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Coda wave attenuation parallel and perpendicular to the Mexican Pacific coast
Journal of South American Earth Sciences 13 (2000) 469±476
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Coda wave attenuation parallel and perpendicular to the Mexican Paci®c coast D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez* Instituto de GeofõÂsica, UNAM, C.P. 04510, Mexico, DF, Mexico
Abstract We calculated the quality factor, Qc, at frequencies from 6 to 24 Hz using coda waves of 97 aftershocks of the Petatlan, Mexico, earthquake (March 14, 1979; MS 7.6). The data were recorded parallel (between Acapulco and Playa Azul) and perpendicular (between Petatlan and Mexico City) to the coast. The results are the following: at 12 and 24 Hz there is no signi®cant difference in the attenuation (Qc21) along the two paths; at 6 Hz, Qc21 has a large scatter in both directions. This observation indicates strong site effects at this frequency; average Qc21 is slightly higher between Petatlan±Acapulco (toward SE) than between Petatlan±Playa Azul (toward NW); and at high frequencies, Qc21 remains essentially constant perpendicular to the coast. These results show that the large seismic wave ampli®cations in Mexico City are caused by shallow site effects. q 2000 Elsevier Science Ltd. All rights reserved.
Resumen Hemos calculado el factor de calidad Qc para las frecuencias de 6 a 24 Hz, usando las ondas de coda de 97 reÂplicas de sismo de PetatlaÂn, MeÂxico (Marzo 14, 1979; MS 7.6). Los datos fueron obtenidos de un per®l paralelo a la costa (entre Acapulco y Playa Azul) y un per®l perpendicular a la costa (entre PetatlaÂn y la Ciudad de MeÂxico). Los resultados son los siguientes: entre 12 y 24 Hz no hay diferencias signi®cativas en la atenuacioÂn (Qc21) a lo largo de dos trayectorias; a los 6 Hz, Qc21 tiene gran dispersioÂn en ambas direcciones. Esta observacioÂn indica fuertes efectos de sitio a esta frecuencia; la Qc21 promedio es un poco mayor entre PetatlaÂn±Acapulco (hacia el SE) que entre Petatlan±Playa Azul (hacia el NW); y a altas frecuencias, Qc21 se mantiene esencialmente constante en la direccioÂn perpendicular a la costa. Estos resultados muestran que la ampli®cacioÂn sIÂsmica en la Ciudad de MeÂxico es debida a efectos locales someros. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: Coda wave attenuation; Quality factor; Mexican Paci®c coast; Petatlan earthquake
1. Introduction Coda waves have been extensively used in seismology to study the scattering and attenuation properties of the lithosphere. The theoretical models proposed include single scattering (Aki and Chouet, 1975), diffusion (Aki and Chouet, 1975; Dainty and ToksoÈz, 1977), and energy ¯ux (Frankel and Wennerberg, 1987). These models assume that the coda consists of scattered waves that have sampled and traversed a broad region surrounding the source and the receiver. The coda is thus thought to yield a spatial average of the Earth's attenuation properties over a large volume (Aki and Chouet, 1975). Spatial or temporal variations in
* Corresponding author. Tel.: 152-5-622-4126; fax: 152-5-616-2547. E-mail address: [email protected] (C. ValdeÂs-GonzaÂlez).
coda decay rate could indicate a change in seismic properties, such as attenuation and the state of stress. Variations in coda decay rate have been suggested as earthquake precursors (Jin and Aki, 1986; Sato, 1988). It has been observed that b-value and Qc variations have the same trend around major earthquakes and an opposite trend around volcanic eruptions (b-value is a parameter that relates the magnitude with its frequency of occurrence). (Wyss, 1985; Novelo-Casanova et al., 1985; Sato, 1986; Jin and Aki, 1986). These observations have been explained assuming that the b-value increases or decreases with the closing of crustal cracks according to the change of stress (Herraiz and Espinoza, 1986). If the increase of Qc (decrease of Qc21) is related to the closing of cracks, this parameter may be a more reliable indicator of tectonic stress than b (Aki, 1985). Temporal variations in the decay rate of coda amplitudes may measure the state of stress accumulation preceding a large earthquake (Chouet, 1979; Sato, 1988).
0895-9811/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S 0895-981 1(00)00037-7
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D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476
Fig. 1. Geologic map of southwestern Mexico (after Ortega-Gutierrez, 1981). Solid circles represent the epicenters of the 97 aftershocks used in the present study. Seismic stations (triangles) radiating from the epicentral area were deployed in a leap-frog fashion for two to three days at each site and they were installed on bedrock and buried when possible. Geological complexes are indicated by the letter C.
