Linearized inverse scattering of teleseismic waves for anisotropic crust and mantle structure: 1. Theory

Abstract

In this study we examine the recovery of vertically varying anisotropic crust and upper mantle structure using converted teleseismic waves recorded on three‐component seismograms from individual broadband stations. Our analysis is cast in terms of inverse scattering theory for a one‐dimensional medium and begins with a derivation of the plane wave Green's function for a homogeneous medium exhibiting arbitrary elastic anisotropy. This Green's function is employed within the single‐scattering approximation to derive formulae that relate the amplitude of the scattered wave in time to perturbations in material properties at corresponding depths. Inclusion of seismograms from multiple events representing a range of azimuths and incident angles leads to the construction of a linear system of equations that is readily solved using singular value decomposition. A useful by‐product of this “amplitude‐versus‐slowness” approach is the identification of simple and compact expressions for linearized reflection and conversion coefficients in anisotropic media that are accurate for small contrasts at near‐vertical angles of incidence. We demonstrate the accuracy of the linearized P‐to‐S transmission coefficient for an idealized upper mantle model. In a companion paper we will examine the application of this approach to field data recorded at stations of the Canadian National Seismograph Network.