Summary
A numerical approach is presented for time domain staggered-grid finite difference modeling of surface waves in porous media, based on the Biot model of poroelasticity. A set of free-surface boundary conditions for solid and fluid are applied based on averaging the medium properties of the nodes along the free surface. The proposed method has higher computional efficiency than that of the previous stress imaging approach at the equivalent precision under the same spatial and temporal discretization.
Introduction
Due to the presence of fluids in near surface, a pure elastic model is insufficient in describing the corresponding seismic wave propagation. Wave motion in a composite medium containing fluids of gas and/or liquid filling the pore space is described in the Biot model (Biot, 1962) of poroelasticity. In Biot's theory, the characterisitics of waves can be used to infer fluid properties such as water distribution and permeability that are useful in many fields. Similarily, numerical simulations of wave propagations in poroelastic media is therefore crucial for near-surface studies using surface waves. Previous works on this subject include finite difference (Masson et al., 2006), finite element (Picotti et al., 2007) and spectral element (Morency and Tromp, 2008) approaches. Due to its computational efficiency and simple model definition, the finite difference method has been the most popular approach.
Finite difference modeling of surface waves is more complex than that for body waves due to the implement of free surface boundary in spatial nodes (e.g., Bohlen and Saenger, 2006). Previously, most of such works are for elastic media. For instance, the simple vacuum formulism in which the boundary conditions are assumed to be implicitly fulfilled by the discontinuity of medium parameters on the nodes (e.g. Moczo et al., 2002). Another popular method is the imaging method, where the stress fields are imaged as odd functions across a free surface (e.g. Levander, 1988; Robertsson, 1996). Several explicit medium averaging approaches are also proposed, where a fictitious layer is always presented to simulate the tractionfree effects on surface waves (e.g. Mittet, 2002; Xu et al., 2007; Zeng et al., 2011). Because of the complex effects of fluids through the free surface (Zhang et al., 2011, 2012), the formulations of finite difference modeling of surface waves in a poroelastic medium is more challenging than that for elastic media.
