KIRCHHOFF-APPROXIMATE INVERSION OF TELESEISMIC WAVEFIELDS

Abstract

We derive Kirchhoff-approximate inversion formulae for elastic wavefields that recover the location of discontinuity surfaces and associated material property contrasts in laterally varying, stratified media. The derivation is cast in the context of teleseismic wavefield scattering in a 2-D medium with allowance made for oblique incidence, although a fully general derivation for 3-D media follows in straightforward fashion. We exploit a little-used variant of the isotropic, elastic Kirchhoff-Helmholtz integral in which individual terms are directly identified with scattered P- and S-wave contributions prior to approximation using ray-theoretic forms. This approach yields relatively simple formulae for Kirchhoff-approximate forward modelling that bear a closer resemblance to their acoustic counterpart than standard elastic formulations cast in terms of traction and displacement. Using micro-local analysis, inversion formulae are readily derived using the generalized Radon transform. Our approach represents an extension of the Kirchhoff-approximate inversion scheme outlined by Beylkin & Burridge (1990) to S-waves and conversions. We demonstrate application of the method to field data recorded during the IRIS-PASSCAL CASC93 experiment.