Benchmarking wave equation solvers using interface conditions: the case of porous media

The correct implementation of the continuity conditions between different media is fundamental for the accuracy of any wave equation solver used in applications from seismic exploration to global seismology. Ideally, we would like to benchmark a code against an analytical Green's function. The latter, however, is rarely available for more complex media. Here, we provide a general framework through which wave equation solvers can be benchmarked by comparing plane wave simulations to transmission/reflection (R/T) coefficients from plane-wave analysis with exact boundary conditions (BCs). We show that this works well for a large range of incidence angles, but requires a lot of computational resources to simulate the plane waves. We further show that the accuracy of a numerical Green's function resulting from a point-source spherical-wave simulation can also be used for benchmarking. The data processing in that case is more involved than for the plane wave simulations and appears to be sufficiently accurate only below critical angles. Our approach applies to any wave equation solver, but we chose the poroelastic wave equation for illustration, mainly due to the difficulty of benchmarking poroelastic solvers, but also due to the growing interest in imaging in poroelastic media. Although we only use 2-D examples, our exact R/T approach can be extended to 3-D and various cases with different interface configurations in arbitrarily complex media, incorporating, for example, anisotropy, viscoelasticity, double porosities, partial saturation, two-phase fluids, the Biot/squirt flow and so on.

Automated summary

The correct implementation of continuity conditions between different media is crucial for the accuracy of wave equation solvers used in seismic exploration and global seismology. Benchmarking against analytical Green's function is ideal, but difficult for complex media. The article proposes a general framework to benchmark wave equation solvers using plane wave simulations and transmission/reflection coefficients, as well as numerical Green's functions from spherical-wave simulations.