Leverage Automatic Differentiation Routines for Seismic Traveltime Tomography in Tunnels

Seismic traveltime tomography calculates the traveltime misfit between observed data and forward modeling data to estimate the subsurface velocity structure. Since no amplitude information is required, it is particularly useful for complex scenarios such as tunnels where observed data is usually of low quality. Seismic traveltime tomography in tunnels has three steps: shortest path searching, traveltime misfit calculation, and parameter updating. However, these steps can be computationally challenging and lead to unstable solutions due to the complex and large systems solving involved. To address this, we leverage automatic differentiation routines, which originated from deep learning and are now playing an increasingly important role in a wide range of fields, to help solve seismic traveltime tomography. Specifically, we build the differentiable computational graph to represent the travel path and compute traveltime in the forward procedure, then use back-propagation to obtain gradients in the backward (inverse) procedure. We then adopt stochastic gradient descent (SGD) to update parameters from several randomly selected paths. In this way, randomness is introduced to avoid local minima, and no large linear systems solving is required. Several representative velocity models are designed to compare seismic traveltime tomography in automatic differentiation routines and traditional ways. Our method shows significant superiority in terms of visual comparison and metric scores from the experiment results.