 April 1845(?), Ms 7.9; 15 April 1907, Ms 7.9; and 28 July 1957, Ms 7.7. Estimates of the seismic potential for this region have been discussed Singh et al. (1982), based on the assumption that both the 1907 and 1957 shocks ruptured the same portion of plate interface. The seismic moment of the 1907 shock is approximately twice that of the 1957 event (see Table 1), and based on the above assumption and the timepredictable model, a possible repeat time of 28 yr was suggested by Singh et al. (1982). Nishenko and Singh (1987), on the other hand, suggest that the 1907 shock may have ruptured both the Acapulco-San Marcos and Ometepec segments. Hence, the difference in moment between the 1907 and 1957 events may reflect the fact that the 1957 shock only ruptured half of the 1907 zone. Like the adjacent Ometepec segment, prior earthquakes in the Acapulco segment are characterized as being both simple and complex (see Table 1). The 1957 shock was followed 5 yr later by two large shocks on 11 and 19 May 1962, suggesting that this segment also exhibits complex rupture patterns. Based on historical observations of great shocks in Acapulco-San Marcos region, there are two possible candidates for a predecessor to the 1907 event: 1820 and The average repeat times, depending on which event actually occurred in this segment, range from 56 to 68 yr and the next Ms ~ 7.7 event would be expected between 2013 and 2024 (see Table 2). In spite of this uncertainty, however, the corresponding conditional probabilities are low for the next 5 and 10 yr. 8. Central Guerrero: 100 to 101 W. Previous shocks Ms >= 7.5, known or estimated to have occurred in this region include: 7 April 1845(?), Ms 7.9; 24 December 1899, Ms 7.7; 26 March 1908, Ms 7.8; 30 July 1909, Ms 7.5; and 16 December 1911, Ms 7.8. With the exception of the 1845 event, there are no welldocumented earthquakes for this region prior to 1899, owing to low population density during the 19th century and perhaps longer than average repeat times. Hence, recurrence estimates are speculative at best. This zone is distinguished by having one of the longest elapsed times since a prior earthquake that has been observed along the Mexican subduction zone. Hence, like the Michoacan and Tehuantepec gaps, recurrence intervals in this region may belong to another periodicity that has not been well-observed historically. Based on the physical dimensions of the Guerrero gap (-100 km length, 80 km width), this segment may be capable of producing a single event of Mw 8.0 (M dyne-cm). The summation of seismic moments for the sequence is approximately dyne-cm, and suggests that, while the exact locations of these events are poorly known, most probably all of these events contributed to filling in the entire gap. While no well-constrained historic observations are available for prior events, we can estimate recurrence times by extrapolating the known M0-recurrence time relationship in Oaxaca, subject to the basic assumptions stated in the data and analysis section. Based on a convergence rate of 6.2 cm/yr, this comparison indicates recurrence periods of approximately 60 to 70 yr for Ms 7.7 to 7.8 events, and 50 yr for Ms 7.5 events. Note that these estimates are in good agreement with the postulated 54-yr recurrence time, if the 1845 shock is actually located in the central Guerrero gap. These estimates are shorter than the amount of time that has already

15 CONDITIONAL PROBABILITIES FOR RECURRENCE OF EARTHQUAKES 2109 elapsed since the previous series of large and great shocks (75 to 87 yr). The corresponding conditional probability estimates for these recurrence times are presented in Table 2 and are significantly higher than those for the surrounding region. In summary, while the data are poorly constrained, the extrapolation of observed recurrence time behavior from other segments of the Mexican subduction zone indicates that central Guerrero should be considered an area of high seismic hazard for the immediate future. In contrast to the seismic quiescence anomaly noted for the Ometepec-San Marcos region, no similar anomaly has been noted as yet for the central Guerrero gap (McNally, 1981). 