# Generalized ray models of strong ground motion

Abstract (Summary)

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A method for synthesizing local ground displacement from a model consisting of a finite fault located within a layered half-space is demonstrated. The response of a three-dimensional fault is evaluated by integrating the responses of point shear dislocations over the fault plane (Green's function technique). The response of each point shear dislocation is evaluated by using generalized ray theory in conjunction with the Cagniard-de Hoop technique. A basic review of these methods is given. In general, the complete solution to a three-dimensional fault in a layered half-space is complex and computationally unwieldy. Various simplifying approximations, whose validity depends upon the source to receiver geometry and seismic frequency, are discussed. The records from three Southern California earthquakes of different magnitudes and source to receiver geometries are modeled and appropriate approximations are demonstrated.
The smallest earthquake that is modeled is the largest earthquake (M 4.9) in the November, 1976 Brawley swarm. Long-period strong-motion instruments were located at distances of 33 km (IVC) and 36 km (ELC). The IVC record consists almost entirely of transversely polarized motion, whereas the ELC record contains an approximately equal proportion of transversely and radially polarized motion. A simplified shear wave velocity model was determined from the compressional wave refraction studies of Biehler, Kovach and Allen (1964). The epicentral location and focal mechanism (right-lateral strike-slip) computed from P wave first arrival studies were used to locate and orient a double-couple point source within the layered half-space. Essentially, the far-field time function and source depth were the only parameters without good independent constraints. A far-field time function with a duration of 1.5 seconds along with a source depth of 7 km was sufficient to model the first 25 seconds of transverse ground motion. Although it seems clear that faulting had finite dimensions, the source to receiver geometries and small source dimension make it possible to model this earthquake with a single point dislocation having the appropriate far-field time function. It appears that the effects of velocity structure on the propagation of long period SH waves are predictable in the Imperial Valley. A study of the synthetic Fourier amplitude spectra indicates that wave propagation effects should be included in studies of source spectra and seismic wave attenuation.
Several synthetic models are constructed to fit the first 40 seconds of transversely polarized displacement, as recorded at El Centro (ELC), of the April 9, 1968 Borrego Mountain earthquake (M 6.5). Unfortunately, there are complications involving the non-planar seismic velocity structures which lie between source and receiver. A simplified structure of a layer over a half-space is used to roughly approximate the effect of the thick sequence of sediments in the Imperial Valley. The beginning 10 seconds of the observed record is used to model the spatial and temporal distribution of faulting, whereas the remaining portion is used to determine the upper crustal structure based on surface-wave periodicity. A natural depth criterion is provided by comparing the amplitude of the direct arrival with the surface-wave excitations. Considerable non-uniqueness is present in the modeling process. If strong midcrustal seismic discontinuities are present, then it is possible to model the ground motion with a single point dislocation. Within the framework of a single layer over a half-space model, faulting of finite vertical extent is required, whereas the horizontal dimensions of faulting are not resolvable. A model which is also consistent with the teleseismic results of Burdick and Mellman (1976) indicates massive faulting near a depth of 9 km with a fast rise time producing a 10 cm displacement pulse of 1 second duration at El Centro. The faulting appears to slow down as it approaches the free surface. The moment is calculated to be approximately 7 x [...] dyne-cm which is somewhat smaller than that found from teleseismic body waves by Burdick and Mellman (1976).
Because of the special source to receiver geometries present for the Brawley and Borrego Mountain earthquakes, it is necessary only to model SH waves. Furthermore, near-field source terms can be neglected and problems associated with fault finiteness are relatively easy to deal with. This is not true in the case of modeling the strong-motion recordings of the February 9, 1971 San Fernando earthquake (M 6.5). Three-dimensional models of a finite fault located in a half-space are constructed to study the ground motions observed at JPL, Palmdale, Lake Hughes and Pacoima Dam. Since the duration of faulting is comparable to the travel times for various wave types, very complex interference of these arrivals makes a detailed interpretation of these waveforms difficult. 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 directivity 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 meters. Fault offsets become very small at depths near 4 km and then grow again to 5 meters 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 shallow faulting. The total moment is 1.4 x [...] ergs.
Bibliographical Information:

Advisor:Donald V. Helmberger

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis

Keywords:geological and planetary sciences

ISBN:

Date of Publication:09/26/1978