Modeling of seismic wave scattering in poroelastic media

Understanding wave scattering in the Earth is considered fundamental in describing seismic wave propagation and providing information on structural features of the Earth’s interior. Petrophysical parameters (especially porosity and permeability) affect the reflection coefficients of subsurface interfaces, which can better explain the field data and infer the subsurface structure. However, the numerical solutions to the scattering problem for efficient modeling of wave propagation in poroelastic earth structures have limitations. We develop a numerical algorithm for solving the poroelastic scattering integral equations. Specifically, applying perturbation theory to Biot’s equations, the solutions are expressed by the Lippman-Schwinger integral equations, which can express the displacement and pressure fields. We derive the contrast source integral equations of the decoupled poroelastic wave equations. We apply a Conjugate Gradient Fast Fourier Transform (CG-FFT) method for fast solutions of the integral equations. We show that despite the complexity of the geological structure, the numerical method enables the modeling of the displacement and pressure fields in both the frequency and time domains. We demonstrate that the wave scattering problem for the Biot model provides a good description to understand the Earth’s interior.