Computing the Scattering From Slightly Deformed Spherical Shells—A Ray-Based Approach

In a previous paper (J. A. Fawcett, IEEE J. Ocean. Eng, vol. 41, no. 3, pp. 682-688, Jul. 2016), the scattering from a spherical shell whose thickness varied with respect to the polar angle (but not azimuthally) was considered. There, it was found that the characteristics of the scattering varied significantly with respect to the monostatic angle and also with respect to the character of the thickness variation. For example, for a wave incident along the vertical axis, the amplitude of the backscattered field depended significantly upon whether a simple shell thickness profile varied from thin to thicker or vice versa. In this paper, the results from the previous paper and some new results are interpreted in terms of a ray theory. This ray theory is simply derived by considering the results from the Sommerfeld-Watson transformation for a constant thickness sphere and substituting integral averages of phase and attenuation where appropriate. For the case of the monostatic angle being off-axis (for example, broadside incidence) these integral values also vary with respect to the raypath. In this case, an integral over the set of contributing raypaths must be performed to compute the scattered pressure field. The ray-predicted scattered pressure fields are compared to those obtained from numerical benchmark computations as a function of frequency and angle of incidence.