Jin and Aki (1986) reported coda Q values about three times lower during the three-year period preceding the Tangshan earthquake of 1976 than afterwards. They also observed a similar temporal behavior in coda Q before and after the Haicheng earthquake of 1975. The Paci®c Coast of Mexico is the site of large (MS $ 7.0) thrust earthquakes that are usually strongly felt at Mexico City at a distance of about 300 to 400 km. For a given magnitude, peak accelerations and horizontal velocities on bedrock near Mexico City are ®ve to eight times larger than those recorded at similar distances along the coast (Singh et al., 1987). On March 14, 1979, an MS 7.6 earthquake occurred offshore the City of Petatlan, Guerrero, Mexico (Valdes et al., 1982). This event was strongly felt in Mexico City and caused the collapse of a building located in the lake sediment zone. Aftershocks from this event were recorded on eight 3-component digital seismographs along two perpendicular pro®les (Ewing and Meyer, 1982). One pro®le was located between Acapulco and Playa Azul (300 km) and the other between Petatlan and Mexico City (310 km) (Fig. 1). Two sets of four instruments were deployed for 2±3 days in a leap-frog fashion along each pro®le (Fig. 1). Due to logistics and to a small number of seismographs it was not possible to deploy them simultaneously at similar distances
along both sections. Seismograph characteristics are presented in Ewing and Meyer (1982). Fig. 1 shows the location of the epicenters and the major geological features of the area. The depth of the aftershocks range from 3 to 45 km. The average magnitude of the analyzed events is ML 2.7 in the range of 1.3 to 3.9. Each seismogram was checked visually for data quality; we rejected those with signal-to-noise ratio of less than 5 and clipped or distorted traces due to malfunctioning geophones. In this work we determine the regional coda-wave attenuation in the frequency band of 6 to 24 Hz for 97 aftershocks of the Petatlan event. The seismic attenuation in Guerrero has been determined previously from strong motion records (Castro et al., 1990; Humphrey and Anderson, 1992; Ordaz and Singh, 1992) and from coda waves (Rodriguez et al., 1983; Novelo-Casanova et al., 1990). Here, we compare the coda-wave attenuation of seismic waves traveling inland with those traveling along the coast. We use the single-scattering model of Sato (1977) to determine Qc. For a detailed discussion of the procedures, see Valdes and Novelo-Casanova (1989); Novelo-Casanova and Lee (1991). Theoretically, the method of Sato (1977) allows estimation of Qc for coda waves arriving immediately after the S-wave arrival; however, the model was developed for deep events, which is not our case. For
D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476 471
Fig. 2. Qc21 values along the Petatlan±Mexico City pro®le for the three components. Stations are plotted as a function of distance from the center of the aftershock activity to Mexico City. Petatlan is considered located at 0 and Mexico City at 320 km. Geological complexes are indicated along the x axis: GC, Guerrero Complex; TCC, Tierra Caliente Complex; TMVB, Trans-Mexican Volcanic Belt (see Fig. 1).
472
D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476
D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476
these reasons, we estimated Qc considering coda windows with lengths of 20 s and starting 10 s after tS. These values were considered because the maximum recording length for the digital seismic records was 65 s. 2. Processing procedures Although the recording stations were deployed at different distances (Fig. 1), calculating Qc from the recorded late coda and using time windows of similar length that start at similar lapse times allowed us to compare results from different areas that sample similar depths. The seismograms were bandpass-®ltered using a recursive 8-pole, zero-phase Butterworth ®lter. Center frequencies at 6, 12, and 24 Hz and corresponding bandwidths of 4, 8, and 16 Hz were used. Window increments of 1 and 2.56 s and window lengths of 2 and 5.12 s were applied to the RMS and FFT calculations, respectively. We did not use lower frequencies because the Qc estimates at these frequencies had large errors. We determined Qc for each component of the records independently. Mean kQcl values for a given distance were determined by weighting each individual measurement by the inverse of its variance (Hellweg et al., 1995): X X 2 2 1 hQc i Qci =s i = 1=s i kQcl was arbitrarily estimated for Qc values with standard deviation, s i, of less than or equal to 35%. Each Qci was weighted by the inverse of its variance before averaging. The variance of the mean was calculated by: X X s m2 1=s i2 Qci 2 kQc l2 = n 2 1 1=s i2 2 where s m is the standard deviation of the mean (Hellweg et al., 1995). 3. Observations Fig. 2 shows the estimates of Qc21 for the Petatlan± Mexico City (Pet±Mex) pro®le using all three components of the events. At 12 and 24 Hz the attenuation values obtained are nearly constant with distance. This is also valid for distances larger than 250 km (Fig. 2a and c). At 6 Hz, despite the high signal-to-noise ratio and the good quality of the seismic records, the scatter of Qc21 is large compared to values at higher frequencies. Fig. 3 displays Qc21 values obtained for the 300 km-long Playa Azul±Acapulco (Azu±Aca) pro®le. We divided this pro®le into two sections, one from Petatlan to Acapulco (Pet±Aca, 180 km) and another from Petatlan to Playa Azul (Pet±Azu, 120 km). Geologically, the sections are different (Fig. 1). Pet±Aca is on the Xolapa Complex,
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composed of migmatites, gneisses, and schists, while Pet± Azu is partly on the Tierra Caliente Complex, composed of greenschist and of siliceous and andesitic volcanics (OrtegaGutierrez, 1981). We observe that Qc21 values are higher toward Acapulco than toward Playa Azul. To determine whether these differences are signi®cant, we calculated average Qc21 values for the two sections and applied Student's t test (Mendenhall, 1975): 2 2 1=2 t kQ c21 l1 2 kQ21 c l2 = s 1 =n1 1 s 2 =n2
3
where kQc21l1 and kQc21l2 are calculated by applying Eq. (1) to the n1 or n2 individual component values Qci of the Pet± Aca and Pet±Azu segments. The results indicate that the observed average Qc21 differences between these two pro®les are signi®cant only for the horizontal components at 12 and 24 Hz (Fig. 3a and b). Figs. 2 and 3 indicate that the attenuation values at 12 and 24 Hz for the coastal segment as well as for the pro®le toward Mexico City are practically the same. Also, in all plots we observe a decrease of attenuation with increasing frequency. This trend has generally been reported for frequencies greater than 1 Hz for Qc21 as well as for QS waves in the lithosphere (Aki, 1980). It was explained by Sato (1984) in terms of a random model of small-scale heterogeneities. 4. Discussion Ordaz and Singh (1992) discussed source spectra and spectral attenuation of seismic waves from Mexican earthquakes. They found that between 0.2 and 0.7 Hz there is no signi®cant difference in the attenuation of S waves along the coast and inland. Singh et al. (1988a), using records of the September 1985 Michoacan earthquakes, observed that stations inland from the coast are characterized by anomalous ampli®cation, but they concluded that this effect could result from wave propagation phenomena associated with the dipping slab or from geological differences between the sites. In agreement with Ordaz and Singh (1992), we do not observe a signi®cant difference of attenuation at 12 and 24 Hz for paths along the coast and toward Mexico City. Our data comes practically from the same source and our recording stations are perpendicular to the coast or aligned toward Mexico City (Fig. 1). Also, we analyzed 3-component seismograms of 97 small magnitude events 1:3 # ML $ 3:9 while Ordaz and Singh (1992) used nine earthquakes with magnitude MS in the range of 4.1 to 8.1. CaÂrdenas et al. (1997), using data from a deep seismic sounding experiment, concluded that attenuation of seismic
Fig. 3. (a) Qc21 values along the Petatlan±Acapulco and Petatlan±Playa Azul pro®les for the three components. Petatlan is considered located at 0 and Acapulco at 200 km. Negative values are toward Playa Azul located at 110 km. The geological complexes along this segment are: TCC, Tierra Caliente Complex; XC, Xolapa Complex (see Fig. 1).
