Inversion of surface wave data in source mechanism studies

Abstract

A least squares method is proposed to invert Rayleigh and Love wave observations in source mechanism studies. When complex spectra is available the inversion scheme is linear and it is carried out in a single step. When only amplitude spectra is available the inversion scheme may be linearized and it converges to a unique solution independent of the orientation of the initial trial source. Source depth is found by minimizing errors in repeated application of the method at different trial depths. Application to real data requires a careful weighting of observations when the path structure is not well‐known. The source representation in term of seismic moment tensor components allows for a simple analysis of the surface wave data resolving power. Complex spectra of Rayleigh waves render a unique solution, but complex spectra of Love waves admit infinite solutions. If a double‐couple source is assumed, the Love wave data may have either one or three equally satisfactory solutions. When only absolute values of surface wave spectra are available, any solution may be rotated 180° in azimuth and/or all the source tensor components may be changed in sign.

Theoretical Rayleigh and Love waves from an explosion in prestressed source regions

“…The far-field forms of the above displacement fields are identical with those of Mendiguren (1977). For a general quadrupole source of arbitrary orientation [Appendix C and equations (49)], ~)(o~).…”

“…We also obtain expressions for the canonical second-or-der moment tensor for comparison with Mendiguren (1977). Finally, we calculate Rayleigh-and Love-wave seismograms for canonical orientations of the pure shear stress field (Harkrider, 1977) and discuss them in terms of their P-and S-wave excitation.…”

Seismic Wave Propagation in Stratified Media

“…The modal contributions to the seismograms are linear in the components of the source moment tensor. Thus, as for body waves, it is possible to make a linear inversion for the source mechanism using distant observations, if a good reference model of the wavespeed distribution with depth can be found for the paths in question (Mendiguren, 1977).…”

Source and Propagation Effects of Rayleigh Waves from Central Asian Earthquakes

“…The first application of the linear inversion was carried out by Dziewonski and Gilbert (1974) on free oscillation datasets for two deep shocks in South America. Extensions of this method to other datasets have been proposed by a number of investigators (Buland and Gilbert, 1976;McCowan, 1976;Mendiguren, 1977).…”