Print version ISSN 0016-7169
Geofís. Intl vol.47 no.4 México Oct./Dec. 2008
An exploratory study for rapid estimation of critical source parameters of great subductionzone earthquakes in Mexico
S. K. Singh1,*, X. PérezCampos1, A. Iglesias1 and J. F. Pacheco1
1 Instituto de Geofísica, Universidad Nacional Autónoma de México, Del. Coyoacán, 04510 México City, México. *Corresponding author: email@example.com
Received: March 5, 2008
Accepted: August 28, 2008
Para una estimación oportuna del potencial de daño y tsunami asociado a los grandes temblores de subducción en México, resulta crítica la determinación rápida y confiable de parámetros sismológicos como lo son la magnitud de momento (Mw), la energía sísmica radiada (Es) y la localización y el tamaño de la ruptura. Para alcanzar este objetivo, la red sismológica de banda ancha mexicana necesita ser complementada con estaciones GPS permanentes localizadas a lo largo de la costa del Pacífico mexicano espaciadas, por lo menos, cada 65 km. Los datos de esta red GPS requieren ser transmitidos a una estación central y procesados en tiempo real para monitorear la posición de las estaciones. Asumiendo que lo anterior estuviera implementado, en este trabajo desarrollamos una metodología para la estimación rápida de parámetros críticos de la fuente sísmica y demostramos su viabilidad aplicándola al análisis del sismo de ColimaJalisco de 1995 (Mw=8.0) y de SumatraAndamán de 2004 (Mw=9.09.3). Para este par de temblores, la metodología propuesta arrojó valores de Mw y Es que son muy similares a los reportados anteriormente, obtenidos a partir de análisis detallados. En el caso del sismo de ColimaJalisco la localización estimada y el tamaño del área de ruptura están de acuerdo con los valores que se pueden inferir a partir de las localizaciones de las réplicas. Actualmente existen 13 estaciones GPS permanentes a lo largo de la costa del Pacífico mexicano con un espaciamiento promedio de ~200 km, las cuales operan de manera autónoma. Es urgente incrementar este número de estaciones a >28 (logrando un espaciamiento de <65 km), así como transmitir los datos y determinar la posición de las estaciones en tiempo real (preferiblemente cada segundo).
Palabras clave: Alerta de tsunami, sismología de tiempo real, grandes temblores mexicanos.
The rapid and reliable estimation of moment magnitude Mw, location, and size of rupture area, and radiated energy Es of great Mexican subduction zone earthquakes is critical for a quick assessment of tsunami and/or damage potential of the event and for issuing an early tsunami alert. To accomplish this goal, the Mexican broadband seismic network needs to be supplemented by permanent GPS stations along the Pacific coast, spaced about 65 km apart or less. The data from the GPS network must be transmitted to a central location and processed in nearreal time to track the position of the stations. Assuming that this can be implemented, we develop a procedure for nearreal time estimation of the critical source parameters. We demonstrate the viability of the procedure by processing nearsource GPS data and regional seismograms for the earthquakes of ColimaJalisco in 1995 (Mw=8.0) and SumatraAndaman in 2004 (Mw=9.09.3). The procedure yields estimates of Mw and Es in excellent agreement with those reported from earlier solutions. In the case of the ColimaJalisco earthquake, the estimated location and size of rupture area agree with that mapped from aftershock locations. Presently, there are 13 permanent GPS stations along the Pacific coast of Mexico with an average spacing of ~200 km which operate in an autonomous mode. It is urgent to increase the number of stations to >28 thus decreasing the spacing of stations to <65 km. Data must be transmitted in nearreal time to a central station to track the position of the stations, preferably every second.
Key words: Tsunami alert, real time seismology, large Mexican earthquakes.
Rapid estimation of critical source parameters of great (Mw > 8.0) subductionzone earthquakes of Mexico is of importance to civil protection authorities in organizing postseismic recovery. These parameters may provide a first glimpse at possible damage and casualties. They are also useful for early tsunami warning, a topic of general concern after the tsunami caused by the 26 December, 2004 SumatraAndaman earthquakes that killed about 200,000 people.
