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:
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).