# On the travel time tomography problem in 3D

## TL;DR

This paper addresses the 3D travel time tomography problem with limited data, introducing a stable numerical method based on Fourier series and Carleman estimates to ensure global convergence.

## Contribution

It develops a novel globally convergent numerical approach for 3D travel time tomography using Fourier series and Carleman estimates, handling non-overdetermined data.

## Key findings

- Lipschitz stability estimate established
- A globally convergent numerical method constructed
- Effective handling of non-overdetermined data

## Abstract

Numerical issues for the 3D travel time tomography problem with non-overdetemined data are considered. Truncated Fourier series with respect to a special orthonormal basis of functions depending on the source position is used. In addition, truncated trigonometric Fourier series with respect to two out of three spatial variables is used. First, the Lipschitz stability estimate is obtained. Next, a globally convergent numerical method is constructed using a Carleman estimate for an integral operator.