Verification of reciprocity in anisotropic poroelastic wave simulation using symmetric Strang splitting

TL;DR

This paper develops a symmetric Strang-splitting scheme for poroelastic wave simulation that preserves reciprocity and energy conservation, addressing a key challenge in numerical modeling of wave propagation in porous media.

Contribution

The authors formulate the Biot equations with a split operator approach and construct a second-order symmetric scheme that maintains reciprocity and stability in discretized simulations.

Findings

The scheme achieves near machine precision reciprocity in 2D VTI media.

Energy conservation is maintained in the reversible wave subsystem.

The method is unconditionally stable and retains Courant limits similar to elastic solvers.

Abstract

Poroelastic wave simulations are important for many applications relating fluid flow and wave characteristics in porous rock formations. Reciprocity is a key physical property of wave propagation in porous media that is important for such applications, even when viscous dissipation is present. However, numerical poroelastic simulations often fail to reproduce reciprocal responses because the discretization does not preserve the balance between reversible wave dynamics and irreversible fluid-solid drag. To address this, we formulate the Biot equations in terms of a continuous evolution operator split into a reversible (skew-adjoint) wave part and an irreversible (self-adjoint, non-positive) Darcy part, including the leading-order Johnson-Koplik-Dashen correction. This structure clarifies why reciprocity holds in the continuous equations and how it is easily broken in discrete form. Guided by this interpretation, we construct a symmetric second-order Strang-splitting scheme with half-step source injection. The method conserves energy in the reversible subsystem, treats Darcy dissipation unconditionally stably, and retains Courant limits similar to elastic solvers. Using a staggered pseudo-spectral discretization, we model multimode propagation in 2D VTI media and obtain cross-component reciprocity with a relative L2 misfit approaching machine precision, demonstrating that the discrete scheme inherits the symmetry properties of the continuous evolution operator.