Generalized Ray Models of the San Fernando Earthquake

The exact Cagniard-de Hoop solut ions for a point dislocation in half-space are used to construct models of the strong ground motion observed during the February 9, 1971 San Fernando earthquake (PC, = 6.4). By summing point dislocations distr ibuted over the fault plane, three-dimensional models of a f inite fault located in a half-space are constructed to study the ground motions observed at JPL (Pasadena), Palmdale, Lake Hughes, and Pacoima Dam. Since the duration of fault ing is comparable to the travel t imes for various wave types, very complex interference of these arrivals makes a detailed interpretation of these wave forms diff icult. By investigating the motion due to small sections of the fault, it is possible to understand how various wave types interfere to produce the motion due to the total fault. Rayleigh waves as well as S to P head waves are shown to be important effects of the free surface. Near-field source effects are also quite dramatic. Strong direct ivi ty is required to explain the difference in amplitudes seen between stations to the north and stations to the south. Faulting appears to have begun north of Pacoima at a depth of 13 km. The rupture velocity, which is near 2.8 km/sec in the hypocentral region, appears to slow to 1.8 km/sec at a depth of 5 km. Displacements on the deeper sections of the fault are about 2.5 m. Fault offsets become very small at depths near 4 km and then grow again to 5 m near the surface rupture. The large velocity pulse seen at Pacoima is a far-field shear wave which is enhanced by directivity. Peak accelerations at Pacoima are probably associated with the large shal low fault ing. The total moment is 1.4 x 102s ergs. INTRODUCTION In this paper we present some preliminary results derived from strong motion modeling of some of the more diagnostic observations obtained from the San Fernando data set. In two related studies (Heaton and Helmberger, 1977, 1978), strong ground motions for several earthquakes located in the Imperial Valley were examined. The records in these situations were taken at distances several times larger than the source dimensions and only transversely polarized motions were modeled. Ground motions for these events were shown to be profoundly affected by seismic velocity structure. Although source characteristics were important, relatively simple source models were all that were necessary to produce adequate synthetic records. This study attempts to understand recordings of the 1971 San Fernando earthquake. Since this earthquake was well recorded by many close stations, a more detailed inspection of source processes is required. Present address: Dames & Moore, Suite 1000, 1100 Glendon Avenue, Los Angeles, California 90024. 1311 1312 THOMAS H. HEATON AND DONALD V. H E L M B E R G E R Several new complications are introduced by the small source-to-receiver distances. Near-field terms can no longer be neglected as in the previous studies. Furthermore, fault finiteness requires that waves from differing parts of the fault must approach the receiver from differing directions. This means that the observed ground motion cannot be rotated into radial and transverse directions. Thus we cannot isolate SHwave forms and we are forced to consider P waves, SVwaves, and Rayleigh waves. For many reasons, life becomes more complicated as we move closer to the earthquake source. Fortunately, as the source-to-receiver distance becomes small, the effects of plane-layered structure become less dramatic. In an attempt to understand the most basic features of the interplay between source and structural effects, we chose first to model the San Fernando earthquake as a threedimensional fault located in an elastic half-space. The purpose of this study is two-fold. We would first like to understand the types of phenomena which should be expected from a three-dimensional fault which is located in a half-space. The second goal is to achieve a better understanding of the particular source processes of the San Fernando earthquake. The second goal is the more important and difficult to achieve. The San Fernando earthquake created a wealth of teleseismic body-wave and surface-wave data and also local static offset data. It thus provides a unique cross-check of several different techniques of studying the slip on the fault plane. Ultimately, we would like to find a single model which explains all of these observations. However, in this study we will not attempt to model these different data sets simultaneously. We will comment on the compatibility of our strong-motion models which have been derived by other authors. A large number of papers have been written about the San Fernando earthquake and we will not attempt to summarize the results of all previous studies. However, these are several papers which we found very useful in constructing our models. The study of teleseismic body waves by Langston (1978), Alewine's (1974) inversion of static offset data and teleseismic surface-wave data, Hanks' study of observed strong ground motion (1975), and the inversion of strong-motion data by Trifunac (1974) all proved very useful in our construction of San Fernando models. Although Trifunac's models were for a finite fault in a whole space, we learned from his synthetic Pacoima Dam ground motion. Thus, there are several similarities between our preferred fault model and Trifunac's final fault model. The numerical calculations involved in our synthetics consist of several relatively laborious and expensive steps. Once a particular fault to station geometry is chosen, it is time and money consuming to change that geometry. We have chosen to model four stations and no attempt was made to find alternate stations or source-to-station geometries which might produce better synthetics. In retrospect, we would have ignored the station at Palmdale since a half-space seems to be a very poor approximation of earth structure near this station. Also, it appears that a different fault dip versus depth relationship might have improved the comparison between synthetic and real data. However, it is not our purpose to discover the best half-space model. We would like to discover the gross features of the model which are required by the data. Because of the large number of parameters involved, a thorough search of the model space can result in an endless groping process. Until we learned the significance of different parameters, we were victims of this grope. The merits of this process are that much can be learned about what will not work. We are now faced with the problem of showing the reader what we have learned from this process and why we have chosen the model presented in this paper. It would be impractical and tedious to present all of our unsuccessful models. Thus GENERALIZED RAY MODELS OF THE SAN FERNANDO EARTHQUAKE 1313 our plan is to preseat several simple models and to then try and understand why they do not work and how they could be improved. THE DATA The 1971 San Fernando earthquake produced by far the largest single strongmotion data set yet available. Shown in Figure 1 are the locations of most of the