Seismic strain release in the Mexican subduction thrust John G. Anderson

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1 Physics of the Earth and Planetary Interiors, 58 (1989) Elsevier Science Publishers By., Amsterdam Printed in The Netherlands Seismic strain release in the Mexican subduction thrust John G. Anderson Seismological Laboratory and Department of Geological Sciences, Mackay School ofmines, Unii ersilr of Nepada-Reno, Reno, N V (U.LA.) Shri Krishna Singh, J.M. Espindola and J. Yamamoto Instituto de Geofisica, Universidad NacionalAutononia de Mexico, Coyoacan 045/0 Mexico, D.F. Mexico (Mexico) (Received January 6, 1989; revision accepted June 13, 1989) Anderson, J.G.. Singh, S.K., Espindola, J.M. and Yamamoto, J., Seismic strain release in the Mexican subduction thrust. Phys. Earth Planet. Inter., 58: In this paper the seismic strain release in the Mexican subduction zone is discussed. The paper is based on a revised catalog of large earthquakes in Mexico. New in this catalog are estimates of the seismic momedt for many of the larger pre-1962 earthquakes of this century, based on instrumental recordings from Uppsala, Sweden. A regression between moment and magnitude is established and used to estimate moments for the remaining events of this and the previous century. The envelopes of the cumulative seismic moment curves can thus be developed, consistent with the nineteenth century seismicity. These indicate that the Guerrero region is currently the most likely, within the Mexican subduction zone, to experience one great event, or several large events, with a moment deficit approaching 20 x 1027 dyn cm. This is comparable with the moment released between 1899 and 1912 in the region. In Guerrero. and also perhaps in Michoacan, the seismic strain release is consistent with plate tectonic expectations for a seismogenic zone 50 km in width. In Oaxaca, either the seismogenic zone is much narrower and there is considerable aseismic slip, or events to rupture the downdip extremes of the subduction zone have not occurred so far this century. This last alternative arises because in Guerrero the 1907 and 1957 earthquakes have relatively strong 40 s surface waves recorded at tjppsala. compared with all the other events. Such events, which we infer are deeper, present new problems for seismic hazard estimation in Mexico since they are not represented in the available strong motion records. 1. Introduction differently. Finally, the behavior of the Rivera plate has been clarified somewhat. Considering all Wang et al. (1982) evaluated the seismic strain this, a re-evaluation of the seismic potential in release in Mexico and Central America and con- Mexico is timely. cluded that by the end of 1985 the moment deficiency would be the equivalent of five magnitude 8 earthquakes. Since their paper was published, 2. Additional moment estimates one disastrous magnitude 8 earthquake has occurred, on September 19, The moments of Espindola et al. (1981) suggested that the additional historical Mexican earthquakes have seismic moments of large earthquakes from the been determined, and a revised catalog in which Mexican subduétion zone could be estimated very magnitudes are determined more consistently has simply from Wiechert seismograms recorded at become available. The focal mechanisms of some Uppsala, Sweden. The station at Uppsala is alearlier earthquakes have now been determined to most unique and of immense value because the be normal, not thrust, and these should be treated same Wiechert seismograph has been operated /89/$ Elsevier Science Publishers By.

2 308 J. ANDERSON ET AL. dvoe ~ -100 Moy~9, A09 Avvj 2, ~ o Jay 30, ~ Nov o time (mm) Fig. 1. Digitized east west component Wiechert seismograms from tjppsala. Sweden, of several recent earthquakes along the Mexican subduction zone. Seismic moments of these events have been determined in other studies. Thus these events are used to calibrate the relationship between moment and spectral level in the period range s. there continuously since The great circle for most of these earthquakes over this range of path to Uppsala is perpendicular to the Mexican periods. subduction trench, and thus the entire subduction Digitized seismograms for the calibration events zone is nearly equidistant. Therefore that station are shown in Fig. 1. Fourier spectra (Fig. 2) were allows direct comparison of seismograms from all obtained from windows of 9 mm duration before the large earthquakes that have occurred along the the arrival of the strong 20 s surface waves. It is Mexican subduction zone since expected that the corner periods of most Espindola et al. measured the amplitude of 40 s earthquakes under consideration are below about surface waves from the east west component at 40 s, but one of the largest events in the catalog, Uppsala for many twentieth century events. Re- that of September 19, 1985, appears on broadband cent events, for which the moments are well de- and short-period teleseisms to have a source duratermined, were used to develop a calibration curve tion of over 60 s (Houston and Kanamori, 1986). for the amplitude of 40 s waves vs. moment. little was to be gained by including the 20 s Moments of the earlier events were determined surface waves, since they are at periods approachfrom these calibration curves. We have used this ing, or below, the corner periods of many of the same method with the procedural difference that earthquakes and thus are less useful for moment the Fourier spectral amplitudes from digitized estimation. The depths of the earthquakes are not seismograms were corrected for instrumenl re- generally well known, and we were concerned that sponse and attenuation and then used to develop the excitation of 20 s waves might be more sensithe calibration curve. The calibration is based on tive to the depth than the s waves. Finally, the spectral level of surface waves with periods when the window includes the 20 s surface waves between 40 and 60 s. On the basis of the ap- with large amplitudes, the spectra are only reliable pearance of the spectra, the signal is above noise after accurate corrections to the seismograms for