In the last century, several earthquakes have generated moderate, local tsunamis along the Pacific coast of Mexico, notably the ColimaJalisco earthquakes of 3, 18, and 22 June, 1932, M=8.2, 7.6, 7.0, respectively; the Michoacan earthquake of 19 September, 1985, Mw=8.0; and the ColimaJalisco earthquake of 9 October, 1995, Mw=8.0 (Farreras, 1997). There is also evidence of much larger tsunamis along the Mexican coast. For example, Suárez and Albini (2008) and NúñezCornu and Ortiz (2008), based on historical documents, suggest that the earthquake of 28 March, 1787 may have caused the largest tsunami in Mexico since 1700. The earthquake probably ruptured a 400 kmlong segment (M~8.4) along the coast of Oaxaca (Suárez and Albini, 2008). Early warning may not be useful to populations in the nearsource region of Mexico unless it can be issued in less than 10 minutes or so. This is because the peak in the tsunami height may reach the coast about 1015 minutes after the origin time of the earthquake (M. Ortiz, personal communication, 2007). Such a warning may, however, be quite useful for more distant coastal areas.
Rapid assessment of tsunami and/or damage potential of a great earthquake requires nearreal time estimation of (1) the moment magnitude (Mw), (2) the location and the size of the rupture area, and (3) the radiated seismic energy (Es). An earthquake of great magnitude whose rupture area partly lies below the continent has relatively enhanced highfrequency radiation and will probably generate severe ground motions, causing damage to engineering structures and loss of life. On the other hand, when the rupture area lies offshore and the highfrequency radiation is relatively depleted, the earthquake may not produce large, destructive ground motions but may have a higher tsunamigenic potential. The challenge is to estimate these parameters rapidly. In this paper, we propose and partly validate a strategy for quick and reliable estimation of the parameters mentioned above. Finally, we discuss the steps needed for its routine implementation in Mexico.
Estimation of Mw, and the location and size of the rupture area
For great earthquakes, the desirable magnitude to be estimated is the moment magnitude, Mw, which is based on very longperiod seismic waves and/or coseismic static deformation. Unlike magnitudes computed from amplitudes of shorterperiod waves, Mw does not saturate. Regional broadband seismograms from the Mexican seismic network, alone, may not be sufficient to estimate Mw as these records may get clipped during great events. Even if the seismograms are on scale, very longperiod waves may not be well developed at regional distances to permit reliable estimation of the seismic moment and, hence, of Mw of great earthquakes. For the SumatraAndaman earthquake, freeoscillation data at periods of about 1 hour were required to obtain a reliable estimate of Mw (Stein and Okal, 2005; Park et al., 2005; Lay et al., 2005). This estimate was later confirmed from modeling of static displacements observed in the near and farfield (e.g., Banerjee et al., 2005; Vigny et al., 2005).
As broadband seismograms are not sufficient to determine Mw of great earthquakes in Mexico, we must complement them with data on static displacements. Double integration of accelerograms might also provide the desired static displacement field: for example, the nearfield accelerogram recorded at Caleta de Campos (CALE) during the Michoacan earthquake of 19 September, 1985, Mw=8.0, when integrated (Fig. 1), indicated an uplift of the coast by 1 m (Anderson et al., 1986). This was independently confirmed from data on mortality of intertidal organisms (Bodin and Klinger, 1986). However, double integration of accelerograms is often unreliable because of baseline offsets in the acceleration time history, hysteresis of the accelerometer, and possible tilt and rotation of the site (e.g., Iwan et al., 1985; Boore, 2001; Clinton, 2004; Emore et al., 2007). As Fig. 1 shows, the static displacement at CALE for the Michoacan earthquake was not obtained by simple double integration of the accelerogram but involved some subjective judgment. It follows that permanent GPS stations, whose positions can be tracked in near real time, may be required for rapid mapping of static displacement field caused by great earthquakes.
