标题： 用深度学习解决旅行时间层析成像 显示英文标题

标题： Solving Traveltime Tomography with Deep Learning

摘要： 本文介绍了一种基于eikonal方程的神经网络方法，用于解决二维旅行时间层析成像（TT）问题。 TT的数学问题是根据通过介质的波的旅行时间的边界测量来恢复介质的慢度场。 这个逆映射是高维且非线性的。 对于圆形层析成像几何结构，扰动分析表明，正向映射可以在角度方向上近似为一个矢量化卷积算子。 受此启发以及滤波反投影的启发，我们提出了一种有效的神经网络架构用于逆映射，使用了最近提出的BCR-Net，其权重通过训练数据集学习得到。 数值结果证明了所提出神经网络的效率。 显示英文摘要

摘要： 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.