3 SEISMIC STRAIN RELEASE, MEXICAN SUBDUCTION THRUST June June May May 1962 :: 10 2 io~ lo ~ io ~ i ~ _i August August January November 1978 : i::: i:::.~ i0 ~ 1D ~ ~ 101 ~o ~ io cycles/miri cycles/mm 14 March September o_~,v,, cycles/mm cycles/mm Fig. 2. Fourier spectra from a 9 mm window of the seismograms in Fig. 1. Spectra have been corrected for instrument response and attenuation from Mexico to Uppsala. The horizontal bar gives the picked spectral level, as described in the text. the curvature introduced by the mechanical pen; The coefficient of log M 0 was constrained to be these corrections were not undertaken. 1.0 in developing eqn. (1); the unit of S in eqn. (1) To be sure that the spectral levels were trust- is millimeter minute and the unit of M0 is dyn worthy, they were picked while looking jointly at centimeter. The calibration events are all fitted to the seismogram and the spectrum. In general, the within a factor of 2; the standard deviation in the picks (Fig. 2) are near the peak of the spectrum in prediction of log M0 is Moments of all the s period range rather than at an average remaining events whose seismograms were availvalue. To avoid systematic errors, all spectral levels able from Uppsala were estimated using eqn. (1). were assigned in the same manner. These moments, determined from Fourier spectral Seismic moments and spectral levels of the amplitudes, are generally close to those estimated calibration events are listed in Table 1. Figure 3 from peak amplitudes by Espindola et al. (1981). shows their spectral amplitudes, S. at a s Two exceptions are the earthquakes of 1907 and period plotted against moment. The calibration 1957, whose moments from peak amplitudes were curve is estimated as 5.8 x 1027 dyn cm and 3.3 >< 1027 dyn log S = 1.0 log M (1) cm respectively (Singh et al., 1982). The corre-

4 ~,./~./. 310 J. ANDERSON ET AL. TABLE I TABLE 2 Calibration earthquakes Earthquakes used in calibration of seismic moments and M~ Date Moment Spectral amplitude Date M~ M 27dyn cm) at Uppsala ~ Year Month Day (lo27dyn 0 cm) Year Month Day (lo (mm mm) ~ See Table 3 for earthquake parameters and references ~ Corrected for instrumental response and for Q. The spectral amplitudes are measured at about s period sponding values from eqn. (1) are 8.4 x 1027 and 5 1 x 1027 d n cm See Table 3 for earthquake parameters and references for all y -... events except the earthquake of March 19, We also calibrated the seismic moment as a ~ Location N, 99.9 W,depth 16km, M from EDR and function of surface wave magnitude M~,using the data in Table 2. This calibration is M 0 from Harvard centroid moment tensor inversion. log M0 = 1.177M (2) moment. Equation (2) was used to estimate M0 The correlation coefficient for this regression is for all subduction events of the nineteenth cen Figure 4 shows that this relationship has a tury. It was also used for some of the events of scatter of about a factor of 2 in estimates of the this century for which neither Uppsala seismograms nor independent M0 values were available..~ tj, J1 -.,~L~ 1 // 1i~0 C / ~ t. / +.. S./. rr Fig. 3. Seismic moments and spectral levels at s periods Fig. 4. Relationship between Mv and M11 for all earthquakes for the seismograms in Figs. I and 2. The solid line is the best listed in Table 2: Solid line, best fit; broken line, fit with slope fit with the slope constrained to 1.0 to these data, fixed to 1.5. in I

5 SEISMIC STRAIN RELEASE. MEXICAN SUBDUCTION THRUST 311 TABLE 3 Catalog of large Mexican earthquakes (15 21 N, W) Date Time Latitude Longitude R Depth M M 0 SR h N E (km) (km) (1027 Year Month Day Hour Mm Sec (deg) (deg) dyn cm) A0 M A0 M I I G I R _ G o I E _97, ,31 E _ ~ o I o _99.1I , G R I R I E E ~ I G _99, G I G I , o _ o : 43: 17.1 _ , GR : 20: 33: 12: 30 20, _105.OI S R : 47: ~ E : 08: _ S ~ G : 03: _~ S G : 45: I 2504 S G : 51: S G : 43: ~I G : 02: ~ 2345 ~ M : 14: ~ G : 55: _ S E : 59: ~ F ii 21 06: 25: S G : 50: I 2978 ~I 6.9 II m : 17: _95, Sm : 19: i ~ : 28: ~_97.6m 2808 ~I1 7, : 01: 01: 50: _ S E : 36: I R : 12: S R : 05: _ ~ R : 47: I ~ E : 17: S G : 09: S1 77 ~ 2.94~ M : 20: M : 23: E : 25: E : 15: S G

6 312 1 ANDERSON ET AL. TABLE 3 (continued) Date Time Latitude Longitude R~ Depth M M 0 SRb N E (km) (km) (1027 Year Month Day Hour Mm Sec (deg) (deg) dyn cm) : 40: S G : 11: _99.6m 2609 ~I G : 58: _ ~I G : 19: 22: 46: _ ~ 7.8 ~ F : 06: , : 01: _ ~ M : 50: ~~ 7, F : 52: _ ~ : 07: _ ~ M : 53: ~ 0.63~ F : 22: _ , M : 52: ~ ~ 0.27 ~ G : 59: ~ ~ 7.0 ~ 0.25 ~ G : 17: _ ~ M : 37: _ ~ M : 07: ~ ~ M a R 8, Distance from pole of rotation between Cocos plate and North America plate N, E (Minster and Jordan, 1979). In this model the rotation rate is deg Ma~. b SR, Subregion for moment rate summation. R, Rivera Plate ( km). M, Michoacan ( km). G, Guerrero ( km). 0, Oaxaca ( km). E, Excluded because event is not believed to be an interplate thrust earthquake (reason is given in footnote). Singh 2Nishenko et al. and (1981). Singh (1987a) location for this earthquake. The former location, in Singh et al., 1981, is N, 98.0 W. 3Earthquake was located at depth of 80 km by Gutenberg and Richter (1954). For this paper, seismograms from Uppsala were reviewed, and they indicate that this earthquake was shallow. Magnitude has been revised according to amplitudes from (Jppsala, as in Singh et al., (1984a). 4Gutenberg and Richter (1954). Singh et al. (1981) relocated this earthquake based on felt areas. Felt areas of the September 19, 1985 event resemble those for this event, however, and thus we now use the original location. 5Location and depth from Yamamoto et al. (1984) and M 0 from Gonzalez and McNally (unpublished manuscript). Lay and 6Havskov Wallace (1988) et al. (1983). give a moment of 0.85 x 1027 for this event. 7Astiz and Kanamori (1984). 8UNAM Seismology Group (1986). 9EDR. ~ Abe and Noguchi (1983b). 11 M~from Uppsala seismograms (listed in Singh et al., 1984) Abe (1981). 13 Gutenberg and Richter (1954). 14 M~from Abe (1981) ~ Abe (1984). 16 Chad and Stewart (1982). 17 Reyes et al. (1979). 18 Singh and Wyss (1976). 19 Le Fevre and McNally (1985). 20 Anderson et al. (1986), UNAM Seismology Group (1986), Astiz et al. (1987). 21 Average of M 0 values given by Astiz et al. (1987), Ekstrom and Dziewonski (1986), Priestley and Masters (1986), and Riedesel et al. (1986) reduced to a dip of Average of M0 values given by Astiz et al. (1987), Priestley and Masters (1986), Riedesel et al. (1986) and Harvard centroid moment tensor inversion. 23 Harvard centroid moment tensor inversion.

