Inhomogeneous waves and the plane‐wave reflection coefficient

Abstract

The importance of knowledge of the plane‐wave reflection coefficient R for a horizontally stratified medium at complex angles of incidence ϑ=π/2−iα (α≳0) is established. It is shown that for a point source, when the combined source/receiver height is less than one‐quarter wavelength, these inhomogeneous plane waves can make significant contributions to the reflected field. But irrespective of source/receiver height, they are important when normal modes are excited in slow speed regions of the bottom via inhomogeneous–pure wave conversion, thus giving rise to poles in the reflection coefficient. The theory of inhomogeneous plane‐wave reflection is examined within the context of conservation of energy, and an expression for the intensity of these waves is derived. It is shown that although ‖R‖ is bounded by unity for real incident angles, it can be unbounded for complex angles without violation of energy conservation. A general asymptotic result for R for large horizontal wavenumber is also derived. The computation of R for inhomogeneous waves is illustrated for three canonical bottom examples: (a) impenetrable, (b) isovelocity fluid, and (c) isovelocity fluid layer overlying an isovelocity fluid half‐space.