Geofisica Colombiana N°.7 pp.74-78 dlciembre de 2003 Bogoli\, D.C. ISSN - 0121 - 2974 Application of neural networks to obtain the site response in Mexico city CARLOS A. VARGAS J. Universidad Nacional de Colombia, Bogota, Grupo de Geofisica, cavargasj@unal.edu.co JULIO C. CUENCA S. Instituto de Ingenieria, UNAM, Mexico, D. E, Mexico, jccsa@pumas.iingen.unam.mx RESUMEN Hemos implementado una red neuronal de tres capas escondidas con 40 neuronas por capa para ser usada como funciones de trasferencia suelo/roca en dos estaciones acelerornetricas en Ciudad de Mexico. La red fue entrenada con entrenamiento su- pervisado por medio de vectores de aceleracion de entrada y salida (doce registros de cinco eventos sismicos localizados en la costa de Guerrero y uno al sur de Puebla, 5,8 M 7,3), Yprobado con tres registros no tornados en cuenta en el entrenamiento de la red. Los resultados obtenidos en el dominio de la frecuencia son bastante buenos, encontrandose una amplificacion sismica entre 0,2 a 5 Hz para la zona de Lago (estacion RMCS). En el dominio del tiempo obtuvimos resultados que no son coinciden- tes. Debido a los datos y a la complejidad del fenomeno, es necesario aplicar esta herramienta usando mas registros de movi- mientos fuertes para entrenar la red neuronal, asi el fenomeno puede ser aprendido mejor mediante una base de datos confiable. PALABRAS CLAVE: REDES NEURONALES, RESPUESTA OE SITlO, CIUOAO DE MEXICO ABSTRACT We have implemented a neural network of three hidden layers with 40 neurons each layer to be used as soil/rock transfer func- tions for two stations in Mexico City. The net was trained with supervised learning through input and output vectors of accele- rations (twelve records, from five seismic events from Guerrero and Puebla, 5.8 M 7.3), and tested with three records not taken in account in the training. The results in the frequency domain are good, finding a seismic amplification between 0.2 to 5 Hz for the Lake zone. In the time domain we obtain results that are not coincident. Due to the data and the complex of the phe- nomena, it is necessary to apply this tool using more records for the training net, so the phenomena can be learned better through reliable database. KEY WORDS: NEURAL NETWORKS, SITE RESPONSE, MEXICO CITY INTRODUCTION The modeling of site response and specially the determination of the capacity of amplification from strong lithologic COntrastshave been an aspect of relevant interest for earthquake engineering in the past three decades. A wide variety of methodologies has been pro- posed and applied in searching to establish transfer functions soil/rock oriented to purposes of seismic microzonation and geo- technic. Some techniques were inspired in the capacity of coda waves or ambient tremors to denote changes of stiffness or attenuation of seismic energy, others were based in physical models under visco-elastic conditions in terrain with lateral homogeneity (Borcherdt, 1970; Su et al., 1992; Field and Jacobi, 1993; Kato et al., 1995; Su and Aki, 1995; Steidl et al., 1996; Mucciarelli, 1998; Rielpl et al., 1998; Cultera et al., 1999). Popular techniques such as Nakamura (Nakamura, 1989) and standard technique have been applied in Mexican cities to study the site effect (Lermo and Chavez-Garcia, 1994; Chavez-Garcia and Cuenca, 1996). Due to Mexico City was funded over soft soils (layers of clay surrounded by basaltic material), it was known the amplified seismic waves and its long duration effect (Sing and Ordaz, 1993; Lermo and Chavez-Garcia, 1994). Singh Manuscrito recibido para evaluacton ellS de abril de 2003. Articulo aceptaco para publicacion por el Comrte Editorial el 30 de octubre de 2003. 74 GEOFislCA COLOMBIANA, 7, OICIEMBRE DE 2003 APPLICATION OF NEURAL NETWORKS TO OBTAIN THE SITE RESPONSE IN MEXICO CITY and Ordaz point out that the long duration of acceleration records in the Lake zone (called soft zone) is result of multipath from the source. Recently, the use of artificial intelligence for purposes of site response has put of manifest the practical utility of genetic algo- rithm and artificial neural network for the simulation of transfer functions soil/rock and inversion of others geophysical variables (Anderson, 1990; Aguirre et al., 2000; Moya et al., 2000; Romo et al., 2000; Garcia et al., 200;0;Vargas et al., 2002). In this work, we try to show the importance of neural network for seismic response proposes for the Lake zone in Mexico City. DATA Digital acceleration data associates to five earthquakes were se- lected from the Instituto de Ingenieria UNAM, the Centro Nacional de Prevencion de Desastres (Cenapred) and the Mexican DataBase of Strong Motion. The units are gals and the