7 SEISMIC STRAIN RELEASE, MEXICAN SUBDUCTION THRUST 313 TABLE 3 (continued) 24 G. Cruz, unpublished manuscript. 25 Wang et al., (1982). 26 From P-wave modeling (Singh et al., 1985a). 27 Magnitude given in Singh et at. (1981) is 7.9. An exhaustive study of the damage and felt reports suggests a larger magnitude, probably 8.1 (G. Suarez, personal communication, 1988). 28 Excluded because earthquake is intermediate depth and/or normal fault. 29 Excluded because earthquake is outside area. 30 Excluded because earthquake is an intraplate event close to Mexico City. 31 M 0 from the relation log M0 = log S , where S is the spectral amplitude (mm mm) near s period at LJppsala. 32 M0 from the relation log M0 = 1.177M mb from Abe (1981). m8 from Abe (1984). ~ Jiminez and Ponce ( ). 36 Excluded because earthquake is probably normal faulting at intermediate depth (Gonzalez-Ruiz and McNally, 1988). 3. Revised catalog and from Abe (1981) for if an event is listed in these catalogs. From Table 3 presents our catalog of all known large the Mv values in Table 3 are M~from Mexican earthquakes since 1800 (15 21 N, Abe (1981) plus From 1968 to the present, W),including earthquake times, ap- M~is taken from Earthquake Data Report (EDR), proximate locations, magnitudes and seismic mo- which we take to be the standard (Okal, 1989). M~ ments. To prepare Table 3 we began with the values for a few events, determined from Uppsala catalog of Singh et al. (1981) for the nineteenth seismograms by Singh et al. (1984a), have been century earthquakes. The magnitude Mv of the reduced by 0.18 unit. The earthquake of March earthquake of April 7, 1845 is listed as 7.9 by 26, 1908 was located at a depth of 80 km, by Singh et al. (1981). Exhaustive re-examination of Gutenberg and Richter (1954). The seismograms damage and felt reports of this earthquake sug- from Uppsala indicate a shallow depth. Table 3 gests a larger magnitude (G. Suarez, personal lists broad-band body wave magnitudes, mb, communication, 1988); a revised value of M~= 8.1, for intermediate depth earthquakes (Abe, 1981; listed in Table 3, is perhaps more reliable. All Abe, 1984). All such events for which focal mechaother magnitudes of the nineteenth century nisms are available are normal faulting in the earthquakes are the same as in Singh et al. (1981). subducted Cocos plate. Depths listed in Table 3 It would be circular to re-evaluate the magnitudes for events beginning in 1965 are mostly from of the nineteenth century earthquakes with the body-wave modeling of teleseismic long-period P- relations of Chavez and Castro (1988) since they waves. Finally, the earthquake of January 14, 1903 included these earthquakes in the calibration of is listed at a new location outside the area of their regressions. Abe and Noguchi (1983a) give primary interest (Nunez-Cornu, 1983; Nishenko = 7.9 for the earthquake of January 24, 1899, and Singh, 1987a). which is the same as the value estimated by Singh The reason for the difference in M~values of et al. (1981) from the isoseismal map. Abe and shallow earthquakes listed by Singh et al. (1984a) Noguchi (1983b) revised this magnitude to 7.5. and in Table 3 of this paper is worth pointing out. Because of uncertainties in the response of un- Abe (1981) proposed that the Mv reported in EDR damped Milne Thomson seismographs and in should be 0.18 unit greater than Mv values obview of damage reports we retained M~= 7.9 for tamed from the use of the original definition of this earthquake. Gutenberg (1945). With this in view, Singh et a!. For events of this century, Table 3 differs in (1984a) added 0.18 unit to the M~values of Abe several aspects from the catalog of Singh et al. (1981) to conform them to the current Mv defini- (1984a). For shallow earthquakes the M~ values tion. Furthermore, Abe and Noguchi (1983a, are taken from Abe and Noguchi (1983b) for 1983b) revised turn-of-the-century magnitudes.

8 I 314 J. ANDERSON ET AL. 21 * 1 ~ LARGE MEXICAN EARTHQUAKES, ( 20 * * /~ CITY 19 ~ / MICHOACAN ~ MEXICO ~ ~M0REL~ * * 18 ~ * PUED~( * * * * + * 0800RERO 17 * ~ ~ 16 ~7~ ~ *, ~=~ Epico,I.r 1N, p,5x lox kr~ 15 * * Fig. 5. Map of the Mexican subduction zone and locations of large events in Table 3. I These revisions were not included in the catalog of 4. Cumulative moment and average moment rates Singh et al. (1984). Additionally there is doubt whether 0.18 needs to he added to the catalogs of Our object is to evaluate the seismic slip be- Abe (1981) and Abe and Noguchi (1983b) to tween the North America plate and the underconform them to My values reported by EDR. thrust Cocos and Rivera plates. Some of the earth- Geller and Kanamori (1977) suggest that the quakes in Table 3 do not contribute directly to Gutenberg (1945) definition is essentially identical this relative motion, and for that reason they are with modern measurements, while Linekaemper excluded from our cumulative moment curves. (1984) suggests that adding 0.06 to the My values listed in Abe (1981) for events between 1910 and 1952, at a depth of less than 40 km, would adjust them to a scale compatible with EDR M~values. I As mentioned earlier we have taken M~values for 2, shallow earthquakes between 1900 and 1957 listed. in Abe and Noguchi (1983b) and Abe (1981) to be ~... compatible with EDR M~values. Uncertainties in e~. the My values of this century s earthquakes are ), not very critical for our study since for most earthquakes an Mo estimate is available either.~ from previous studies or from the Uppsala records C (Table 3). I~I Figure 5 shows a map of the study area, includ- Fig. 6. Cumulative seismic moment release curves for the entire ing all epicenters. Generally as one proceeds zone consmdered n this study. The catalog appears incomplete south-east along the subduction zone, the slip rate for the last century s earthquakes. The slope of the parallel lines enveloping the data since about 1870 is 0.93 ~ i0~dyn increases, the age of the subducted sea floor in-. cm per year. Lmnes with different slopes can he drawn to creases, the distance to the volcanic belt increases, envelope the data, depending upon the time period from the and the extreme moment decreases, catalog chosen for analysis, as suggested by broken lines.

