Learning stable seismic wave equations for porous media from real data

Abstract

SUMMARY This work presents a machine-learning-based framework to determine unknown coefficients in seismic wave equations for porous media saturated with fluids by using real data as labels, which are velocities of P and S waves. The coefficients are functions of basic rock physics parameters. By using this framework, the trained neural networks incorporate certain mathematical and physical constraints on the coefficients. Working on a single-fluid model, we train the networks with synthetic as well as real data sets. The prediction results show that the learned model is inherently stable, has good physical properties and can accurately predict synthetic data as well as real logging data of shale reservoirs with relative mean square errors less than 5 per cent. They also demonstrate that the wave propagation phenomenon corresponding to the logging data can be well described with the single-fluid model.