Decomposition and Properties of the Traveltime Sensitivity Kernels in Transversely Isotropic Elastic Media

Abstract

This study discusses the properties and decompositions of the traveltime sensitivity kernels in elastic isotopic and transversely isotropic media. Analytical solutions in homogeneous isotropic elastic media are derived and help better understand their properties. One key component is the kernel phase function which determines the frequency components of the sensitivity kernels, the geometrical setting of the Fresnel zones, and the resolving ability for velocity inversion. For the purpose of exploration seismology, the sensitivity kernels for finite-frequency traveltime inversion in transversely isotropic elastic media are expressed in terms of Thomsen’s anisotropic parameters. The sensitivity kernels in anisotropic media can be decomposed into the summation of the isotropic terms constructed by the elastic properties in the symmetry direction and the correction terms due to the presence of anisotropy. Sensitivity kernels computed from different types of acquisitions contain information for different parameters. We compare the kernels computed using finite-difference with those by dynamic ray tracing. We conclude that the full wave numerical method is able to provide high-resolution kernels, which form the basis for 3D finite-frequency traveltime inversion for velocity and anisotropic parameters.