Raymond Lim

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...

Acoustic scattering by a partially buried three-dimensional elastic obstacle

A formally exact transition‐matrix solution for the spectral scattering response of an elastic object that penetrates a plane‐stratified fluid host is formulated. The field scattered from the segment in each layer is expanded in a global outgoing basis centered on that segment and these segment fields are superimposed at the field point. A manageable structure for the transition matrix is maintained by using the boundary conditions to couple these segment fields to the interior field of the object via a single exterior surface field expansion centered on the origin of the object. The standard set of regular spherical eigenfunctions of the Helmholtz equation are used to expand the exterior surface field. Numerical tests for an axisymmetric spheroid indicate this choice yields a viable solution but convergence is better for flattened shapes (oblate) than elongated shapes (prolate). Examples are presented to illustrate environmental effects on the backscatter by a bubble and an elastic spheroid that penetrat...

A transition‐matrix formulation of scattering in homogeneous, saturated, porous media

Scattering by an obstacle embedded within a homogeneous host is analyzed in the context of Biot’s theory. Both host and scatterer are assumed to be fluid‐saturated poroelastic media. A transition matrix that accounts for the additional slow longitudinal wave is constructed from a Betti’s identity generalized to poroelastic media. Extinction, scattering, and absorption cross sections are defined for objects embedded in nonattenuating hosts. When attenuation is significant in the host (as is typical in saturated porous media), appropriately scaled, far‐field scattering amplitudes are used to investigate scattering dynamics. General results are presented and specialized to spherical objects where the elements of the transition matrix may be obtained in closed form. Using effective medium estimates of Biot parameters where needed, numerical calculations of cross sections and scattering amplitudes are presented for incident plane‐wave fields. Several limiting cases are discussed.

Evaluation of the integrals of target/seabed scattering using the method of complex images

In this paper the integrals which arise in target/seabed scattering problems are examined. These are the integrals which express the propagation of a spherical harmonic term in a fluid above or below a half-space and the integrals which compute the conversion coefficients of outgoing spherical harmonics into incident spherical harmonics after a seabed reflection. A very efficient and accurate method of computing these integrals, using the method of complex images, is derived. Numerical comparisons with the exact integral expressions show the accuracy of this approach.

Double monopole resonance of a gas-filled, spherical cavity in a sediment

The monopole response of a gas-filled, spherical cavity in a sediment is investigated. The sediment is either a fluid, elastic solid, or saturated poroelastic medium. The present method entails the scattering of an incident displacement field that preferentially excites the monopole resonance of the cavity. The main result demonstrates that a gas-filled, spherical cavity in a saturated poroelastic medium can exhibit two distinct monopole resonances. These resonances arise from the two distinct longitudinal modes of propagation in saturated poroelastic medium as described by Biot’s theory.

Scattering by an obstacle in a plane‐stratified poroelastic medium: Application to an obstacle in ocean sediments

A transition‐matrix formulation of the field scattered by a bounded three‐dimensional obstacle buried in a plane‐stratified, saturated, poroelastic environment is described. The formulation yields an exact solution of the vector Biot equations, obeying all boundary conditions prescribed on the layer and obstacle boundaries. This is obtained by combining the recently derived free‐field transition matrix for an obstacle in a porous medium [S. G. Kargl and R. Lim, J. Acoust. Soc. Am. 94, 1527–1550 (1993)] with a generalization of existing acoustic waveguide solutions. The present solution is numerically implemented for an aluminum sphere buried in an ocean sediment half‐space and insonified by an acoustic source in an overlying water half‐space. Attention is paid to assessing the contribution of shear waves and slow compressional waves to the predicted backscatter.

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...

Buried Sphere Detection Using a Synthetic Aperture Sonar

This paper presents observations of a buried sphere detected with a low-frequency (5-35-kHz) synthetic aperture sonar (SAS). These detections were made with good signal-to-noise ratios (SNRs) at both above and below the critical grazing angle. The raw data for the below-critical-grazing angle detection shows that the acoustic penetration is skewed by the 29deg offset of the ripple field relative to the sonar path. This observed skew is in agreement with T-matrix calculations carried out to model penetration into the bottom via ripple diffraction. Additionally, measured SNRs over different frequency bands are compared to predictions made using both first- and second-order perturbation theory for ripple diffraction. Both the data and the models indicate a peak detection region around 25 kHz for the environmental conditions present during the test. These results confirm that ripple diffraction can play a critical role in long range (subcritical angle) buried target detection.

Acoustic transmission across a roughened fluid–fluid interface

A set of tank experiments was performed to investigate acoustic transmission across a roughened fluid-fluid interface with the intention to test heuristic Bragg scattering predictions used to explain observations of anomalous transmission in field experiments. In the tank experiments, two immiscible fluids (vegetable oil floating on glycerin) formed the layers. Small polystyrene beads were floated at the interface to simulate roughness. An array of hydrophones placed in the bottom layer (glycerin) was used to measure the acoustic levels transmitted across the interface. This array was also employed as a beamformer to determine the apparent angle and sound speed of the scattered signals. Data were acquired at subcritical grazing angles in the frequency range of 100-200 kHz for three different bead diameters and for various configurations in which the locations of the beads floating on the interface were varied. Results of these measurements demonstrated that a significant amount of acoustic energy can be scattered into the bottom layer by beads floating at the interface. The scattered levels increased with increasing bead diameter. However, discrepancies occurred between observed propagation properties and the Bragg predictions. By comparing the processed tank data to a computer simulation of the same it was determined that these discrepancies are a consequence of near-field reception of the scattering by the bead array and ignoring the directionality of the scattering by the beads. Consequences to observations made in field experiments are discussed.

A formulation of multiple scattering by many bounded obstacles using a multicentered, T supermatrix

The acoustic scattering from many interacting, bounded, three‐dimensional obstacles has been treated by several authors [see, for example, V. Twersky, J. Math. Phys. 8, 589 (1967) or B. Peterson and S. Strom, J. Acoust. Soc. Am. 56, 771 (1974)]. In particular, Peterson and Strom extended the single‐obstacle, transition (T) matrix formalism to several obstacles (including all orders of multiple scattering) by using the translation properties of the spherical basis functions to translate the multiply scattered fields of each obstacle to a common origin. Later, their formalism was extended to treat elastic wave scattering by using spherical vector basis functions [A. Bostrom, J. Acoust. Soc. Am. 67, 399 (1980)]. However, for numerical results, the present state of development is cumbersome to apply to more than two obstacles and convergence of the rescattering matrices is sensitive to obstacle separation. In this paper, a multicentered, T‐matrix formalism for acoustic and elastic wave scattering is given, ba...