Index of content:
Volume 73, Issue 2, February 1983

A model for wave propagation in gassy sediments
View Description Hide DescriptionA variational method of deriving equations of motion for mixtures is used to obtain a theory for a granular sediment saturated by a liquid which contains bubbles of gas. The theory is an extension of the Biot–Stoll model for wave propagation in saturated sediments. Wave velocity and attenuation are determined for a water‐saturated model sediment containing a small volume of air bubbles. It is verified that the model predicts the qualitative features that have been observed experimentally in gassy sediments. At frequencies below the bubble resonance frequency (BRF), the phase velocity is substantially decreased by the presence of the bubbles. Near the BRF, the attenuation increases markedly. Above the BRF, the phase velocity and attenuation approach the values which they would have if no bubbles were present.

Piezo‐acoustic rotation in crystals
View Description Hide DescriptionA relationship between acoustic and optical gyrotropic tensors is given. The effect of stress on acoustical activity for crystals belonging to D _{3}, S _{4}, and T _{ d } point groups is studied and it is found that in the acoustically inactive S _{4} and T _{ d } point groups, for unaxial stress along x direction and for propagation along z direction, the degeneracy of the shear wave is lifted giving rise to left‐elliptical and right‐elliptical polarized modes. The experimental method of observing such splittings is suggested.

Inverse ray tracing in elastic solids with unknown anisotropy
View Description Hide DescriptionThe problem of inverse ray tracing in a homogeneous anisotropicelastic solid is considered. The wave speeds in the solid are assumed unknown, and must be obtained in the course of the inversion. The specific problem of locating a crack tip in a two‐dimensional geometry is investigated. The data are assumed to be in the form of travel times of diffractedultrasonic signals between transducers positioned on an exterior surface of the solid. Both pulse–echo and pitch–catch data are considered. It is found that travel‐time data on the exterior surface suffices to locate the crack tip only if the material is isotropic. If the material is anisotropic, we must be able to move the source and/or receiver in the direction normal to the surface. The same problem is considered with the source and receiver positioned in a surrounding isotropic material, e.g., a water bath. It is shown that the ray inversion is now possible only if the solid is isotropic, the problem being underdetermined for an anisotropic solid. This indicates that the problem of inverse ray tracing, in the context of crack sizing, is not possible in a medium which is both inhomogeneous and anisotropic. Numerical results are presented for a synthetic experiment in which a finite crack is present in some transversely isotropic homogeneous elastic solids. It is demonstrated that an initial presumption of isotropy can lead to very erroneous results.

Back reflection of ultrasonic waves from a liquid–solid interface
View Description Hide DescriptionA new acoustic phenomenon has recently been observed in experiments where a bounded beam of ultrasound is incident upon a smooth liquid–solid interface. A significant amount of coherent radiation is found to be backscattered in the general direction of incidence. The angle of back reflection is observed to be equal to the critical Rayleigh angle or leaky wave angle. Most of these observations were made during experiments on the Schoch displacement effect, and therefore it has been tacitly assumed that the back reflection is strongly dependent upon the angle of incidence, as is the case for the beam shifting in the Schoch effect. We present a theoretical basis for this new phenomenon. A two‐dimensional incident beam of Gaussian profile is considered. By a careful analysis we isolate that part of the field on the interface which has Fourier components corresponding to backward propagating waves in the liquid. This subset of the total wave field is then considered separately and it is shown to display a maximum in a certain direction, close to the critical Rayleigh angle. This peak in the angular pattern of the scattered field corresponds to an evanescent reflection boundary. We discuss the dependence of the effect upon certain parameters. The amplitude is shown to decrease as the beam width is increased, and it increases with increasing Schoch displacement. This backscattering is present for all angles of incidence; there is nothing inherently special about the Rayleigh angle.

Reflection of ultrasonic waves at a liquid–cubic–solid interface
View Description Hide DescriptionThe results of numerical calculations are presented for the reflection coefficient of sound waves incident on a liquid–cubic–solid interface. The reflection coefficient is calculated numerically for the (001) face of various cubic crystals. It is found that for certain orientations there is a null in the reflection coefficient. At this orientation all the power is coupled into a quasishear wave inside the solid. An explanation based on impedance theory is presented. The explanation given predicts that there might be reflection nulls for other liquid–solid interfaces where the solid is any anisotropicsolid not just cubic.