series of time are 100 and 200 samples/sec depending on the local network and ins- trument. Four earthquakes used are located at the Mexican coast of Guerrero State and one at south of Puebla city (see Figure I) co- vering principally three different azimuths. The accelerographic sta- tions in Mexico City taken on count due to quality of the data are RMCS (called Roma "C" in surface on clay layers or lake zone) and Cena (called Cenapred over basaltic deposits). The station called CUP4 (called C. U. Patio 4 on similar basaltic deposits as in Cena) was used in the case when Cena not registered the events numbers I and 2 (see Table 1). METHODOLOGY In this work, we have tried to determine a non-analytic transfer function capable to predict seismic response under the soft forma- tionslhard rock relation, which can consider non-linear aspects of that relation. For that reason, we have selected to train a neural network on the basis of spectral observations ofthe N-S, E-Wand Z components for five seismic events. Taking in consideration some conclusions mentioned by Vargas et al. (2002), who computed seismic amplification factor for the Armenian area (Colombia) using neural networks with ac- celeration data, pointing out that the simulations with any com- ponent must keep a similar tendency in the results. For this reason, from fifteen records (5 events with 3 components) we ap- plied twelve records in the training phase and the others three for the evaluation phase. The utility of neural network has seen limited its use for spectral analysis. Justly, the analysis on the time domain becomes a not very practical procedure due to the high computation de- manding (Vargas et al., 2002; Garcia et al., 2000). In our case, it was proposed that inversion of the spectral acceleration for RMCS station on soil of Mexico City with data of spectral accele- ration from stations on rock (CUP4 and Cena) through the use of neural networks based on the following criteria: 1. Spectra of the events coming from the seismic zones of Gue- rrero and Puebla, principal seismic sources, recorded in Mexico City show components that rarely exceed the 5 Hz 2. The longitudes of data accelerographic for seismic events with 5.7< Mc < 7.3, generally not exceed their strong movements so far than 4 minutes. Figure 2 is one example of this si- tuation. For the 12 records of the training phase we applied Fast Fourier Transform (FFT) to spectral acceleration determination, with an analysis of 50 seconds beginning from S wave. The fo- llowing step was used a neural network with supervised learning; the inputs are the spectral accelerations in the reference station (rock) and the output the spectral acceleration on other station (soil). That network must have capacity of generalization with certain detail the spectrum (training with 12 records), for that it is necessary a good number of neurons; it was selected a back-propagation topology (Johansson et al., 1990) with three hidden layers of 40 neurons and activation functions [TanSigmod LogSigmod Linear]. The first two activation functions have the capacity of learning I.inear and non-linear patrons, while that the Table J. Earthquake of acceleration data analyzed in this work registered in RMCS (soil) and Cena (rock) I I 1 I I Ti- Mag.M I Dist.e) - Azi. Location# Date Lat.N( 0) Lon.W(O) meHh:mm:ss c 1 10 December 19-~--t:17:40.9 6.3 18.02 101.56 2.7239 NW Guerrero __--i 2 14 Seotember 1995 14:04:30.5 7.3 16.31 98.88 3.1 176 South Coast Guerrero I 3 15 June 1999 20:42:07.1 6.7 18.18 97.51 1.9 129 South Puebla I I4 21 June 1999 17:43:05.5 15.8 17.99 101.72 2.7241 NW Guerrero 5 29 December 1999 05:19:46 5.9 18.02 101.68 NW Guerrero I GEOFISICA COLOMBIANA, 7, OICIEMBRE DE 2003 75 third scale magnitudes of output. The learning was based in the method of conjugated gradient (Hagan et aI., 1996), a powerful al- gorithm with rapid capacity of error convergence. Finally, we tried to invert the waveform using Inverse Fost Fourier Transform (IFFT) in the band 0.02 to 10 Hz with intervals of 0.02 Hz in the time domain. Figure 3 shows the fidelity of the recorder interloper versus the true one. RESULTS AND DISCUSSION It has been appreciated in several works of site response for Mexico City, the amplification due to the contrast soil/rock is important in low frequencies mainly between 0.2 to 5 Hz (Lermo and Cha- vez-Garcia, 1994; Chavez-Garcia and Cuenca, 1996). These obser- vations detailed with the data of this work were simulated from the neural network. Figure 4 shows an example of the capacity of re- construction of neural network with the learned information of 12 records. We see (top of Figure 4) a real amplification effect as product of