Volume 79, Issue 2, February 1986
Index of content:

Inverse elastic scattering in three dimensions
View Description Hide DescriptionIt is shown how to find the density and the elastic constants in the half‐space x _{3}≥0 from the value of the scattered displacement field u _{ s } on the plane x _{3}=0. The source of the field is a time‐harmonic force applied at a source point x ^{ s } on x _{3}=0, and the field is measured at a geophone position x ^{ g } on this plane. The medium is assumed to differ slightly from a uniform medium so that u _{ s }(x ^{ g }, x ^{ s }, ω) can be calculated by the single scattering or Born approximation. As is to be expected, u _{ s } contains more than enough information for the desired reconstruction. Therefore, a subset of the data, involving only longitudinal waves, is used. From it the density and the elastic constants are determined explicitly. A similar problem in which the elastic medium occupies all of space, with perturbations confined to a half‐space, is treated also.

Determination of the resonance spectrum of elastic bodies via the use of short pulses and Fourier transform theory
View Description Hide DescriptionA method which permits a rapid determination of the resonance spectrum of submerged elastic cylindrical wires is described. A portion of the backscattering signal is selected by a gate, and the gated echo is Fourier‐transformed into the frequency domain. Depending on the temporal position of the gate in comparison with the specular signal, either the form function (gate includes the rigid contribution) or the resonance spectrum (gate excludes the specular echo) was determined. According to the attenuation properties of the surface waves in cylindrical targets, the first (n, 1), or Rayleigh, resonances can be separated from the (n, l=2,3,...) resonances corresponding to the Whispering Gallery waves. The use of a broadband transducer is necessary in order to achieve a clear separation of specular and circumferential wave echoes.

An exact resonance decomposition of the acoustic transmission and reflection coefficients of a fluid layer
View Description Hide DescriptionPreviously, a resonancetheory had been devised by us for the acoustic transmission (T) and reflection coefficient (R) of a fluid layer, or elastic plate imbedded in a fluid. This theory, based on the use of a ‘‘resonance approximation,’’ was restricted to the case of light fluid loading, or of a large impedance mismatch at the boundaries between the external fluid and the fluid layer or plate. In the present paper, the meromorphic function T (together with R) for a fluid layer is represented by a (Mittag–Leffler type) series expansion which not only directly exhibits resonance properties, but also furnishes the value of each resonance peak correctly, including the effect of the underlying tails of all other resonances. Being exact, this expansion is now applicable to the case of heavy fluid loading, or of a close impedance match between the external fluid and the layer.

Traveling wave and SEM representations for transient scattering by a circular cylinder
View Description Hide DescriptionWhen observed over long observation times, scattered returns from targets illuminated by broadband acoustic signals reveal distinctive features in the early and late time regimes. The features can be explained in terms of the different wave phenomena, progressive and oscillatory, that are dominant during these respective intervals. The former represent wave front arrivals, and the latter full body resonances. A hybrid theory, recently developed by Heyman and Felsen [IEEE Trans. Antennas Propag. A P ‐ 3 1, 426–437 (1983)], has formalized the connection between them and has provided new interpretations that have not emerged from more conventional treatments. These interpretations can clarify issues which have arisen within the resonance expansion procedure, in particular, the adequacy of the expansion at early times. In this paper, the canonical problem of scattering by a circular cylinder serves as a rigorous test for general observations made elsewhere [E. Heyman and L. B. Felsen, IEEE Trans. Antennas Propag. A P ‐ 3 1, 706–718 (1985)], concerning the t r a v e l i n g w a v e interpretation of the resonance series, and especially the role of the entire function in the complex frequency plane that is included to repair resonance series deficiencies of the Singularity Expansion Method (SEM).
The resonance series of damped global oscillatory wave fields corresponding to the complex resonant frequencies represents, collectively, the multiple effects of diffracted (creeping) waves traveling around the cylinder in the positive and negative directions, but it cannot incorporate the specularly reflected field in the lit region, which has not sampled the obstacle surface a s a w h o l e. This contribution remains as a free term that can be identified in the complex frequency plane as an i n t r i n s i c (nonremovable) entire function. The analysis also shows how delaying the turn‐on time of the resonance series, by retaining some early creeping wave front arrivals intact, can generate, in addition, a n o n i n t r i n s i c (i.e., removable) entire function. These considerations, having rigorous foundation and appealing physical content, aid in the understanding of wave phenomena associated with broadband scattering from targets observed over early and late time periods.

