A Scoping Review of Physics Informed Machine Learning for Wave Propagation Modeling in Seismology

\emph{Background:} Standard numerical methods accurately simulate seismic waves but are computationally expensive, particularly for inverse problems.

Machine learning approaches have been proposed as alternatives that can reduce computational cost while maintaining acceptable physical accuracy. \emph{Objective:} To map how physics-informed machine learning methods have been applied to seismic wave propagation modeling based on partial differential equations. \emph{Methods:} A scoping review was conducted using the OpenAlex and Scopus databases.

Selected studies were classified by problem type (forward or inverse) and machine learning strategy to identify research trends, methodological patterns, and gaps in the literature. \emph{Results:} Physics-informed machine learning has been applied to both forward modeling and inversion in seismology, often reaching accuracy comparable to standard numerical methods at lower computational cost.

Application of three mechanisms for incorporating physical knowledge were identified: observational bias, inductive bias, and learning bias.

To evaluate methodological reproducibility of a representative method, the original PINN framework was replicated in PyTorch, obtaining results consistent with and in most cases more accurate than those originally reported.

From the reviewed literature, limitations remain in benchmarking consistency, training cost, and scalability to three-dimensional and experimentally validated problems. \emph{Conclusions:} Standard numerical methods remain the basis of seismological workflows, while physics-informed machine learning offers complementary approaches that are useful for inverse problems and surrogate modeling.

Future work should focus on consistent benchmarking, hybrid formulations, and validation under realistic geophysical conditions.