In this paper, a model for the bistatic reverberation associated with seafloor scattering of sound from a moving, narrowband source in an ocean waveguide is developed. Studies of the Doppler effect for moving sources in waveguides have typically focused on the forward propagating field where the Doppler shift leads to a splitting or broadening of the received spectrum. In contrast, the contributions to the scattered field come from all directions and as a consequence the spectrum of the received energy is spread across the entire range of Doppler-shifted frequencies possible for the speed of the source. The model developed here uses rays for the incident field, ray-mode analogies for the scattering, and normal modes to propagate the scattered field to the receiver. Results from this model are compared with data collected using a towed source during the Target and Reverberation Experiment 2013. The possible applications of this Doppler reverberation for seafloor characterization are also considered.

The primary goal of the Target and Reverberation Experiment in spring 2013 (TREX13) was to identify the major physical mechanisms responsible for midfrequency reverberation. While both the sea surface and seafloor can contribute to reverberation, the seafloor is typically dominant in shallow water environments. To determine the level of this contribution at the TREX13 site, the bottom backscatter sonar (BBS) was deployed from a dive boat at multiple locations around the site. The BBS consists of a source and a receiver mounted on a short bracket that is suspended above the seafloor to measure direct-path bottom backscatter at 3 kHz. Data near normal incidence were interpreted as bottom reflectivity, which was used to quantitatively explain the range-dependence of the sediment composition at the experiment site. Two factors restricted the estimates of the bottom backscatter strength to the minimum grazing angle of 21°: the currents at the experiment site made it difficult to position the system close to the seafloor, and the shallow water depth resulted in sea surface scatter contaminating small angle bottom backscatter. From the measured backscatter strength and by utilizing available environmental data, initial models of scattering strength indicate that at the shallow grazing angles of importance to reverberation, the scattering on the sand ridges is dominated by roughness scattering while in the muddy areas of the ridge swales, volume scattering dominates. The volume scattering from these mud areas is significantly stronger than the roughness scattering on the ridges by as much as 10 dB and may explain the substantial fluctuations observed in the reverberation as a function of range.

The Target and Reverberation EXperiment 2013 (TREX13) included a comprehensive reverberation field project in the frequency band of 2–10 kHz, and was carried out off the coast of Panama City, FL, USA, from April 21 to May 17, 2013. A spatially fixed transmit and receive acoustic system was used to measure reverberation over time under diverse environmental conditions, allowing study of reverberation level (RL) dependence on bottom composition, sea surface conditions, and water column properties. Extensive in situ measurements, including a multibeam bathymetric survey, chirp sonar subbottom profiling, gravity/diver cores, sediment sound speed and attenuation, interface roughness, wind-generated sea surface waves, and water column properties, were made to support studies of environmental effects on RL. Beamformed RL data are categorized to facilitate studies emphasizing physical mechanisms of 1) bottom reverberation; 2) sea surface impact; and 3) biological impact. This paper is an overview of RL over the entire sea trial, intending to summarize major observations and provide both a road map and suitable data sets for follow-up efforts on model/data comparisons. Emphasis is placed on the dependence of RL on local geoacoustic properties and sea surface conditions.

Bottom scattering is important for a number of underwater applications: it is a source of noise in target detection and a source of information for sediment classification and geoacoustic inversion. While current models can predict the effective interface scattering strength for layered sediments, these models cannot directly compute the ensemble averaged mean-square pressure. A model for bottom scattering due to a point source is introduced which provides a full-wave solution for mean-square scattered pressure as a function of time under first-order perturbation theory. Examples of backscatter time series from various types of seafloors will be shown, and the advantages and limitations of this model will be discussed.