Effective wave speeds in an SiC‐particle‐reinforced Al composite
View Description Hide DescriptionPlane‐wave propagation in an SiC‐particle‐reinforced aluminum‐alloy composite was studied. Considering the composite to possess orthotropic symmetry (nine independent elastic constants), by a pulse‐echo method, nine independent ultrasonic velocities were measured.Measuredelastic stiffnesses departed negatively up to 40% from a rule‐of‐mixture model. Using ensemble‐average, scattered‐plane‐wave methods, the composite was modeled as SiC particles represented as prolate spheroids distributed randomly, both in position and in orientation. Wave speeds of plane waves, both longitudinal and shear, were calculated in the long‐wavelength limit. These wave speeds lead to equations for the effective static bulk and shear moduli of the composite. Further, a nonhomogeneous particle distribution was considered. Wave‐speed equations were derived for the case where the composite contains particle‐free aluminum‐alloy regions that were represented by oblate spheroids. The resulting anisotropic composite behaves transversely isotropicly. For all elastic constants, the model agrees with measurements, within a few percent.

Excitation of surface waves of different modes at fluid–porous solid interface
View Description Hide DescriptionThe presence of ultrasonicsurface waves of various modes on a fluid–porous solid interface is demonstrated and their velocitiesmeasured. The experimental technique (developed earlier by one of the authors for a fluid–isotropic solid interface) utilizes reflected broadband spectra from periodic surfaces. Three sharp minima corresponding to three mode‐converted waves coupled to the porous solid are observed. The velocities of these ‘‘surface’’ waves are in qualitative agreement with theoretical predictions [S. Feng and D. L. Johnson, J. Acoust. Soc. Am. 7 4, 906 (1983) and 7 4, 915 (1983)] and are identified as pseudo Rayleigh, pseudo Stoneley, and true Stoneley waves.

Gas‐filled spherical resonators: Theory and experiment
View Description Hide DescriptionGas‐filled spherical resonators are excellent tools for routine measurement of thermophysical properties. The radially symmetric gas resonances are nondegenerate and have high Q’s (typically 2000–10 000). Thus they can be used with very simple instrumentation to measure the speed of sound in a gas with an accuracy of 0.02%. We have made a detailed study of a prototype resonator filled with argon (0.1–1.0 MPa) at 300 K, with the objective of discovering those phenomena which must be understood to use gas‐filled spherical resonators to measure the thermodynamictemperature and the universal gas constant R. The resonance frequencies f _{ N } and half‐widths g _{ N } were measured for nine radially symmetric modes and nine triply‐degenerate nonradial modes with a precision near 10^{−} ^{7} f _{ N }. The data were used to develop and test theoretical models for this geometrically simple oscillating system. The basic model treats the following phenomena exactly for the case of a geometrically perfect sphere: (1) the thermal boundary layer near the resonator wall, (2) the viscous boundary layer (for nonradial modes), (3) bulk dissipation, and (4) the coupling of shell motion and gas motion. In addition, the following phenomena are included in the model through the use of perturbation theory: (5) ducts through the shell, (6) imperfect resonator geometry, and (7) the seam where the two hemispheres comprising the shell are joined. Some estimates of the effects of (8) roughness of the interior of the shell have also been made. Much of the lower pressure f _{ N } and g _{ N } data can be explained by our model of these phenomena to within ±5×10^{−} ^{6} f _{ N } when a single parameter c _{0}/(V _{0})^{1} ^{/} ^{3} is fit to a single resonance frequency at a single pressure. In this parameter, c _{0} is the ideal‐gas speed of sound and V _{0} is the resonator volume. If this volume were known, the prototype resonator could be used to measure the speed of sound of a gas with an accuracy approaching ±0.0005%. Improvements in resonator design which will circumvent difficulties discovered in this work are expected to lead to much better agreement between theory and the measuredf _{ N } and g _{ N }.

