Numerical modeling has been crucial for addressing problems across various scientific and engineering disciplines involving partial differential equations. In particular, wave propagation modeling has seen significant development in scientific computation. Standard numerical modeling methods have demonstrated notable accuracy; however, their computational cost can be substantial. Recently, alternative methods based on machine learning have emerged, offering a promising balance between computational cost and accuracy when applied to wave propagation problems. In this work, we present a review of methods developed and used to model wave propagation, with a special emphasis on computational seismology. We discuss the fundamentals of wave propagation modeling, standard numerical methods, and recent advances in solving differential equations through these approaches. We conduct a systematic review of the literature to identify applications where these methods, either standalone or in hybrid approaches with standard numerical methods, have demonstrated efficiency in terms of computational time. The results of this review provide insights into the potential of machine learning techniques for wave propagation modeling and their impact on computational seismology.

We recommend setting up a new Python environment with conda. You can do this by running the following commands:

conda env create -f environment.yml
conda activate review-seismic-waves-env

To verify the packages installed in your review-seismic-waves-env conda environment, you can use the following command:

conda list -n review-seismic-waves-env