Scattering by a spherical inhomogeneity in a fluid-saturated porous medium

Journal Article · Sat Jun 01 04:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526955· OSTI ID:5747183

Berryman, J G

A fast compressional wave incident on an inhomogeneity in a fluid-saturated porous medium will produce three scattered elastic waves: a fast compressional wave, a slow compressional wave, and a shear wave. This problem is formulated as a multipole expansion using Biot's equations of poroelasticity. The solution for the first term (n = 0) in the multipole series involves a 4 x 4 system which is solved analytically in the long-wavelength limit. All higher-order terms (n > or = 1) require the solution of a 6 x 6 system. A procedure for solving these equations by splitting the problem into a 4 x 4 system and a 2 x 2 system and then iterating is introduced. The first iterate is just the solution of the elastic wave scattering problem in the absence of fluid effects. Higher iterates include the successive perturbation effects of fluid/solid interaction.

• Research Organization: Lawrence Livermore National Laboratory, University of California, P.O. Box 808, L-201, Livermore, California 94550
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5747183
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:6; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657004* -- Theoretical Physics-- Acoustics-- (-1987)
658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
ATTENUATION
COUPLING
ELASTIC SCATTERING
ITERATIVE METHODS
MATERIALS
PERTURBATION THEORY
POROUS MATERIALS
SCATTERING
SOUND WAVES
WAVE PROPAGATION