Inversion of Strong Ground Motion and Teleseismic Waveform Data for the Fault Rupture History of the 1979 Imperial Valley, California, Earthquake by Stephen H. Hartzell and Thomas H. Heaton

A least-squares point-by-point inversion of strong ground motion and teleseismic body waves is used to infer the fault rupture history of the 1979 Imperial Valley, California, earthquake. The Imperial fault is represented by a plane embedded in a half-space where the elastic properties vary with depth. The inversion yields both the spatial and temporal variations in dislocation on the fault plane for both right-lateral strike-slip and normal dip-slip components of motion. Inversions are run for different fault dips and for both constant and variable rupture velocity models. Effects of different data sets are also investigated. Inversions are compared which use the strong ground motions alone, the teleseismic body waves alone, and simultaneously the strong ground motion and teleseismic records. The inversions are stabilized by adding both smoothing and positivity constraints. The moment is estimated to be 5.0 x 102s dyne-cm and the fault dip 90 ° + 5 °. Dislocation in the hypocentral region south of the United States-Mexican border is relatively small and almost dies out near the border, Dislocation then increases sharply north of the border to a maximum of about 2 m under Interstate 8. Dipslip motion is minor compared to strike-slip motion and is concentrated in the sediments. The best-fitting constant rupture velocity is 80 per cent of the local shear-wave velocity. However, there is a suggestion that the rupture front accelerated from the hypocenter northward. The 1979 Imperial Valley earthquake can be characterized as a magnitude 5 earthquake at the hypocenter which then grew into or triggered a magnitude 6 earthquake north of the border. INTRODUCTION The 15 October 1979 (23:16:54) Imperial Valley earthquake (ML = 6.6) provided a wealth of strong-motion records. Twenty-two records were obtained from the U.S. Geological Survey network in the Imperial Valley within an epicentral distance of 60 km (Brady et al., 1980) and seven records were obtained from the northern Baja California strong-motion array (Brune et al., 1982). The strong-motion records, together with the teleseismic recordings, make the 1979 Imperial Valley earthquake the best-instrumented, moderate-sized event to date, with the possible exception of the 1971 San Fernando earthquake. The complicated topographic and geologic setting of the San Fernando earthquake makes it difficult to study. In comparison, the structure of the Imperial Valley is relatively simple, consisting of a deep sedimentary basin with relatively fiat-lying layers. Furthermore, a recent seismic refraction study of the area (Fuis et al., 1982) yielded fairly detailed information on the P-wave velocity structure. Thus, recordings of the 1979 Imperial Valley earthquake provide us with a unique opportunity to construct detailed and physically realistic models of the rupture history and wave propagation for this earthquake. Failure to adequately model records from this earthquake would seriously undermine our confidence in the validity of previous modeling studies of earthquakes for which less data is available. To date, the strong-motion data set has formed the basis of a number of studies. 1553 1554 STEPHEN H. HARTZELL AND THOMAS H. HEATON Niazi (1982) determined acceleration directions using the horizontal ground motions across a differential array at E1 Centro (station locations indicated by DIF in Figure 7). This array consists of five digital accelerometers positioned on a north-south line 210 m long. From these data, Niazi inferred that the rupture propagated northwestward from the epicenter in Mexico. Niazi further estimated an average rupture velocity of 2.7 km/sec during the first 6 sec of faulting. Spudich and Cranswick (1982) have also analyzed the E1 Centro differential array data. They calculated apparent velocities of particular phases by cross-correlating records. Their work implies an average rupture velocity of 2.5 km/sec at depth, but also suggests that the rupture velocity was lower during the first few seconds of faulting and that the rupture accelerated as it moved to the north. Their analysis also suggests that large high-frequency vertical accelerations (0.6 to 1.74 g) recorded on several strong-motion records near E1 Centro are due to P waves originating from the vicinity of the Imperial fault where it crosses Interstate 8 and at a depth of approximately 8 km. Archuleta (1982) proposed the alternative interpretation that the large vertical accelerations are a surface-reflected PP phase originating further to the south near Bonds Corner at a depth of about 4 km. By examining polarization diagrams of particle velocity for stations near the trace of the fault, Archuleta (1982) estimated an average rupture velocity of 2.5 to 2.6 km/sec. Three previous studies have used the strong-motion data to estimate the distribution of slip for the 1979 earthquake: Hartzell and Helmberger (1982), Olson and Apsel (1982), and Le Bras (1983). Hartzell and Helmberger (1982) used forward modeling to deduce the slip distribution. Their model is characterized by an average rupture velocity of 2.5 to 2.7 km/sec (0.8 to 0.9 times the basement shear-wave velocity). The slip is predominantly below a depth of 5 km, north of the hypocenter and south of the E1 Centro area. Two regions of noticeably larger slip were suggested, particularly one located under Interstate 8, which is held to be responsible for the large vertical accelerations recorded near E1 Centro. They estimated the moment from strong-motion records to be 5.0 × 1025 dyne-cm, which was shown to be consistent with the amplitudes of teleseismic shear waves. Olson and Apsel (1982) used a least-squares inversion. They parameterized the problem by dividing the Imperial fault plane into sections, 2 with depth and 10 along the strike of the fault. Each section, or subfault, is allowed to rupture during five separate time intervals, each separated by 0.75 sec. Their slip distribution is significantly smoother than the model of Hartzell and Helmberger (1982). The major differences