Mixed acousto-elastic problems are treated in one of two different ways. The first approach is to simply incorporate all of the elastic effects into a boundary condition. The particular boundary condition was already written down in Eq. (). The coefficients of that boundary condition require the solution of Eq. () which is accomplished using a simple explicit integrator. Specifically, we employ the modified midpoint method which for a first-order system takes the form:

and,

The integration is carried out in succession through each of the elastic
layers to compute the coefficients of the impedance boundary condition.
This approach is used in * KRAKEN*
and * KRAKENC*
.

The other approach, which is implemented in * KRAKEL*
, is simply to apply
finite differences directly to the stress-displacement equations
(). The result is a somewhat complicated 9-diagonal
matrix whose characteristic is evaluated using a LINPACK routine
(DGBDI).

Tue Oct 28 13:27:38 PST 1997