Fig. 2 shows theoretical surface displacements in the near field caused by shallow dipping, thrust earthquakes of Mw=8.0 and 8.4 buried in a half space. The calculations are based on Okada's model (1992). For both earthquakes, the fault is approximated by a rectangle of width, W, of 80 km and dip, δ, of 150. The rake, λ, is taken as 900. The deep edge of the fault is at a depth d of 25 km. Numerous studies on seismicity, and on large earthquakes and their aftershocks show that these parameters are reasonable for earthquakes with Mw>7.8 along the Mexican subduction zone, from Jalisco to Tehuantepec (see, e.g., Chael and Stewart, 1982; Singh et al., 1985; Singh and Mortera, 1992; Suárez et al., 1990; Pacheco and Singh, 2008). The fault parameters used in generating Fig. 2 are listed in Table 1.
The coordinate system used in the computation is the same as in Okada (1992). From frames on the right of Fig. 2 we note that: (1) the hinge line for vertical displacement, Uz, is at a distance of ~13 km toward the trench from the projection of the deepest part of the fault. With respect to the hinge line, Uz is negative towards the continent and positive towards the trench. (2) While magnitude and polarity of Uz are very sensitive to the position of observation point with respect to the hinge line, the horizontal displacement in the direction perpendicular to the strike of the fault (Uy, blue triangles) is much less so. (3) Uy falls off quickly beyond the edge of the fault.
These properties may be used to delimit the rupture areas of great earthquakes from observed static displacements along the Pacific coast of Mexico. For example, if Uz is negative along the coast (subsidence), the horizontal projection of the edge of the fault can be no further inland than 13 km from the coast. If, however, Uz is positive (uplift), then the fault projection must be more than 13 km inland. Consider the Michoacán earthquake of 19 September 1985 (Mw = 8.0). The earthquake caused an uplift of the coast by 1 m (Fig. 1). In this case, we would expect the rupture to extend more than 13 km inland. In fact, an aftershock study indicated that nearly half the rupture area was below the continent (UNAM Seismology Group, 1986). For this reason, only about half the rupture area would have been involved in the uplift of the ocean floor and in tsunami generation. In fact, the earthquake caused only a minor, local tsunami (Farreras, 1997).
The length of the fault can be roughly estimated from the amplitude of horizontal displacement vectors, since their amplitudes decay rapidly beyond the edge of the fault. Once the approximate dimension of the fault is known, the static horizontal displacements can be used to estimate M0, and, hence, Mw of the earthquake. As we discuss later, a relatively dense array of GPS stations along the Pacific coast of Mexico will be required for reliable estimation of Mw.
We recall that the trench from Puerto Vallarta to Puerto Angel is ~80 km offshore. As W of Mw >7.6 earthquakes is ~80 km, the horizontal projection of the deepest part of the rupture lies only slightly inland or offshore. As discussed above, in this case the location and size of the rupture can be estimated from static displacements observed on the coast. This may not be so for the subduction segment between Tehuantepec and Tapachula since the trench here is ~150 km offshore. In this case, it will be difficult to find the location and the size of the rupture from coastal static field data without careful analysis.
A large magnitude earthquake with a location near the trench of a subduction zone is potentially a tsunamigenic event. Such events may also be deficient in highfrequency radiation and, hence, give rise to relatively low accelerations on land. Tsunami earthquakes which, by definition, generate disproportionately large tsunamis in relation to their surfacewave magnitudes (Kanamori, 1972), are deficient in highfrequency radiation. Such events are characterized by large (MsMw) and (mbMw) disparity (Kanamori and Kikuchi, 1993; Kanamori, 2006), and anomalously low value of Es/M0 (Newman and Okal, 1998; Ammon et al., 2006), where Ms and mb are surfacewave and shortperiod bodywave magnitudes, respectively. Clearly, a rapid estimation of Es is important for understanding the nature of the source and detecting tsunami potential and/or damage potential of the earthquake. In fact, for early tsunami warning, the Pacific Tsunami Warning Center (PTWC) now calculates both longperiod magnitude and Es/M0 in nearreal time (Weinstein and Okal, 2005). The radiated energy at PTWC is estimated from the integration of velocitysquared P wave spectra at teleseismic distances following the method of Boatwright and Choy (1986).