A seafloor laser scanner was deployed in the Gulf of Mexico during the 2013 Target and Reverberation Experiment (TREX13). This system collected digital elevation maps at 14 locations along the main reverberation track, and these measurements provide roughness power spectra for modeling seafloor acoustic scattering. The spectra were divided into two regimes according to the mid and high-frequency acoustic measurements made during the experiment. For the wave numbers corresponding to the midfrequency regime (2–4 kHz), the spectra could be approximated using the mean spectral exponent derived from the all of the spectra. With this spectral exponent, the best fit spectral strengths were found to be negatively correlated to the backscatter levels measured at 400 kHz using a multibeam echosounder (MBES). While the scattering mechanisms at 400 kHz are not influenced by the roughness at these low wave numbers, this correlation may be indirectly related to the bioturbation and the spatial variation of the shell content. A more pronounced correlation was found for the high wave numbers, where again a single spectral exponent could be used to a good approximation. In this case, the spectral strengths were also linearly related to the MBES backscattering level but with a positive correlation. For these wave numbers, the roughness is largely influenced by the shell content, which is also the dominant scattering mechanism at 400 kHz. The correlations between the roughness and the MBES measurements provide a means to approximate the seafloor roughness parameters in both wave number regimes throughout the experiment site. For the low wave number spectrum, an alternative approach is also proposed, which uses the spectral parameters for the mean spectrum to approximate the roughness throughout the TREX13 site.

Ripples on the seafloor affect acoustic scattering and transmission loss, wave attenuation, and the amount of sediment transported in shallow water. Historically, seafloor roughness (a function of ripples, bedforms, sediment type, and size) is assumed to be spatially homogeneous and temporally static in hydrodynamic and acoustic models despite the often dynamic nature of the seafloor in the nearshore region. We present a spectral ripple model, Navy Seafloor Evolution Archetype (NSEA), which simulates the variations in seafloor roughness given measured or predicted wave conditions in sandy environments. NSEA simulates sand ripple formation and evolution based on bottom velocities either measured or predicted by a wave model. The time dependency is a function of equilibrium ripple geometries and the amount of sediment transport needed to reach an equilibrium state, which is dependent on the relict ripples. Spectral decay due to bioturbation is incorporated as a diffusive process. NSEA was validated with time series observations obtained in water depths of 7.5 and 20 m from April 20, 2013 to May 23, 2013 during the 2013 Target and Reverberation Experiment (TREX13) offshore of Panama City, FL, USA. The model predicted spectral ripple wavelengths that were in good agreement with observed spectral ripple wavelengths obtained using a fixed platform, high-frequency (2.25 MHz) sector scanning sonar. Likewise, the variations in the predicted normalized ripple heights and orientations were similar to the normalized spectral decay and orientations estimated from the sector scanning sonar imagery.

In this paper, a method for performing underwater acoustic navigation using a spiral wave-front beacon is examined. A transducer designed to emit a signal whose phase changes by 360°in one revolution can be used in conjunction with a reference signal to determine the aspect of a remote receiver relative to the beacon. Experiments are conducted comparing spiral wave-front beacon navigation to Global Positioning System (GPS) onboard an unmanned surface vehicle. The advantages and disadvantages of several outgoing signals and processing techniques are compared. The most successful technique involves the use of a phased array projector utilizing a broadband signal. Aspect is determined by using a weighted mean over frequencies. Sources of error for each of the techniques are also examined.

A screw dislocation in a wavefront is characterized by a phase dependence about the dislocation axis that varies as exp(–i m φ), where m is an integer and φ is the angle about the axis. This talk discusses two sources which generate an acoustic field with a screw dislocation but for very different applications. The first is the helicoidal wave transducer which generates a beam with a screw dislocation along its axis [Hefner and Marston, J. Acoust. Soc. Am. 106, 3313 (1999)]. At the axis, the phase is indeterminate and as a result there is a corresponding null in the pressure magnitude. The screw dislocation is found to exist in both the far- and near-fields of the transducer. This null then clearly indicates the axis of the beam at all distances and has the potential to be used as an aid in the alignment of objects in sonar experiments or other similar applications. This beam is also shown to carry angular momentum. The second source utlizes a screw dislocation but far from the null axis. It generates a wavefront in the x-y plane that has a phase which is proportional to the azimuthal angle about the source (m = 1). This transducer is combined with an omnidirectional, reference source to produce a spiral wavefront beacon. The phase difference between these sources contains information about a distant receiver's azimuthal angle relative to the beacon and can be used for underwater navigation [Hefner and Dzikowicz, J. Acoust. Soc. Am. 129, 3630 (2011)]. Navigation using this beacon has been demonstrated experimentally and propagation models have been developed to assess the performance of the beacon for the general case of propagation in a horizontally stratified waveguide [Hefner and Dzikowicz, J. Acoust. Soc. Am. 131, 1978 (2012)]. This talk discusses both of these unique sources and their applications as well as the underlying physics which connects them.

