Solving Traveltime Tomography with Deep Learning

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 backprojection,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.