Weak and short waves in inhomogeneous isotropic elastic materials. I.
View Description Hide DescriptionWave propagation in an elastic material is investigated theoretically. The material is assumed to be isotropic and inhomogeneous and to have a nonlinear stress–strain relation, and the prestrain is assumed to be dynamic and inhomogeneous. Geometrical acoustics is applied, and the wave is assumed to be weak and short and to have an arbitrarily curved wave front. The amplitude is less than the wavelength, and the wavelength is less than the distances over which such wave quantities as prestrain and stress are subject to considerable change. By equating first‐order terms, a principal longitudinal and two principal transverse waves are shown to exist and their speeds of propagation are evaluated. Likewise, by equating second‐order terms, amplitude equations which govern the growth and decay of amplitude are derived. The variation of amplitude depends upon the curvature of the wave front, the velocity gradient and prestrain and material inhomogeneities, the nonlinearity of the stress–strain relation, and the waveform. The results obtained in simple cases are identical with those derived using the method of singular surface.

Weak and short waves in one‐dimensional inhomogeneous materials with memory.II
View Description Hide DescriptionWave propagation in a material with memory is investigated theoretically. The material is assumed to be one‐dimensional and inhomogeneous and to possess effects due to memory. Geometrical acoustics is assumed to hold for a weak wave with short wavelength. Order of magnitude estimations are made via the equation of motion. By equating first‐order terms, the propagation velocity is determined and in general found to depend upon waveform. When the material has weak memory the propagation velocity is independent of waveform. Likewise, by equating second‐order terms, an amplitude equation is obtained for a material with weak memory and found to depend upon waveform. The propagation velocity on the wave front and the amplitude equation of acceleration on it are identical with those derived using the method of singular surface.

Steady‐state oscillations of gas bubbles in liquids: Explicit formulas for frequency response curves
View Description Hide DescriptionThe steady‐state nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid subject to an acoustic pressure field are investigated by the multiscale perturbation method. As a result, simple formulas for the frequency response curves in the regions of the main resonance, first and second ultraharmonic and first and second subharmonic, are obtained to second order in the expansion.

Anomalous infrasound from Space Shuttle II and Skylab I
View Description Hide DescriptionInfrasound from Space Shuttle II and Skylab I recorded at Palisades, New York had characteristics strikingly different from all previous signals recorded from large rockets launched at Cape Canaveral. In the case of Space Shuttle, the reentry signal is unusually weak and lacking normal low frequency components. This anomaly is traced to the horizontal attitude of the reentry boosters and their slower speed. In the case of Skylab, the reentry signal arrives unusually early and the ratio of launch to reentry signal amplitude is inverted from past values. A combination of a different launch direction and weak stratospheric sound channel is responsible for the signal anomalies.

The role of the seabottom attenuation profile in shallow water acoustic propagation
View Description Hide DescriptionThe effect of the seabottom upon acoustic propagation in the frequency range from 20 to 2000 Hz in shallow water is analyzed. In particular, the role of depth and frequency variations of attenuation is considered. The point of view that attenuation in the seabottom varies linearly with frequency and changes with depth is taken. Normal mode calculations which demonstrate the interplay between depth variations of attenuation and the frequency dependence of propagation loss and mode attenuation coefficients are presented. It is shown that, if in the course of data analysis, attenuation were erroneously constrained to be constant with depth, then a nonlinear estimate for frequency dependence of attenuation could result. Calculations based upon attenuation profiles from the geophysical literature are compared with reported propagation loss data from the acoustics literature.

Modeling of acoustic propagation across warm‐core eddies
View Description Hide DescriptionA theoretical investigation has been made into the effect on acoustic propagation of oceanic fronts at the edge of warm‐core eddies. The investigation utilized modeling of acoustic propagation using the parabolic approximation to the wave equation. Propagation was examined using typical parameters for a wintertime warm‐core eddy in the Tasman Sea. Propagation across the eddy boundary (at a frequency of 100 Hz) is shown to create a second series of convergence zones, in addition to the normal series. This occurred for propagation both into and out of the eddy. For a source outside the eddy, energy is shown to strongly couple from deep refracted paths to mixed layer paths within the eddy. The eddy boundary was found to have significant effects on convergence zone properties. Acoustic propagation was also modeled using parameters from a particular realization of a summertime warm‐core eddy in the Tasman Sea (for which realization there was environmental and acoustic data available). This eddy had a surface duct and a separate subsurface duct. Reasonable agreement between model and experiment was found for source and receiver both in the subsurface duct at frequencies from 50 to 1000 Hz; disagreement occurred at 25 Hz. However, for source in surface duct but receiver in subsurface duct, the agreement was poor at most frequencies. The effect of minor variations in oceanic and experimental parameters was examined to determine the experimental resolution required of these parameters.

