  Seismic tomography solves high-dimensional optimization problems to image
subsurface structures of Earth. In this paper, we propose to use random batch
methods to construct the gradient used for iterations in seismic tomography.
Specifically, we use the frozen Gaussian approximation to compute seismic wave
propagation, and then construct stochastic gradients by random batch methods.
The method inherits the spirit of stochastic gradient descent methods for
solving high-dimensional optimization problems. The proposed idea is general in
the sense that it does not rely on the usage of the frozen Gaussian
approximation, and one can replace it with any other efficient wave propagation
solvers, e.g., Gaussian beam methods and spectral element methods. We prove the
convergence of the random batch method in the mean-square sense, and show the
numerical performance of the proposed method by two-dimensional and
three-dimensional examples of wave-equation-based travel-time inversion and
full-waveform inversion, respectively. As a byproduct, we also prove the
convergence of the accelerated full-waveform inversion using dynamic
mini-batches and spectral element methods.