In the spring of 2013, a shallow water reverberation experiment was conducted to measure contemporaneous acoustic and sufficient environmental data so detailed model/data comparisons could be achieved and important environmental factors could be identified for different applications. The Target and Reverberation Experiment (TREX13) was sponsored by the US Office of Naval Research and the Strategic Environmental Research and Development Program. It was conducted from April to June of 2013 off the coast of Panama City Beach, Florida, in collaboration with multiple institutions and involving three research vessels: The R/V Sharp, R/V Walton Smith, and the Canadian Force Auxiliary Vessel Quest. From a SONAR viewpoint, reverberation consists of two-way propagation and a single backscatter. Therefore, reverberation, transmission loss, and bottom backscatter were repeatedly measured over a time period of several weeks in the frequency band of 2-10 kHz, along with extensive environmental measurements. To reduce the area over which environmental measurements were needed, the reverberation was measured using a horizontal line array mounted 1 m above the seafloor in 19 m of water. The reverberation, transmission loss, and bottom backscatter were measured along a single beam of the array out to a distance of 7 km. Discussed will be planning and execution of the field experiments, strategies and steps for data analysis, and modeling efforts.

In the Spring of 2012, high-frequency backscattering from a sandy sediment was measured in the Gulf of Mexico at the site of the upcoming, ONR-sponsored reverberation experiment. The measurements were made using an array of sources and receivers that collected data from 200 to 500 kHz and that could be rotated such that the incident grazing angles varied from 10 to 50 degrees. This array was used previously to measure scattering from a sand/mud sediment during the Sediment Acoustics Experiment 2004 (SAX04). To support data/model comparisons, the seabed roughness, sediment shell content, sediment sound speed, and sediment attenuation were also measured. For scattering below the critical grazing angle, sediment roughness is found to be the dominant scattering mechanism while above the critical angle, roughness scattering underpredicts the measured scattering strength. To understand the scattering strength at high grazing angles, scattering from shells and shell hash is considered. The measured scattering strengths and environmental properties at the experiment site are also compared to those made during SAX04.

n the time period from 1981 to 2011 understanding of the acoustic behavior of sand matured via the combination of experiments, modeling and data/model comparisons. At the core of the issues addressed is the question of whether the sand is best described as a viscoelastic solid or a porous medium. Progress in answering this question has involved examining transmissioninto/ propagation-within/scattering-from sand. A perspective is presented that is based on the premise that results of experiments examining transmission/propagation/scattering must be explained in terms of one unified physical model of sand. The 30 year time span will be divided into three periods: 1981-1997, 1997-2004, and 2004-2011. Experiments, modeling and data/model comparisons from each of these periods will be used to arrive at a perspective on the acoustic behavior of sand.

Transducers for acoustic beacons which can produce outgoing signals with wave fronts whose horizontal cross sections are circular or spiral are studied experimentally. A remote hydrophone is used to determine its aspect relative to the transducers by comparing the phase of the circular signal to the phase of the spiral signal. The transducers for a %u201Cphysical-spiral%u201D beacon are made by forming a strip of 1%u20133 piezocomposite transducer material around either a circular or spiral backing. A %u201Cphased-spiral%u201D beacon is made from an array of transducer elements which can be driven either in phase or staggered out of phase so as to produce signals with either a circular or spiral wave front. Measurements are made to study outgoing signals and their usefulness in determining aspect angle. Vertical beam width is also examined and phase corrections applied when the hydrophone is out of the horizontal plane of the beacon. While numerical simulations indicate that the discontinuity in the physical-spiral beacon introduces errors into the measured phase, damping observed at the ends of the piezocomposite material is a more significant source of error. This damping is also reflected in laser Doppler vibrometer measurements of the transducer%u2019s surface velocity.

Downward looking sonar, such as the chirp sonar, is widely used as a sediment survey tool in shallow water environments. Inversion of geo-acoustic parameters from such sonar data precedes the availability of forward models. An exact numerical model is developed to initiate the simulation of the acoustic field produced by such a sonar in the presence of multiple rough interfaces. The sediment layers are assumed to be fluid layers with non-intercepting rough interfaces.

A spiral wave front source generates a pressure field that has a phase that depends linearly on the azimuthal angle at which it is measured. This differs from a point source that has a phase that is constant with direction. The spiral wave front source has been developed for use in navigation; however, very little work has been done to model this source in an ocean environment. To this end, the spiral wave front analogue of the acoustic point source is developed and is shown to be related to the point source through a simple transformation. This makes it possible to transform the point source solution in a particular ocean environment into the solution for a spiral source in the same environment. Applications of this transformation are presented for a spiral source near the ocean surface and seafloor as well as for the more general case of propagation in a horizontally stratified waveguide.