For nearreal time estimates of Esof large Mexican earthquakes, we propose to use broadband records at regional distances. Es can be estimated from integration of velocitysquared spectra of the Swave group after applying corrections for anelastic attenuation and site effects (Singh and Ordaz, 1994; PérezCampos et al., 2003). Es can also be estimated using the empirical Green's function (EGF) technique. This method has the advantage that it does not require corrections for attenuation and local site effects. Recordings of a smaller earthquake from the same region where a great earthquake has just occurred can be used as EGF. The location and focal mechanism of the EGF and the large, target event should be similar. However, a study by Venkataraman et al. (2002) suggests that the estimates are robust with respect to moderate difference in the focal mechanisms of the mainshock and the EGF. The magnitude of the target event should be at least 2 units greater than that of the EGF. Assuming pointsource, farfield approximation to be valid, Es can be written as (Vassiliou and Kanamori, 1982):
where M0(f) is the moment rate spectrum, ρ is the density and β is the shearwave velocity in the source region. Let fc be the corner frequency of the earthquake. At frequencies f << fc , M0( f ) = M0, so that Es in the frequency range of 0 to fi, where fi << fc, is given by
For a Brune ω2source model (Brune, 1970)
so that for f >> fc, M0( f )( fc /f )2. In this case, Es in the frequency band of fu to ∞, where fu >> fc, is given by
The following steps would be required for a rapid estimation of Es of a great earthquake using the EGF technique:
(1) Locate the earthquake and determine its focal mechanism from regional moment tensor inversion.
(2) From computer archives containing recordings of moderate earthquakes with known location, M0, corner frequency, and focal mechanism, retrieve the event whose location and mechanism is similar to that of the large earthquake.
(3) Compute spectral ratio of Swave group of the large earthquake to the EGF event at each station.
(4) Multiply the ratios by the seismic moment of the EGF to obtain the median M0(f).
(5) Use equations (1a) to (1c) to estimate Es. The choice of the upper limit of integration, fu, is critical since the corner frequency of the EGF affects M0(f) (e.g., Iglesias and Singh, 2007). If Mw of the EGF is less than or equal to 6, then the upper limit of integration could be set to 0.2 Hz. The contribution to Es from f > 0.2 Hz can be estimated assuming an ω2 source model, using equation (1c).
An important factor in tsunami generation may be the depth of the source. If so, then rapid and reliable depth estimation would be helpful in early tsunami alert. Shapiro et al. (1998) report that the ratio of total to highfrequency energy, Er, is a useful parameter in depth discrimination. These authors show that Er of earthquakes along the Pacific coast of Mexico, recorded on a broadband seismograph at CUIG, a station in the UNAM campus in Mexico City (3° < Δ < 5°), is sensitive to the depth of the event: shallower, neartrench events have larger Er values than deeper ones (see also Iglesias et al., 2003). They suggest that earthquakes with large Mw and large Er would have high tsunami potential. Such events also give rise to, relatively, lower accelerations (Iglesias et al., 2003).
The dependence of Er on depth arises from the fact that seismograms of shallower events at regional distance are enhanced at longer periods as compared to the deeper ones. In fact, slowness of the source would cause an effect on seismograms similar to the shallowness of the event. Since Er is a ratio, the effect of focal mechanism is cancelled out. If path and distance from different events to a given station are roughly the same (thus requiring a minor correction to normalize the data to a common distance), then it should be possible to compare Er values of different earthquakes in a meaningful manner. For this reason, Er seems a useful parameter to compliment Mw, location of the earthquake, and Es /M0. Shapiro et al. (1998) and Iglesias (et al., 2003) computed Er from the relation:
where V2(f) = VN2(f) + VE2(f)+ VZ2(f), and VI (f) is the Fourier spectrum of the ith component of the velocity recorded at CUIG, normalized to a distance of 400 km. For normalization, geometrical spreading was assumed to be as R1 for R<100 km (body waves) and as R1/2 (surface waves) beyond 100 km. The quality factor, Q, was taken as Q( f )=273f 0.67 (Ordaz and Singh, 1992). Fig. 3 illustrates Er versus Mw plot for 21 earthquakes. It includes two earthquakes from Peru (events 18 and 19). Event 18 (21 February, 1996;=7.5, Ms=6.6; mb=5.8) was a "tsunami" earthquake (as also indicated by a large disparity between Mw and Ms). This event has the largestvalue in the figure. On the other hand, Er of event 19 (12 November, 1996) is small. Aftershocks locations suggest that events 18 and 19 occurred near the trench and near the coast, respectively (Shapiro et al., 1998). Dashed curve in Fig. 3 illustrates Er versus Mw curve for ω2source model of Brune (1970) at a distance of 400 km. In computing the theoretical curve, we have taken the same Q( f ) and the geometrical spreading as used in the normalization of the data. A constant stress drop of 2 MPa has been taken in the calculation. With two exceptions, the events above the dashed curve in Fig. 3 occurred offshore while those that fall below it were located near the coast. The figure suggests that farther above the Er value of an earthquake with respect to the reference ω2 curve, the higher is its tsunami potential. Since such an earthquake is deficient in highfrequency radiation, it is expected to produce smaller acceleration. Conversely, lower the Er value with respect to the reference curve, smaller is the tsunami potential but higher is the expected acceleration.