An equivalent bottom for use with the split‐step algorithm
View Description Hide DescriptionThe split‐step algorithm is the standard method for calculating complex (i.e., amplitude and phase) sound fields in a range dependent ocean environment. However, in ocean areas with strong bottom interaction, density discontinuities, sediment rigidity, and bottom roughness should be taken into account. It is easy to incorporate the effects of density discontinuities and rigidity in a specular bottom reflection coefficientR, and it is reasonable to assume that some of the complications of moderately rough bottom interfaces can also be included. Once R has been defined, a systematic procedure is given for generating an equivalent bottom that is compatible with the split‐step algorithm and provides an accurate accounting of bottom interaction.

Sound absorption measurements at 10–650 kHz in arctic waters
View Description Hide DescriptionThe absorption of sound in near‐freezing seawater was measured from ice floes in northern waters during April 1979, March 1980, and September 1980. Analysis of the data obtained shows that the relaxation frequency for the magnesium sulfate contribution is appreciably lower than predicted by extrapolating the Schulkin–Marsh equation or the Fisher–Simmons equation to temperatures below 0 °C. There is good agreement, however, with the Glotov equation. The measuredabsorption is lower than the Schulkin–Marsh equation predicts at all frequencies. The results are in good agreement with the Fisher–Simmons equation except near the magnesium sulfate relaxation frequency. Specifically, for the excess absorption equation α_{ E }=A S f _{2} f ^{2}/(f ^{2} _{2}+f ^{2})—with frequency f in kilohertz, salinity S of 32%–34%, and temperature at −1.6 °C—we find for the constants, A×10^{3}=14±2 dB/km and f _{2}=36±3 kHz.

Underwater acoustic sensor arrays using angle of arrival diversity to counteract fading in a multipath medium
View Description Hide DescriptionThe statistical properties of the output of a sparse array of independently suspended acoustic sensors submerged in the sea and exposed to vertically dispersed multipath signal arrivals typical of deep underwater propagation, are studied here. Horizontal components of element positions are subject to drift and defusion and are not accessible to manipulation; vertical components are assumed nontime varying once element depth has been set. Element positions are assumed known having been obtained using an independent measurement procedure not dealt with in this paper. The mean power pattern of such arrays in two dimensions with all elements at one depth and in three dimensions with different distributions of vertical positions, are obtained assuming conventional beamforming. Conventional focusing is found to be inefficient for signal energy collection and the output obtained is subject to variation typical of fading environments. To overcome these effects, multiple vertical beams are formed using the three‐dimensional array, the beams looking at different angles to resolve the multipath rays. The multiple beams, constituting a collection of angle‐of‐arrival diversity branches are combined in customary ways. Beam separation to minimize noise correlation between branches is determined. Simulation results for such a system using various diversity combining techniques are presented and the improvements obtained are discussed.

Acoustic reflection from transversely isotropic consolidated sediments
View Description Hide DescriptionMeasurements of an excess of horizontal to vertical velocity (averaging 10% for shales) have been made in consolidated marine sediments and in sedimentary rocks. In this paper, the proposed causes of such anisotropies are reviewed, and the reflection coefficient for a homogeneous, solid, transversely isotropic seafloor is derived from plane‐wave solutions of the anisotropicwave equations. Bottom loss calculations are used to show that anisotropy can affect the reflectivity of exposed consolidated sediments at the ocean floor. Studies of bottom loss are also used to develop a method for estimating the elastic parameter C _{1} _{3} (frequently not measured for sedimentary material) for consolidated materials.

An improved Kirchhoff formula for reflection loss at a rough ocean surface at low grazing angles
View Description Hide DescriptionThe calculation of specular reflection loss at a rough oceansurface is a time‐consuming procedure if the boundary perturbation or mode‐coupling methods are used. The simple Kirchhoff formula is often used as an estimate of reflection loss, but this is shown to severely underestimate the loss at small grazing angles. A formula is derived using the large correlation length limit of the boundary perturbation calculation, and is shown to be a more accurate estimate of the reflection loss at small grazing angles than the Kirchhoff formula. The new formula is identical with the Kirchhoff formula at large grazing angles.

A wake‐scattering experiment in thermally stratified water
View Description Hide DescriptionAn underwater object moving through a stable thermocline leaves a trail of fluctuations in pressure,velocity, and temperature; the attendant nonuniformities in the index of refractionscatteracoustic waves. An acoustic scatteringexperiment was performed in a flooded quarry, which has a stable thermocline with a typical gradient of 1.0 to 1.5 °C/ft and a Brunt–Väissälä period of about 70 s. The experiment used a self‐propelled, slender model about 9 in. in diameter and 48 in. long. The speed was 3 ft/s, the Froude number was 300, and the Reynolds number was 1.5×10^{5} based on the body diameter. A 75‐kHz directional sonar, driven with 0.1‐ms pulses at a rate of 10/s, insonified the wake; the scattered return was received by a directional hydrophone. The transducer‐wake geometries included vertical, horizontal, and 45° backscatter. A strong backscattered signal was received for several Brunt–Väissälä periods; in one instance, for ten periods. The amplitude of the scattered return compares favorably with theory.

