Diana F. McCammon

The influence of the physical properties of ice on reflectivity

A model for the plane‐wave reflection coefficient from a layered elastic solid bounded on either side by a fluid half‐space is developed and applied to study environmental factors affecting the reflectivity of smooth arctic ice. Experimental measurements of the internal friction in ice and snow are reviewed and applied to compute realistic attenuation profiles. An examination of the effect of ice layers conforming with measured temperature profiles in floe ice shows that the use of average values for sound speed and attenuation is an acceptable approximation for modeling purposes. A study of the reflectivity due to the absorption of shear and compressional waves demonstrates that shear wave attenuation is the most important loss mechanism from 20° to 60° incidence. The effect of an additional snow layer is to produce more attenuation without shifting the pattern of reflection nulls. Major results are presented for a frequency of 2 kHz. Data comparisons are performed from 0.5–3 kHz that show a limited qual...

The design of Tonpilz piezoelectric transducers using nonlinear goal programming

The design of Tonpilz piezoelectric transducers often involves the satisfaction of multiple, conflicting design specifications. To arrive at an optimal compromise solution to a specific design formulation, nonlinear goal programming techniques can be applied. For this optimization technique, a mathematical model of the transducer and its associated housing is constructed and the values of the desired transducer responses and attributes—the design objectives—are computed. The nonlinear goal programming formulation minimizes the differences between the objectives and their specifications. The use of priorities and weights in this minimization process is the key to the great utility of the technique. An example of the application of nonlinear goal programming in a simple hypothetical transducer design is presented to demonstrate the value of the optimal compromise approach for this or more complex systems.

Surface reflection: On the convergence of a series solution to a modified Helmholtz integral equation and the validity of the Kirchhoff approximation

In the problem of scattering from a pressure release boundary, the Helmholtz integral equation may be expressed as a Fredholm equation of the second kind with the unknown surface velocity as the independent variable. The method of successive approximations was employed by Meecham [J. Ration. Mech. Anal. 5, 323–333 (1956)] to obtain a series solution to this equation, where the first term of this series is, in fact, the unshadowed Kirchhoff approximation to the solution. Meecham attempted to formulate the region of validity of the Kirchhoff approximation by determining when the remaining terms of the series could be neglected, however, his arguments used to select ‘‘smallness’’ have been questioned. An exact solution to the integral equation for a sinusoidal boundary is employed to examine the series, term by term, for convergence; and it is found that (1) the alternating nature of the series does not bring convergence when the series diverges absolutely, and (2) the absence of any propagating side orders ...

Application of a new theoretical treatment to an old problem; sinusoidal pressure release boundary scattering

The scattering of sound from a sinusoidal pressure release boundary has long been the subject of study among researchers. Recently, R. L. Holford [J. Acoust. Soc. Am. 70, 1116–1128 (1981)] outlined an exact solution to a variant of the Helmholtz integral equation that permits calculation of the unknown velocity potential on the surface by the solution to a matrix equation. Application of this solution is made to the sinusoid to generate plane wave reflection coefficients. The reflection coefficients are then compared with two sets of model tank data as well as with the approximate solutions of Kirchhoff, Eckart, Rayleigh, and Brekhovskikh. The exact solution compares most favorably with the data, particularly on the rougher surfaces. The principal errors produced by the approximate solutions are a shift in the location of the reflection nulls, an inability to correctly predict unity when all side orders are evanescent, and the absence of Rayleigh reflection anomalies. These errors appear regardless of the...

Linear and nonlinear measures of ocean acoustic environmental sensitivity

This letter defines linear, linearized, and nonlinear measures of environmental sensitivity for ocean acoustic propagation that account for realistic uncertainties in various environmental parameters (water-column sound-speed profile and seabed geoacoustic properties). Simple interpretations of sensitivity are based on the implicit assumption of a linear relationship between parameter sensitivity and parameter uncertainty. This assumption is examined by comparing the three sensitivity measures over a range of parameter uncertainties about the actual assumed environmental uncertainty. Sensitivity range and depth dependencies are illustrated for realistic geoacoustic uncertainties and oceanographic variability of the sound-speed profile.

Composite‐roughness theory applied to scattering from fetch‐limited seas

The prediction of surface scattering strength using composite‐roughness theory requires a detailed knowledge of the ocean wave spectrum. While extensive research in the past has produced a good empirical representation of the wavenumber spectrum of a fully developed sea, only recently have the spectra of fetch‐limited seas been examined. A fetch‐limited sea spectrum is similar in most respects to a spectrum at reduced windspeed except that a small region of ‘‘overshoot’’ occurs on the high‐frequency side of the swell peak. Scattering strength computations show that the fetch‐limited condition has an effect only on the near‐specular returns where values can be 2–10 dB higher than those for a fully developed sea. Computations with composite‐roughness theory including the Fresnel phase approximation and source beam patterns are also made. Comparisons are shown with surface scattering data in both monostatic backscattering and bistatic forward scattering geometries.

Mode coupling and the environmental sensitivity of shallow‐water propagation loss predictions

Variations of seabed parameters, particularly the acoustic compressional velocity relative to that of the water column, have a very strong effect on the predicted magnitude of the propagated acoustic field. In many cases, the sensitivity of the predicted losses to the assumed seabed parameters is sufficiently severe to render the predictions meaningless. In this article, coupled‐mode theory is employed to study how the presence of lateral seabed inhomogeneities affects this sensitivity. The dependence of predicted propagation losses on sediment sound speed is first examined for horizontally stratified sediments; then a rough layered structure of clay–silt interbedded with sand is assumed. With the introduction of rough sub‐bottom layering, coupling occurs between modes, so that the conversion of energy into progressively higher‐order modes, which attenuate rapidly, becomes an important loss mechanism. The extent to which acoustic energy penetrates the seabed and interacts with the sub‐bottom inhomogeneiti...

Surface velocity, shadowing, multiple scattering, and curvature on a sinusoid

The Kirchhoff approximation is frequently invoked in the solution of scattering problems because it greatly reduces the computational complexity. This paper compares the actual surface velocity distribution on a sinusoidal pressure release surface to that assumed by the Kirchhoff approximation and examines more closely the reasons for its successes and failures. Corrections designed to improve the result by including the effects of shadowing, surface curvature, and multiple scattering are also investigated. In the cases examined, curvature correction appears to offer the most improvement while the multiple scattering contribution is practically negligible.

Spectral spreading from surface bubble motion

At low frequencies, surface bubbles contribute to acoustic backscattering in aggregate, and the motion of these bubble masses causes spectral spreading of the acoustic signals. This motion of the bubbles entrained in the surface waves is used to obtain the power spectrum of a low-frequency surface-scattered signal at a low grazing angle. A spectral distribution of the deterministic surface drift, augmented by breaking wave crests, is developed for the wave frequency components that are actively breaking. This motion is combined with the random motion in a wave cycle to predict the spectral widths of low-angle backscattered sound. To permit comparisons with measured data, convolutions of these spectra with simple square pulses of various durations are performed. >

The use of goal programming in the design of electroacoustic transducers and transducer arrays

Abstract The design of piezoelectric transducers or of acoustic transducer arrays often involves the satisfaction of multiple conflicting design specifications. To arrive at an optimal compromise solution to a specific design formulation, nonlinear goal programming techniques can be applied. In this paper, the section on transducer design contains a discussion of the mathematical model of a particular type of transducer and its associated housing. An example is given of a transducer constructed using the parameters indicated by the Goal Programming technique. In the section on array design, the compromise between beamwidth and side lobe level necessary in designing beam patterns is discussed and an example of the application of Goal Programming to the selection of array shading coefficients is given.