Modeling of the Surface Static Displacements and Fault Plane Slip for the 1979 Imperial Valley Earthquake By

Synthesis of geodetic and seismological results for the 1979 Imperial Valley earthquake is approached using three-dimensional finite element modeling techniques. The displacements and stresses are calculated elastically throughout the modeled region. The vertical elastic structure in the model is derived from compressional and shear wave velocities as used in the seismic data analysis (Fuis et al., 1981) combined with a sediment density profile. Two strategies for applying initial conditions are followed in this modeling. In the first strategy, a sample seismological estimate for fault plane slip is used to predict the resultant surface motions. We show that the geodetic strain results over distances of tens of kilometer from the fault (Snay et al., 1982) are basically consistent with the model seismic fault displacements. Geodetic results from within a few kilometers of the fault trace (Mason et al., 1981) seem to require more slip at shallow depths than appears at seismic time scales. This is consistent with the occurrence of aftercreep at shallow depths in less well-consolidated material, which would bring surface displacements into line with maximum slip at depth, but not greatly affect the net moment. In the second strategy, we consider stresses on the fault plane, rather than displacements, as model variables. To constrain this part of our numerical modeling, we assume that the fault driving stress is governed by ambient tectonic stress and an opposing Coulomb friction derived from experiment. The coseismic stress drop from point to point on the failed fault is given by the difference between the tectonic shear stress and the frictional stress. After arriving at such a uniform model which adequately represents the Snay et al. results, we further modify a small region near the seismic "asperity" to make the fault plane motions qualitatively and quantitatively resemble the model of coseismic motions used in the first strategy. The observed offset on the fault trace (Sharp et al., 1982) is approximated in this final stress-driven model by removing the driving stress on the southern third of the fault. Thus, the principal features of the coseismic slip pattern are explained by a stress-driven fault model in which: (a) a spatially unresolved asperity is found equivalent to a stress drop of 18 MPa averaged over an area of 15 km 2, and (b) driving stress is essentially absent on the fault segment overlapping the 1940 earthquake rupture zone. INTRODUCTION The Imperial Valley is one of the most seismically active regions in California and represents an important transition zone as follows. The character of the plate boundary in the Imperial Valley is predominantly strike-slip, with east-west extensional tectonics superposed. To the south in the Gulf of California, the plate boundary is a spreading ridge-transform fault system (Lomnitz et al., 1970; Elders et al., 1972). Northward from the Imperial Valley, the Transverse Ranges are characterized by north-south compression of ~0.17/~strain/yr (Savage et al., 1981). The Salton trough in general appeared to be in uniaxial north-south contraction at the rate of 0.3 strain/yr, with no rift-opening strain perpendicular to the axis of the 2413 2414 MARTIN A. SLADE 1, GREGORY A. LYZENGA, AND ARTHUR RAEFSKY trough (Savage et al , 1979). However, the directions and rates of strain in Southern California may be time variable, since the more recent observations (Savage et al., 1981) find these strains are now comparable. In order to study the regional tectonics of this important area, we have performed numerical modeling, using the finite element technique, of the most recent significant earthquake there. The 15 October 1979, Imperial Valley earthquake was a large event [ML 6.6 (Chavez, 1982)] in a well-instrumented area with a fairly well-characterized vertical seismic velocity structure (Fuis et al., 1981). The data from this event and its aftershocks have been the subject of a large number of investigations (see, e.g., U.S. Geological Survey Professional Paper 1254, 1982). Our finite element studies attempt to synthesize the results of several specific analyses of the Imperial Valley main event into a self-consistent static description of the coseismic displacements and stresses. The strategy pursued in this work consists of two principal steps (Figure 1). In the first step, we take the seismologically derived (Hartzell and Heaton, 1983) coseismic fault slip as a function of position in the fault plane and apply this directly to a three-dimensional dislocation model. Since this approach entails considerable inhomogeneity, both in the distribution of slip and in constitutive parameters, we have chosen to employ the finite element method for these calculations. The surface displacements and strains obtained from this step of the modeling is then compared with available geodetic data, with the purpose of identifying components (if any) of the observed geodetic changes which are not explained by the seismic slip. This step of the modeling, therefore seeks to work from the seismic slip observation toward an insight into any unmodeled processes occurring in the fault zone. In the second step of the modeling presented here, we invert this strategy by beginning with a physical model of stresses and constitutive parameters, and subsequently perturb it in order to reproduce the observed fault slip (and by assumption, geodetic displacements). These two approaches are complementary, but not redundant or trivially equivalent. This is apparent because for any given set of seismological and/or geodetic data, there exists a broad set of nonunique physical models to explain these. The purpose of the first step'then, is to provide an adequate empirical description of the event under consideration, while the second seeks to select a physically plausible scenario to reproduce this description. This finite element modeling procedure does not, therefore represent a formal inversion for very specific details in the local stress field, but rather is an attempt to reconcile a range of observational data within a basic physical framework. BACKGROUND MODEL INFORMATION Our analysis of the 1979 coseismic motions utilizes as input the results from seismological studies. A brief description of these is given below. All of the models have in common a vertical elastic profile derived from the vertical velocity structure of Fuis et al. (1981), as used in the seismic data analysis (Figure 2). The density profile given in Table 1 as a function of depth (Hartzell, personal communication, 1982), was used. The model values used here for Lam~'s modulus X and shear modulus # are also given in Table 1. The depths in Table 1 are also the vertical divisions of our finite element grid. The finite element models constructed are compared with various results, as explained below, in order to judge their success. The coseismic displacements on the Imperial fault obtained from analysis of a combination of strong-motion and MODELING TECHNIQUES FOR THE IMPERIAL VALLEY EARTHQUAKE 2415 teleseismic data by Hartzell and Heaton (1983) are used as input to the dislocation model. Figure 3 (top) shows the seismically determined strike-slip displacements interpolated onto the nodal points of our finite element grid (discussed below), where the contour levels are in centimeters. The values shown are half the dislocation; these values are imposed in opposite senses (for right-lateral motion) on the opposing fault walls, by employing the "split node" finite element procedure deI ' SEISMO I 1 i,,,,o,,,=,.., I 1 i o,=OOES,'! DRIVEN BY SEISMOLOGICALLY DETERMINED FAULT DISPLACEMENTS PHYSICAL I PARAMETERS J / ~ i , ~