Site and frequency dependence of ambient noise in the Northeastern Pacific Ocean
View Description Hide DescriptionOne‐hour averages of omidirectional ambient noise measurements at 60 and 165 Hz are analyzed for two nearby, deep ocean sites in the Northeastern Pacific during February and March 1981. Site A is a high noise site and is located near major east–west shipping lanes and near major Pacific storm paths. Site B is a lower noise site and is located approximately 450 nm from site A away from major shipping lanes and near major Pacific storm paths. The site and frequency dependence of ambient noise is found to be highly variable with shipping noise being totally dominant at 60 Hz at site A and stormnoise being totally dominant at 165 Hz at site B. Both shipping and stormnoise can dominate the 165‐Hz site A or 60‐Hz site B noise levels depending on weather conditions. Storms have a possible indirect effect on shipping noise, since very low noise periods occur in between storms, especially when the storm passes nearby the site. A limited number of WMO ships sampled indicate that ships slow down or stay in port during storms. Average omnidirectinal noise levels at 60 Hz at both sites and at 165 Hz at site A were 3 to 4 dB lower during a stormy week than they were during a relatively calm week. Array noise gain measurements at site B indicate that the coherence of noise during stormy periods is much less than it is during calm periods. Generally, this implies that the increase in beam level at 165 Hz, caused by stormnoise, will be significantly less than corresponding increase in omnidirectional noise levels.

Time of day noise adjustments or ‘‘penalties’’
View Description Hide DescriptionCommunity response descriptors, such as Day‐Night Average Sound Level (DNL), have included a nighttime adjustment or ‘‘penalty’’ in their formulation. Typically this nighttime penalty has been 10 dB. Some models incorporate an evening penalty in addition to the nighttime penalty. The basis for these penalties is examined in this paper. This analysis is based on results from a community attitudinal survey conducted in the vicinity of a large Army base. The survey sought to compare blast noise (e.g., artillery) and helicopters in the context of all noise such as airplane, traffic, and children. The analysis shows that there are at least two factors which contribute to a ‘‘penalty’’ during any time period. One factor occurs when individual events are intrinsically more bothersome or annoying during one period of time than during another time period. The second factor occurs because a greater percentage of events are most likely to be noticed and found bothersome during one period of time as compared with another. The results show that single bothersome events are more or less equally annoying during all time periods of the day. There is only a small growth in annoyance during the night and this growth occurs primarily with the more impulsive sources such as artillery and helicopters. The results indicate that the second factor described above is more important in contributing to a total nighttime adjustment of penalty. That is, for a given number of available events, respondents are more likely to notice and be bothered by events during the night than during the day. This factor appears to be a primary contributor to any nighttime adjustment. The nighttime penalty indicated by these two factors is of the order of 5 to 10 dB. These results tend to support retention of a nighttime penalty in descriptors such as DNL. Based on the results, one would not be tempted to depart from the long‐established 10‐dB value for the penalty.

Relative hazard of weapons impulses
View Description Hide DescriptionArguments in favor of a theoretically based damage‐risk criterion (DRC) for intense noise [G. R. Price, J. Acoust. Soc. Am. 6 9, 171–177 (1981); 6 6, 456–465 (1979); J. Acoust. Soc. Am. Suppl. 1 6 2, S95 (1977)] are further developed here to make a crucial prediction. Based on measured spectral differences, it was predicted that rifle impulses would cause permanent threshold shifts at approximately 9 dB lower peak pressures than cannon impulses. In contrast, DRCs in use in the world predict that the cannon would be more hazardous than the rifle by 7 to 10 dB. Electrophysiological measures of sensitivity were used in 38 cats (76 ears) which were exposed to 60 impulses, approximately 3 s apart, at various peak pressures, from either a rifle or a 105‐mm Howitzer. Hearing changes were followed until recovery was complete (2 months). Permanent threshold shifts began at about 140 dB for rifle impulses and 150–155 dB for cannon impulses, confirming the prediction and supporting the contention that there is a spectrally dependent critical level for the ear at high intensities. Implications for present DRCs and future risk assessment schemes are discussed.