The National Seismological Service (SSN) of Mexico reports magnitudes of moderate and large earthquakes based on broadband seismograms recorded at CUIG (Singh and Pacheco, 1994). This algorithm may be modified to compute both the magnitude and Er in nearreal time.
1. The ColimaJalisco earthquake of 1995
The coseismic static displacement caused by this earthquake was obtained from campaignmode GPS measurements carried out before and after the earthquake (Melbourne et al., 1997). The data, shown in Fig. 4, provide a test for the estimation of the seismic moment, the location and the size of the rupture area. We note that the vertical displacement, Uz, was negative along the coast. The tide gauge record at Manzanillo also shows a subsidence (Ortiz et al., 2000). The subsidence of the coast implies that the rupture extended less than ~13 km inland from the coast. The horizontal displacement rapidly decreases between stations CHAM and CHAC to the NW and between CRIP and SJDL to the SE. This suggests that the fault extended from ~50 km NW of CHAM to ~50 km SE of CRIP, for a total rupture length, L, of ~180 km. As mentioned earlier, the width, W, of the coupled interface along the Mexican subduction zone that ruptures in great earthquakes is about 80 km. These estimates are in excellent agreement with those obtained from a detailed aftershock study by Pacheco et al. (1997): rupture reaching up to the coast, L=170 km, and W=70 km. The average of horizontal displacement at CHAM and CRIP is 75 cm. This observation, along with L=180 km and W=80 km, requires an average dislocation of 2.5 m on the fault. This yields a seismic moment, M0 = µLWD, of 1.3x1021 Nm (Mw=8.0), surprisingly close to M0=1.15x1021 Nm (Mw=8.0) reported in Harvard CMT catalog. This case demonstrates that closelyspaced, continuouslyoperating GPS stations along the Mexican coast, with the capacity to track the positions of the stations in near real time, would be very useful in quick estimation of the seismic moment, and the location and size of the rupture area of Mw >8.0 earthquakes.
As mentioned above, a rapid estimation of the radiated energy, Es, can provide a clue to the tsunami potential or the damage potential due to intense ground motion. For the ColimaJalisco earthquake of 1995 we follow the step outlined above. We use the aftershock of 12 October, 1995 (Mw=5.9) as the EGF. Fig. 5 shows the moment rate function M0( f ) of the target event. The figure also gives theoretical M0( f ) for ω2source model with a stress drop of 4 MPa. We estimate Es at frequencies f<0.2 Hz from M0( f ) shown in the figure using equation (1a). The contribution to Es of frequencies f >0.2 Hz is obtained assuming ω2 fall off of M0( f ) above 0.2 Hz (green line), using equation (1c), with M0( fu ) = 2.88x1019 Nm at fu=0.2 Hz (Fig. 5). The total Es is 8.84x1015 J. This gives Es/M0=7.7x106, a slightly lower that normal value for large/great subduction zone earthquakes (Venkataraman and Kanamori, 2004; Weinstein and Okal, 2005). For comparison, Venkataraman and Kanamori (2004) report Es of 48x1015 J from telesesimic P waves. This suggests that a rapid and reliable estimation of Es of great Mexican earthquakes is possible using the EGF technique provided that a library of properly cataloged seismograms of earthquakes of M0 <6.0 are available in the computer memory for immediate retrieval. Since the upper limit of integration, fu, in equation (1) is critical; its value should be known for each EGF event in advance.
