  Seismic traveltime tomography using transmission data is widely used to image
the Earth's interior from global to local scales. In seismic imaging, it is
used to obtain velocity models for subsequent depth-migration or full-waveform
inversion. In addition, cross-hole tomography has been successfully applied for
a variety of applications, including mineral exploration, reservoir monitoring,
and CO2 injection and sequestration. Conventional tomography techniques suffer
from a number of limitations, including the use of a smoothing regularizer that
is agnostic to the physics of wave propagation. Here, we propose a novel
tomography method to address these challenges using developments in the field
of scientific machine learning. Using seismic traveltimes observed at seismic
stations covering part of the computational model, we train neural networks to
approximate the traveltime factor and the velocity fields, subject to the
physics-informed regularizer formed by the factored eikonal equation. This
allows us to better compensate for the ill-posedness of the tomography problem
compared to conventional methods and results in a number of other attractive
features, including computational efficiency. We show the efficacy of the
proposed method and its capabilities through synthetic tests for surface
seismic and cross-hole geometries. Contrary to conventional techniques, we find
the performance of the proposed method to be agnostic to the choice of the
initial velocity model.

Computational Physics;Geophysics