Solving Traveltime Tomography with Deep Learning
This addresses a high-dimensional, nonlinear inverse problem in geophysics, but appears incremental as it adapts existing neural network methods to a specific domain.
The paper tackles the problem of recovering the slowness field in two-dimensional traveltime tomography using a neural network approach based on the eikonal equation, demonstrating efficiency in numerical results.
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.