Transient radiation from axially symmetric sources
View Description Hide DescriptionA method is presented for the efficient calculation of radiated acoustic fields from a radially symmetric source in a rigid baffle excited by an arbitrary time excitation. The technique is a modal analysis based on the series expansion of the source velocity excitation in terms of either of two basis functions. Each mode is propagated by the technique with rapid convergence of the solution evident in 30 or less terms, allowing rapid and efficient computer‐based solutions to be obtained. Several numerical field simulations are given.

Acoustic resonance frequencies of deformed spherical resonators. II
View Description Hide DescriptionThe effects of imperfect spherical shape on the modes of a spherical acoustic resonator are considered. The resonator boundary is described by a series of spherical harmonics r=a+εa∑ c _{ l k } Y _{ l k }, where ε is a small parameter. It is convenient to summarize the results by considering deformations which do not change the resonator volume. Earlier work showed, for pure radial modes subject to axisymmetric shape perturbations, that the fractional shift of the resonance frequency is proportional to ε^{2}. This work extends this result to arbitrary shape perturbations. Nonradial modes, for which the acoustic pressure is proportional to j _{ n } (k _{ n s } r) Y _{ n m } (θ, φ) with n≥1 are (2n+1)‐fold degenerate for a perfect spherical resonator. Deformation of the resonator normally shifts the resonance frequencies by an amount which is linear in ε. However, the average shift of a degenerate set of modes with indices {n s} is of order ε^{2}. Axisymmetric shape perturbations normally reduce the degeneracy of the nonradial modes to (n+1)‐fold, and arbitrary deformations normally lift the degeneracy completely. The modes with indices {n s} are sensitive only to the terms c _{ l k } with even values of l in the range l≤z n. A formalism for quantitative estimates is developed. Numerical results are obtained for some n=1 and n=2 cases.

A comparison of high‐resolution seismic methods for determining seabed velocities in shallow water
View Description Hide DescriptionThe ability to resolve both the seismicvelocity of the seabed in shallow water and the lateral variability of these measuredvelocities using four conventional seismic methods is compared. The four methods described here differ in the ease and efficiency in which the field data are collected and interpreted, and in the resolution of the velocity of the seabed they provide. Narrow‐aperture refraction studies provide limited constraints due to the frequent absence of first‐arriving sediment refractions in the narrow portion of the wave field that is sampled. Wide‐aperture refraction experiments using ocean bottom seismometers provide high resolution of both the compressional‐ and shear‐wave velocities of the seabed but are time‐consuming to perform and to interpret. Narrow‐aperture multichannel reflection data are easily collected, and are ideal for areal mapping of sedimentary sequences, but resolution of seismicvelocities is low unless the aperture of the multichannel streamer is several water depths in length. Wide‐aperture multichannel reflection profiling generally provides the highest resolution in velocity in all geoacoustic environments, including those which produce little or no precritical reflected energy and little dispersion of the acoustic normal modes. Moreover, difference seismic wave fields calculated by subtracting a reference seismic wave field from adjacent wave fields provide an objective means of rapidly mapping the lateral variability of the seabed.

Acoustic reciprocal transmission experiments, Florida Straits
View Description Hide DescriptionAn acoustic approach for the measurement of range‐ and depth‐averaged current and temperature is successfully demonstrated for the bottom‐limited acoustic transmission of the Florida Straits. The shallow water environment prohibits the use of deep oceantomography methods since there are usually no separable arrivals associated with eigenrays. Instead, multipath groupings of arrivals are shown to have stable envelopes if averaged sufficiently long to eliminate effects of interference. The shape of the envelope is controlled to some extent by the source–receiver depth and has characteristics which can be used for very precise travel time measurements. Ray models predict a unique relation between ray height above the bottom and arrival time allowing for unambiguous inversion. Two three‐point reciprocal transmission experiments were conducted in the Florida Straits (ranges approx. 25 and 45 km). Two‐way channel pulse responses are analyzed to give travel times which are then inverted to give depth averages of temperature and current; the depth and extent of the average is determined by ray models. The method is shown to be precise in resolving variations in temperature of 0.002 °C and current of 2 cm/s. The spatially averaged tomographic results are compared with point measurements of current and temperature from current meter moorings along the path of propagation.