in the two models may be due to the different parameterizations of the problem. Hartzell and Helmberger (1982) used a constant rupture velocity, with fixed timing, requiring that the waveforms be explained by spatial variations in slip. Olson and Apsel (1982) set the problem up with more capacity for temporal variation and less spatial variation in slip. They obtained a trend in dynamic slip which implied a horizontal rupture velocity between 4.0 and 5.0 km/sec, which is greater than the local shearwave velocity. This slip, although more smoothly distributed than the patch of large dislocation in the Hartzell and Helmberger (1982) model, is located in the same place and may be a manifestation of the same phenomenon. The present study has a more balanced trade-off between spatial and temporal model parameters than these previous two studies. Olson and Apsel (1982) obtained a moment of 9.1 × 1025 dyne-cm. Le Bras (1983) used an inversion scheme which minimizes a cross-correlation error function between the synthetic waveform and the data. A constant rupture velocity is used, but the mechanism (strike, dip, and rake) of each subfault is allowed FAULT RUPTURE HISTORY OF THE IMPERIAL VALLEY EARTHQUAKE 1555 to vary somewhat about a pure right-lateral, strike-slip, 90°-dipping fault. He found that the fits to the strong-motion records are improved by allowing the strike, dip, and rake to vary by _+10". As in the previous studies, the Le Bras (1983) model is characterized by an average rupture velocity of about 2.5 km/sec, with most of the slip below 5 km and north of the hypocenter but south of the E1 Centro area. He estimated the moment to be 5.0 × 1025 dyne-cm. In this paper, unlike the previous studies, we model both the teleseismic body waves and the local strong-motion records. The teleseismic data are included in an attempt to add additional constraints on the rupture process. We also wish to address a basic question: What details of the rupture history can be deduced from (1) teleseismic data alone, (2) near-source data alone, and (3) the combined teleseismic and near-source data sets? This is an important question, since good local instrument coverage is rare and most earthquake source studies must depend on teleseismic data alone. Heaton (1982) recently demonstrated the difficulties involved in modeling teleseismic body waves and strong ground motions simultaneously with a forward modeling approach and showed the inconsistencies which can develop between models obtained by forward modeling of limited data sets. Thus, one of the objectives of this paper is to explore the similarities and differences of inversion models based on different data sets. The data are modeled by using a constrained, stabilized, least-squares inversion technique. The problem is parameterized to yield the best-fitting (in a least-squares sense) dislocation on a spatially and temporally discretized fault. FORWARD PROBLEM Before pursuing the inverse problem, several forward models of the teleseismic body waves were run. These calculations are done to investigate the dip of the Imperial fault and to see what contributions individual phases make to the teleseismic waveforms. Hartzell and Helmberger (1982) obtained a model of the distribution of dislocation for the 1979 earthquake by forward modeling of just the strongmotion data. It is also of interest to see how well this model predicts the teleseismic body waves. Figure I shows the seismic velocity structures used throughout this study to compute strong ground motion (dashed curves) and teleseismic synthetics (solid curves). The local P-wave velocity structure (Table 1) is based closely on the refraction results of Fuis et al. (1982) and is an average velocity structure for profile 6NNW-13SSE of that study, which runs approximately down the axis of the Imperial Valley. The S-wave velocities are obtained by assuming (1) a Poisson solid (a = ~f3 ~) below a depth of 5 km and (2) linearly increasing Poisson's ratio for depths less than 5 km such that a = 2.37/~ at the free surface. TiLe structure used to compute the teleseismic waveforms (Table l) consists of three layers over a halfspace and approximates the gradient structure used in the near-source region. This simplified structure greatly reduces the computational effort required to model teleseismic body waves from a finite fault. Use of the layered structure to compute the teleseismic body waves is justified by their longer period and the steep teleseismic take-off angles. The computation of teleseismic body-wave synthetics for a threedimensional finite fault is done by a Green's function summation technique. Heaton (1982) gives a full explanation of the method. The teleseismic synthetics in this paper include the responses of all rays with up to two internal reflections in the layered stack. All conversions between phases occurring at the free surface are included as well as the more important internal conversions. The amplitudes of 1556 STEPHEN H. HARTZELL AND THOMAS H. HEATON rays having a greater number of internal reflections are much smaller and can be omitted. Point source responses for sources embedded within the gradient structure (approximated by many layers) were computed using a Haskell propagator matrix technique and compared favorably with responses computed using the generalized ray technique and assuming the simplified velocity model. The Haskell matrix method is not used in the rest of this study because the analysis requires the separation of the responses of down-going (P, S) and up-going (pP, sP) phases, a modification not yet implemented in the Haskell method. The teleseismic, long-period P and S H waves predicted by the Hartzell and Helmberger (1982) model 9WM are shown in Figures 2 and 3, respectively. All WWSSN P and SH waveforms of acceptable quality between 30 ° and 90 ° are shown. In both figures the synthetic is the second, lighter trace. The amplitude in microns is given for each synthetic assuming a moment of 5.0 × 1025 dyne-cm. This moment was obtained by Hartzell and Helmberger in their study of the strong-motion records. The waveforms and amplitudes of the P waves are fairly well-matched. The Velocity, km/sec 0 0 2 4 6 N " . i ' ' I ,