Verification of reciprocity in anisotropic poroelastic wave simulation using symmetric Strang splitting
This work provides a numerical method that accurately preserves a fundamental physical property (reciprocity) in poroelastic simulations, which is important for applications in geophysics and reservoir engineering.
The authors developed a symmetric Strang-splitting scheme for anisotropic poroelastic wave simulation that preserves reciprocity, achieving cross-component reciprocity with a relative L2 misfit approaching machine precision.
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.