9. Petatlan: 101 to W. Previous shocks in this region include: 22 February 1943, Ms 7.7 and 14 March 1979, Ms 7.6. In contrast to the Oaxaca earthquakes, there appears to be much variability in the mode of rupture for this region. Comparison of body waveforms for the 1943 and 1979 events indicate significant differences which Singh et al. (1984b) attributed to either different rupture zones or varying styles of rupture. The occurrence of a significant number of aftershocks updip from the 1979 rupture zone, following the 21 September 1985 Michoacan earthquake (UNAM Seismology Group, 1986), is also problematic, and it is not known whether this occurrence represents sympathetic slip (or rerupture) or a fresh rupture of an area that was unbroken during the 1979 shock. Using the simple assumption that the sequence represents an actual recurrence interval for this segment, the estimated date of the next Ms 7.6 to 7.7 shock in this segment is 2015, and conditional probabilities for the next 5, 10, and 20 yr are negligible (see Table 2). MICHOACAN 10. Michoacan: to 103 W. This segment, like the Tehuantepec gap, is coincident with the intersection of a bathymetric feature, the Orozco fracture zone, with the Middle American trench. Kelleher and McCann (1976) have suggested that collisions of this sort may severely modify the subduction process locally, resulting in longer than average recurrence times. The occurrence of the 19 September 1985 Ms 8.1 earthquake in this gap appears to support the model of infrequent great shocks with longer than average repeat times. An earlier event, 7 June 1911 Ms 7.9, is located in this gap on the basis of locally recorded S-P times and similarities in intensity with the 1985 event (UNAM Seismology Group, 1986; Eissler et al., 1986). Hence, while still poorly known, recurrence times of 75 yr or longer for great earthquakes appear to be appropriate for this region, and the hazard estimate for the recurrence of a great earthquake in this segment in the immediate future appears to be small. Note, that the complex nature of the 1985 main shock (two sources with equal moments and source time functions; Eissler et al., 1986; UNAM Seismology Group, 1986) is consistent with the regional observation for complex events to occur northwest of 99 W and simple events to occur southwest of 99 W (Singh et al., 1984b). 11. Colima: 103 to W. Previous large earthquakes associated with this segment include 15 April 1941 Ms 7.9 and 30 January 1973, Ms 7.5. Body waveforms for the 1973 event indicate a complex mode of rupture (Chael and Stewart, 1982) as is suggested for the 1941 event as well (Singh et al., 1984b). A comparison of locally recorded S-P times and felt intensities indicate that the rupture zone of the 1941 event was larger than that of the 1973 event and may have extended into the 1985 Michoacan rupture zone (UNAM Seismology Group, 1986). The variable

16 2110 S. P. NISHENKO AND S. K. SINGH rupture history observed in Colima and Petatlan may help to explain why the log T/log M0 relationship developed by Astiz and Kanamori (1984) systematically tends to underestimate the observed recurrence times in this area. If we base our forecast on the historically observed interval , the next Ms >= 7.5 event is expected in 2005, and the conditional probabilities are negligible for the next 5 and 10 yr (see Table 2). Note that like the eastern Oaxaca segment, the degree of resolution available with only one recurrence estimate is quite low. COLIMA 12. Coliraa gap: to W. The Colima gap is defined on the basis of relocations of aftershocks of the great 3 June 1932 Jalisco earthquake (Singh et al., 1985) and covers a zone approximately 60 km long between the 1932 zone and the 1973 Colima shock. The Colima gap is approximately coincident with the coastal extension of the Colima graben--an arm of an incipient triple junction in Jalisco (Luhr et al., 1985). The lack of any major shocks in this region during the last 80 yr may indicate the existence of a modified stress regime in this area. Given this, any further discussion of this gap is outside the scope of this paper, with the exception of noting that the Jalisco graben system is also capable of producing large shocks (i.e., 11 February 1875, Guadalaraja, Ms 7.5). JALISCO 13. Jalisco: to I05.7 W. Previous large and great earthquakes that have occurred in the state of Jalisco include: 25 March 1806, Ms 7.5; 31 May 1818, Ms 7.7; 20 January and 16 May 1900, Ms 7.6 and 7.1; and 3 and 18 June 1932, Ms 8.1 and 7.8. The 3 June 1932 event is one of the largest events to have occurred in Mexico during this century. Analysis of intermediate-period body waves indicate that it was a complicated, multiple event with an estimated rupture length of 220 km (Singh et al., 1984b). Relocations of aftershocks recorded by stations in Mexico and compilation of intensity data (Singh et al., 1985) indicate that this event ruptured the shallow portion of the Rivera plate. The low population density along the coast of Jalisco, however, makes the positive identification of rupture zones of