Partial Global Recovery in the Elastic Travel Time Tomography Problem for Transversely Isotropic Media

TL;DR

This paper investigates the partial recovery of material parameters in transversely isotropic media using travel times of different wave types, providing stability estimates and conditions for parameter identifiability.

Contribution

It introduces a pseudolinearization approach for inverting parabolic-type operators in elastic travel time tomography and establishes stability and injectivity results for parameter recovery.

Findings

Stability estimates for recovering parameters from wave speeds.

Injectivity conditions for parameters with small set differences.

Analysis of parabolic-type operators in the inversion process.

Abstract

We consider the problem of recovering material parameters in a transversely isotropic medium from the qP and qSV waves' travel times, given the axis of isotropy and the material parameters associated to the qSH wave speed. The operators obtained from the pseudolinearization argument are of parabolic type, and so we discuss inverting operators whose symbols are of parabolic type. We present stability estimates for recovering either one parameter from one wave speed or two parameters from two wave speeds with the remaining parameters either known or with a known functional relationship, and these estimates provide injectivity among parameters that differ on sets of small width.