Deep-neural-networks-based approaches for Biot–squirt model in rock physics

A new cost-effective surrogate model using deep neural network (DNN) for seismic wave propagation in rocks saturated with fluid is presented. In this field, the dispersion/attenuation analysis and wave-field simulation are two key measurements which can be carried out by solving wave equations. The Biot–squirt (BISQ) equation is a classical wave propagation model in geophysical forward modeling and has been widely used. The solution of such equation, especially by numerical method, is often complex and time-consuming. In this work, a DNN model is trained with the dataset of velocity and inverse quality factor generated from BISQ model. The results show that the relative mean square error between the predictions of DNN model and that of BISQ model on the test sets are all less than 3%. It indicates that the DNN model has learned the high-dimensional space well and then can realize the dispersion/attenuation analysis for any given rock physical parameters. Besides, the other well-trained DNN model is used to obtain the simulation results with second-order accuracy according to results by finite difference scheme with first-order accuracy. It reveals that the fast wave-field simulation can be implemented once the results with lower accuracy are obtained.