Modeling and simulation of underwater acoustic propagation through a random distribution of ice blocks.

Acoustic propagation through a random distribution of 1 m ice cubes, from 100 to 1000 Hz, was simulated in a 3D finite element model. The effective sound speed and attenuation as functions of frequency were calculated from the simulated signals. Attempts were made to fit a number of models to the wave speed and attenuation, including single scattering, lossy water, and Biot approximations. An extended Biot model, developed for acoustic propagation in granular seabed sediments, was able to fit the simulation up to 300 Hz. Beyond this frequency, the simulation shows that multiple scattering dominates.

Connecting poro- and visco-elastic acoustic models of marine sediments: Salinity, force chains, creep, and permeability.

A poro-elastic model for both sandy and muddy marine sediments is used to derive a visco-elastic approximation, and compared to the existing measurements of wave speeds, attenuations, and reflection. The poro-elastic model is the modified, corrected, Revil, extended Biot (mCREB) model. Its derivation, which includes a force chain approximation and a creep mechanism, is reviewed and equations for implementation are provided. It fits the existing measurements over a broad range of frequencies from a few Hertz to almost a megaHertz. Salinity is essential to the poro-elastic behavior of mud. A visco-elastic approximation is derived, based on the zero permeability condition. It is a simpler model with fewer input parameters, and practically identical to the popular viscous grain shearing (VGS) model, although their derivations are very different. Comparisons between the measurements, the poro-elastic model, and its visco-elastic approximation are made in order to identify the circumstances in which the latter may be used. Generally, the visco-elastic approximation may be used for frequencies below 1 kHz in mud and sand. At higher frequencies, poro-elastic effects dominate rendering the visco-elastic approximation inaccurate.

Simulation of acoustic reflection and backscatter from arctic sea-ice.

The rapidly warming Arctic ocean demands new ways to monitor and characterize changes in sea-ice distribution, thickness, and mechanical properties. Upward-looking sonars mounted on autonomous underwater vehicles offer possibilities for doing so. Numerical simulations were made of the signal received by an upward-looking sonar under a smooth ice sheet using a wavenumber integration code. Demands on sonar frequency and bandwidth for pulse-echo measurements were analyzed. For typical sea-ice physical properties found in the Arctic ocean, even in highly attenuating sea-ice, there is significant information to be extracted from the received acoustic signal. Discrete resonance frequencies in the signal may be related to leaky Lamb waves, and the frequencies are connected to the ratio of the shear wave speed-to-thickness of the ice sheet. The periodicity of the multiple reflections of a pulse-compressed signal may be related to the ratio of compressional wave speed-to- thickness. Decay rates of both types of signals are indicative of the wave attenuation coefficients. Simulations of the acoustic reflection by rough water-ice interfaces were made. Smaller levels of roughness were found to enhance the acoustic signal, while greater levels of roughness are detrimental to the sea-ice characterization process.

Inversion of surficial sediment thickness from under-ice acoustic transmission measurement.

The under-ice acoustic transmission experiment of 2013, conducted under ice cover in the Fram Strait, was analyzed for bottom interactions for the purpose of developing a model of the seabed. Using the acoustic signals, as well as data from other sources, including cores, gravimetric, refraction, and seismic surveys, it was deduced that the seabed may be modeled as a thin surficial layer overlaid on a deeper sediment. The modeling was based on the Biot-Stoll model for acoustic propagation in porous sediments, aided by more recent developments that improve parameter estimation and depth dependence due to consolidation. At every stage, elastic and fluid approximations were explored to simplify the model and improve computational efficiency. It was found the surficial layer could be approximated as a fluid, but the deeper sediment required an elastic model. The full Biot-Stoll model, while instrumental in guiding the model construction, was not needed for the final computation. The model could be made to agree with the measurements by adjusting the surficial layer thickness.

A porous medium model for mud.

The extended Biot model for sands and silts is repurposed to include mud, but modifications are needed. The boundary between pore water and skeletal frame needs to be redefined because a significant fraction of the pore fluid is adsorbed onto the solid frame by electrostatic forces, and a proportion of the solid particles may be suspended in the pore fluid. Revil's relationships are used to simplify the input parameters. The frame elasticity equations are corrected to accommodate the sparse skeletal frame, which is supported by electrostatic forces, and behaves differently to a mechanical packing of grains. The corrected, Revil, extended Biot model has just four fitting parameters and is compared with published measurements of wave speeds and attenuations in the literature of clay, silty clay, and clayey silt sediments including recently published measurements from the Seabed Characterization Experiment. The results indicate that the skeletal frame in clay has a high water-content and the pore water contains suspended particles. To fit all the currently available data, it was necessary to modify corrected, Revil, extended Biot by flattening the creep related relaxation loss spectrum. There is a similarity with the Viscous Grain Shearing models in the use of a fractional exponent.

Connecting the grain-shearing, creep, and squirt flow models for wave propagation in the seabed.

The generalized creep and squirt flow models are shown to be stationary creep processes. A fractional exponent is used to develop a new generalized squirt flow model. The responses of the grain-shearing and generalized creep models are identical, although based on entirely different concepts: a single spring and time-varying damper versus a continuous distribution of parallel Maxwell elements. The random structure of marine sand is more consistent with the latter, implying absence of strain-hardening. The generalized squirt flow model has a high frequency cutoff suited to practical systems, limited by the speed with which underlying physical changes can occur.

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.

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.

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.

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.

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.

Normal incidence reflection loss from a sandy sediment.

Acoustic reflection loss at normal incidence from a sandy sediment, in the Biodola Gulf on the north side of the island of Elba, Italy, was measured in the frequency band 8-17 kHz, using a self-calibrating method. The water depth was approximately 11 m. The mean and standard deviation of the sand grain diameter were 2.25 (0.21 mm) and 0.6 phi, respectively. The reflection loss was measured using an acoustic intensity integral method, which is insensitive to roughness effects within the selected frequency band. The measured value of reflection loss was 11 dB, +/- 2 dB. The result is consistent with previous measurements in the published literature. The computed reflection loss for a flat interface between water and a uniform fluid or visco-elastic medium with the same properties is 8 dB, +/- 1 dB. The theoretical and experimental values do not significantly overlap, which leads to the conclusion that the visco-elastic model is inappropriate. The Biot model is suggested as a better alternative but more work is needed to ascertain the appropriate parameter values.