Convexification for the 3D Problem of Travel Time Tomography

TL;DR

This paper introduces a new convexification method for solving the 3D travel time tomography problem modeled by the eikonal equation, with applications in seismic imaging, demonstrating promising numerical results.

Contribution

A novel globally convergent convexification approach tailored for 3D travel time tomography in a cylindrical setting is developed and tested.

Findings

Numerical studies confirm the effectiveness of the convexification method.

The method achieves global convergence in the 3D travel time tomography problem.

Results indicate potential for improved seismic imaging techniques.

Abstract

The travel time tomography problem is a coefficient inverse problem for the eikonal equation. This problem has well known applications in seismic. The eikonal equation is considered here in the circular cylinder, where point sources run along its axis and measurements of travel times are conductes on the whole surface of this cylinder. A new version of the globally convergent convexification numerical method for this problem is developed. Results of numerical studies are presented.