# Finite difference modeling of Biot's poroelastic equations atseismic frequencies

## Abstract

Across the seismic band of frequencies (loosely defined as<10 kHz), a seismic wave propagating through a porous material willcreate flow in the pore space that is laminar; that is, in thislow-frequency "seismic limit," the development of viscous boundary layersin the pores need not be modeled. An explicit time steppingstaggered-grid finite difference scheme is presented for solving Biot'sequations of poroelasticity in this low-frequency limit. A key part ofthis work is the establishment of rigorous stability conditions. It isdemonstrated that over a wide range of porous material properties typicalof sedimentary rock and despite the presenceof fluid pressure diffusion(Biot slow waves), the usual Courant condition governs the stability asif the problem involved purely elastic waves. The accuracy of the methodis demonstrated by comparing to exact analytical solutions for both fastcompressional waves and slow waves. Additional numerical modelingexamples are also presented.

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

- Sponsoring Org.:
- USDOE. Assistant Secretary for Fossil Energy.Petroleum

- OSTI Identifier:
- 927822

- Report Number(s):
- LBNL-61829

Journal ID: ISSN 0148-0227; JGREA2; R&D Project: G32801; BnR: AC1005000; TRN: US200816%%1074

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Geophysical Research; Journal Volume: 111; Journal Issue: B10305; Related Information: Journal Publication Date: 10/14/2006

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54; ACCURACY; ANALYTICAL SOLUTION; BOUNDARY LAYERS; DIFFUSION; POROUS MATERIALS; SEDIMENTARY ROCKS; SEISMIC WAVES; SIMULATION; STABILITY

### Citation Formats

```
Masson, Y.J., Pride, S.R., and Nihei, K.T.
```*Finite difference modeling of Biot's poroelastic equations atseismic frequencies*. United States: N. p., 2006.
Web.

```
Masson, Y.J., Pride, S.R., & Nihei, K.T.
```*Finite difference modeling of Biot's poroelastic equations atseismic frequencies*. United States.

```
Masson, Y.J., Pride, S.R., and Nihei, K.T. Fri .
"Finite difference modeling of Biot's poroelastic equations atseismic frequencies". United States.
doi:.
```

```
@article{osti_927822,
```

title = {Finite difference modeling of Biot's poroelastic equations atseismic frequencies},

author = {Masson, Y.J. and Pride, S.R. and Nihei, K.T.},

abstractNote = {Across the seismic band of frequencies (loosely defined as<10 kHz), a seismic wave propagating through a porous material willcreate flow in the pore space that is laminar; that is, in thislow-frequency "seismic limit," the development of viscous boundary layersin the pores need not be modeled. An explicit time steppingstaggered-grid finite difference scheme is presented for solving Biot'sequations of poroelasticity in this low-frequency limit. A key part ofthis work is the establishment of rigorous stability conditions. It isdemonstrated that over a wide range of porous material properties typicalof sedimentary rock and despite the presenceof fluid pressure diffusion(Biot slow waves), the usual Courant condition governs the stability asif the problem involved purely elastic waves. The accuracy of the methodis demonstrated by comparing to exact analytical solutions for both fastcompressional waves and slow waves. Additional numerical modelingexamples are also presented.},

doi = {},

journal = {Journal of Geophysical Research},

number = B10305,

volume = 111,

place = {United States},

year = {Fri Feb 24 00:00:00 EST 2006},

month = {Fri Feb 24 00:00:00 EST 2006}

}