474 D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476 Fig. 4. Vertical seismograms of aftershocks recorded along the Petatlan±Mexico City; Petatlan±Acapulco, and Petatlan±Playa Azul pro®les at different distances from the center of the aftershock activity. Observe that the coda wave envelope toward Mexico City is similar at the different distances. Toward Acapulco, coda waves decay faster than toward Playa Azul. Empty squares indicate that seismograms were not available at that distance.
D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476
energy is higher for paths along the coastline than into the continent. They used three seismic pro®les from sea-bottom explosions, and they evaluated Q for frequencies between 0.5 and 5.0 Hz. The depth of the source may be a possible factor that explains the difference between the results of CaÂrdenas et al. (1997) and ours. CaÂrdenas et al. (1997) used shots of 300 and 500 kg of explosive. We use earthquakes with an average magnitude of 2.7 in the depth range from 3 to 45 km. Coda waves at frequencies higher than 10 Hz consist of backscattered body waves from heterogeneities in the deep lithosphere (Aki and Chouet, 1975). The geologic structure along the coast is dominated by the subduction of the Cocos Plate under the North-American Plate. Thus, the similar behavior of Qc21 values at 12 and 24 Hz might be associated with the mean attenuation sampled by coda waves over a large volume, including parts of the accretionary block, the edge of the continental block, and the oceanic lithosphere. The consistency of the Qc21 values at 12 and 24 Hz for vertical and horizontal components (Figs. 2 and 3) suggests that the in¯uence of strati®cation is small. The increase of velocity with depth will tend to refract the scattered waves upward and will lead to Qc differences with respect to the horizontal component. Thus, the similarity of values of Qc21 between the horizontal and vertical components may indicate that several wave modes are thoroughly mixed by the time they are sampled as coda waves at the recording site. The smooth trend of Qc21 at 12 and 24 Hz along the pro®les, with no sharp changes from station to station, suggests little or no in¯uence of local site conditions at these frequencies. Our approximately constant Qc21 values at 12 and 24 Hz in the Petatlan±Mexico City pro®le (Fig. 2) represent evidence that the seismic wave ampli®cations observed at lake-bed sites with respect to hill-zones sites in Mexico City (Singh et al., 1988b) are due to site conditions. Thus, the local conditions would be the primary cause of damage suffered by Mexico City from coastal earthquakes. This result is in discrepancy with Ordaz and Singh (1992) who attributed ampli®cation of seismic waves in the hill zone to a large-scale geological structure, a lake which covered the Valley of Mexico and extended to the South down to Taxco in late Oligocene to Pliocene. The large scatter of Qc21 at 6 Hz observed in Figs. 2 and 3 suggests that coda seismic waves in both directions are in¯uenced by local site conditions at this frequency. Spudich and Bostwick (1987) showed that near-site reverberations can be the dominant component of the coda at time t, where tS , t , 2tS ; for frequencies less than about 10 Hz. For our data t , 1:5tS : As mentioned above, the Pet±Aca and Pet±Azu sections are geologically different and this accounts for the larger average Qc21 value observed along Pet±Aca than toward Pet±Azu for the horizontal components at 12 and 24 Hz (Fig. 3a and b). Both regions, however, were in different states of stress at the time the data were collected. Pet±Aca has been ruptured by large events in 1899 (MS 7.7), 1908 (MS 7.8), 1909 (MS 7.5), and 1911 (MS 7.8), and is
475
presently considered a seismic gap (Nishenko and Singh, 1987). Pet±Azu had not experienced a large earthquake in 74 years. This segment was probably in a high state of stress prior to its partial rupture in the 1981 Playa Azul earthquake of MS 7.3, and prior to its total rupture during the great 1985 Michoacan earthquake (MS 8.1). Castro et al. (1994) compared Q for the regions of Guerrero and Oaxaca, Mexico. They found that Q values estimated from coda waves are consistently lower than those calculated from S waves of ªbackground seismicityº. They suggested that the differences may be related to the state of stress prevailing when Q was measured, due to the density of fractures and perhaps ¯uid content in the upper crust. The geology and/or the state of tectonic stress in the areas may be responsible for differences in Qc21 values along the coast. However, from the present experiment, it is dif®cult to evaluate the amount of contribution from each of these two factors. Our interpretations are supported by Fig. 4 which shows recorded seismograms for the Z component along the two sections. Observe that the coda envelope in the Mexico City direction is similar at different distances. However, the envelope toward Playa Azul, decays more slowly than toward Acapulco. 5. Conclusions Our results indicate that Qc21 between 12 and 24 Hz: is essentially constant toward Mexico City; increases between Petatlan and Acapulco but remains almost constant between Petatlan and Playa Azul; and has practically the same values toward Mexico City or along the coast. These observations are evidence that the seismic wave ampli®cations in Mexico City are due to local site conditions. The ef®cient transmission of coda seismic energy inland from the coast between Petatlan and Acapulco, and the ampli®cation of seismic waves at lake-bed sites with respect to hill-zone sites in Mexico City, suggest that a large subduction earthquake rupturing along the dip of the Cocos Plate has the potential for causing signi®cant damage in this city. Acknowledgements The authors are grateful to S.K. Singh, R.P. Meyer, and M. GuzmaÂn for helpful criticism and discussions. We also thank an anonymous reviewer for his/her thoughtful review of this work. We thank P. Medina for her assistance in typing this paper. References Aki, K., 1980. Attenuation of shear waves in the lithosphere for frequencies from 0.05 to 25 Hz. Physics of the Earth and Planetary Interiors 21, 50± 60. Aki, K., 1985. Theory of earthquake prediction with special references to
