Roger H. Hackman

Scattering by objects buried in underwater sediments: Theory and experiment

The scattering of sound by objects buried in underwater sediments is studied in the context of an exactly soluble model. The model consists of two fluid half‐spaces separated by a planar, fluid, transition layer of arbitrary thickness. Attenuation is included in any of these regions by using complex wave numbers. A directional source field, generated in the upper half‐space by a continuous line array, insonifies an object placed in the lower half‐space. The scattered field detected by another line array placed anywhere in the system may be calculated. The solution is determined from the T matrix for the bounded scattering system and is exact (in linear acoustics) to all orders of multiple scattering among the interfaces and object. Numerical results are presented to investigate the effect of the local acoustic environment on the free‐field, in‐water scattering resonances of thin spherical shells. The field scattered by a shallowly buried object is discussed with emphasis on the importance of evanescent wa...

The acoustic scattering by a submerged, spherical shell. I: The bifurcation of the dispersion curve for the spherical antisymmetric Lamb wave

The acoustic scattering by thin‐walled, evacuated, elastic spherical shells immersed in water is studied. The analytic structure of the scattering amplitude in the complex‐k plane is directly analyzed using Cauchy’s residue theorem, and dispersion curves are presented for the lowest elastic modes of the fluid‐loaded shell. It is found that fluid loading has a profound effect on the vacuum dynamical characteristics of the shell; the spherical equivalent of the first antisymmetric, flat‐plate Lamb wave for the fluid‐loaded shell bifurcates into two distinct modes near the frequency that the vacuum dispersion curve transitions from a subsonic to a supersonic phase velocity. By way of contrast, the spherical equivalent of the first symmetric Lamb wave is essentially unaffected. The salient features of the free‐field scattering process are also analyzed in terms of the resonance excitation of these modes.

Multiple‐scattering analysis for a target in an oceanic waveguide

A multiple‐scattering approach is developed for the acoustic scattering from a target in a range‐independent oceanic waveguide. The multiple‐scattering series is explicitly summed and a solution is obtained in closed form. The final result is algebraically much simpler than that obtained in earlier work, and the individual terms may be straightforwardly interpreted in terms of scattering events in the waveguide. The formalism is applied to the scattering from a target (1) near a sound‐soft boundary, and (2) in a waveguide with a single, homogeneous fluid layer over a homogeneous, fluid half‐space. Numerical examples are given that illustrate the importance of contributions involving rescattering among the target and the waveguide boundaries.

The transition matrix for acoustic and elastic wave scattering in prolate spheroidal coordinates

A spheroidal‐coordinate‐based transition matrix is derived for acoustic and elastic wave scattering. The formalism is based on Betti’s third identity and an appropriately chosen set of vector spheroidal basis functions. Transition matrices are obtained for the scattering from an elastic inclusion in an elastic medium and in an inviscid fluid.

Acoustic scattering in a homogeneous waveguide

The acoustic scattering from an elastic spherical shell in a homogeneous, range‐independent waveguide is studied. New phenomena are observed that have no counterpart in free‐field scattering. First, the free‐field resonance spectrum exhibits fine structure, that is, the lth resonance splits into (l+1) distinct components. This splitting is most pronounced near the waveguide boundaries. Second, ‘‘superresonances’’ are observed. It is found that at certain water column heights and scatterer depths, significant enhancements of the resonance strength occur. In some cases, more than 100‐fold enhancement is observed.

Acoustic scattering in an inhomogeneous waveguide: Theory

A transition matrix formalism is developed for the acoustic scattering from a target in a layered, inhomogeneous waveguide. The connection is made with the normal mode model of propagation and the total acoustic wave is expressed as a sum over waveguide modes. For a target in a deep ocean environment, the scattering solution may be expressed in terms of the free‐field T matrix and the normal mode wavefunctions for the empty waveguide. Both homogeneous and inhomogeneous layers are considered.

An application of the spheroidal‐coordinate‐based transition matrix: The acoustic scattering from high aspect ratio solids

In a previous paper [R. H. Hackman, J. Acoust. Soc. Am. 75, 35–45 (1984)] a spheroidal‐coordinate‐based transition matrix formalism was established for acoustic and elastic wave scattering. In this paper, we consider the acoustic scattering by a solid elastic cylinder with hemispherical endcaps and a length‐to‐diameter ratio of 10. Numerical results are presented for the backscattered form function as a function of frequency for various angles of incidence. These results are compared with experimental measurements taken at the Naval Coastal Systems Center and given a physical interpretation.

High‐frequency scattering from rigid prolate spheroids

The scattering of an acoustic plane wave by a rigid, immovable prolate spheroid is investigated over a broad frequency range (0<kL/2≤300). An unexpectedly large, off‐axis radiation lobe dominates the bistatic beam pattern for axial incidence and aspect ratios larger than unity, over the entire frequency range considered. This lobe is found to be due to an amplitude‐modulated creeping wave. A new asymptotic expansion of the spheroidal radial functions is introduced that gives an improved estimate of the functions for moderate values of the azimuthal index at high frequency.

A parametric analysis of attenuation mechanisms in composites designed for echo reduction

The fundamental attenuation mechanisms operating in a particular class of composites are investigated for their viability as underwater anechoic materials. The type of composites of interest consists of dense (visco‐) elastic inclusions in rigid, low‐density, water impedance‐matched, elastic hosts. Composites similar to this have been studied by Kinra2 and shown to attenuate transmitted elastic waves in a resonant regime of the imbedded inclusions. Our calculations indicate that the processes giving rise to the attenuation would also be appropriate for echo reduction. As a reference material, a composite of lead‐loaded silicone rubber spheres in a rigid epoxy is studied. The processes operating at both the water–epoxy and epoxy–rubber interfaces are studied theoretically. Using the spherical elastic T matrix, effects due to resonant scattering are analyzed by reference to the scattered and absorption cross sections calculated for both a single rubber sphere and two rubber spheres imbedded in an infinite e...

The acoustic scattering by a submerged, spherical shell. II: The high-frequency region and the thickness quasiresonance

This article presents a fundamentally oriented analysis of the complex-ka plane pole structure of the S matrix for spherical shells in the thickness range 0.02a⩽h⩽0.10a (a is the outer radius of the sphere) for the high-frequency region (100<ka<1000); the Poisson’s ratio for these shells is fixed at σ=0.34 (aluminum). Surprisingly, this analysis reveals that the most dominant feature in the backscattered form function of a thin spherical shell is a single prominent high-frequency peak. The underlying modal structure and accompanying regions of negative group velocity are related to this feature, which is interpreted as a thickness “quasiresonance.” In particular, the significance of stationary values of the group velocity to the relative amplitude of modal excitation is emphasized.