Modeling surface scatter in the channel impulse response with a Helmholtz-Kirchhoff integral

Abstract

Several experimental measurements of channel impulse responses (CIRs) using underwater communication bandwidths have shown distinct striation features arriving up to 10 milliseconds after the main surface bounce, e.g. Badiely et al. [J. Acoust. Soc. Am. 132, EL290 (2012)]. Choo et al. [J. Acoust. Soc. Am. 136, 1046 (2014)] used an intuitive geometric ray model to argue that the source of these arrivals was the reflection from a wave trough near the receiver. This presentation extends Choo's approach and focuses on a quadrature solution of the time domain Helmholtz-Kirchhoff (HK) integral in a half space. This approach provides the same intuitive geometric ray perspective on the surface scattering, but additionally models arrival amplitudes near caustics and higher order catastrophe phenomena induced by surface waves. It is shown that a simple shadowing correction of the HK result produces all of the major features of the full Helmholtz scattering integral solution. The HK integral is computationally tractable, accurate, and can show the path from the surface that contributes to each CIR arrival.