Kevin L. Williams

An effective density fluid model for acoustic propagation in sediments derived from Biot theory

In this paper we present an acoustic propagation model that approximates a porous medium as a fluid with a bulk modulus and effective density derived from Biot theory. Within the framework of Biot theory it is assumed here that the porous medium has low values of frame bulk and shear moduli relative to the other moduli of the medium and these low values are approximated as zero. This leads to an effective density fluid model. It is shown that, for saturated sand sediments, the dispersion, transmission, reflection, and in-water backscattering predicted with this effective density fluid model are in close agreement with the predictions of Biot theory. In this agreement we demonstrate that the frame bulk and shear moduli play only a minor role in determining several aspects of sand acoustics. Thus, for many applications the effective density fluid model is an accurate alternative to full Biot theory and is much simpler to implement.

An overview of SAX99: acoustic measurements

A high-frequency acoustic experiment was performed at a site 2 km from shore on the Florida Panhandle near Fort Walton Beach in water of 18-19 m depth. The goal of the experiment was, for high-frequency acoustic fields (mostly In the 10-300-kHz range), to quantify backscattering from the seafloor sediment, penetration into the sediment, and propagation within the sediment. In addition, spheres and other objects were used to gather data on acoustic detection of buried objects. The high-frequency acoustic interaction with the medium sand sediment was investigated at grazing angles both above and below the critical angle of about 30/spl deg/. Detailed characterizations of the upper seafloor physical properties were made to aid in quantifying the acoustic interaction with the seafloor. Biological processes within the seabed and the water column were also investigated with the goal of understanding their impact on acoustic properties. This paper summarizes the topics that motivated the experiment, outlines the scope of the measurements done, and presents preliminary acoustics results.

Tests of models for high-frequency seafloor backscatter

The interaction of high-frequency sound with the seafloor is inherently a stochastic process. Inversion techniques must, therefore employ good stochastic models for bottom acoustic scattering. An assortment of physical models for bottom backscattering strength is tested by comparison with scattering strength data obtained at 40 kHz at three shallow water sites spanning a range of sediment types from fine silt to coarse sand. These acoustic data are accompanied by sediment physical property data obtained by core sample analysis and in situ probes. In addition, stereo photography was used to measure the power spectrum of bottom relief on centimeter scales. These physical data provided the inputs needed to test the backscatter models, which treat scattering from both the rough sediment-water interface and the sediment volume. For the three sites considered here, the perturbation model for scattering from a slightly rough fluid seafloor performs well. Volume scattering is predicted to be weak except at a site having a layer of methane bubbles.

Bistatic bottom scattering: Model, experiments, and model/ data comparison

A model is presented for bistatic scattering from ocean sediments. It treats scattering due to both roughness of the seabed and volume inhomogeneities within the sediment. Accordingly, the scattered intensity is assumed to be a sum of two terms, one proportional to the roughness-scattering cross section and the other proportional to the volume-scattering cross section. The model is tested against data acquired as part of the Coastal Benthic Boundary Layer (CBBL) research program. As part of that program, an autonomous, circularly scanning sonar system was deployed in well-characterized regions. This sonar operated at 40 kHz, had a 5° horizontal beam, and acquired backscattering data over a 50-m radius. During part of the deployment, it operated in conjunction with a mobile receiving array so as to acquire bistatic data. The experimental apparatus and procedures are presented, and results are compared with model predictions.

Characterization of interface roughness of rippled sand off Fort Walton Beach, Florida

As part of the environmental characterization to model acoustic bottom scattering during the high-frequency sediment acoustics experiment (SAX99), fine-scale sediment roughness of a medium sand was successfully measured within a 600 /spl times/ 600-m area by two methods: stereo photography and a technique using a conductivity system. Areal coverage of the two methods, representing approximately 0.16 m/sup 2/ of the sea floor, was comparable, resulting in the depiction and quantification of half-meter wavelength sand ripples. Photogrammetric results were restricted to profiles digitized at 1-mm intervals; sediment conductivity results generated gridded micro-bathymetric measurements with 1- to 2-cm node spacing. Roughness power spectra give similar results in the low-spatial-frequency domains where the spectra estimated from both approaches overlap. However, spectra derived from higher resolution photogrammetric results appear to exhibit a multiple-power-law fit. Roughness measurements also indicate that spectrum changes as a function of time. Application of statistical confidence bounds on the power spectra indicates that roughness measurements separated by only 1-2 m may be spatially nonstationary.

