  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.
