Subcritical detection of targets buried under a rippled interface: extended perturbation theory

Previous comparisons between controlled measurements and model predictions for shallow grazing angle acoustic backscatter by underwater targets buried in sand with a rippled surface have shown good agreement except for some of the higher roughness height cases. This lends confidence to the hypothesis that roughness diffraction can significantly improve target detection performance with sonar operated at grazing angles shallower than the critical grazing angle. The exceptions to model agreement showed even greater detection signal-to-noise due to roughness diffraction than predicted. Because the modeling was based on low-order perturbation theory to handle sound transmission through bottom roughness, these exceptions have been attributed to failure of the perturbation theory. Here we report on the effect of including higher-order perturbation corrections using a recursive algorithm to generate corrections to arbitrary order for an idealized sinusoidal ripple. Straightforward summation of terms is seen to lead to divergence beyond third order as the acoustic wavelength gets smaller than the ripple height. However, reformulations of perturbation theory, such as applying Pade approximants or using Voronovich´s small-slope approximation, are shown to remain stable for most problems of interest