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A method of determining focal mechanisms and quantifying the uncertainty of the determined focal mechanisms for microearthquakes

DEPARTMENT OF GEOSCIENCE NATIONAL DEFENSE ACADEMY, YOKOSUKA, Japan, 239

Abstract

A practical method of determining focal mechanisms suitable for microearthquakes was designed and its characteristics were investigated. The method consists of three parts: (1) determining the focal-mechanism solutions using the Fourier method (Aoki, 1986) improved by Maeda (1988): (2) selecting the final focal-mechanism solutions; and (3) evaluating the uncertainty of the final focal-mechanism solutions.

The characteristics of the method are summarized as follows. (1) In determining the focal-mechanism solutions, the Fourier method (Aoki, 1986) improved by Maeda (1988) was adopted. The precision of this method is of the same degree as that by the grid search with a grid interval of 10°, although the calculation time is one fifth of that by the grid search. Therefore, the method is convenient for use on minicomputers or personal computers. (2) The uncertainty indices u for the final focal-mechanism solutions were defined as the root-mean-square of the angle of deviation for respective axes. The uncertainty of the focal-mechanism solutions selected by using the amplitudes of first motions can be estimated at 15° at most. Accordingly, if the solutions with the uncertainty indices larger than 15° are omitted out of those determined by using only polarities, we can obtain the data set of final focal-mechanism solutions with the same degree of uncertainty as those selected by using the amplitudes of first motions. (3) It should be noted that the data set of the focal-mechanism solutions having uncertainty indices less than a threshold value is not uniform about the faulting type, because the focal-mechanism solutions with a strike-slip faulting type is not better constrained than that with a thrust or normal faulting type. (4) The direction of the predominant stress can be estimated by this method even if the uncertainty of the focal-mechanism solutions is large.

Using the method designed in this study, we can obtain abundant focal-mechanism solutions of microearthquakes that are routinely observed by seismic networks.