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monitoring of the quality factor of lithosphere by coda method. Earthquake Prediction Research 3, 219±230. Aki, K., Chouet, B., 1975. Origin of coda waves: source, attenuation, and scattering effects. Journal of Geophysical Research 80, 3322±3342. CaÂrdenas, M., NuÂnÄez-CornuÂ, F., Lermo, J., GonzaÂlez, A., 1998. Seismic energy attenuation in the region between the coast of Guerrero and Mexico City: differences between paths along and perpendicular to the coast. Physics of the Earth and Planetary Interiors 105, 47±57. Castro, R.R., Anderson, J.G., Singh, S.K., 1990. Site response, attenuation and source spectra of S waves along the Guerrero, Mexico, subduction zone. Bulletin of the Seismological Society of America 80, 1481±1503. Castro, R.R., Munguia, L., Rebollar, C.J., Acosta, J.G., 1994. A comparative analysis of the quality factor Q for the regions of Guerrero and Oaxaca, Mexico. Geo®sica Internacional 33, 373±383. Chouet, B., 1979. Temporal variation in the attenuation of earthquake coda near Stone Canyon, California. Geophysical Research Letters 6, 143±146. Dainty, A.M., ToksoÈz, M.N., 1977. Elastic wave scattering in a highly scattering medium: a diffusion approach. Journal of Geophysical Research 43, 375±388. Ewing, J.I., Meyer, R.P., 1982. Rivera Oceanic Seismic Experiment (ROSE) Overview. Journal of Geophysical Research 87, 8345±8357. Frankel, A., Wennerberg, L., 1987. Energy-¯ux model of seismic coda: separation of scattering and intrinsic attenuation. Bulletin of the Seismological Society of America 77, 1223±1251. Hellweg, M., Spudich, P., Fletcher, J.B., Baker, L.M., 1995. Stability of coda Q in the region of Park®eld, California: View from the U.S. Geological Survey Park®eld Dense Seismograph Array. Journal of Geophysical Research 100, 2089±2102. Herraiz, M. Espinoza, A.F., 1986. Scattering and attenuation of highfrequency seismic waves: development of the theory of coda waves U.S.G.S. Open File Report, Number 86±455. Humphrey, J.R., Anderson, J.G., 1992. Shear-wave attenuation and site response in Guerrero, Mexico. Bulletin of the Seismological Society of America 81, 1622±1645. Jin, A., Aki, K., 1986. Temporal change in coda Q before the Tangshan earthquake of 1976 and the Haicheng earthquake of 1975. Journal of Geophysical Research 91, 665±673. Mendenhall, W., 1975. Introduction to Probability and Statistics. Duxbury, Boston, MA, p. 460. Nishenko, S.P., Singh, S.K., 1987. Conditional probability for the recurrence of large and great interplate earthquakes along the Mexican subduction zone. Bulletin of the Seismological Society of America 77, 2095±2114. Novelo-Casanova, D.A., Lee, W.H.K., 1991. Comparison of techniques that use the single scattering model to compute the quality factor Q from coda waves. PAGEOPH 135, 77±89. Novelo-Casanova, D.A., Berg, E., Helsley, C.E., 1990. S-wave coda Q
from 3 to 20 Hz and P wave Q for foreshocks and afershocks of the Petatlan earthquake. Journal of Geophysical Research 95, 4787±4795. Novelo-Casanova, D.A., Berg, E., Hsu, V., Helsley, C.E., 1985. Time±space variation of seismic S-wave coda attenuation (Qc21) and magnitude distribution (b-values) for the Patatlan earthquake. Geophysical Research Letters 12, 789±792. Ordaz, M., Singh, S.K., 1992. Source spectra and attenuation of seismic waves from Mexican earthquakes, and evidence of ampli®cation in the hill zone of Mexico City. Bulletin of the Seismological Society of America 82, 24±43. Ortega-Gutierrez, F., 1981. Metamorphic belts of southern Mexico and their tectonic signi®cance. Geo®sica International 20, 65±82. Rodriguez, M., Havskov, J., Singh, S.K., 1983. Q from waves near Petatlan, Guerrero, Mexico. Bulletin of the Seismological Society of America 73, 321±326. Sato, H., 1977. Energy propagation including scattering effects, single isotropic approximation. Journal of Physics of the Earth 25, 27±41. Sato, H., 1984. Attenuation and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. Journal of Geophysical Research 89, 1221±1241. Sato, H., 1986. Temporal change in attenuation intensity before and after the eastern Yamanashi earthquake of 1983 in central Japan. Journal of Geophysical Research 91, 2049±2061. Sato, H., 1988. Temporal change in scattering and attenuation associated with the earthquake occurrence Ð a review of recent studies on coda waves. PAGEOPH 126, 465±497. Singh, S.K., Mena, E., Castro, R., 1988a. Some aspects of source characteristics of the 19 September 1985 Michoacan earthquake and ground motion ampli®cation in and near Mexico City from strong-motion data. Bulletin of the Seismological Society of America 78, 451±477. Singh, S.K., Lermo, J., DomIÂnguez, T., Ordaz, M., Espinosa, J.M., Mena, E., Quass, R., 1988b. A study of ampli®cation of seismic waves in the Valley of Mexico with respect to a hill zone site. Earthquake Spectra 4, 653±673. Singh, S.K., Mena, E., Castro, R., Carmona, C., 1987. Empirical prediction of ground motion in Mexico City from coastal earthquakes. Bulletin of the Seismological Society of America 77, 1862±1867. Spudich, P., Bostwick, T., 1987. Studies of the seismic coda using an earthquake cluster as a deeply buried seismograph array. Journal of Geophysical Research 92, 10526±10546. Valdes, C.M., Novelo-Casanova, D.A., User manual for Q coda, in: Toolbox for Plotting Seismic and Other Data, IASPEI Seismological Software Library, 1, 1989, pp. 237±255. Valdes, C., Meyer, R., ZunÄiga, R., Havskov, J., Singh, S.K., 1982. Analysis of Petatlan aftershocks: numbers, energy release, and asperities. Journal of Geophysical Research 87, 8519±8527. Wyss, M., 1985. Precursors to large earthquakes. Earthquake Prediction Research 3, 519±543.