Beyond bathymetry: Mapping acoustic backscattering from the deep seafloor with Sea Beam
View Description Hide DescriptionIn its standard mode of operation, the multibeam echosounder Sea Beam produces high resolution bathymetric contour charts of the seafloor surveyed. However, additional information about the nature of the seafloor can be extracted from the structure of the echo signals received by the system. Such signals have been recorded digitally over a variety of seafloor environments for which independent observations from bottom photographs or sidescan sonars were available. An attempt is made to relate the statistical properties of the bottom‐backscattered sound field to the independently observed geologicalcharacteristics of the seafloor surveyed. Acoustic boundary mapping over flat areas is achieved by following trend changes in the acoustic data both along and across track. Such changes in the acoustics are found to correlate with changes in bottom type or roughness structure. The overall energy level of a partial angular‐dependence function of backscattering appears to depend strongly on bottom type, whereas the shape of the function does not. Clues to the roughness structure of the bottom are obtained by relating the shape of the probability density function of normal‐incidence echo envelopes to the degree of coherence in the backscattered acoustic field.

The effects of variations in sound speed on coupling coefficients between acoustic normal modes in shallow water over a sloping bottom
View Description Hide DescriptionThe conventional method for determining the coupling coefficient between acoustic normal modes in shallow water over a hard sloping bottom gives an incorrect result because it assumes the derivative normal to the bottom to be equal to the depth derivative. This problem can be circumvented by measuring depth normal to the bottom. The coupling coefficients determined in this manner are found to be at least three times smaller or larger than the corresponding conventional results (the exact ratio depends on the mode numbers). For well‐trapped modes in isospeed water over a sloping bottom with a finite sound speed, the coupling coefficient is approximately the same as would occur if there were a virtual pressure release surface at a fixed distance beneath the actual seafloor. This distance is typically about 30% greater than the cutoff water depth for the frequency under consideration. If the water column is not isospeed, then the depth functions of the modes can be expressed as perturbation series of the sinusoidal functions that correspond to the isospeed case. A negative sound‐speed gradient increases the coupling coefficients and, providing the sound speed does not exceed the phase velocity of the unperturbed modes, the increase is proportional to the relative variability of the sound‐speed profile.

Hamiltonian perturbation theory for acoustic rays in a range‐dependent sound channel
View Description Hide DescriptionA perturbation theory for acoustic ray propagation is presented which is based on the analogy between Hamilton’s Principle of Least Action (independent variable: time) and Fermat’s Principle of Least Time (independent variable: space coordinate). In a vertical ocean section with x positive to the right and z positive upward, the Lagrangian variables z and ż (a dot denotes differentiation with respect to x; ż=d z/d x) are first replaced by the canonical variables (z, p) of the corresponding Hamiltonian formulation. For the zeroth‐order case, where the soundc(x,z) reduces to the form c _{0}(z), a canonical transformation, z, p → ω_{0}, J _{0}, can be made. The new variables are the analogs of angles‐action variables in dynamics, and are constants. The generator for this transformation is just the Eikonal function for zeroth order and, hence, is recognized as the travel time between a source and receiver of sound. Finally, when the x‐dependent perturbations are turned on, ω_{0} and J _{0} cease to be constants and a second, infinitesimal, canonical transformation, ω_{0}, J _{0} → ω, J, is made. For range‐dependent sound channels, ω=ω(x) and J=J(x). The canonical equations for these variables are exhibited, and how they may be solved by standard perturbation theory techniques is shown. Finally, some examples of the theory as applied to perturbations which vary slowly in x or, alternatively, which vary rapidly in x compared with the basic variation in the range‐independent channel are given. The various perturbations to travel time are included in these calculations.

Acoustic scattering by ocean irregularities: Aspects of the inverse problem
View Description Hide DescriptionExpressions are derived for the autocorrelation and structure functions of the acoustic refractive index for oceaninternal waves in the presence of fine structure. The transverse autocorrelation and structure functions required in acoustic scattering formulas are obtained from these. The spectra and correlation functions of acoustic phase, complex amplitude, and intensity are considered in the case of multiple scattering, and it is shown that the effect of fine structure on the fourth moment of the acoustic field is fundamentally different from that exerted on the second moment or the phase. The problem of deducing the correlation function of ocean irregularities from the acoustic signal is considered, and it is shown that, under certain circumstances, the full inverse problem can be solved by using the second moment of acoustic complex amplitude. Finally, the effect of tides on the phase, second moment, and the spectrum of intensity fluctuations of the acoustic signal is considered. It is shown that this effect must be taken into account when seeking a solution to the inverse problem.