9 I SF1SMIC STRAIN RELEASE. MEXICAN SUBDUCTION THRUST 315 2~ - I I r 4 101, 4 Fig. 7. Cumulative seismic moment release curve for the Rivera Fig. 9. Cumulative seismic moment release curve for Guerrero. plate subduction zone. The slope of the parallel lines envelop- Catalog of the past century s earthquakes appears reasonably ing the data, 0.112x 1027 dyn cm per year, is constrained from complete. The slope of the parallel lines enveloping the data. the plate slip rate (2.0 cm per year) assuming L = 280 km x 1027 dyn cm per year, suggests that seismic slip equals 2. plate slip and gives a current moment deficit of about 20 x 1027 W = 50 km, and a rigidity of 4x loll dyn cm dyn cm. The reasons for excluding an event, given in Table 3, include the following: (a) intermediate depth distance from the estimated pole of rotation beand/or normal fault event, and (b) the event is tween the Cocos and North America plate (Table intraplate and thus outside the zone of interest. 3). An additional feature on each of Figs is Figures 6 10 show the cumulative moment re- a plausible envelope of the cumulative moment lease for the entire Mexican subduction zone and release curves. The slope of each envelope is given for four distinct subregions along the zone. These in Table 4, together with the corresponding infour subregions are the Rivera plate and the ferred seismic slip rate based on a seismogenic Michoacan, Guerrero and Oaxaca segments of the width of 50 km and shear modulus of 4 x 1011 dyn Cocos plate subduction. The earthquakes were cm -2~ On the basis of the locations of aftershocks sorted into these four regions according to their and other small earthquakes, 50 km is apparently a lower bound for the seismogenic width (UNAM 01 H I I..0~. Fig. 8. Cumulative seismic moment release curve for Michoa- - - can. Either the catalog for last century s events is grossly Fig. 10. Cumulative seismic moment curve for Oaxaca. The incomplete or else the recurrence period of earthquakes of catalog appears complete since A slope of 0.23 x 1027 dyn September 19, 1985 type is larger than 185 years. Two sets of cm per year envelopes the data and suggests that the seismic parallel lines with slopes of 0.17x 1027 and 0.35 x 1027 dyn cm slip is about 60% of the plate slip and a current moment deficit per year are drawn to envelope the data. of about 8 x 1027 dyn cm.

10 316 J. ANDERSON ET AL. TABLE 4 Moment rates in Mexico Region or dm 0/dt Length Width Slip rates M0 deficit subregion (1027 dyn cm per year) (km) (km) Infer Expect ~ (1027 dyn cm) (cm per year) (cm per year) Mexico entire Rivera Michoacan <1 Guerrero Oaxaca ah Inferred Expected slip rates are based onathe shear Minster modulus and of Jordan 4.Ox 1011 (1978, dyn 1979) cmmodel for present-day plate motion between the Cocos and North America plates and between the Rivera and North America plates. Seismology Group, 1986; Singh et al., 1985a), could follow excursions outside the limits without although Nava et al. (1988) suggested, from mi- violating any physical constraints, either because croearthquake focal mechanisms and locations in the slopes are uncertain or because of periods of Guerrero, that seismic slip only occurs over a high or low seismicity. band km wide. There is uncertainty on how to draw the en- Figure 6 shows the results for the entire region velope on the moment release. Our preferred model and allows comparison with the results of Wang et was defined from a lower bound ( time-predictal. (1982). The moment release rate for the past able model of Shimazaki and Nakata) with a century appears smaller than that for this century, slope of 0.94 x 1027 dyn cm per year that interprobably at least in part because of incomplete- sects several corners of the staircase function since ness and/or underestimation of the magnitudes of Extrapolation of this moment rate line sugthe nineteenth century earthquakes (Singh et al., gests that for the catalog is deficient by 1981). (12 24) x 1027 dyn cm moment release. This is Since the 1860s, our estimate for the cumulative consistent with our belief that the catalog is inmoment curve has stayed between bounds with a complete by less than 24 x 1027 dyn cm since slope of 0.94 X 1027 dyn cm per year. The upper 1840, Two extreme alternatives for an upper bound bound is violated before the 1860s in a manner envelope for the moment release curve would seem that is consistent with incompleteness in the his- to be (a) the catalog from 1840 onwards which torical record. The appearance of the cumulative gives a rate of 0.83 x 1027 dyn cm per year, and curve changes qualitatively before the 1860s also, (b) the data from 1900 onwards which yields a showing fewer events. There is no physics in the rate of 1.44 x 1027 dyn cm per year. The extension boundaries to the cumulative moment curve drawn of the line corresponding to case (b) suggests that in Fig. 6, but rather only about 120 years of between 1840 and 1899 the catalog has either statistical experience. For a region of this size, missed events and/or their magnitudes have been these cumulative curves cannot have any time- or underestimated, corresponding to a moment reslip-predictable significance, since many source lease of about 50>< 10~ dyn cm (about five magareas are involved. Neither time predictability nor nitude 8 earthquakes). This is most unlikely. Case slip predictability (Shimazaki and Nakata, 1980) is (a) suggests that there is almost no current mooperating in the region as a whole. Many earth- ment deficit, defined by the separation of the quakes occur before the year corresponding to the cumulative moment curve and the upper envelope. intersection of the cumulative curve with the lower We interpret a small moment deficit as a statistiboundary, or release too little moment to reach cal statement that implies large earthquakes are the upper boundary. The cumulative moment curve unlikely, and a large moment deficit as a statisti-