The ratio of total to highfrequency energy, Er, for the ColimaJalisco earthquake was 258 (event 9, Fig. 3, a value slightly below the reference curve corresponding to the ω2source model. For comparison, Er for the 1985 Michoacan earthquake was 46 (event 1, Fig. 3). While Er of the 1995 earthquake does not suggest a "tsunami" earthquake, it does point towards a more tsunamigenic earthquake than the 1985 earthquake. This, indeed, was the case as documented by inundation heights (M. Ortiz, personal communication, 2008).
Thus, a coherent picture of the ColimaJalisco earthquake emerges from GPS displacement vectors, and estimates of Es and Er: the rupture was essentially offshore of L~180 km and W probably 80 km, M0=1.3x1021 Nm (Mw=8.0), Es/M0=7.7x106, and Er=258. Offshore rupture, and relatively low value of Es/M0 and high value of Er suggest an earthquake with somewhat high tsunamigenic potential. It is noteworthy that these parameters are very similar to those obtained from detailed analyses. This gives us confidence that rapid and reliable estimation of these parameters for great Mexican earthquakes may be possible if, in addition to the broadband seismographic network, a dense GPS network becomes operational along the coast so that the positions of the stations can be tracked in near real time.
2. The SumatraAndaman earthquake of 2004
Finally, we test whether rapid and automatic analysis of nearfield static displacements could have yielded a reliable seismic moment of the giant SumatraAndaman earthquake (26 December, 2004), had the data been available in nearreal time. We also test whether the EGF technique would have provided reasonable estimate of the radiated energy, Es.
We note that the nearfield static displacements for the 2004 earthquake were obtained from GPS measurements carried out before and after the earthquake, in a campaign mode. Near and far field geodetic data have been analyzed by themselves (e.g., Vigny et al., 2006; Banerjee et al., 2005, 2007; Gahalaut et al., 2006; Rajendran et al., 2007) as well as in conjunction with the seismic data (e.g., Chlieh et al., 2007) to invert for the slip distribution on the fault. As expected, the slip distribution is complex. For our test, we selected the nearfield static deformation reported in Gahalaut et al. (2006). These values have not been corrected for postseismic slip, which was small (Banerjee et al., 2007; V. Gahaluat, personal communication, 2008). Fig. 6 shows the horizontal coseismic displacement on the surface. Note that the nearfield data are available only between 7° and 14° N. The average amplitude of the horizontal vectors in Fig. 6 is 4.1 m. Since the epicenter was located near 3°N, we assume that the average displacement was the same above the fault segment between 2° and 7°N (the inversion of seismic and geodetic data, in fact, yield larger displacement above this segment). Although the rupture propagated along an arc, we approximate the fault by a rectangle of length, L, of 1330 km (from 2° to 14° N). We take the dip of the fault, δ, as 15°, the width W as 150 km, and the depth of the deep edge of the fault as 50 km. These parameters are supported by seismicity of the region (e.g., Engdahl et al., 2007). Finally, we assume that the static displacements were measured at points above the deep edge of the fault (along a line defined by z=0, y=0 in Fig. 2). This is incorrect since the field observations and the geodetic data from GPS campaign demonstrate that some islands in the Andaman and Nicobar region were uplifted, while others suffered subsidence. However, as Fig. 2 shows, the horizontal displacement is not very sensitive to the exact location of the observation point with respect to the rectangular fault area below. Under these reasonable assumptions, an average dislocation, D, of 12 m is needed to produce a horizontal displacement of 4.2 m at the surface. Assuming µ=6x104 MPa, this yields a seismic moment M0=µLWD of 1.17x1023 Nm (Mw=9.3). The magnitude of the SumatraAndaman earthquake has been controversial; the estimates, using different data sets and techniques, vary between Mw=9.0 and 9.3 (see Bilek et al., 2007 for a summary). Our estimate is in the range of the values reported in studies based on detailed analysis of the data. We reiterate that this estimate could have been obtained within about 20 minutes after the earthquake, had the positions of GPS stations in the near field been available in near real time.