Source depth distribution for uniform intensity in a surface sound channel
View Description Hide DescriptionA single acoustic source in a surface sound channel will produce an average acoustic intensity which varies with measurement depth, and the question is how to calculate the source concentration down a vertical array which will produce an intensity independent of depth. It is the long‐range or range‐averaged problem which is treated, using, initially, a high‐frequency or energy flux approximation. The chosen approach works first from the uniform intensity back to the necessary depth distribution of quasimodes, and then from the quasimode distribution to the source distribution. We arrive at a universal curve specified in terms of elliptic integrals, which has a high concentration at the bottom of the duct. The same curve is reached using numerical methods. Comments cover wave theory effects and the efficiency of coupling. PACS numbers: 43.30.Bp, 43.30.Es

An experimental study of the penetration of a water–sediment interface by a parametric beam
View Description Hide DescriptionA recent theoretical study [D. J. Wingham, J. Acoust. Soc. Am. 7 6, 1192–1200 (1984)] presented calculations of the farfield secondary pressure in sediment due to a parametric array incident on a water–sediment interface, assuming the array to be completely truncated at the interface. An experimental investigation of this theory is undertaken and the measured secondary pressure contours throughout the sediment are compared with the theoretical estimates. The theory is shown to provide good estimates of the secondary field. The measured secondary pressure variation as a function of beam incidence angle at various ranges is presented and it is apparent that only when the array is truncated in its primary nearfield does the performance of the parametric array differ significantly from a conventional array. It is concluded that the anomalous behavior of parametric arrays, at postcritical angles, relies on virtual sources which are both close to the interface and suitably phased to radiate into the sediment.

Free vibration of axisymmetrical solid bodies with meridionally varying profile
View Description Hide DescriptionAn analysis is presented for the three‐dimensional vibration problem of determining the natural frequencies and the mode shapes of axisymmetrical solid bodies, with meridionally varying profiles, expressed as an arbitrary function. For this purpose, the body is transformed into a circular cylinder with unit axial length and unit radius, by a transformation of variables. With the displacements of the transformed cylinder assumed in the forms of algebraic polynomials, the dynamical energies of the cylinder are evaluated, and the frequency equation is derived by the Ritz method. This method is applied to barrel or hourglass‐type bodies and frustums of cone, under two combinations of boundary conditions at the ends, and the natural frequencies and the mode shapes are calculated, numerically giving the results.

Accurate determination of object–image distance for planar objects in acoustical imaging
View Description Hide DescriptionA new technique of processing the image data for accurately determining the object distance from the image plane, when a planar object is illuminated by a plane acoustic wave, is presented in this paper. Typical illustrations are presented, which establish the validity of the proposed technique.

Accuracy of distance measurement in the bat E p t e s i c u s f u s c u s: Theoretical aspects and computer simulations
View Description Hide DescriptionBehavioral experiments of Simmons [J. Acoust. Soc. Am. 5 4, 157–173 (1973) and Science 2 0 4, 1336–1338 (1979)] on the ranging accuracy in the bat E p t e s i c u s f u s c u s have led to far‐reaching postulates on the existence of optimal and phase‐conserving processing mechanisms in the bat. In this paper, the results of computer simulations of these experiments are presented. Two receiver types are investigated: the fully coherent cross‐correlation receiver and the cross‐correlation receiver with envelope processing (semicoherent). It is shown that Simmons’ experiments cannot be treated as a simple estimation of distance, but require at least two (range difference experiment; see Simmons, 1973) or four (range jitter experiment; see Simmons, 1979) echolocation sounds for one decision. The performance of the bat in both experiments is much worse than predicted for a coherent and a semicoherent receiver type. The bat’s accuracy in Simmons’ range difference experiment is at least 18 dB worse than predicted for an optimal receiver. The results of the jitter experiment cannot be interpreted in a simple way as proof that bats are able to evaluate phase information as in a fully coherent cross‐correlation receiver.