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Seismic traveltime tomography using transmission data is widely used to imagethe Earth's interior from global to local scales. In seismic imaging, it isused to obtain velocity models for subsequent depth-migration or full-waveforminversion. In addition, cross-hole tomography has been successfully applied fora variety of applications, including mineral exploration, reservoir monitoring,and CO2 injection and sequestration. Conventional tomography techniques sufferfrom a number of limitations, including the use of a smoothing regularizer thatis agnostic to the physics of wave propagation. Here, we propose a noveltomography method to address these challenges using developments in the fieldof scientific machine learning. Using seismic traveltimes observed at seismicstations covering part of the computational model, we train neural networks toapproximate the traveltime factor and the velocity fields, subject to thephysics-informed regularizer formed by the factored eikonal equation. Thisallows us to better compensate for the ill-posedness of the tomography problemcompared to conventional methods and results in a number of other attractivefeatures, including computational efficiency. We show the efficacy of theproposed method and its capabilities through synthetic tests for surfaceseismic and cross-hole geometries. Contrary to conventional techniques, we findthe performance of the proposed method to be agnostic to the choice of theinitial velocity model.

PINNtomo: Seismic tomography using physics-informed neural networks