We estimated Es of the 2004 earthquakes using an aftershock which occurred on 2 January, 2005 (6.25°N, 92.47°E, Mw=6.3) as the EGF. The depth of the EGF is given as 12 km in Harvard CMT catalog and 25 km in Engdahl et al. (2007). Fig. 7 (top) shows M0(f) of the Sumatra earthquake retrieved from the EGF technique (continuous black curve). The figure includes M0(f) reported by Stein and Okal (2005) at ultralow frequencies and in Global Centroid MomentTensor (GCMT) catalog (http://www.globalcmt.org/CMTsearch.html) at about 0.0025 Hz. Also included in the figure is the M0(f) corresponding to the source time function of model III of Ammon et al. (2005). We note that M0(f) from the EGF technique and from model III are fairly consistent in the frequency range of 0.0050.1 Hz. We computed Es in this frequency band using equation (1a), assuming ρ=3.2 gm/cm3 and β=4.62 km/s. The result is shown in Fig. 7 (bottom) as a function of azimuth. For the entire data set, log Es=16.97±0.30 which gives a median Es=9.29x1016 J. Es in the frequency band 00.005 Hz is 7.0x1015 J. Median M0(fu) at fu=0.1 Hz is 1.72x1020 Nm (Fig. 7). This yields Es=1.11x1016 J for f >0.1 Hz (equation 1c). Thus, our estimate of total Es is 1.11x1017 J. For comparison, Choy and Boatwright (2007) and Kanamori (2006) report Es=1.4x1017 J and 3.0x1017 J, respectively. These values are unexpectedly close to the one reported here. Our estimate of radiated energy differs from that by Kanamori (2006) mostly at frequencies higher than 0.1 Hz: 1.11x1016 J versus 1.6x1017 J.
From Es=1.11x1017 J and M0=1.2x1023 Nm estimated here, Es/M0=1.1x106. If we consider the range of the reported values of Es (1.13.0x1017 J) and M0 (0.61.3x1023 Nm), then Es/M0 ranges between 1.1 x1066 and 5.0x106, values smaller than that of other large/great subduction zone earthquakes.
Some further considerations and future work
This exploratory study is based on some assumptions and expectations that deserve further validation and checking. For example, in our discussion of GPS data we have assumed a uniform slip on the fault. The slip during a large/great earthquake will be heterogeneous. The assumption of uniform slip is expected to have relatively small effect on the estimation of the seismic moment and the length of the rupture (provided that the coast GPS coverage is adequate). However, the location of the rupture area, estimated from the sense of the vertical motion, may be more sensitive to this assumption. Clearly, a more exhaustive testing is warranted.
The permanent GPS network of the Instituto de Geofísica, UNAM, presently includes 13 autonomous stations along the coast with an average separation of ~200 km (Fig. 8). If rapid information is required for only Mw>8.0 earthquakes (length of rupture greater than ~130 km), then the station separation along the coast should be ~65 km. Since the coast from Puerto Vallarta to Tapachula is ~1600 km long, the total number of GPS stations should be 28; thus 15 additional stations along the coast will be needed. This would be the minimum number of stations required. However, more redundancy in the system would be highly desirable. The system may be complimented with data from inland GPS stations. It will be advantageous to install tiltmeters along the coast and add these stations to the network. Some limitations of tiltmeters is discussed by Lomnitz (1997). Realtime transmission of the data from the stations to a central location and tracking of the position of the stations in nearreal time will be crucial. We are not the first to suggest supplementing broadband seismograms with tracking of GPS station positions to estimate magnitudes for tsunami warning (see, e.g., Blewitt et al., 2006). A GPS shield has recently been proposed for early tsunami warning in Sumatra (Sobolev et al., 2007).