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Coda wave attenuation parallel and perpendicular to the Mexican Paci®c coast D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez* Instituto de GeofõÂsica, UNAM, C.P. 04510, Mexico, DF, Mexico
Abstract We calculated the quality factor, Qc, at frequencies from 6 to 24 Hz using coda waves of 97 aftershocks of the Petatlan, Mexico, earthquake (March 14, 1979; MS 7.6). The data were recorded parallel (between Acapulco and Playa Azul) and perpendicular (between Petatlan and Mexico City) to the coast. The results are the following: at 12 and 24 Hz there is no signi®cant difference in the attenuation (Qc21) along the two paths; at 6 Hz, Qc21 has a large scatter in both directions. This observation indicates strong site effects at this frequency; average Qc21 is slightly higher between Petatlan±Acapulco (toward SE) than between Petatlan±Playa Azul (toward NW); and at high frequencies, Qc21 remains essentially constant perpendicular to the coast. These results show that the large seismic wave ampli®cations in Mexico City are caused by shallow site effects. q 2000 Elsevier Science Ltd. All rights reserved.
Resumen Hemos calculado el factor de calidad Qc para las frecuencias de 6 a 24 Hz, usando las ondas de coda de 97 reÂplicas de sismo de PetatlaÂn, MeÂxico (Marzo 14, 1979; MS 7.6). Los datos fueron obtenidos de un per®l paralelo a la costa (entre Acapulco y Playa Azul) y un per®l perpendicular a la costa (entre PetatlaÂn y la Ciudad de MeÂxico). Los resultados son los siguientes: entre 12 y 24 Hz no hay diferencias signi®cativas en la atenuacioÂn (Qc21) a lo largo de dos trayectorias; a los 6 Hz, Qc21 tiene gran dispersioÂn en ambas direcciones. Esta observacioÂn indica fuertes efectos de sitio a esta frecuencia; la Qc21 promedio es un poco mayor entre PetatlaÂn±Acapulco (hacia el SE) que entre Petatlan±Playa Azul (hacia el NW); y a altas frecuencias, Qc21 se mantiene esencialmente constante en la direccioÂn perpendicular a la costa. Estos resultados muestran que la ampli®cacioÂn sIÂsmica en la Ciudad de MeÂxico es debida a efectos locales someros. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: Coda wave attenuation; Quality factor; Mexican Paci®c coast; Petatlan earthquake
1. Introduction Coda waves have been extensively used in seismology to study the scattering and attenuation properties of the lithosphere. The theoretical models proposed include single scattering (Aki and Chouet, 1975), diffusion (Aki and Chouet, 1975; Dainty and ToksoÈz, 1977), and energy ¯ux (Frankel and Wennerberg, 1987). These models assume that the coda consists of scattered waves that have sampled and traversed a broad region surrounding the source and the receiver. The coda is thus thought to yield a spatial average of the Earth's attenuation properties over a large volume (Aki and Chouet, 1975). Spatial or temporal variations in
* Corresponding author. Tel.: 152-5-622-4126; fax: 152-5-616-2547. E-mail address: [email protected] (C. ValdeÂs-GonzaÂlez).
coda decay rate could indicate a change in seismic properties, such as attenuation and the state of stress. Variations in coda decay rate have been suggested as earthquake precursors (Jin and Aki, 1986; Sato, 1988). It has been observed that b-value and Qc variations have the same trend around major earthquakes and an opposite trend around volcanic eruptions (b-value is a parameter that relates the magnitude with its frequency of occurrence). (Wyss, 1985; Novelo-Casanova et al., 1985; Sato, 1986; Jin and Aki, 1986). These observations have been explained assuming that the b-value increases or decreases with the closing of crustal cracks according to the change of stress (Herraiz and Espinoza, 1986). If the increase of Qc (decrease of Qc21) is related to the closing of cracks, this parameter may be a more reliable indicator of tectonic stress than b (Aki, 1985). Temporal variations in the decay rate of coda amplitudes may measure the state of stress accumulation preceding a large earthquake (Chouet, 1979; Sato, 1988).
0895-9811/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S 0895-981 1(00)00037-7
470
D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476
Fig. 1. Geologic map of southwestern Mexico (after Ortega-Gutierrez, 1981). Solid circles represent the epicenters of the 97 aftershocks used in the present study. Seismic stations (triangles) radiating from the epicentral area were deployed in a leap-frog fashion for two to three days at each site and they were installed on bedrock and buried when possible. Geological complexes are indicated by the letter C.
Jin and Aki (1986) reported coda Q values about three times lower during the three-year period preceding the Tangshan earthquake of 1976 than afterwards. They also observed a similar temporal behavior in coda Q before and after the Haicheng earthquake of 1975. The Paci®c Coast of Mexico is the site of large (MS $ 7.0) thrust earthquakes that are usually strongly felt at Mexico City at a distance of about 300 to 400 km. For a given magnitude, peak accelerations and horizontal velocities on bedrock near Mexico City are ®ve to eight times larger than those recorded at similar distances along the coast (Singh et al., 1987). On March 14, 1979, an MS 7.6 earthquake occurred offshore the City of Petatlan, Guerrero, Mexico (Valdes et al., 1982). This event was strongly felt in Mexico City and caused the collapse of a building located in the lake sediment zone. Aftershocks from this event were recorded on eight 3-component digital seismographs along two perpendicular pro®les (Ewing and Meyer, 1982). One pro®le was located between Acapulco and Playa Azul (300 km) and the other between Petatlan and Mexico City (310 km) (Fig. 1). Two sets of four instruments were deployed for 2±3 days in a leap-frog fashion along each pro®le (Fig. 1). Due to logistics and to a small number of seismographs it was not possible to deploy them simultaneously at similar distances
along both sections. Seismograph characteristics are presented in Ewing and Meyer (1982). Fig. 1 shows the location of the epicenters and the major geological features of the area. The depth of the aftershocks range from 3 to 45 km. The average magnitude of the analyzed events is ML 2.7 in the range of 1.3 to 3.9. Each seismogram was checked visually for data quality; we rejected those with signal-to-noise ratio of less than 5 and clipped or distorted traces due to malfunctioning geophones. In this work we determine the regional coda-wave attenuation in the frequency band of 6 to 24 Hz for 97 aftershocks of the Petatlan event. The seismic attenuation in Guerrero has been determined previously from strong motion records (Castro et al., 1990; Humphrey and Anderson, 1992; Ordaz and Singh, 1992) and from coda waves (Rodriguez et al., 1983; Novelo-Casanova et al., 1990). Here, we compare the coda-wave attenuation of seismic waves traveling inland with those traveling along the coast. We use the single-scattering model of Sato (1977) to determine Qc. For a detailed discussion of the procedures, see Valdes and Novelo-Casanova (1989); Novelo-Casanova and Lee (1991). Theoretically, the method of Sato (1977) allows estimation of Qc for coda waves arriving immediately after the S-wave arrival; however, the model was developed for deep events, which is not our case. For
D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476 471
Fig. 2. Qc21 values along the Petatlan±Mexico City pro®le for the three components. Stations are plotted as a function of distance from the center of the aftershock activity to Mexico City. Petatlan is considered located at 0 and Mexico City at 320 km. Geological complexes are indicated along the x axis: GC, Guerrero Complex; TCC, Tierra Caliente Complex; TMVB, Trans-Mexican Volcanic Belt (see Fig. 1).
