Semi-analytical and numerical methods for computing transient waves in 2D acoustic / poroelastic stratified media

TL;DR

This paper develops and compares semi-analytical and numerical methods for modeling transient wave propagation in 2D stratified acoustic and poroelastic media, validated through benchmarks with realistic soil parameters.

Contribution

It introduces a combined analytical and numerical framework with improved stability and accuracy for simulating wave behavior in complex stratified media.

Findings

Excellent agreement between methods confirms validity

Mesh refinement improves interface wave accuracy

Tools applicable to realistic soil conditions

Abstract

Wave propagation in a stratified fluid / porous medium is studied here using analytical and numerical methods. The semi-analytical method is based on an exact stiffness matrix method coupled with a matrix conditioning procedure, preventing the occurrence of poorly conditioned numerical systems. Special attention is paid to calculating the Fourier integrals. The numerical method is based on a high order finite-difference time-domain scheme. Mesh refinement is applied near the interfaces to discretize the slow compressional diffusive wave predicted by Biot's theory. Lastly, an immersed interface method is used to discretize the boundary conditions. The numerical benchmarks are based on realistic soil parameters and on various degrees of hydraulic contact at the fluid / porous boundary. The time evolution of the acoustic pressure and the porous velocity is plotted in the case of one and four interfaces. The excellent level of agreement found to exist between the two approaches confirms the validity of both methods, which cross-checks them and provides useful tools for future researches.