Acoustic scattering from a solid aluminum cylinder in contact with a sand sediment: Measurements, modeling, and interpretation

Understanding acoustic scattering from objects placed on the interface between two media requires incorporation of scattering off the interface. Here, this class of problems is studied in the particular context of a 61 cm long, 30.5 cm diameter solid aluminum cylinder placed on a flattened sand interface. Experimental results are presented for the monostatic scattering from this cylinder for azimuthal scattering angles from 0 degrees to 90 degrees and frequencies from 1 to 30 kHz. In addition, synthetic aperture sonar (SAS) processing is carried out. Next, details seen within these experimental results are explained using insight derived from physical acoustics. Subsequently, target strength results are compared to finite-element (FE) calculations. The simplest calculation assumes that the source and receiver are at infinity and uses the FE result for the cylinder in free space along with image cylinders for approximating the target/interface interaction. Then the effect of finite geometries and inclusion of a more complete Greens function for the target/interface interaction is examined. These first two calculations use the axial symmetry of the cylinder in carrying out the analysis. Finally, the results from a three dimensional FE analysis are presented and compared to both the experiment and the axially symmetric calculations.

High-frequency subcritical acoustic penetration into a sandy sediment

During the sediment acoustics experiment, SAX99, a hydrophone array was deployed in sandy sediment near Fort Walton Beach, Florida, in a water depth of 18 m. Acoustic methods were used to determine array element positions with an accuracy of about 0.5 cm, permitting coherent beamforming at frequencies in the range 11-50 kHz. Comparing data and simulations, it has been concluded that the primary cause of subcritical acoustic penetration was diffraction by sand ripples that were dominant at this site. These ripples had a wavelength of approximately 50 cm and RMS relief of about 1 cm. The level and angular dependence of the sound field in the sediment agree within experimental uncertainties with predictions made using small-roughness perturbation theory.

Backscattering from an elastic sphere: Sommerfeld–Watson transformation and experimental confirmation

The Sommerfeld–Watson transformation (SWT) of the partial wave series for the acoustical scattering from a fluid‐loaded elastic sphere is examined. This research specifically focuses on the specular reflection and Rayleigh wave contribution to scattering at small backscattering angles. In a previous paper the angular dependence of the Rayleigh contribution to near backward scattering was measured and modeled [Williams and Marston, J. Acoust. Soc. Am. 78, 722–728 (1985)]. The SWT confirms the physical picture used and, for the first time, predicts the absolute Rayleigh contribution associated with one or more circumnavigations of the sphere. To test the SWT, tungsten carbide spheres in water were ensonified by tone bursts having central frequencies in the range 24<ka<80. Measurements were made of the first and second Rayleigh contributions to the backscattered pulse train. Plots of these measured distinct Rayleigh amplitudes as a function of ka confirm the results of the SWT and illustrate the significance...

Sound speed and attenuation measurements in unconsolidated glass-bead sediments saturated with viscous pore fluids

As part of a recent ocean sediment acoustics experiment, a number of independent sound speed and attenuation measurements were made in a well-characterized sandy sediment. These measurements covered a broad frequency range and were used to test both Biot-Stoll theory and Buckingham’s more recent grain-to-grain shearing model. While Biot theory was able to model the sound speed well, it was unable to predict the attenuation measured above 50kHz. This paper presents a series of measurements made in the laboratory on a simple glass-bead sediment. One goal of these measurements was to test the hypothesis that the attenuation measured at-sea was a result of scattering from shells within the sediment. The laboratory sediments used were saturated with fluids with different viscosities in order (assuming that Biot-Stoll theory is correct) to shift the dispersion into the frequency range of the measurement system. The measured attenuation in the glass-bead sediments exhibited the same frequency dependence as obser...

Fine-scale volume heterogeneity measurements in sand

As part of the effort to characterize the acoustic environment during the high frequency sediment acoustics experiment (SAX99), fine-scale variability of sediment density was measured by an in situ technique and by core analysis. The in situ measurement was accomplished by a newly developed instrument that measures sediment conductivity. The conductivity measurements were conducted on a three-dimensional (3-D) grid, hence providing a set of data suited for assessing sediment spatial variability. A 3-D sediment porosity matrix is obtained from the conductivity data through an empirical relationship (Archies Law). From the porosity matrix, sediment bulk density is estimated from known average grain density. A number of cores were taken at the SAX99 site, and density variations were measured using laboratory techniques. The power spectra were estimated from both techniques and were found to be appropriately fit by a power-law. The exponents of the horizontal one-dimensional (1-D) power-law spectra have a depth-dependence and range from 1.72 to 2.41. The vertical 1-D spectra have the same form, but with an exponent of 2.2. It was found that most of the density variability is within the top 5 mm of the sediment, which suggests that sediment volume variability will not have major impact on acoustic scattering when the sound frequency is below 100 kHz. At higher frequencies, however, sediment volume variability is likely to play an important role in sound scattering.