2-D poroelastic wave modelling with a topographic free surface by the curvilinear grid finite-difference method

Abstract

The curvilinear grid finite-difference method, which is suitable for accurate modelling of seismic waves in the presence of topographic free surfaces, is applied in this study to model poroelastic waves. Poroelastic wave equations of Biot’s theory are expressed in curvilinear coordinates and solved on a collocated grid by utilizing the fourth-order Runge–Kutta time integral scheme with alternative applications of forward and backward MacCormack finite differences. Discretization of the irregular free surface with the curvilinear coordinate grid enables a good fit of the topographic surface, and this good fit results in higher numerical accuracy in comparison with stair-case approximation. The formulas of the free-surface boundary conditions for poroelastic media are also derived for the curvilinear coordinates and subsequently implemented with the traction-imaging method, which is a generalization of the stress-imaging method and can maintain high accuracy in curvilinear coordinates. To verify the performance of the proposed algorithm and determine its accuracy, we conduct numerical simulations on several different models, and compare our numerical solutions with other solutions that are calculated by analytical expressions, generalized reflection/tranmission method and spectral-element method. Besides, the fluid–solid dynamic compatibility of porous media is demonstrated using a three-layered half-space model, and effects of the irregular free-surface on poroelastic waves are investigated for a four-layered model with strong irregular free-surface topography. The good performance of the proposed algorithm suggests that the curvilinear grid finite-differece method is a useful tool for the study of poroelastic wave propagation.