11 SEISMIC STRAIN RELEASE. MEXICAN SUBDUCTION THRUST 317 cal statement that large earthquakes could occur. plate motion in the region is about 2 cm per year The size of the moment deficit gives an estimate (Minster and Jordan, 1979; Eissler and McNally, for the largest size earthquake that it is reasonable 1984). Assuming a length of 280 km, a seismoto anticipate. By the slip-predictable model of genic width of 50 km, and shear modulus of Shimazaki and Nakata (1980), a small moment 4 X 1011 dyn cm 2 we obtain a moment rate of deficit would imply that no earthquakes should be 0.11 x 1027 dyn cm per year. The envelope to the expected in the region in the near future because cumulative curve on Fig. 7 has this slope, and it is the seismic slip is at present caught up with reasonable as a lower bound to the cumulative plate tectonic motions. As will be discussed, we curve. At this rate, it takes 145 years to accubelieve that the Mexican subduction zone is cur- mulate the seismic moment that was released in rently likely to experience one or more large earth- the 1932 earthquakes. The recurrence is perhaps quakes, particularly in Guerrero (Fig. 9), and thus delayed by smaller events such as those that apthe conclusion from case (a) that large earth- pear on Fig. 7 before the 1932 sequence. An quakes are unlikely on either statistical or physical estimated recurrence interval of 77 years was given grounds would be erroneous. earlier by Singh et al. (1985) on the basis of Wang et al. (1982) obtained dm 0/dt = 1.6 X W= 280(see kmalso andnishenko a shear modulus and Singh, of 1987c). 5 x lollcon- moment dyn cm deficiency per year, of and 42 x suggested 1027 dyn acm. current The cm sidering the short historical record compared with dyn 1027 southeastern limit of their study area extended to these possible repeat times, it is not possible to 900 W, while our limit is 950 W. We exclude events differentiate between these two assumptions. southeast of Oaxaca because these represent inter- The cumulative moment release for the Michoaction of the Cocos plate with the Caribbean acan segment is likewise dominated by one large plate, not the North America plate. The dif- event, in September 1985 (Fig. 8). Assuming ferences arise for more reasons than geographic (without good justification) that the cumulative coverage. Their rate is defined by the peaks corre- moment curve is currently near an upper bound, sponding to case (b) above. The revised magni- the range of moment rates which we can estimate tudes in Table 3, while still somewhat uncertain, from the historical catalog is ( ) x 1027 have reduced these peaks. Because of this and the dyn cm per year. The lower rate depends on inconsistency with the nineteenth century record catalog completeness since 1818, which we conmentioned above, Wang et al. probably overesti- sider unlikely. The higher rate is defendable only mated the moment deficit, if the moment of the 1911 earthquake is under- Now we explore whether the envelopes of estimated from the Uppsala record and the hiscumulative moment curves of subregions (Figs. torical record is substantially incomplete in the 7 10) lead to conclusions that are more informa- 1800s. (There is uncertainty about the earthquake tive than those obtained from treating the region of June 19, This event is one of the most as a unit. Within smaller units, the repeat of major strongly felt earthquakes in the history of Mexico earthquakes becomes more dominant in the City. The damage distribution suggests a normal cumulative moment curves, and thus the results faulting event in the subducted Cocos plate (Singh might more nearly represent the fundamental et al., 1985a), and is the basis for it being excluded physical process. from the cumulative moment curve in Fig. 8. Figure 7 shows the cumulative moment release However, it is possible that it was an interplate from the Rivera plate subduction. The seismic event in the Michoacan region. If so, it may have activity is dominated by earthquakes of June 3 released more moment than the earthquake of and June 18, These two events ruptured a September 19, 1985.) On the basis of the assumplength of about 280 km (Singh et al. 1985b). The tions above and in Table 4, the moment rates moment release during the nineteenth century mentioned above imply a slip rate of cm events and the two earthquakes in 1900 is only per year compared with the rate of 6.0 cm per year about 40% of the 1932 earthquakes. The relative obtained from the Minster and Jordan (1978)

