Kirchhoff Approximation for a Cylinder Breaking Through a Plane Surface and the Measured Scattering

When considering the application of quantitative ray theory to the backscattering of sound at grazing incidence by a circular cylinder partially buried in sediment, the analysis is complicated by a transition in the number of reflected rays. For broadside insonification, the number of rays geometrically backscattered may be 0, 1, 2, or 3 depending on the exposure of the cylinder. A formulation for the scattering based on the Kirchhoff approximation is given, which avoids discontinuities associated with transitions in the number of rays. The formulation is tested for the experimentally simpler case of a steel cylinder hung through a free surface with a 30^?? grazing angle relative to the air-water interface. Tone burst insonification was used with a wave number radius product ka from 9.6 to 16. The measured dependence of the backscattering on exposure is similar to predictions except for extra features present for a slightly exposed cylinder. The approximation is also supported by comparison with an exact theory for backscattering by a half-exposed rigid cylinder in a flat pressure-release surface. Predictions for the dependence on exposure are also shown for the case of a cylinder emerging from a flat rigid surface.