We have proposed the use of the empirical Green's function (EGF) technique to compute the radiated energy, Es. To a great extent, the success of the EGF method depends on an appropriate selection of the EGF event. A library of seismograms for earthquakes of Mw<6.0, which sample the entire Pacific coast of Mexico, should be saved in computer memory so that they may be retrieved quickly. The source parameters of the EGF events (location, depth, seismic moment, focal mechanism, corner frequency) would have to be carefully determined beforehand. As nearsource broadband seismograms are likely to saturate during great earthquakes, the recordings of EGF events should also be available at large distances (R>500 km). In view of the fact that a scarcity of M~6 earthquakes has previously been reported for the Mexican subduction zone (Singh et al., 1983), a critical issue is whether recordings of adequate EGFs are presently available. We searched the GCMT catalog beginning 1995 for shallow, thrust earthquakes along the Mexican coast with Mw<6.2. The events are plotted in Fig. 9. These earthquakes have been recorded by the Mexican broadband seismographic network. The figure shows some large gaps along the coast and suggests that smallermagnitude earthquakes would have to be used as EGFs in some segments of the subduction zone. Although recordings of such events exist, we need to carefully assess the suitability these events as appropriate EGFs and estimate their relevant source parameters. Generally, the use of different EGFs yields estimates of Es which only differ by a factor of about two (e.g., Venkataraman et al., 2002; Singh et al., 2004). Thus, all EGFs which fall in the estimated rupture area of the mainshock can be used in the calculation of Es without requiring further selection criterion.
We have shown that a rapid and reliable estimation of the moment magnitude (Mw), the location and the size of the rupture area, the radiated energy (Er), and the ratio of total to highfrequency energy (Er) is viable for great earthquakes (Mw>8.0) along the Mexican subduction zone, provided that regional BB seismograms and continuous GPS position are available in nearreal time. This information can be obtained within about 1520 minutes after the occurrence of an earthquake: it would be very helpful for a quick assessment of tsunami occurrence and/or damage potential of the event, and in issuing an early tsunami alert. The peak tsunami wave occurs at the nearsource coast of Mexico 10 to 20 minutes after the earthquake. Thus an early alert, based on the estimation of the source parameters mentioned above, is not possible for the coastal area close to the source. However, it may be useful in adjacent areas. If, however, an early alert is to be based only on Mw, then this may be accomplished in less than 67 minutes from the analysis of the GPS data. It is worth noting that an estimate of Mw may also be possible in short time (about 67 minutes) from the analysis of Wphase recorded on the regional broadband seismographs (H. Kanamori, personal communication, 2008). Wphase is a longperiod wave that is predicted from theory to arrive between P and S phases. It is observed on broadband seismograms (see, e.g., Kanamori and Kikuchi, 1993).
A rapid estimation of the critical source parameters will complement some other initiatives of nearrealtime seismology in Mexico. These initiatives are: (1) the seismic alert system (SAS) for Mexico City, in operation since 1992. (2) Rapid estimation of ground motion parameters in Mexico City, in a first stage of development at the Instituto de Ingenieria (II), UNAM. (3) Contours of observed groundmotion in Mexico, presently under development at II, UNAM. The alert and the groundmotion maps can only be understood in proper perspective if the critical source parameters of the earthquake are known.
A highsampling, preferably 1 Hz, GPS is an ideal strongmotion seismograph which records displacement. Thus, an improved and enlarged 1 Hz GPS network, along with the existing broadband seismographic and accelerographic networks of Mexico, will provide valuable data for inversion of spatiotemporal evolution of rupture on the fault plane. The GPS data is critical in the study of earthquake cycle, interplate coupling, seismotectonics, and geodynamics. Observations based on GPS in Mexico (e.g., Kostoglodov et al., 2003; Iglesias et al., 2004; Larson et al., 2007) and elsewhere have led to the discovery of silent earthquakes on the plate interface. An enlarged network may answer some of the critical questions which remain unanswered, e.g., the precise location of the area below Mexico that slips during a silent earthquakes.
We thank V. Gahalaut for helpful discussions and for providing us with Fig. 6. Incisive comments and suggestions by Gregory Beroza and an anonymous reviewer are greatly appreciated. The research was partially funded by DGAPA, UNAM project IN114307 and IN11027 and FOPREDENGDF.
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