older earthquakes difficult. For both the 1806 and 1818 events, the available data for this time period are not sufficient to either construct an isoseismal map or accurately estimate an epicenter. As noted by the question marks in Figure 1, one or both of these events may have ruptured either the Jalisco (1932) segment or the Colima (1973) segment. In addition, a pronounced asymmetry in isoseismal patterns also obscures the ability to differentiate between sources in Colima and Jalisco during the 19th century. Hence, the locations and recurrence periods of large and great earthquakes in the region are uncertain. Singh et al. (1985) estimate a recurrence time of about 77 yr based on the measured long-period seismic moments and rupture areas of the 3 and 18 June 1932 events, and assuming that the total convergence rate of 2 cm/yr is taken up by seismic slip. This direct estimate is shorter than the historically suggested intervals of 114 to 126 yr (i.e., or ), if either of these events actually did rupture this segment of the margin. Based on the historic data, the estimated hazard level for great earthquakes like the 1932 shock appears to be negligible for at least the next 20 yr (see Table 2). Note, a comparison of seismic moments in Oaxaca with the 1932 event to determine a recurrence time is not feasible, due to the complex nature of the 1932 event. At present, lacking a clear recurrence history for great earthquakes in Jalisco, the direct estimate based on the size of the 1932 shock

17 CONDITIONAL PROBABILITIES FOR RECURRENCE OF EARTHQUAKES 2111 provides a minimum recurrence time for this region. Based on the 77-yr recurrence estimate of Singh et al. (1985), and assigning a ~ = 0.33, the resulting conditional probabilities are somewhat higher than those based on the historic estimates. Although poorly constrained, our best recurrence time estimates for great earthquakes in Jalisco range from 77 to 126 yr. Additionally, we have no information about the recurrence of large (i.e., 7 =< Ms <= 7.7) earthquakes, like the 20 January 1900 event, for this region. Hence, probability estimates for large shocks in the state of Jalisco are not possible at this time. DISCUSSION At present, the central Oaxaca (zone 4, 97.3 to 97.7 W), Ometepec-San Marcos {zone 6, 98.5 to 99.5 W), and central Guerrero (zone 8, 100 to 101 W) segments of the Mexican subduction zone stand out has having the highest likelihood for the recurrence of large or great earthquakes in the near future. For both central Oaxaca and central Guerrero, the history of prior earthquakes is poorly known and recurrence estimates are based on comparison with other segments of the margin, subject to a few simplifying assumptions. For the Ometepec-San Marcos segment, the history of prior earthquakes is more complete. The demonstrated variable rupture history for the Ometepec region, however, cautions against more precise estimates of future behavior in this region. Hence, for all three segments, the absolute probability levels are less well-constrained. In a relative sense, however, the hazard for these three areas is higher than for all the other zones along the Mexican margin. At this point, it is also interesting to note that these zones coincide with those segments of the margin which have not had a major earthquake in the last 25 yr, and therefore have the most incomplete earthquake histories. While the majority of these results could have been anticipated qualitatively via the seismic gap hypothesis, presenting the historical and instrumental data in a probabilistic framework has improved our overall perception of the seismic hazard for this region. In particular, the a priori information contained in the lognormal model has resulted in improved estimates of Tare, and more importantly, a quantitative description of the overall uncertainties present in our forecasts for each segment. By adopting a predetermined confidence interval (i.e., 90 per cent), we can convey more information about the precision of the forecast than is available by using a single number. The observation of a constant coefficient of variation for the lognormal distribution also provides valuable information as to how much temporal resolution we can reasonably expect from using either historic or instrumental data for recurrence time calculations. Inspection of Table 2 shows that all of the 90 per cent confidence windows are _10 to 20 yr in duration and hence are best considered as long-term earthquake predictions. The observation of variable rupture geometries for many segments of the Mexican margin highlights one of the basic problems