Backscattering of an Isotropic, Spherical, Acoustic Pulse of Arbitrary Shape from a Rough-Sea Surface

Abstract

When an isotropic spherical pulse generated by an underwater source at A reflects from a rough-sea surface S, the pressure p(A) subsequently measured at the backscatter point depends on the shape of the incident pulse and the displacement-slope properties of S. If A is at a large distance D from S and approximate boundary conditions appropriate to surfaces of small slope are assumed, then Kirchhoff's general integral formula can be transformed into the sum of two surface integrals over modified source distributions on the zero-level surface So. The first integral po reduces to an “image pulse” reflected from a mirror surface at D + ζo, where ζo is the vertical displacement of S from the specular point on So. The second integral ps is the scattered pulse that interferes with po and persists after the latter disappears. At time t, ps is composed of a superposition of pulselet contributions that have propagated to A from a limited portion So(t) of So. The functional form of the pulselet source at dSo(t) is generally quite different from that of the incident pulse since the “amplitude scattering coefficient” σ that determines the pulselet-source strength is actually a differential operator. Pulselet-source strength also depends directly on the slope of S near dSo(t). This approximate formulation gives physical insight into the causes of surface scattering and is convenient for treating certain problems that arise in underwater sound and model experiments. [Hudson Laboratories, Columbia University Informal Documentation No. 31. This work was supported by the U. S. Office of Naval Research.]