Study of Love and Rayleigh waves from earthquakes with fault plane solutions or with known faulting. Part 1. A phase difference method based on a new model of earthquake source

Abstract

ABSTRACT For the purpose of examining the basic assumptions underlying the surface wave method of earthquake mechanism study, we investigated Love and Rayleigh waves from earthquakes with known faulting and/or fault plane solutions obtained from initial motion studies. In order to eliminate the effect of the source time function and finiteness of the fault and to concentrate on the nature of the earthquake force system and its space parameters, we are primarily concerned with the phase differences between Love and Rayleigh waves and their amplitude ratios. We studied about 30 earthquakes which occurred in the Mediterranean region, California, and Japan. The results are given in Part 2, and the method used is described in the present paper. The theoretical phase and amplitude of Love and Rayleigh waves were computed on the basis of observed faulting or fault plane solution under various hypotheses about the equivalent force system. Then, we obtained from the record, the Fourier phase difference of Love and Rayleigh waves, corrected it for propagation in a layered earth and compared it with the corresponding theoretical value. In computing the theoretical values, we assumed a homogeneous half space for Rayleigh waves. For Love waves, the layered structure of the earth was taken into account in an approximate way. We have constructed a table of the theoretical values for all possible parameters of fault system and also for various focal depths. A part of the table is given in a concise form in Part 3. The measurement of the phase difference between Love and Rayleigh waves was made by two methods. One is the stationary phase analysis, first applied to seismograms by Brune, Nafe and Oliver (1960), and the other is a filtering-correlation method. The latter method is appropriate for those records where the waves are less dispersed and noise is a factor. It was found that the single couple hypothesis fails to explain the observations on surface waves, and must be modified in some way. A modified single couple hypothesis is proposed which appears to explain the observations generally better than the double couple hypothesis as will be shown in Part 2.