Abstract of the paper ``Generalized ray expansion for pulse propagation and
attenuation in fluid-saturated porous media'' (with R. C. Y. Chin
and G. W. Hedstrom)
A theory suitable for studying pulses propagating through a layered
fluid-satruated porous medium is presented. Biot's theory is used to
describe the constitutive equation of a fluid-saturated porous solid.
Since fast and slow compressional waves exist in a Biot solid even at
normal incidence, there is mode conversion at the interface and, therefore,
the transmission and reflection coefficients are 2x2 matrices.
We use matrix methods in developing the solution of the wave propagation
problem. A generalized ray expansion algorithm is obtained by using the
Gauss-Seidel matrix iterative method. The arrivals of the fast and slow
waves are easily identified. A compact computational algorithm is
developed using combinatorial analysis and the Cayley-Hamilton theorem.
Electronic copies of this paper are not available.