Stable components of sound fields in the ocean

Abstract

A method is proposed for finding the wave field components which are weakly sensitive to the sound speed perturbation in the ocean acoustic waveguides. Such a component is formed by a narrow beam of rays whose spread in vertical direction, up to the observation range, remains less than the vertical scale of perturbation. These rays pass through practically the same inhomogeneities and therefore their phases are incremented by the same amount. If the ray amplitudes vary insignificantly, then (i) the stable components of the monochromatic field in the perturbed and unperturbed waveguide differ by only a constant phase factor, and (ii) in the case of transient wave field the perturbation causes only an additional time delay of the stable component as a whole. It is shown how the stable components can be selected from the total wave field using the field expansions in the coherent states and in the normal modes. The existence of stable components is demonstrated by numerical simulation of sound field in a deep water waveguide. It turns out, that even though the assumptions (i) and (ii) are not met exactly, the stable components in the perturbed and unperturbed waveguides are quite close.

Matched shadow processing

“…In Ref. [7] some considerations are given explaining the stability of field components formed by coherent states associated with small areas of the phase space. These considerations can be used to justify the stability of the intensity distribution |a µ | 2 in phase space.…”

“…The coherent state associated with the point of the phase plane µ = (P, Z) is given by the function [6,7,10] Y (z; P, Z)…”

Beamforming in multipath environment using the stable components of wave field

“…If the eigenbeam is narrow enough, then it forms a component, which in Ref. [2] is called stable. Let us dwell on this issue.…”

“…Two heuristic methods for isolating stable components from the total field u (z) are proposed in Ref. [2]. Both methods come from the relationship between the ray-based and wave-based descriptions of sound fields and give similar results.…”

“…In Ref. [2], the field component formed by such a beam is called stable. If the wave field is excited by a tonal source, then the stable components in the perturbed and unperturbed waveguide differ by only a constant phase factor exp(iφ).…”