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these reasons, we estimated Qc considering coda windows with lengths of 20 s and starting 10 s after tS. These values were considered because the maximum recording length for the digital seismic records was 65 s. 2. Processing procedures Although the recording stations were deployed at different distances (Fig. 1), calculating Qc from the recorded late coda and using time windows of similar length that start at similar lapse times allowed us to compare results from different areas that sample similar depths. The seismograms were bandpass-®ltered using a recursive 8-pole, zero-phase Butterworth ®lter. Center frequencies at 6, 12, and 24 Hz and corresponding bandwidths of 4, 8, and 16 Hz were used. Window increments of 1 and 2.56 s and window lengths of 2 and 5.12 s were applied to the RMS and FFT calculations, respectively. We did not use lower frequencies because the Qc estimates at these frequencies had large errors. We determined Qc for each component of the records independently. Mean kQcl values for a given distance were determined by weighting each individual measurement by the inverse of its variance (Hellweg et al., 1995): X X 2 2 1 hQc i Qci =s i = 1=s i kQcl was arbitrarily estimated for Qc values with standard deviation, s i, of less than or equal to 35%. Each Qci was weighted by the inverse of its variance before averaging. The variance of the mean was calculated by: X X s m2 1=s i2 Qci 2 kQc l2 = n 2 1 1=s i2 2 where s m is the standard deviation of the mean (Hellweg et al., 1995). 3. Observations Fig. 2 shows the estimates of Qc21 for the Petatlan± Mexico City (Pet±Mex) pro®le using all three components of the events. At 12 and 24 Hz the attenuation values obtained are nearly constant with distance. This is also valid for distances larger than 250 km (Fig. 2a and c). At 6 Hz, despite the high signal-to-noise ratio and the good quality of the seismic records, the scatter of Qc21 is large compared to values at higher frequencies. Fig. 3 displays Qc21 values obtained for the 300 km-long Playa Azul±Acapulco (Azu±Aca) pro®le. We divided this pro®le into two sections, one from Petatlan to Acapulco (Pet±Aca, 180 km) and another from Petatlan to Playa Azul (Pet±Azu, 120 km). Geologically, the sections are different (Fig. 1). Pet±Aca is on the Xolapa Complex,
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composed of migmatites, gneisses, and schists, while Pet± Azu is partly on the Tierra Caliente Complex, composed of greenschist and of siliceous and andesitic volcanics (OrtegaGutierrez, 1981). We observe that Qc21 values are higher toward Acapulco than toward Playa Azul. To determine whether these differences are signi®cant, we calculated average Qc21 values for the two sections and applied Student's t test (Mendenhall, 1975): 2 2 1=2 t kQ c21 l1 2 kQ21 c l2 = s 1 =n1 1 s 2 =n2
3
where kQc21l1 and kQc21l2 are calculated by applying Eq. (1) to the n1 or n2 individual component values Qci of the Pet± Aca and Pet±Azu segments. The results indicate that the observed average Qc21 differences between these two pro®les are signi®cant only for the horizontal components at 12 and 24 Hz (Fig. 3a and b). Figs. 2 and 3 indicate that the attenuation values at 12 and 24 Hz for the coastal segment as well as for the pro®le toward Mexico City are practically the same. Also, in all plots we observe a decrease of attenuation with increasing frequency. This trend has generally been reported for frequencies greater than 1 Hz for Qc21 as well as for QS waves in the lithosphere (Aki, 1980). It was explained by Sato (1984) in terms of a random model of small-scale heterogeneities. 4. Discussion Ordaz and Singh (1992) discussed source spectra and spectral attenuation of seismic waves from Mexican earthquakes. They found that between 0.2 and 0.7 Hz there is no signi®cant difference in the attenuation of S waves along the coast and inland. Singh et al. (1988a), using records of the September 1985 Michoacan earthquakes, observed that stations inland from the coast are characterized by anomalous ampli®cation, but they concluded that this effect could result from wave propagation phenomena associated with the dipping slab or from geological differences between the sites. In agreement with Ordaz and Singh (1992), we do not observe a signi®cant difference of attenuation at 12 and 24 Hz for paths along the coast and toward Mexico City. Our data comes practically from the same source and our recording stations are perpendicular to the coast or aligned toward Mexico City (Fig. 1). Also, we analyzed 3-component seismograms of 97 small magnitude events 1:3 # ML $ 3:9 while Ordaz and Singh (1992) used nine earthquakes with magnitude MS in the range of 4.1 to 8.1. CaÂrdenas et al. (1997), using data from a deep seismic sounding experiment, concluded that attenuation of seismic
Fig. 3. (a) Qc21 values along the Petatlan±Acapulco and Petatlan±Playa Azul pro®les for the three components. Petatlan is considered located at 0 and Acapulco at 200 km. Negative values are toward Playa Azul located at 110 km. The geological complexes along this segment are: TCC, Tierra Caliente Complex; XC, Xolapa Complex (see Fig. 1).
