Biot's theory-based dynamic equation modeling using a machine learning auxiliary approach

Characterizing seismic wave propagation in a fluid-saturated porous media well enhances the precision of interpreting seismic data, bringing benefits to understanding reservoir properties better. Some important indicators, including wave dispersion and attenuation, along with the wavefield, are widely used for interpreting the reservoir, and they can be obtained from a rock physics model. In existing models, some of them are limited in scope due to their complexity, for example, numerical solutions are difficult or costly. In view of this, this study proposes an approach of establishing equivalent dynamic equations of existing models. First, the framework of the equivalent model is derived based on Biot's theory, while the elastic coefficients are set as unknown factors. The next step is to use deep neural networks (DNNs) to predict these coefficients, and surrogate models of unknowns are established after training DNNs. The training data is naturally generated from the original model. The simplicity of the equation forms, compared to the original complex model and some other equivalents such as the viscoelastic model, enables the framework to perform wavefield simulation easier. Numerical examples show that the established equivalent model can not only predict similar dispersion and attenuation, but also obtain wavefields with small differences. This also indicates that it may be sufficient to establish an equivalent model only according to dispersion and attenuation, and the cost of generating such data is very small compared to simulating the wavefield. Therefore, the proposed approach is expected to effectively improve the computational difficulty of some existing models.