Bi-orthogonality relationships involving porous media.

Bi-orthogonality relationships are established for a vertically heterogeneous porous media in contact with a fluid, a solid, a second porous medium, and a free surface. Fraser's bi-orthogonality relation for propagation of Rayleigh-Lamb modes in a plate with traction-free surfaces is shown to be a special case of the bi-orthogonality relations derived herein in which the medium can be thought of as a porous slab with zero porosity. [ABSTRACT FROM AUTHOR]