Variable-Order Finite Difference Scheme for Numerical Simulation in 3-D Poroelastic Media

The numerical simulation of wave fields in 3-D poroelastic media can give a better understanding of elastic properties, deformation characteristics of rocks, and interaction with pore fluids. However, the wave equations in 3-D poroelastic media include more equations, and the size of geophysical model for practical reservoir is immense. Therefore, numerical simulation is time consuming. In order to improve the efficiency, we proposed variable-order staggered-grid (SG) finite difference (FD) method to solve 3-D poroelastic wave equations. In this method, different orders of SGFD scheme can be selected for different velocities in a heterogeneous poroelastic model by restricting the dispersion parameters within a tolerable threshold. We derive the dispersion relation, numerical dispersion relation, and stability condition for 3-D poroelastic media using plane wave analysis and SGFD scheme. Based on the numerical dispersion relation of slow P-wave, S-wave, and fast P-wave, we restrict the average of dispersion parameters of the three waves within a given range; the orders of the SGFD scheme can be calculated for different velocities. Dispersion analysis shows that the variable-order SGFD method can maintain the accuracy compared with the fixed-order SGFD method. We use three numerical examples, which include laterally homogeneous model, a simplified overthrust model, and a geophysical model in a desert area in China, to demonstrate the accuracy and efficiency of the proposed method. The numerical results confirm that the variable-order SGFD method can reduce the computation time efficiently and still ensure the accuracy.