Reflection and reverberation in normal incidence echo-sounding

A mathematical model of normal incidence sediment backscatter, based on the Helmholtz integral and the Kirchhoff approximation, was developed. This model is different from existing models in that it is able to account for the effects of sonar beamwidth and wavefront curvature, including a first-order correction for the effects of local slope. Bottom roughness was modeled as a spatial correlation function, constructed from a distribution of Gaussian functions. A probabilistic measure of the validity of the Kirchhoff approximation was also developed. Two bottom models, for a sand and a mud sediment, based on measured roughness spectra of real sediments in situ, were used to generate numerical results. The results confirm the ability of current narrow-beam, high-frequency systems to detect sub-bottom interfaces in mud, and the ability of most systems to estimate the magnitude of the reflection coefficient of the sediment surface. They also predict that measurement of the phase of the reflection coefficient will be considerably more difficult due to the low coherence of the signal.