474 D.A. Novelo-Casanova, C. ValdeÂs-GonzaÂlez / Journal of South American Earth Sciences 13 (2000) 469±476 Fig. 4. Vertical seismograms of aftershocks recorded along the Petatlan±Mexico City; Petatlan±Acapulco, and Petatlan±Playa Azul pro®les at different distances from the center of the aftershock activity. Observe that the coda wave envelope toward Mexico City is similar at the different distances. Toward Acapulco, coda waves decay faster than toward Playa Azul. Empty squares indicate that seismograms were not available at that distance.
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energy is higher for paths along the coastline than into the continent. They used three seismic pro®les from sea-bottom explosions, and they evaluated Q for frequencies between 0.5 and 5.0 Hz. The depth of the source may be a possible factor that explains the difference between the results of CaÂrdenas et al. (1997) and ours. CaÂrdenas et al. (1997) used shots of 300 and 500 kg of explosive. We use earthquakes with an average magnitude of 2.7 in the depth range from 3 to 45 km. Coda waves at frequencies higher than 10 Hz consist of backscattered body waves from heterogeneities in the deep lithosphere (Aki and Chouet, 1975). The geologic structure along the coast is dominated by the subduction of the Cocos Plate under the North-American Plate. Thus, the similar behavior of Qc21 values at 12 and 24 Hz might be associated with the mean attenuation sampled by coda waves over a large volume, including parts of the accretionary block, the edge of the continental block, and the oceanic lithosphere. The consistency of the Qc21 values at 12 and 24 Hz for vertical and horizontal components (Figs. 2 and 3) suggests that the in¯uence of strati®cation is small. The increase of velocity with depth will tend to refract the scattered waves upward and will lead to Qc differences with respect to the horizontal component. Thus, the similarity of values of Qc21 between the horizontal and vertical components may indicate that several wave modes are thoroughly mixed by the time they are sampled as coda waves at the recording site. The smooth trend of Qc21 at 12 and 24 Hz along the pro®les, with no sharp changes from station to station, suggests little or no in¯uence of local site conditions at these frequencies. Our approximately constant Qc21 values at 12 and 24 Hz in the Petatlan±Mexico City pro®le (Fig. 2) represent evidence that the seismic wave ampli®cations observed at lake-bed sites with respect to hill-zones sites in Mexico City (Singh et al., 1988b) are due to site conditions. Thus, the local conditions would be the primary cause of damage suffered by Mexico City from coastal earthquakes. This result is in discrepancy with Ordaz and Singh (1992) who attributed ampli®cation of seismic waves in the hill zone to a large-scale geological structure, a lake which covered the Valley of Mexico and extended to the South down to Taxco in late Oligocene to Pliocene. The large scatter of Qc21 at 6 Hz observed in Figs. 2 and 3 suggests that coda seismic waves in both directions are in¯uenced by local site conditions at this frequency. Spudich and Bostwick (1987) showed that near-site reverberations can be the dominant component of the coda at time t, where tS , t , 2tS ; for frequencies less than about 10 Hz. For our data t , 1:5tS : As mentioned above, the Pet±Aca and Pet±Azu sections are geologically different and this accounts for the larger average Qc21 value observed along Pet±Aca than toward Pet±Azu for the horizontal components at 12 and 24 Hz (Fig. 3a and b). Both regions, however, were in different states of stress at the time the data were collected. Pet±Aca has been ruptured by large events in 1899 (MS 7.7), 1908 (MS 7.8), 1909 (MS 7.5), and 1911 (MS 7.8), and is
475
presently considered a seismic gap (Nishenko and Singh, 1987). Pet±Azu had not experienced a large earthquake in 74 years. This segment was probably in a high state of stress prior to its partial rupture in the 1981 Playa Azul earthquake of MS 7.3, and prior to its total rupture during the great 1985 Michoacan earthquake (MS 8.1). Castro et al. (1994) compared Q for the regions of Guerrero and Oaxaca, Mexico. They found that Q values estimated from coda waves are consistently lower than those calculated from S waves of ªbackground seismicityº. They suggested that the differences may be related to the state of stress prevailing when Q was measured, due to the density of fractures and perhaps ¯uid content in the upper crust. The geology and/or the state of tectonic stress in the areas may be responsible for differences in Qc21 values along the coast. However, from the present experiment, it is dif®cult to evaluate the amount of contribution from each of these two factors. Our interpretations are supported by Fig. 4 which shows recorded seismograms for the Z component along the two sections. Observe that the coda envelope in the Mexico City direction is similar at different distances. However, the envelope toward Playa Azul, decays more slowly than toward Acapulco. 5. Conclusions Our results indicate that Qc21 between 12 and 24 Hz: is essentially constant toward Mexico City; increases between Petatlan and Acapulco but remains almost constant between Petatlan and Playa Azul; and has practically the same values toward Mexico City or along the coast. These observations are evidence that the seismic wave ampli®cations in Mexico City are due to local site conditions. The ef®cient transmission of coda seismic energy inland from the coast between Petatlan and Acapulco, and the ampli®cation of seismic waves at lake-bed sites with respect to hill-zone sites in Mexico City, suggest that a large subduction earthquake rupturing along the dip of the Cocos Plate has the potential for causing signi®cant damage in this city. Acknowledgements The authors are grateful to S.K. Singh, R.P. Meyer, and M. GuzmaÂn for helpful criticism and discussions. We also thank an anonymous reviewer for his/her thoughtful review of this work. We thank P. Medina for her assistance in typing this paper. References Aki, K., 1980. Attenuation of shear waves in the lithosphere for frequencies from 0.05 to 25 Hz. Physics of the Earth and Planetary Interiors 21, 50± 60. Aki, K., 1985. Theory of earthquake prediction with special references to
