Riccati equations for wave propagation in planarly-stratified solids

Wave propagation and scattering are investigated in three-dimensional, dissipative, anisotropic bodies with one-dimensional inhomogeneity. The constitutive equations are taken to be linear. The incidence is allowed to be oblique. Three different procedures are set up which involve the impedance matrix and two local reflection matrices. All three matrix functions are shown to satisfy appropriate Riccati equations and jump conditions (at discontinuities). The operative aspects are examined to solve reflection–transmission problems for a layer sandwiched between two half spaces. The unknown field within the layer is determined through the impedance or the reflection matrices.