12 318 J. ANDERSON ET At.. model for present-day plate motions. Thus relative tion, the 1982 earthquakes, although small. repreto our assumptions, there might be some aseismic sent major stress-relieving earthquakes in Ometeslip in the Michoacan region. However, given the pec, and the repeat of an event there would not be tendency of the region to break in infrequent large expected in the near future. We cannot contradict earthquakes, the seismic moment rate here is very that conclusion, but observe that none of the poorly determined. earthquakes in the Ometepec region have been The cumulative moment release for Guerrero very large. The moments of the December 23, (Fig. 9) is estimated to be 0.37 X 1027 dyn cm per 1937, December 14, 1950 and June doubyear. Thts corresponds to a slip rate of 6.2 cm per let are only 1.6 x 1027 dyn cm, 0.9 x 1027 dyn cm, year, which is about 90% of the plate tectonic 27 0,27 x 10 dyn cm and 0.25 x 10 dyn cm respecvalue of 6.8 cm per year. On the basis of this tively, and the sum is only about 3>< 1027 dyn cm. envelope the moment deficit in Guerrero is about compared with 9 x 1027 dyn cm that would accu- 20 x 1027 dyn cm. There is a general consensus mulate in 92 years, , under our assumpamong seismologists that this segment includes a tions of a seismogenic zone 50 km wide and a mature seismic gap (e.g. Kelleher et al., 1973; shear modulus of 4 x 1011 dyn cm 2. The year McCann et a!. 1979, Singh et al. 1981, 1982; 1890 is taken as the start of the interval because McNally, 1981; UNAM Seismology Group, 1986; the 1890 event was the prior earthquake in the Nishenko and Singh, 1987b, 1987c; Gonzalez-Ruiz Ometepec region. Thus perhaps only one-third of and McNally, 1988). For part of this gap Astiz et the slip in Ometepec occurs as coseismic strain al. (1987) suggest a moment release of 10 x 1027 release, but it is also possible that a larger earthdyn cm in a single great earthquake or sequence of quake might rupture Ometepec, and adjacent resmaller earthquakes. Their estimate is based on gions, and increase the fraction of seismic slip. the relation between the average seismic moment Finally, the cumulative moment curve for (M 0 in dyn cm) and average recurrence period (T Oaxaca is shown in Fig. 10, The bounds, which in years) for large earthquakes in the Mexican appear to he relatively unambiguous, have a slope zone, i.e. of 0.23 x 1027 dyn cm per year, and a current log T=O.333 log M deficit of 8 x 1027 dyn cm from the bound drawn... in that figure. Converted to slip rate, this gives an Our estimate of the moment deficit is con- unexpectedly low value of 4,4 cm per year, cornsistent with Astiz et a!. (1987) since the Guerrero pared with the plate convergent rate of 7.5 cm per subregion defined in this study is about two times year for this subregion (Minster and Jordan, 1978). the length considered by them, The seismic events McNally and Minster (1981) suggested that the between 1899 and 1912 released a moment of seismic slip rate matches the plate convergence about 20>< 1027 dyn cm. With 1845 as the prior rate locally in Oaxaca. There are several difoccurrence of an earthquake in the zone, one ferences in the details to account for this disobtains a repeat time of about 62 years (1907 crepancy. They only used earthquakes since 1928, 1845), and a perfectly periodic repetition would the moments were estimated from M0 or the have implied a repeat in about Similarly, aftershock area, they included the earthquake of Gonzalez-Ruiz and McNally (1988) have found January 15, 1931 (My 8.1) which we have excluded variability in the character and repeat times of because it was a normal faulting event (Singh et earthquakes in Ometepec, in the southwest quarter al. 1985a), and they used a different shear modof the Guerrero region. ulus, a different seismic width, and have defined It may be informative to divide the Guerrero their average for a smaller length of the trench. region into even smaller regions. Gonzalez-Ruiz While for our assumptions the seismic slip rate in and McNally (1988) consider Ometepec to be Oaxaca, averaged over a length of 300 km (Table most likely a distinct segment of the Mexican 4), is about 60% of the plate convergence rate, it trench that ruptures independently from the parts may be that in some smaller areas of the Oaxaca of Guerrero to the northwest, In their interpreta- subregion the seismic slip and the plate conver-

13 SEISMIC STRAIN RELEASE. MEXICAN SUBDUCTION THRUST 319 gence rates are equal as suggested by McNally and aseismic slip but the fraction is poorly determined. Minster. The two Guerrero events below the correlation line (at My values of 6.9 and 7.0, and M 0 below 0.3 >< 1027) are the 1982 Omtepec earthquakes. 5. Discussion The Omtepec region was discussed above for its low historical fraction of seismic slip. Omtepec is There appears to be some correlation between in the south-eastern-most section of Guerrero. and the fraction of tectonic slip that is coseismic and so could have been wholly or partly included in one characteristic of the seismic radiation. The the Oaxaca region instead, By the criterion of the radiation characteristic is the relative excitation of My_~M0 residual the 1982 earthquakes seem to 20 s surface waves, represented by My, and have a greater affinity with Oaxaca than with s surface waves, represented by M0 estimated from Guerrero but the 1950 and 1962 Omtepec earth- Uppsala. Figure 11 replots M0 as a function of My quakes, which are farther from Oaxaca than the for all events in our catalog, with different sym earthquakes (Table 3). fall above the rebols to represent the region of origin. gression on Fig. 11. suggesting affinity with Guer- Events on the regression curve in Fig. 11 were rero instead. mostly determined from the regression; therefore Physically, events above the regression show a it is the events that fall off the regression that are richer excitation of s or longer period enmost interesting. Events from Oaxaca on Fig. 11 ergy compared with 20 s periods, while events mostly fall well below the regression; from Table below the regression show a relatively lower cxci- 4 Oaxaca had an estimated 60% seismic slip. Events tation of the longer periods. From another viewfrom Guerrero mostly fall well above the regres- point, the events in Oaxaca have apparently been sion; in Guerrero we estimated that essentially all more efficient at generating 20 s surface waves the slip is seismic. Events from Michoacan gener- than the events with the same moment to the ally fall between those from Guerrero and Oaxaca; northwest. We do not believe that the difference is in Michoacan our calculations suggested some entirely a result of systematic errors in moment determinations, as could result from changing dip of the subduction zone or propagation path. The I I I I I I 1 o / path to Uppsala begins to cross the Gulf of Mexico 10 // from events in Oaxaca, but not for events from / Michoacan or Guerrero. However, seismograms 4. with comparable levels of 40 and 20 s surface / waves can be found for events in Michoacan and a o F Oaxaca. Figure 12 shows the Uppsala seismo- A grams from six events. Two Guerrero events, 1907 and 1957, have abnormally high moments corno,,7 pared with regression, one Michoacan event (1941) ~ ~o / ~ and one Oaxaca event (1928) are near the re- A gression. and two Oaxaca events, 1978 and 1965, // are substantially below the regression in Fig. 11. / The 1907 and 1957 events clearly have excited much stronger 40 s surface waves than those from A Oaxaca, Although teleseismic P-wave modeling suggests a shallow depth (h <20 km) for all large interplate earthquakes of Mexico which have oc- Fig II M0 as a function of M: G, Oaxaca; ~, Guerrero: ~ curred since 1928 (e.g. Chael and Stewart, 1982; Michoacan. For events falling on the line, M0 has been con- Singh et al., 1984b; Astiz et al., 1987; Singh et al., verted to M1, using eqn. (2). in preparation), the stronger excitation of 40 s

