AN OPTI~[AL STRATEGY FOR SEARCHING THE BEST FAULT-PLANE SOLUTION USING WAVE-AMPLITUDE DATA.pdf

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AN OPTI~[AL STRATEGY FOR SEARCHING THE BEST FAULT-PLANE SOLUTION USING WAVE-AMPLITUDE DATA.pdf

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AN OPTI~[AL STRATEGY FOR SEARCHING THE BEST FAULT-PLANE SOLUTION USING WAVE-AMPLITUDE DATA

Bulletin of the Seismological Society of America. Vol. 67, No. 5, pp. 1355-1362. October 1977 AN OPTI~[AL STRATEGY FOR SEARCHING THE BEST FAULT-PLANE SOLUTION USING WAVE-AMPLITUDE DATA B Y I4~AILASH I~HATTRI* ABSTRACT This paper presents an optimum search procedure known as the Fibonacci Tech- nique for abstracting the earthquake-source parameters from the amplitude data of seismic waves. The power of the method has been demonstrated by determining the fault-plane solution of a deep-focus earthquake using the P-wave spectral ampli- tude data. INTRODUCTION The fault-plane studies found an early use as a means of inferring geological faults. They have seen many years of widespread and successful applications in seismo- tectonic investigations. The growing interest in such studies has led to the develop- ment of some powerful techniques for abstracting the fault parameters. Among the methods available for this purpose, the techniques using the amplitude of seismic waves is particularly versatile (Teng and Ben Menahem, 1965; Khattri, 1969; Chan- dra, 1970; I(anamori, 1970). As in.many inverse problems of geophysics, the inversion of amplitude data for abstracting the source parameters requires an exhaustive random search for a fault model that gives the best fit of the theoretical amplitudes with the observed data. There are three parameters that define a fault model, namely, the strike T, the dip ~, and the slip direction k. The search space is thus very large (0 ° T 180 °, 0 ° 180 °, 0 ° k 360°). This implies a time-consuming and costly process and the formulation of an optimal search procedure is acutely needed. In the present study, we briefly expose the Fibonaccian search technique and dem- onstrate its power in earthquake source studies by determining the fault-plane solu- tion of a deep-focus earthquake using P-wave spectral amplitude data. AN OPTIMAL SEARCH SCHEME Suppose we are given a function f ( x ) and it is desired to