REFLECTION AND TRANSMISSION OF PLANE COMPRESSIONAL WAVES

Abstract

The reflected and transmitted waves generated by a plane, monochromatic, compressional wave incident at a plane interface between two half‐spaces are analyzed. Energy ratios and the phase angles for the vertical displacement have been tabulated for over two thousand choices of the elastic parameters and densities. Computations for the solid‐fluid and solid‐air cases show that a large fraction of the incident energy goes into the shear wave over a large range of angles of incidence. The conditions for perfect reflection (with no conversion and no transmission) at the critical angles are derived. Within the critical angle, the requirement that the instantaneous energy flux be continuous is given by Knott’s equation. Beyond the critical angle, Knott’s equation gives continuity of the net flux but not continuity of the instantaneous flux. To achieve continuity of the instantaneous flux, Knott’s equation and two additional equations must be satisfied.