INVERSION OF THE BODY WAVES FROM THE BORREGO EARTHQUAKE TO THE SOURCE

The generalized linear inverse technique has been adapted to the problem of determining an earthquake source model from body-wave data. The technique has been successfully applied to the Borrego Mountain earthquake of April 9, 1968. Synthetic seismograms computed from the resulting model match in close detail the first 25 sec of long-period seismograms from a wide range of azimuths. The main shock source-time function has been determined by a new simultaneous short period-long period deconvolution technique as well as by the inversion technique. The duration and shape of this time function indicate that most of the body-wave energy was radiated from a surface with effective radius of only 8 kin. This is much smaller than the total surface rupture length or the length of the aftershock zone. Along with the moment determination of Mo = 11.2 x 102s dyne-cm, this radius implies a high stress drop of about 96 bars. Evidence in the amplitude data indicates that the polarization angle of shear waves is very sensitive to lateral structure. I N T R O D U C T I O N Since the introduction of simple theoretical fault models, many investigators have attempted to infer details of earthquake faulting by comparing far-field body-wave recordings with model predictions, They have found that most deep and intermediate events have simple wave shapes which can be easily explained with smooth dislocation models, (Mikumo, 1971, a and b; Teng and Ben Menahem, 1965; Burdick and Helmberger 1974) but that shallow earthquakes have very complex wave forms. Until recently, this was interpreted to mean that shallow events have fundamentally more complex fault surfaces and time histories. By determining the response of a layered half-space to a shallow double-couple point source, Helmberger (1974), Fukao (1971), and Hudson (1969), among others, have shown that this interpretation is not entirely correct because much of the wave-form complexity is caused by the interaction of the source with the free surface. Thus, it will once again be worthwhile to address the question of whether or not a smooth dislocation is appropriate for shallow earthquakes. This time, however, the fleesurface interaction should be included in the analysis. Many of the previous investigators of body waves from shallow events have focused their attention on the Fourier transform of the entire body-wave pulse. They employed a technique which enabled them to determine important source parameters such as seismic moment, stress drop and source dimensions from the rough characteristics of the amplitude spectrum (Hanks and Wyss, i972; Wyss and Hanks, 1972, a and b; Molnar and Wyss, 1972; Molnar, Tucker and Brune, 1973). Since reflected or converted phases such as pP, sP or sS can affect both the long-period level and the shape of the amplitude spectrum, it will be important to see if the results change when the free surface is correctly accounted for. Langston and Helmberger (1975) have outlined a simple procedure for including the surface interaction in the computation of a synthetic seismogram from a model of a shallow dislocation source. In other words, they have presented a tractable solution to the forward problem of computing the data given the model. We have demonstrated in a related work (Mellman and Burdick, 1976), that the existence ofa soluti6n to the forward