A spiral wave front source produces an acoustic field that has a phase that is proportional to the azimuthal angle about the source. The concept of a spiral wave front beacon is developed by combining this source with a reference source that has a phase that is constant with the angle. The phase difference between these sources contains information about the receiver's azimuthal angle relative to the beacon and can be used for underwater navigation. To produce the spiral wave front, two sources are considered: a "physical-spiral" source, which produces the appropriate phase by physically deforming the active element of the source into a spiral, and a "phased-spiral" source, which uses an array of active elements, each driven with the appropriate phase, to produce the spiral wave front. Using finite element techniques, the fields produced by these sources are examined in the context of the spiral wave front beacon, and the advantages of each source are discussed.

During the Sediment Acoustics Experiment in 1999 (SAX99), measurements were made of the sound speed and attenuation in a sandy sediment, supplemented by detailed environmental characterization. While the dispersion was consistent with Biot theory, the attenuation at high frequencies had a linear frequency dependence that was consistent with models based on losses at grain contacts. These results led to the development of a number of competing models of sound propagation in sand sediments. Subsequent to SAX99, measurements of sound speed and attenuation have been made in several ocean sediments as well as in a number of laboratory sediments composed of either sand or glass beads. Many of these experiments have been accompanied by careful measurements of the sediment properties and, in some cases, these properties have been varied to assess their impact on sound propagation. An overview of these results will be given and the implications of these measurements for high frequency sediment acoustics modeling will be discussed.

At frequencies of about 1 kHz and higher, forward scattering from a rough sea surface (and/or a rough bottom) can strongly affect shallow water propagation and reverberation. The need exists for a fast, yet accurate method for modeling such propagation where multiple forward scattering occurs. A transport theory method based on mode coupling is described that yields the first and second moments of the field. This approach shows promise for accurately treating multiple forward scattering in one-way propagation. The method is presently formulated in two space dimensions, and Monte–Carlo rough surface PE simulations are used for assessing the accuracy of transport theory results.

While Biot theory can successfully account for the dispersion observed in sand sediments, the attenuation at high frequencies has been observed to increase more rapidly than Biot theory would predict. In an effort to account for this additional loss, perturbation theory is applied to Biot's poroelastic equations to model the loss due to the scattering of energy from heterogeneities in the sediment. A general theory for propagation loss is developed and applied to a medium with a randomly varying frame bulk modulus. The theory predicts that these heterogeneities produce an overall softening of the medium as well as scattering of energy from the mean fast compressional wave into incoherent fast and slow compressional waves. This theory is applied to two poroelastic media: a weakly consolidated sand sediment and a consolidated sintered glass bead pack. The random variations in the frame modulus do not have significant effects on the propagation through the sand sediment but do play an important role in the propagation through the consolidated medium.

During the recent 2004 sediment acoustics experiment (SAX04), a buried hydrophone array was deployed in a sandy sediment near Fort Walton Beach, FL. The array was used to measure both the acoustic penetration into the sediment and sound speed and attenuation within the sediment while a smaller, diver-deployed array was also used to measure sound speed and attenuation. Both of these systems had been deployed previously during the 1999 Sediment Acoustics Experiment (SAX99). In that experiment, the buried array was used to make measurements in the 11-50-kHz range while the diver-deployed array made measurements in the 80-260-kHz range. For the SAX04 deployment, the frequency range for the measurements using the buried array was lowered to 2 kHz. The diver-deployed array was also modified to cover the 40-260-kHz range.

Unlike the SAX99 deployment, there were no obvious sand ripples at the SAX04 buried array site at the time of the measurements. To examine the role of sand ripples in acoustic penetration over this new frequency range, artificial ripple fields were created. For the high frequencies, the penetration was consistent with the model predictions using small-roughness perturbation theory as in SAX99. As the frequency of the incident acoustic field decreased, the evanescent field became the dominant penetration mechanism. The sound speed measured using the buried array exhibits dispersion consistent with the Biot theory while the measured attenuation exceeds the theory predictions at frequencies above 200 kHz.

