Stability and Statistical Inversion of Travel time Tomography

TL;DR

This paper investigates the stability and statistical inversion methods for travel time tomography, focusing on conformal metrics, and demonstrates the consistency of Bayesian techniques with noisy data.

Contribution

It provides new stability estimates for conformal metrics and applies these to validate Bayesian inversion methods in travel time tomography.

Findings

Established forward and inverse stability estimates for conformal metrics.

Proved the consistency of Bayesian statistical inversion with noisy measurements.

Enhanced understanding of stability in travel time tomography applications.

Abstract

In this paper, we consider the travel time tomography problem for conformal metrics on a bounded domain, which seeks to determine the conformal factor of the metric from the lengths of geodesics joining boundary points. We establish forward and inverse stability estimates for simple conformal metrics under some a priori conditions. We then apply the stability estimates to show the consistency of a Bayesian statistical inversion technique for travel time tomography with discrete, noisy measurements.