Testing the theoreticians.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

Method of numerical Green's function determination for far-field scattering solutions from objects at a water-sediment interface.

A method is presented for numerically determining Green's functions for the purpose of calculating the far-field scattering from objects resting on or buried within the seafloor. To obtain the far-field scattering, initial evaluation of the three-dimensional near-field solution is required, through finite element analysis or other means. The Green's function and its spatial derivatives are then numerically evaluated for input into the Helmholtz-Kirchhoff integral, yielding the far-field scattering solution. This numerical technique determines the Green's function directly and avoids requiring analytic forms of Green's functions, which may be difficult or time consuming to evaluate for complex environments. This paper demonstrates the effectiveness of applying the numerical Green's function determination technique in conjunction with near-field results from finite element models to determine the far-field scattering for various elastic targets in free-field and flat seafloor environments. The method may be generalizable to arbitrary targets at complicated interfaces, incorporating interface roughness, layering, and volume inhomogeneities.

A comparison of three geoacoustic models using Bayesian inversion and selection techniques applied to wave speed and attenuation measurements.

Many geoacoustic models have been developed to study sandy sediments. In this work, Bayesian inference techniques are used to compare three such models: the VGS(λ) model, the most recent of Buckingham's viscous grain-shearing models, the Biot-Stoll poroelastic model, and an extension to the Biot-Stoll model proposed by Chotiros called the corrected and reparametrized extended Biot (CREB) model. First, Bayesian inversion is applied to wave speed and attenuation measurements previously made in the laboratory to determine the degree to which each of the model input parameters can be resolved by wave speed and attenuation data. Then, Bayesian model selection techniques are utilized to assess the degree to which the predictions of these models match the measured data and to ascertain the Bayesian evidence in favor of each. Through these studies it is determined that the VGS(λ) and CREB models outperform the Biot-Stoll model, both in terms of parameter resolution and in their ability to produce predictions in agreement with measurements. The VGS(λ) model is seen to have the highest degree of Bayesian evidence in its favor.

Observation and modeling of acoustic scattering from a rubber spherical shell.

Acoustic backscattering from a rubber spherical shell in water is observed to contain a delayed enhancement, demonstrated to be associated with a waveguide path along the shell. This path is somewhat analogous to that of the Lamb wave observed on metallic shells. Rubber is a unique material because of its subsonic sound speed relative to water, and because shear coupling is often small enough to be neglected in typical models, making it fluid-like. This makes rubber a material of interest for coating and cloaking underwater devices and vehicles. Both fluid and elastic rubber partial wave series models are tested, using experimentally measured longitudinal and shear speeds, attenuation, and rubber density. A finite element model for the shell is also developed. Comparison of the models and experiments highlights the importance of the waveguide path to the overall scattering. Estimates for the group and phase velocities of the lowest order propagating mode in the shell are determined through waveguide normal mode analysis and Sommerfeld-Watson theory, and are shown to give good agreement with experiments in predicting the time of arrival of the waveguide path.

A comparison of finite element and analytic models of acoustic scattering from rough poroelastic interfaces.

The finite element method is used to model acoustic scattering from rough poroelastic surfaces. Both monostatic and bistatic scattering strengths are calculated and compared with three analytic models: Perturbation theory, the Kirchhoff approximation, and the small-slope approximation. It is found that the small-slope approximation is in very close agreement with the finite element results for all cases studied and that perturbation theory and the Kirchhoff approximation can be considered valid in those instances where their predictions match those given by the small-slope approximation.

On the validity of the effective density fluid model as an approximation of a poroelastic sediment layer.

The effective density fluid model (EDFM) was developed to approximate the behavior of sediments governed by Biots theory of poroelasticity. Previously, it has been shown that the EDFM predicts reflection coefficients and backscattering strengths that are in close agreement with those of the full Biot model for the case of a homogeneous poroelastic half-space. However, it has not yet been determined to what extent the EDFM can be used in place of the full Biot-Stoll model for other cases. Using the finite element method, the flat-interface reflection and rough-interface backscattering predictions of the Biot-Stoll model and the EDFM are compared for the case of a poroelastic layer overlying an elastic substrate. It is shown that considerable differences between the predictions of the two models can exist when the layer is very thin and has a thickness comparable to the wavelength of the shear wave supported by the layer, with a particularly strong disparity under the conditions of a shear wave resonance. For thicker layers, the predictions of the two models are found to be in closer agreement, approaching nearly exact agreement as the layer thickness increases.

Shear wave attenuation and micro-fluidics in water-saturated sand and glass beads.

An improvement in the modeling of shear wave attenuation and speed in water-saturated sand and glass beads is introduced. Some dry and water-saturated materials are known to follow a constant-Q model in which the attenuation, expressed as Q(-1), is independent of frequency. The associated loss mechanism is thought to lie within the solid frame. A second loss mechanism in fluid-saturated porous materials is the viscous loss due to relative motion between pore fluid and solid frame predicted by the Biot-Stoll model. It contains a relaxation process that makes the Q(-1) change with frequency, reaching a peak at a characteristic frequency. Examination of the published measurements above 1 kHz, particularly those of Brunson (Ph.D. thesis, Oregon State University, Corvalis, 1983), shows another peak, which is explained in terms of a relaxation process associated with the squirt flow process at the grain-grain contact. In the process of deriving a model for this phenomenon, it is necessary to consider the micro-fluidic effects associated with the flow within a thin film of water confined in the gap at the grain-grain contact and the resulting increase in the effective viscosity of water. The result is an extended Biot model that is applicable over a broad band of frequencies.