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monitoring of the quality factor of lithosphere by coda method. Earthquake Prediction Research 3, 219±230. Aki, K., Chouet, B., 1975. Origin of coda waves: source, attenuation, and scattering effects. Journal of Geophysical Research 80, 3322±3342. CaÂrdenas, M., NuÂnÄez-CornuÂ, F., Lermo, J., GonzaÂlez, A., 1998. Seismic energy attenuation in the region between the coast of Guerrero and Mexico City: differences between paths along and perpendicular to the coast. Physics of the Earth and Planetary Interiors 105, 47±57. Castro, R.R., Anderson, J.G., Singh, S.K., 1990. Site response, attenuation and source spectra of S waves along the Guerrero, Mexico, subduction zone. Bulletin of the Seismological Society of America 80, 1481±1503. Castro, R.R., Munguia, L., Rebollar, C.J., Acosta, J.G., 1994. A comparative analysis of the quality factor Q for the regions of Guerrero and Oaxaca, Mexico. Geo®sica Internacional 33, 373±383. Chouet, B., 1979. Temporal variation in the attenuation of earthquake coda near Stone Canyon, California. Geophysical Research Letters 6, 143±146. Dainty, A.M., ToksoÈz, M.N., 1977. Elastic wave scattering in a highly scattering medium: a diffusion approach. Journal of Geophysical Research 43, 375±388. Ewing, J.I., Meyer, R.P., 1982. Rivera Oceanic Seismic Experiment (ROSE) Overview. Journal of Geophysical Research 87, 8345±8357. Frankel, A., Wennerberg, L., 1987. Energy-¯ux model of seismic coda: separation of scattering and intrinsic attenuation. Bulletin of the Seismological Society of America 77, 1223±1251. Hellweg, M., Spudich, P., Fletcher, J.B., Baker, L.M., 1995. Stability of coda Q in the region of Park®eld, California: View from the U.S. Geological Survey Park®eld Dense Seismograph Array. Journal of Geophysical Research 100, 2089±2102. Herraiz, M. Espinoza, A.F., 1986. Scattering and attenuation of highfrequency seismic waves: development of the theory of coda waves U.S.G.S. Open File Report, Number 86±455. Humphrey, J.R., Anderson, J.G., 1992. Shear-wave attenuation and site response in Guerrero, Mexico. Bulletin of the Seismological Society of America 81, 1622±1645. Jin, A., Aki, K., 1986. Temporal change in coda Q before the Tangshan earthquake of 1976 and the Haicheng earthquake of 1975. Journal of Geophysical Research 91, 665±673. Mendenhall, W., 1975. Introduction to Probability and Statistics. Duxbury, Boston, MA, p. 460. Nishenko, S.P., Singh, S.K., 1987. Conditional probability for the recurrence of large and great interplate earthquakes along the Mexican subduction zone. Bulletin of the Seismological Society of America 77, 2095±2114. Novelo-Casanova, D.A., Lee, W.H.K., 1991. Comparison of techniques that use the single scattering model to compute the quality factor Q from coda waves. PAGEOPH 135, 77±89. Novelo-Casanova, D.A., Berg, E., Helsley, C.E., 1990. S-wave coda Q
from 3 to 20 Hz and P wave Q for foreshocks and afershocks of the Petatlan earthquake. Journal of Geophysical Research 95, 4787±4795. Novelo-Casanova, D.A., Berg, E., Hsu, V., Helsley, C.E., 1985. Time±space variation of seismic S-wave coda attenuation (Qc21) and magnitude distribution (b-values) for the Patatlan earthquake. Geophysical Research Letters 12, 789±792. Ordaz, M., Singh, S.K., 1992. Source spectra and attenuation of seismic waves from Mexican earthquakes, and evidence of ampli®cation in the hill zone of Mexico City. Bulletin of the Seismological Society of America 82, 24±43. Ortega-Gutierrez, F., 1981. Metamorphic belts of southern Mexico and their tectonic signi®cance. Geo®sica International 20, 65±82. Rodriguez, M., Havskov, J., Singh, S.K., 1983. Q from waves near Petatlan, Guerrero, Mexico. Bulletin of the Seismological Society of America 73, 321±326. Sato, H., 1977. Energy propagation including scattering effects, single isotropic approximation. Journal of Physics of the Earth 25, 27±41. Sato, H., 1984. Attenuation and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. Journal of Geophysical Research 89, 1221±1241. Sato, H., 1986. Temporal change in attenuation intensity before and after the eastern Yamanashi earthquake of 1983 in central Japan. Journal of Geophysical Research 91, 2049±2061. Sato, H., 1988. Temporal change in scattering and attenuation associated with the earthquake occurrence Ð a review of recent studies on coda waves. PAGEOPH 126, 465±497. Singh, S.K., Mena, E., Castro, R., 1988a. Some aspects of source characteristics of the 19 September 1985 Michoacan earthquake and ground motion ampli®cation in and near Mexico City from strong-motion data. Bulletin of the Seismological Society of America 78, 451±477. Singh, S.K., Lermo, J., DomIÂnguez, T., Ordaz, M., Espinosa, J.M., Mena, E., Quass, R., 1988b. A study of ampli®cation of seismic waves in the Valley of Mexico with respect to a hill zone site. Earthquake Spectra 4, 653±673. Singh, S.K., Mena, E., Castro, R., Carmona, C., 1987. Empirical prediction of ground motion in Mexico City from coastal earthquakes. Bulletin of the Seismological Society of America 77, 1862±1867. Spudich, P., Bostwick, T., 1987. Studies of the seismic coda using an earthquake cluster as a deeply buried seismograph array. Journal of Geophysical Research 92, 10526±10546. Valdes, C.M., Novelo-Casanova, D.A., User manual for Q coda, in: Toolbox for Plotting Seismic and Other Data, IASPEI Seismological Software Library, 1, 1989, pp. 237±255. Valdes, C., Meyer, R., ZunÄiga, R., Havskov, J., Singh, S.K., 1982. Analysis of Petatlan aftershocks: numbers, energy release, and asperities. Journal of Geophysical Research 87, 8519±8527. Wyss, M., 1985. Precursors to large earthquakes. Earthquake Prediction Research 3, 519±543.