Open AccessPropagation of harmonic plane waves in a general anisotropic porous solid
Author(s) -
Sharma M. D.
Publication year - 2008
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2007.03659.x
Subject(s) - slowness , poromechanics , biot number , porous medium , wave propagation , anisotropy , mechanics , physics , boundary value problem , mathematical analysis , dissipation , classical mechanics , mathematics , geometry , porosity , geology , optics , geotechnical engineering , thermodynamics , quantum mechanics
SUMMARY Wave propagation is studied in a general anisotropic poroelastic solid. The presence of dissipation due to fluid‐viscosity as well as hydraulic anisotropy of pore permeability are also considered. Biot's theory is used to derive a system of modified Christoffel equations for the propagation of plane harmonic waves in porous media. A non‐trivial solution of this system is ensured by a determinantal equation. This equation is separated into two different polynomial equations. One is the quartic equation whose roots represent the complex velocities of four attenuating waves in the medium. The other is a eighth‐degree polynomial whose roots represent the vertical slowness values for the four waves propagating upward and downward in a finite porous medium. Procedure is explained to associate the numerically obtained roots with the waves propagating in the medium. The slowness surfaces of waves reflected at the boundary of the medium are computed for a realistic numerical model. The behaviours of phase velocity surfaces are analysed with the help of numerical examples.