which confronts efforts in earthquake forecasting and prediction. The concept of seismic gaps and the statistical analysis presented in this study are fundamental for identifying the most probable sites and times of occurrence of future large and great shocks. Based on the previously observed patterns of earthquake occurrence, these techniques appear to be most appropriate for the Oaxaca segment of the margin (i.e., 95 to 98 W). As Singh et al. (1983) note, the plate interface in Oaxaca appears to be divided into a few (3 or 4) large segments which cyclically rupture their entire dimension. In Oaxaca, the long-period body waveforms are indicative of simple ruptures, and the rupture zones appear relatively constant in size and location from cycle to cycle. Along the

18 2112 S. P. NISHENKO AND S. K. SINGH Guerrero, Michoacan, Colima, and Jalisco segments of the margin, the earthquake sources are more complex and involve the rupture of a number of asperities. This complexity also appears to manifest itself by a greater variability of both magnitudes and rupture dimensions from cycle to cycle. This variability results in a reduced ability to accurately forecast the extent and times of future events. Nevertheless, the analysis presented in this study provides a crucial first step in identifying future earthquake source zones and relative likelihoods of occurrence along the Mexican subduction zone. Mindful of the previous complications, we can discuss a number of scenarios, based on historical observations, for possible future activity in the central Guerrero segment. The sequence of large and great earthquakes that occurred in central Guerrero during is similar to the episode of subduction seen in Oaxaca during 1928 (see Figure 1). In other words, a large segment of the margin, encompassing a number of separate earthquake source zones, ruptured in a series of events over a time interval that is short in comparison to the average recurrence time. This clustering of activity in time presents a possible scenario for future activity in the Guerrero region, i.e., the segment reruptures in a series of large and great shocks clustered together in time, as it did previously in Alternatively, the central Guerrero region could rupture in a single great earthquake of about Mw 8.0, similar to the 19 September 1985 Michoacan earthquake. Note that the 1985 shock was preceded by a smaller shock in 1981 (Playa Azul, Ms 7.3, Havskov et al., 1983). Hence, the similar occurrence of large shocks in the central Guerrero region may provide a crucial intermediate-term indication as to the imminence of future great earthquakes in this region. These two scenarios of possible seismic failure also have important implications for seismic hazard and risk assessment of major Mexican cities. The Guerrero gap is located closer to Mexico City than was the Michoacan gap and has the potential for a similar sized event. In other words, depending upon the size and rupture history of the next gap-filling Guerrero earthquake, there is a good possibility that the same patterns of damage associated with the 1985 Michoacan earthquake may again be repeated. In the state of Oaxaca, the earthquakes of 1965, 1968, and 1978 were preceded by seismicity anomalies (Ohtake et al., 1977; Habermann, 1981; Tajima and McNally, 1983). Both the 1965 and 1978 events were preceded by reductions in the rate of background seismicity or seismic quiescence. In contrast, the 1968 event was preceded by an increase in the rate of background seismicity. If pronouced seismicity chages prior to large and great earthquakes are characteristic features of the earthquake cycle in this region, then the identification of future anomalies would provide an intermediate to short-term improvement of our recurrence time estimates. The identification of such anomalies in the central Oaxaca gap would provide a crucial constraint for the hazard level of that region. Similarly, a clarification of the Ometepec-San Marcos seismic quiescence anomaly (McNally, 1981) is crucial toward evaluating the intermediate-term seismic hazard in that region. ACKNOWLEDGMENTS Conversations with K. McNally, D. Perkins, L. Ponce, and G. Suarez throughout the course of this study are gratefully acknowledged. Thanks to Jim Dewey, Dave Perkins, and Bill Spence for critically reading the manuscript and offering a number of helpful suggestions. This study was supported by Agency for International Development agreement BOF-0000-P-IC (S.P.N.) and by Consejo Nacional de Ciencia y Technologia (CONACYT), Mexico (S.K.S.).

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