Relationship between strong-motion array parameters and the accuracy of source inversion and physical waves

Abstract

We develop general rules for a strong-motion array layout on the basis of our method of applying a prediction analysis to a source inversion scheme. A systematic analysis is done to obtain a relationship between fault-array parameters and the accuracy of a source inversion. An overdetermined least-squares inversion scheme is used, where the spatial resolution is predetermined by the subfault size and the model variance is used as the accuracy of the source inversion. The accuracy of source inversion is efficiently estimated by using Wolberg's prediction analysis. Vertical strike-slip and inclined dip-slip faults are assumed to be located at the center of a circular array. Several fault and array parameters, which are all normalized to make the results applicable to a general case, are separately varied and their effects on the accuracy of the source inversion are estimated. We use exact solutions in a homogeneous half-space. A relationship σ ∝ 1/ Ns 1/2 holds regardless of the fault mechanics, where σ is the accuracy of the source inversion; in other words, the maximum standard deviation of subfault moment and Ns is the number of stations. The most appropriate array radius is found to be 0.75 to 2.0 times the fault length. Good azimuthal coverage of the source is required to retrieve the source structure accurately. Also, a subduction zone simulation does not lead to a strong incentive to deploy permanent ocean bottom seismographs. The accuracy of the source inversion is much less dependent on fault-array parameters for the exact solutions than when only far-field S waves are used, because of the contribution of different seismic waves. Our study of the effects of various physical waves indicates that surface waves at distant stations contribute significantly to the inversion accuracy for the inclined fault plane, whereas only far-field body waves at both small and large distances contribute to the inversion accuracy for the vertical fault, which produces more phase interference. These observations imply the adequacy of the half-space approximation used throughout our present study and suggest rules for actual array designs.