A three-dimensional, longitudinally-invariant finite element model for acoustic propagation in shallow water waveguides.

A three-dimensional, longitudinally-invariant finite element (FE) model for shallow water acoustic propagation is constructed through a cosine transform of a series of two-dimensional FE models at different values of the out-of-plane wavenumber. An innovative wavenumber sampling method is developed that efficiently captures the essential components of the integral as the out-of-plane wave number approaches the water wavenumber. The method is validated by comparison with benchmark solutions of two shallow water waveguide environments: a flat range independent case and a benchmark wedge.

Quantifying the effects of roughness scattering on reflection loss measurements.

Seafloor reflection loss and roughness measurements were taken at the Experimental Validation of Acoustic Modeling Techniques experiment in 2006. The magnitude and phase of the reflection loss was measured at frequencies from 5 to 80 kHz and grazing angles from 7° to 77°. Approximately 1500 samples were taken for each angle. The roughness was measured with a laser profiler. Geoacoustic parameters such as water and sediment sound speed and density were measured concurrently. The reflection loss data were compared with three models: A flat interface elastic model based on geoacoustic measurements; a flat interface poro-elastic model based on the Biot/Stoll model; and a rough interface model based on the measured interface roughness power spectrum. The data were most consistent with the poro-elastic model including scattering. The elastic model consistently predicted values for the reflection loss which were higher than measured. The data exhibited more variability than the model due to layering and fluctuations in the propagating medium.

Shear and compressional wave speeds in Hertzian granular media.

It is shown that the shear wave speed in a granular medium is less than that in an elastic solid of the same shear modulus-to-density ratio. Shear and compressional wave speeds are derived for granular media using a conservation of energy approach. The grains are assumed to be spherical with elastic Hertzian contacts of constant stiffness. The affine approximation is used to determine the relative displacements of grain centers, and it is also assumed that the grains are small compared to a wavelength, consistent with the effective medium approximation. Potential and kinetic energies associated with linear motion are the same as those in an elastic solid, but it is found that shear wave propagation in a granular medium involves additional energies associated with grain rotation. The partition of energies results in a reduction in the shear wave speed, relative to an elastic solid of the same shear modulus-to-density ratio. It is shown that the reduction is an inherent property of granular media, independent of any departure from the affine approximation or fluctuations in coordination number or contact stiffness. The predicted wave speed ratios are consistent with published measurements.

Finite element modeling of reverberation and transmission loss in shallow water waveguides with rough boundaries.

A finite element model for the reverberation and propagation in a shallow water waveguide with a sandy bottom was calculated for five different environments at a center frequency of 250 Hz. The various environments included a rough water/sediment interface, a rough air/water interface, roughness at both interfaces and downward and upward refracting sound speed profiles with roughness at both interfaces. When compared to other models of reverberation such as ray theory, coupled modes, and parabolic equations, finite elements predicted higher levels of reverberation. At early times, this is due to the "fathometer" return, energy that is normally incident on the boundaries at zero range. At later times, the increased reverberation was due to high angle scattering paths between the two interfaces. Differences in reverberation levels among the environments indicated that scattered energy from the air/water interface is transmitted into the bottom at steep angles. This led to a large decrease in reverberation for a rough air/water interface relative to a rough water/sediment interface. Sound speed profile effects on reverberation were minimal at this frequency range. Calculations of the scintillation index of the different environments indicated that most of the reverberation was relatively Rayleigh-like with heavier tailed distributions at longer ranges.

Comments on "On pore fluid viscosity and the wave properties of saturated granular materials including marine sediments" [J. Acoust. Soc. Am. 122, 1486-1501 (2007)].

The ability of the grain shearing (GS) and viscous grain shearing (VGS) models to relate geophysical and acoustic properties is tested by a method based on the claimed tight coupling between compressional and shear wave speeds and attenuations, which allows the test result to be quantified in a single parameter. The VGS model is claimed to provide a better fit to the measured sound speed and attenuation in sandy sediments below 10 kHz. In situ measurements of wave speeds and attenuations from the Sediment Acoustics Experiment 1999 (SAX99) and published laboratory measurements by Prasad and Meissner [Geophysics 57, 710-719 (1992)] on a number of sand samples were used to test the models. By this metric, the SAX99 data show that the VGS model is no better than the original GS model because the improved agreement of compressional wave speeds at low frequencies is achieved at the expense of gross overestimation of the shear wave attenuation. When applied to the measurements by Prasad and Meissner, it is shown that the GS models are not applicable at any significant confining pressures, and at zero pressure they may only be applicable to a small subset of the sand samples.

High-frequency dispersion from viscous drag at the grain-grain contact in water-saturated sand.

Shear viscous drag within the thin fluid film at the contact between grains in water-saturated sand is an important loss mechanism for high-frequency sound in the Biot-Stoll plus contact squirt flow and shear viscous drag (BICSQS) model [J. Acoust. Soc. Am. 116, 2011-2022 (2004)]. Couette flow was assumed for the shear drag but it breaks down when inertial effects within the film become significant. Using Biot's method, a correction is derived for the shear drag and inserted into the BICSQS model. The result is a prediction of negative sound speed dispersion, consistent with dynamic theories of fluid-filled poroelastic bodies.

Acoustic virtual mass of granular media.

Mechanical coupling between grains in a randomly packed unconsolidated granular medium is shown to cause an increase in the effective inertia, hence, a reduction in sound and shear wave speeds, relative to predictions by the standard expressions for a uniform elastic solid. The effect may be represented as a virtual mass term, and directly related to the scintillation index of the grain-to-grain contact stiffness.