The same group theory that applies to elastic media can also be extended to incorporate coupling effects. We can do so by replacing the elastic stiffness matrix with the generalized stiffness matrix in a form which groups coefficients related to normal and tangential components. The elastic stress and strain is thereby extended to the generalized stress and strain. Consequently, in order to calculate the group elements correctly, we have to specify the components of the generalized stress and strain vectors which are continuous across boundaries. In general, when crossing a layer boundary, those components of the generalized stress vector normal to the horizontal layers are continuous and the tangential components of the generalized strain vector are also continuous. This allows us finally to compute average properties of packets of layers efficiently, not only for elastic wave propagation but also for any coupled waves propagating in the medium.

1/13/1998