Numerical simulation of the seismic wave propagation and fluid pressure in complex porous media at the mesoscopic scale

In this study, we apply an improved high-order staggered-grid finite difference method to model seismic wave propagation in complex heterogeneous porous media with cracks. Upon changing the mesh step and applying a broadband wavelet, we obtain numerical simulation results at the mesoscopic scale. As a fundamental result of applying Biot's theory, three types of waves are also found. We discuss the relationship between the shear wave splitting parameter and the crack density of an equivalent medium in detail. Based on Darcy's law, the finite element method is used to investigate the distribution of the fluid pressure field in porous media at the mesoscopic scale. A flat ellipse is used as an approximation of a crack. According to the simulation results, we further study the influence of variations in the crack angle on the distribution of the fluid pressure. Moreover, the formulas derived from the Fourier transform are used to calculate the inverse attenuation quality factors and phase velocities of the fast compressional wave, slow compressional wave and shear wave. The effects of the porosity and elastic modulus of an equivalent medium on wave attenuation are also taken into account in this study.