THE INVERSION OF TRANSIENT REFLECTION DATA TO DETERMINE SOLID GRAIN-STRUCTURE

In this paper we consider the direct and inverse scattering problem fo r an inhomogeneously oriented linearly elastic anisotropic material. W e use the invariant imbedding method to formulate a class of one-dimen sional reflection problems for the scalar case of obliquely incident h orizontally polarized shear waves travelling in a transversely isotrop ic solid. Particular attention is given to the case when the material parameters are such that the advancing wavefront suffers total interna l reflection. The implications of this phenomenon for the wave splitti ng formalism are discussed and the results from several example comput ations are presented. We also show that the field satisfies a certain temporally non-local boundary condition at the transition layer where the energy flow is reversed. This condition suggests an intuitively re asonable approximate relationship between the components of the wave s plitting there.