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Published October 2008 | Published
Journal Article Open

Spectral-element simulations of wave propagation in porous media

Abstract

We present a derivation of the equations describing wave propagation in porous media based upon an averaging technique which accommodates the transition from the microscopic to the macroscopic scale. We demonstrate that the governing macroscopic equations determined by Biot remain valid for media with gradients in porosity. In such media, the well-known expression for the change in porosity, or the change in the fluid content of the pores, acquires two extra terms involving the porosity gradient. One fundamental result of Biot's theory is the prediction of a second compressional wave, often referred to as 'type II' or 'Biot's slow compressional wave', in addition to the classical fast compressional and shear waves. We present a numerical implementation of the Biot equations for 2-D problems based upon the spectral-element method (SEM) that clearly illustrates the existence of these three types of waves as well as their interactions at discontinuities. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well suited to simulations on parallel computers. Effects associated with physical dispersion and attenuation and frequency-dependent viscous resistance are accommodated based upon a memory variable approach. We perform various benchmarks involving poroelastic wave propagation and acoustic–poroelastic and poroelastic–poroelastic discontinuities, and we discuss the boundary conditions used to deal with these discontinuities based upon domain decomposition. We show potential applications of the method related to wave propagation in compacted sediments, as one encounters in the petroleum industry, and to detect the seismic signature of buried landmines and unexploded ordnance.

Additional Information

© 2008 The Authors. Journal compilation © 2008 RAS. Accepted 2008 June 29. Received 2008 June 27; in original form 2008 January 7. Published Online 2 October 2008. This research was supported in part by a grant from the Strategic Environmental Research Development Program (SERDP) under contract number W912HQ-06-C-0006. We are grateful to Julien Diaz, who helped us carry out most of the 2-D benchmarks, and to Dimitri Komatitsch for providing the randomly perturbed mesh. The program used to evaluate the analytical solutions for the two layered models may be found at http://www.spice-rtn.org/library/software/Garcimore2D/. We thank Dimitri Komatitsch, Abdelaâziz Ezziani, Julien Diaz, Roland Martin from the University of Pau, France and Josep de la Puente from the University of Munich, Germany, for valuable discussions and advice. Finally, we also wish to acknowledge the Editor Johan Robertsson and two anonymous reviewers for pertinent comments which helped to improve the manuscript. This is contribution No. 8999 of the Division of Geological & Planetary Sciences (GPS), California Institute of Technology.

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Created:
August 22, 2023
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October 17, 2023