Microlocal Methods for The Elastic Travel Time Tomography Problem for Transversely Isotropic Media

TL;DR

This paper develops microlocal analysis techniques, including a modified pseudodifferential calculus, to solve the elastic travel time tomography problem in transversely isotropic media, advancing mathematical methods in seismic imaging.

Contribution

It introduces a new microlocal framework with a modified calculus to address degenerately elliptic operators in elastic travel time tomography.

Findings

Constructed a new pseudodifferential calculus for degenerately elliptic operators.

Provided parametrices for the elastic travel time tomography problem.

Extended boundary rigidity analysis to transversely isotropic media.

Abstract

We study the travel time tomography problem for transversely isotropic media using the artificial boundary method used in works in X-ray tomography and boundary rigidity problems. The analysis involved requires a modification of the scattering pseudodifferential calculus in order to provide parametrices for operators which are degenerately elliptic; such a calculus is constructed in this paper and used to solve the tomography problem of interest.