Sandy sediment ripples impact sonar performance in coastal waters through Bragg scattering. Observations from data suggest that sandy ripple elevation relative to the mean seafloor as a function of the horizontal coordinates is not Gaussian distributed; specifically, peak amplitude fading over space associated with a random Gaussian process is largely absent. Such a non-Gaussian nature has implications for modeling acoustic scattering from, and penetration into, sediments. An algorithm is developed to generate ripple fields with a given power spectrum; these fields have non-Gaussian statistics and are visually consistent with data. Higher order statistics of these ripple fields and their implications to sonar detection are discussed.

Acoustic backscattering from a diver-smoothed sand sediment was measured at frequencies from 200 to 500 kHz as a function of grazing angle. The residual roughness of this smoothed surface was measured using a laser line scanning system capable of measuring sub-millimeter heights over a 4-meter track. Using the measured sediment roughness, perturbation theory underestimates the scattering strength at all frequencies for angles greater than the critical grazing angle. The absence of large, discrete scatterers in the sediment suggests that scattering from fluctuations in the sediment properties may be the dominant scattering mechanism for these angles. The sound speed and attenuation were also measured in this sediment and the attenuation was found to exhibit a linear frequency dependence similar to that observed for other sand sediments.

To account for this linear attenuation, a theory that incorporated scattering losses due to porosity fluctuations into the effective density fluid model has been developed. This theory suggests that the propagation losses may be connected by the same physical mechanism to the scattering of sound from the sediment. This connection is explored in the context of these scattering and propagation measurements.

The topography of the seabed is influenced by sediment transport due to wave motion, current disturbance, and biological activities. The bottom roughness generated by these processes can substantially alter acoustic wave penetration into and scattering from the bottom, and therefore, it is essential to make accurate measurements of the bottom roughness for such acoustic applications. Methods to make direct measurements of bottom roughness include stereo photography, laser line scanning, and sediment conductivity. Roughness can also be measured indirectly using high-frequency sound backscatter. For optically-based methods, the accuracy of these measurements is typically evaluated using the elevations, lengths, or diameters of simple surface features of known dimensions. However, for acoustic applications, the statistical characteristics of the surface, e.g., the roughness spectrum, are more meaningful.

In this paper, we present a fabricated rough surface milled into a 40 times 60 cm² plastic block for use as a benchmark in the assessment of two in situ roughness measurement systems: a laser scanning system and a digital stereo photography system. The surface has a realistic roughness power spectrum that is derived from the bottom roughness measured during the 1999 Sediment Acoustics Experiment (SAX99) and was fabricated by a computer numerical controlled milling machine. By comparing the fabricated surface spectrum to the measured spectrum, a determination of the accuracy of the roughness measurement is evaluated, which is of direct relevance to acoustic applications.

Sand sediments are inherently heterogeneous due to the random packing of the grains. For sound propagation through fluid-saturated sediments, these heterogeneities may lead to scattering from the coherent fast compressional wave into incoherent slow compressional waves or shear waves. This loss of energy from the fast compressional wave may account for the increase in high-frequency attenuation above that predicted by Biot theory.

In a previous talk, we presented preliminary results of applying perturbation theory to Biot theory in order to model scattering from heterogeneities in the porosity [Hefner et al., J. Acoust. Soc. Am. 120, 3098 (2006)]. This theory has since been refined to properly account for scattering into both the slow compressional wave and the shear wave. In order to apply this theory to a given sand sediment, knowledge of the covariance function for the spatial variations in the porosity is required. Results of the theory will be presented for several different analytic covariance functions, as well as for covariance functions measured in simulated and real unconsolidated granular materials.

The comparison of sediment sound speed and attenuation measurements to predictions has been the primary method used to test Biot theory and the grain-shearing model. Examples of data–model comparisons will be shown. Subsequent refinements made to these models result in similar predictions for sound speed and attenuation. However, the underlying physics is substantially different suggesting other, more indirect means for discriminating between sediment propagation theories. One technique that has received recent attention is the measurement of forward scattering from the sediment interface. Model predictions of these measurements depend not only the sound speed and attenuation, but also on the acoustic impedance of the medium. Examination of the physics incorporated into Biot Theory shows that the "effective density" seen by the acoustic wave is lower than the bulk density, thus lowering the acoustic impedance. This results in a difference in the predicted flat surface reflection coefficient for Bio-type models as compared to grain-shearing models. The flat surface reflection coefficients derived from experiment will be compared with predictions using the Biot model and the viscosity grain shearing (VGS) model for a sand sediment. The validity of obtaining reflection coefficients using forward scattering from rough surfaces will also be discussed.