14 320 J. ANDERSON ET AL. Apr.I , Cuerre~ C ~P~ 7A07~J\/L/f\~C\f/ I~, f ~JlP/~Ii~~1JI[II. f~,~ ~ 7 S Joy 25, 1957, Gye~re1 E ~ 1/, C 3, Ap~ 15, 941, ~ 00 - ~ /1 ~ -o Jolle 17, 1928, Dyacca ~ ~//~[5-of r0//1fvj~n~f~foo~ 5f5 J/o 3jCi~t~ 30 ni 0/ 1 - ri Coo7IJ~f,/fC1~. 77 ~ Aog 23, 1985, Oaeacc niir if ~ Fig. 12. Six selected seismograms showing differing relative levels of 20 s and 40 s period surface waves. surface waves may suggest a source which involves differ at high frequencies, and therefore it is not faulting at greater depths. There are of course clear that they will fall in the same category as the several geophysical explanations for the observa- existing data. This is a practical matter of great tion. One is that the brittle failure region of the importance for earthquake design practices on the subduction zone is not as wide in Oaxaca, so that coast of Mexico, since the peak ground accelerathe downdip part of the subduction zone tends to tions from the 1985 Michoacan earthquake and fail by creep or slow earthquakes (e.g. Kanamori, the 1978 Oaxaca earthquake were unexpectedly 1988). Another possibility is that failure of the small (Anderson et a!., 1985). deeper part of the subduction zone in Oaxaca has not occurred in the twentieth century but still might happen. Another way to look at the anomaly 6. Conclusions in Fig. 11 is in terms of stress drop. The greater excitation of 20 s surface waves, indicated by the Our study of the cumulative seismic strain enhigher magnitudes in Oaxaca, could be interpreted ergy release along the Mexican subduction zone as representing a higher stress drop for the Oaxaca (up to 95 0 west) is based on revised magnitude earthquakes. We have no reason to expect this on and moment values and therefore is more reliable the basis of the sea-floor topography or the surface than previous such studies. The envelopes of the geology, and we do not know why this difference cumulative moment curves in Figs are, of in stress drop would occur. course, only statistical interpretations of imperfect There is an important corollary to this. None of data, not physical constraints. If the cumulative the earthquakes since the beginning of strong mo- moment stays within these envelopes in the future, tion recordings in Mexico have excited the strong then these figures give current moment deficits 40 s waves relative to the 20 s waves. Thus such and an estimate of the longest duration that a events are not represented in the strong motion subduction zone element could have without an data set in Mexico. It is unknown how these might earthquake. We find that from the cumulative

15 321 SEISMIC STRAIN RELEASE. MEXICAN SUBDUCTION THRUST moment curve for the entire subduction zone (up to west) a reliable estimate of current mornent deficit cannot be obtained. If the zone is divided into smaller segments a clearer picture for the Guerrero and Oaxaca (but not for the Rivera plate and Michoacan) subregions emerges. While in Guerrero and perhaps along the Rivera plate and in Michoacan the seismic slip roughly equals the plate slip (when the seismogenic width and the rigidity are taken as 50 km and 4 x 1011 dyn cm2 respectively), it is only about 60% of the plate slip in Oaxaca. The most likely scenario for the next 15 years is about (20 25) X 1027 dyn cm moment release along the entire zone considered here. The current seismic gaps are Guerrero, areas in Oaxaca, and northwest of Colima, with possible moment releases of 77 (15 20) x 1027 dyn cm. 5 X 10- dyn cm, and 3 2< lo27dyn cm respectively. 950 Acknowledgements actermstmcs of earthquakes in the Michoacan seismic gap in Mexico. Bull. Se,smol. Soc. Am., Chad. E. and Stewart. G.S Recent large earthquakes along the Middle America trench and their implications for the subduction process. J. Geophys. Res.. 87: Chavez. M. and Castro. R Attenuation of Modified Mercalli Intensity with distance in Mexico. Bull. Seismol, Soc. Am.. 78: ics of the Rivera plate and implications for the 1932 Jalisco, Mexico. earthquake. J. Geophys. Res.. 89: Ekstrom, G. and Dziewonski, A A very broad band Eissler, H.K. and McNally. K.C Seismicity and tecton- analysis of the Michoacan. Mexico earthquake of Septem- ber Geophys. Res. Lett., Seismic moments of large Mexican subduction earthquakes since 1907 (abstract). EOS. Trans. Am. Geophys. Espindola, J.M.. Singh. 5K.. Yamamoto. J. and Havskov. J.. Union, 62: 948. Geller, Ri. and Kanamori, H Magnitudes of great shallow earthquakes from 1904 to Bull. Seismol. Soc. Am., 67: Gonzalez-Ruiz, JR. and McNally, K.C Stress lation and release since 1882 in Ometepec. Guerrero. Mexico: Implications for failure mechanisms and risk assessments of a seismic gap. J. Geophys. Res.. 93: Gutenberg. B Amplitudes of surface waves and magnitudes of shallow earthquakes. Bull. Seismol. Soc. Am.. 35: This paper benefitted from a careful review by George Purcaru. The work was supported by the National Science Foundation under grants CEE , ECE and CES References Abe, K Magnitudes of large shallow earthquakes from 1904 to Phys. Earth Planet. Inter.. 27: Abe, K., Complements to Magnitudes of large shallow earthquakes from 1904 to Phys. Earth Planet. Inter., 34: Gutenberg. B. and Richter, CF Seismicity of the earth and associated phenomena, 2nd edn.. Princeton University Press. Princeton. NJ, 310 pp. Haskov, J., Singh, S K, Nava. E.. Dominguez. T. and Rodriguez. M Playa Azul, Michoacan. Mexico earthquake of 25 October 1981 (My = 7.3). Bull. Seismol. Soc. Am.. 73: Houston, H. and Kanamori, H., Source characteristics of the 1985 Michoacan, Mexico earthquake at short periods. Geophys. Res. Lett.. 13: , Jiminez. Z. and Ponce. L Focal mechanism of six large earthquakes in northern Oaxaca. Mexico. for the period Geofis. mt., 17: Kanamori. H Mechanism of low frequency earthquakes (abstract). EOS. Trans. Am. Geophys. Union. 69: Abe. K. and Noguchi, S., 1983a. Determination of magnitude Kelleher, J.A.. Sykes, L.R. and Oliver. J Possible criteria for large shallow earthquakes Phys. Earth Planet. Inter.. 32: Abe. K. and Noguchi. S b. Revision of magnitudes of for predicting earthquake locations and their applications to major plate boundaries of the Pacific and Caribbean. J. Geophys. Res., 78: Lay. T. and Wallace, T.C., Multiple ScS attenuation and travel times beneath western North America. Bull. Seismol. large shallow earthquakes, Phys. Earth Planet. Inter., 33: Anderson, J.G.. Bodin. P., Brune. in.. Prince, J., Singh, S.K.. Quaas, R. and Onate, M Strong ground motion and Soc. Am., 78: LeFevre, LV. and McNally. K.C Stress distribution source mechanism of the Mexico earthquake of September (My = 8.1). Science 233: and subduction of aseismic ridges in the Middle America subduction zone. J. Geophys. Res.. 90: Astiz, L. and Kanamori. H An earthquake doublet in Linekaemper, J.J Comparison of two surface-wave magnitude scales: M of Gutenberg and Richter (1954) and My of Preliminary Determination of Epicenters. Bull. Seismol. Soc. Am., 74: Omlepec. Guerrero. Mexico. Phys. Earth Planet. Inter., 34: Astiz, L., Kanamori, H. and Eissler, H., Source char-

