Moment tensor inversion of local earthquake data-I. Investigation of the method and its numerical stability with model calculations

Abstract

SUMMARY Two methods for moment tensor inversion of waveform data (Sipkin 1982) are examined for applicability to high-frequency near-source data. This study focuses on two subjects, namely the numerical aspects of the inversion method and the various kinds of assumptions being made from the theory. It is shown that the moment tensor inversion methods are theoretically unstable if only far-field SH seismograms are used due to dependencies and vanishing of different Green's functions. Additional instabilities are found even for the P–SV problem, which are caused by numerical effects. In order to remove these problems the inversion methods are modified by a damped least-squares algorithm, estimating the useful range of damping parameters from singular value analysis. Numerical tests are performed on synthetic near-source data with simulated traveltime errors assuming a wrong source location or misidentification of phases. Bias from extended sources with directivity is investigated. It is concluded that the modified inversion method is robust with respect to such data sets.