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Solving Traveltime Tomography with Deep Learning

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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.

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Acknowledgements

The work of Y.F. and L.Y. is partially supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program. The work of L.Y. is also partially supported by the National Science Foundation under award DMS-1818449.

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  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Yuwei Fan & Lexing Ying

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  1. Yuwei Fan
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Correspondence to Lexing Ying.

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Fan, Y., Ying, L. Solving Traveltime Tomography with Deep Learning. Commun. Math. Stat. 11, 3–19 (2023). https://doi.org/10.1007/s40304-022-00329-z

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