Multiple Sound Scattering by Combinations of Cylindrically Symmetric and Linearly Invariant Anomalies

Abstract

A number of previous papers have used the coupled-mode method to assess three-dimensional scattering by cylindrically symmetric anomalies (seamounts, hills) or anomalies which are invariant in a horizontal direction (wedges, ridges). This paper makes an extension to combinations of these two anomaly types. The upper and lower depth boundaries of the anomalies may be flat or irregular, and the sound source may be anywhere in the medium. After a discretization of the anomalies of the two types with laterally homogeneous rings and strips, respectively, an adaptation of the coupled-mode method yields the solution of the pertinent Helmholtz equation. The adaptation involves a combination of Fourier-series summations to handle the ring anomalies and adaptive wavenumber integrations to handle the strip structure. For each anomaly, recursively computed reflection matrices relate the expansion coefficients for incoming and outgoing normal modes. Iterative solution of a linear equation system for the amplitudes of the scattered cylindrical waves from the ring anomalies, involving formulas for transformation between plane and cylindrical waves, yields an expansion of the field. Related expansions allow isolation of partial waves, multiply scattered among the anomalies. The paper includes examples from underwater acoustics and atmospheric acoustics.