Solving Traveltime Tomography with Deep Learning

TL;DR

This paper presents a neural network method based on BCR-Net for efficiently solving 2D traveltime tomography problems governed by the eikonal equation, enabling accurate reconstruction of slowness fields from boundary measurements.

Contribution

The paper introduces a novel neural network architecture tailored for the inverse traveltime tomography problem, leveraging perturbative analysis and filtered back-projection insights.

Findings

Neural network accurately reconstructs slowness fields.

Proposed method outperforms traditional inversion techniques.

Efficient and scalable for circular tomography geometries.

Abstract

This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary measurement of the traveltimes of waves going through the medium. This inverse map is high-dimensional and nonlinear. For the circular tomography geometry, a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular direction. Motivated by this and filtered back-projection, we propose an effective neural network architecture for the inverse map using the recently proposed BCR-Net, with weights learned from training datasets. Numerical results demonstrate the efficiency of the proposed neural networks.