soil/rock relation. However, we can obtain an simulated amplification effect similar to real one when we use as input for the net a spectra from the rock (bottom of Figure 4). This procedure allows us to considerate the neural network as a well approximation for infering empirical transfer functions soil/rock by means of its generalization capability. To evaluate the inference capacity of the neural network with data unknown, we used 3 records on rock (not taken in account in the training phase) to establish what similar are the deduction of the net with respect to the true spectral accelerations on the soil. In the Figure 5, we can appreciate simulated and true accelerations that follow the same tendencies, the dominants period obtained are best coincident (0.02-5 Hz). Thus, it is clear that the neural network has a well behavior as a transfer function soil/rock with unknown data and it can be used for inferring spectra an soil from spectra on rock. On the other hand, it looks attractive to use a net for infering the waveform on the soil from the waveform on the rock. Several tests were made to obtain a transfer function in the time domain that should reach this objective. Figure 6 shows real signal on the time domain (top) where we see different amplitudes as answer of the amplification effect of the soil. Similarly, we see the true and simulated records on the soil with the learned data. These results satisfy in the first instance our requirements with a little change of the wave-phase. However, when we use records not taken in ac- count in training, the waveforms were very different (see Figure 7). This situation is answer of the very complex problem asso- ciated to lateral heterogeneity of soils, scattering and the structure of Mexican basin. Obviously, it is necessary to use more records for the training phase that can assure optima learning and permit obtain more reliable records. 76 VARGASET AL. CONCLUSION We have used five triaxial accelerographic records to determine soil/rock transfer functions for two stations in Mexico City with neural networks. In this case it was used a topology with three hidden layers of 40 neurons by layer. The net was trained with su- pervised learning through input and output vectors of accelerations (12 records), and tested with three records not taken in account in the training. In the frequency domain the results were good and the net has a valuable behavior as reliable tool for studies of site res- ponse. However, in the time domain the results were not coincident. Due to the complex of the phenomena, it is necessary to use more records for the training net that can learn the nature of phenomena. We suggest to made more works on this sense where exit reliable databases that permit to show the great capacity of this technology for proposes of site response. BIBLIOGRAPHY AGUIRRE,1., CONTRERAS,M. G. and FLORES,H. C. 2000. "Obtencion de efectos de sitio utilizando algoritmos geneticos y el modelo de fuente w-2". Memorias del Simposio Intemacional "Riesgos Geologicos y Ambientales en la Ciudad de Mexico", UNAM. ANDERSON,K. R. 1990. "Programming as a geophysical inverse problem". Bull. 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Earthquake 1O-Dec-94,16:17- Guerrero 10~---,....-r---r----r----..-----, -100'-------:':50:-------;-1 0::::0:-----'::5:;;-D-----;;2:';;00:;----;;-;250 Time(s) PowerSpectrumDensity o '----JLC:.flW"'--J..M>,."-----<>-----:-----_:------:-_---;--------; o 3 5 Frequency (HZ) Figure 3. Signal in time (top) and frequency domain (bottom). Note the spectrum ra- rely exceed the 5Hz. 77 104 6 8'~':C'".,"''"'''''''''k'."''" o 2 4 6 8 Frequency (Hz) 10 Figure 4. On the top, spectra of soil (soft line) and rock (heavy line). On the bottom, the true (soft line) and simulated (heavy line) spectral acceleration on soil, from learned data. 4 5 6 Frequency(Hz) 10 Figure 5. True (soft line) and simulated (heavy line) spectral acceleration on soil for three different records. The simulated data obtained from spectral acceleration on rock not taken in account in the training. 78 V ARGAS ET AL. True Aceieratron on Rock and 5011 ~:~N~ 0 u .10 -20~o 5 10 15 20 25 30 35 40 45 50 "~ 10 N~ 0 u -10 ·20 o 5 10 15 20 25 Time(s) 30 45 5035 40 Figure 6. On the top, true acceleration on rock (heavy line) and (soft line) soil. On the bottom, true (soft line) and simulated (heavy line) acceleration for the same time win- dow of soil. True and Simulated Aceieranon::~o 5 10 15 20 25 30 35 40 45 50<:~o 5 10 15 20 25 30 35 40 45 50 .~~o 5 10 15 20 25 30 35 40 45 50 Time(s) Figure 7. True (soft line) and simulated (heavy line) acceleration for three different events. GEOfislCA COLOMBIANA, 7. OiCIEMBRE OE 2003