Previously, we presented the results of applying perturbation theory to the problem of fast compressional wave propagation through a Biot medium with heterogeneities in the frame bulk modulus [B. T. Hefner et al., J. Acoust. Soc. Am. 119, 3447 (2006)]. It was found that the heterogeneities scattered energy into both the slow and fast compressional waves, thus increasing the attenuation of the fast compressional wave. This theory has since been generalized to account for heterogeneities in both the frame bulk and shear moduli. For the fast compressional wave, energy is now scattered into the shear wave as well as the fast and slow compressional waves, further increasing the attenuation of the coherent field. While shear wave propagation is unaffected by variations in the frame bulk modulus, scattering does occur when there are heterogeneities in the shear modulus. Energy in the shear wave is scattered into both shear and compressional waves as well. The generalized theory depends on the autocorrelation functions of both the shear and bulk moduli variations as well as the cross-correlation function between the moduli. Efforts are underway to estimate these statistics in simple random packings of spherical grains using discrete-element modeling.

Knowing the temporal change of the seabed, we can understand the nature of the undersea environment in more details. The scale of the features on the seabed varies from meters for large sandwaves, and down to less than one millimeter for the prints left by marine creatures. So far, there is not a single instrument that can cover the whole range and still preserve the resolution. For measuring small-scale roughness of seabed, laser scanning is an alternative. In this work, we report the integration of Seabed Laser Scanner (SLS), developed by Institute of Undersea Technology, Sun Yat-sen University, on the linear stage of In Situ Measurement of Porosity 2 (IMP2), developed by Applied Physics Laboratory, University of Washington to carry out deep sea sediment 2D roughness measurement and comparison. IMP2 consists of a 4 meter long scaffold and a linear stage. SLS is mounted on the linear stage to carry out the scanning. To simplify the integration and avoid the possible failure coming from the additional underwater connections, SLS is designed to be a self-contained system. It runs on a PC104 with Windows XP and feeds on its own battery pack. The only interaction between the two systems is achieved by the proximity of a set of magnets and a relay. As the linear stage starts, the first magnet triggers SLS to power up and standby. As the stage comes to the end of the rack, the second magnet triggers the image acquisition. The integrated system was deployed three times during the Shallow Acoustics Experiment 2006, about eighty miles off the coast of New Jersey. We successfully retrieved data from SLS for the first two trials; the third trial failed due to the aborted mission of IMP2. A 300 cm times 30 cm and a 350 cm times 25 cm seafloor were mapped at 80-meter water depth. From the reconstructed 3D surfaces, we found that the seafloor is full of shell debris and covered by mud-like sediment. The 2D spectra were estimated from the 3D surface. The results indicated that the seafloor roughness follows a power-law spectrum and isotropic. These spectra estimated provide the boundary condition for modeling the acoustic propagation and scattering.

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 50 kHz. 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 observed in the ocean experiment even though no shells were present. The laboratory results motivated development of a sediment model which incorporates both fluid viscosity and grain-to-grain interactions as embodied in a simple frequency-dependent, imaginary frame modulus first suggested by Biot.

Efforts to model sound speed and attenuation in sandy sediments have centered on the use of theories for which either the relative motion of the pore fluid is the dominant attenuation mechanism, such as Biot theory, or the dominant loss mechanism is grain-to-grain friction. A recent model which attempts to incorporate grain-to-grain loss mechanisms into a model of sandy sediments was proposed by Buckingham. This model can fit the frequency dependence of the attenuation measured in ocean sediments and laboratory glass bead sediments, but it does not capture the sound speed dispersion as effectively as Biot theory. The relative success of each model suggests that both attenuation mechanisms may play important roles in sediment acoustics. In order to explore this possibility, a hybrid model has been developed which incorporates Buckingham's grain-to-grain shearing mechanisms into the frame moduli used in Biot theory. In the hybrid model, the grain-to-grain losses dominate at high and very low frequencies while pore fluid attenuation dominates at mid-frequencies where the sound speed dispersion is the most pronounced. As a consequence, the hybrid model is able to describe both the measured sound speed and attenuation in ocean and laboratory sediments.