16 322 McCann, W.R., Nishenko, S.P., Sykes, L.R. and Krause, i.h., Seismic gaps and plate tectonics: seismic potential for major boundaries. Pure AppI. Geophys.. 117: McNally, K.C Plate subduction and prediction of earthquakes along the Middle America trench. In: D.W. Simpson and PG. Richards (Editors), Earthquake Prediction, J. ANDERSON ET AL. Reyes, A., Brune, J.N. and Lomnitz, C Source mechanism and aftershock study of the Colima, Mexico earthquake of January 30, 1973, Bull. Seismol. Soc. Am.. 69: An International Review, Maurice Ewing Series 4, Amen- Riedesel. MA., Jordan. T.H.. Sheehan. A.F. and Silver. PG Moment tensor spectra of the 19 Sept and 21 Sept Michoacan. Mexico, earthquakes. Geophys. Res. can Geophysical Union, Washington, D.C., pp McNally, K.C. and Minster, J.B., Nonuniform seismic slip rates along the Middle America trench. J. Geophys. Lett.. 13: Shimazaki, K. and Nakata, T Time-predictable recurrence model for large earthquakes. Geophys. Res. Lett., 7: Res., 86: Minster. J.B. and Jordan. TI-I Present day plate motions. J. Geophys. Res., 83: Minster. J.B. and Jordan, T.H., Rotation vectors for Philippine and Rivera plates (abstract), FOS. Trans. Am. Geophys. Union, 60: 958. Nava. A., Gonzalez-Ruiz, L., McNally. K.C.. Simila, G.W., Singh. 5K. and Wyss, Orizaba earthquake M Source parameters of the of August Geofis. Int., 16: Singh. 5K., Astiz. L. and Havskov, J., Seismic gaps and recurrence periods of large earthquakes along the Mexican the lnterinstitutional Working Group for Deep Seismic Profiling in Guerrero, Mexico A microearthquake study in the Guerrero-Ometepec, Mexico. region and the shallow earthquake generation band of the Middle America trench (abstract). EOS, Trans. Am. Geophys. Union. 69: Nishenko, S.P. and Singh, 5K., 1987a. Relocation of the great Mexican earthquake of 14 January Bull. Seismol. Soc. Am., 77: subduction zone: a reexamination. Bull. Seismol. Soc. Am.. 71: Singh, 5K., Espindola, i.m., Yamamoto, J. and Havskov, i., Seismmc potential of Acapulco-San Marcos Region along the Mexican Subduction Zone. Geophys. Res. Lett., 9: Singh. 5K.. Rodriguez. M. and Espindola, J.M., 1984a. A catalog of shallow earthquakes of Mexico from 1900 to Bull. Seismol. Soc. Am., 74: Singh, 5K., Dominguez. T.. Castro, R. and Rodriguez, M., 1984b. P waveforms of large shallow earthquakes along the Nishenko. S.P. and Singh. 5K., 1987b. The Acapulco-Omete- Mexican subduction zone. Bull. Seismol. Soc. Am., 74: Munguia. L., Gonzalez-Ruiz, JR., Gonzalez-Garcia, i. and pee, Mexico, earthquakes of : evidence of varia ble recurrence history. Bull. Seismol. Soc. Am., 77: Singh. 5K.. Suarez. G. and Dominguez, T., 1985a. The Oaxaca, Nishenko. S.P. and Singh, 5K., 1987c. Conditional prohahilities for the recurrence of large and great interplate earthquakes along the Mexican subduction zone. Bull. Seismol. Soc. Am.. 77: Mexico earthquake of 1931: lithospheric normal faulting in the subducted Cocos plate. Nature (London), 317: Singh. 5K.. Ponce. L. and Nishenko, S.P b. The great Jalisco. Mexico earthquakes of 1932: subduction of the Rivera plate. Bull. Seismol. Soc. Am.. 75: Nunez-Cornu, F.J Seismotectonica del Estado de Oaxaca. Mexico basado en el analisis de temblores fuertes (My> 7.0), MS. Thesis, Facultas de Ciencias. U.N.A.M.. Mexico. UNAM Seismology Group, The September 1985 Michoacan earthquakes: aftershock distribution and history of rupture. Geophys. Res. Lett., 13: Wang. S-C.. McNally. K.C. and Geller, Ri Seismic Okal, E.A., A theoretical discussion of time-domain magnitudes: the Prague formula for M~and the mantle magnitude Mm. i. Geophys. Res.. 94: Pniestley, K.F. and Masters, T.G Source mechanism of the September 19, 1985 Michoacan earthquake and its implications. Geophys. Res. Lett., 13: strain release along the Middle America Trench. Mexico. Geophys. Res. Lett.. 9: Yamamoto. i., iiminez, Z. and Mota. R., El temblor de Huajuapan de leon. Oaxaca, Mexico, de 24 de octubre de Geofis. Int., 23: