Low- to mid-frequency model of attenuation and dispersion.

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. [Work supported by ONR.]

Marine sediments exist universally as the lower boundary for sound propagation in ocean waveguides, and knowledge of the properties of these sediments is important for accurate modeling of sound propagation and reverberation. In order to test theory predictions of the frequency dependence of sound speed and attenuation, it is necessary to have accurate information on the sediment properties, which is most easily done in a laboratory environment. Initial results reported here were done at high frequency in a small tank, as a preliminary step before making similar low frequency measurements in a much larger tank. A sandy sediment was used and the sound speed and attenuation were measured through different thicknesses of the sample. In the frequency range of 90–170 kHz, the measured sound speed was 1757–1767 m/s, and the attenuation was 22–30 dB/m. The sound speed dispersion was found to be very weak, as expected, and much smaller than the measurement uncertainty. The attenuation was found to increase approximately linearly with frequency. The measured sound speed agrees well with Biot theory predictions, while the measured attenuation is higher than Biot predictions, most likely because the measurement include effects such as volume scattering not taken into account in the theory.

During the Sediment Acoustics Experiment in 1999 (SAX99), the in Situ Sediment geoAcoustic Measurement System (ISSAMS), transmitting tone bursts containing an integer number of cycles, was used to measure the speed and attenuation of compressional waves in a weakly dispersive, medium-sand sediment in the Gulf of Mexico. ISSAMS was deployed at seven stations and operated mostly at a frequency of 38 kHz, but at two of the sites, a succession of pulses was transmitted with frequencies extending from 25 to 100 kHz, in 5-kHz increments, yielding the phase speed, the group speed and the attenuation as a function of frequency. An analysis of a tone-burst transmission in a dispersive medium illustrates that several subtle factors, including the narrow bandwidth of the source, along with dispersion and attenuation in the medium, have the potential for introducing significant errors into travel-time measurements. It is concluded that, in general, the timing is best performed between two receivers rather than between the source and a receiver, the difficulty in the latter case being that the output from a narrow-band source is not a replica of the input. A correlation applied to the arrivals at the two receivers yields the travel time, from which a good approximation to the group speed is immediately available. Alternatively, a Fourier decomposition yields the phase speed as a function of frequency, which would be an advantage in a highly dispersive medium. The two techniques return almost identical wave speeds when applied to the ISSAMS tone-burst data from the weakly dispersive SAX99 sediments: at 38 kHz, the mean wave speed from the six primary stations is 1778 m/s. Attenuation was also estimated from receiver-to-receiver travel paths, using three different techniques: the ratio of the mean-square values of the arrivals, the ratio of the Fourier magnitudes of the arrivals and transposition. All three methods yield similar results when applied to the SAX99 data, returning a mean attenuation from the six stations of 12 dB/m at 38 kHz, which is comparable with previously reported measurements of attenuation in marine sands. From the broadband measurements, between 25 and 100 kHz, the dispersion is found to be weak but detectable and the attenuation scales almost linearly with frequency, which corresponds to a nearly constant Q.

Section 1 Physical properties and laboratory measurements.- Shear waves in marine sediments-bridging the gap from theory to field applications (Opening paper).- Surface waves in poro-viscoelastic marine sediments.- An investigation of causality for Biot models by using Kramers-Kronig relations.- Soil properties for shear wave propagation (Invited).- The relevance of shear waves for structural subsurface investigations.- Experimental investigation of seismic surface waves in the seafloor.- Laboratory studies on pulsed leaky Rayleigh wave components in a water layer over a solid bottom.- Assessment of shear strength of the sea bottom from shear wave velocity measurements on box cores and in-situ.- Numerical modelling and laboratory experiments on underwater sound propagation over a shear supporting bottom.- A review of laboratory shear wave techniques and attenuation measurements with particular reference to the resonant column (Invited).- Relationship between acoustic and mechanical properties of two marine clays.- A laboratory method to investigate shear waves in a soft soil consolidating under self weight.- Laboratory measurements of acoustic properties of periplatform carbonate sediments.- Comparison of measured compressional and shear wave velocity values with predictions from Biot theory.- Wave velocities in sediments.- Shear wave attenuation in unconsolidated laboratory sediments.- Shear wave velocities of glacio-marine sediments: Barents Sea.- Rock acoustics: relevance of the porous viscoelastic model.- Influence of stress state and stress history on acoustic wave propagation in sedimentary rocks.- Section 2 Field experiments and interpretation.- A summary of DREA observations of interface waves at the seabed.- Observations of the relative contributions of waterborne and sediment paths to the received acoustic signal.- Shear-wave anisotropy in marine sediments around Britain from surface sources.- Refraction measurement of shear wave anisotropy in shallow marine sediments and implications for reflection processing.- Spatial variability in ground motion: effects of material heterogeneity in seafloor sediments.- Implications of deep-water seismometer array measurements for Scholte wave propagation.- Shear wave velocity structure from interface waves at two deep water sites in the Pacific ocean.- The effects of shear velocity structure on seafloor noise.- Concurrent observations of directional spectra of ocean surface waves and microseisms from an ocean subbottom seismometer (OSS) array.- Wave propagation in a borehole (Invited).- Application of shear wave measurements in boreholes.- Experience with the seismic cone penetrometer in offshore site Investigations.- Comparison of techniques for shear wave velocity and attenuation measurements.- Shear wave velocity gradients in near-surface marine sediment.- ISSAMS: an in situ sediment acoustic measurement system.- Small-scale in situ measurements of S-H velocity in surficial sedimentary deposits: localised textural and biological controls.- In situ measurements of shear-wave velocity in ocean sediments.- Seafloor shear wave velocity data acquisition: procedures and pitfalls.- Mapping of the sea bed via in situ shear wave (SH) velocities.- Observations of split shear-waves from young ocean crust.- Estimation of shear-wave speed in ocean-bottom sediments by comparing oblique-angle reflectivity measurements with normal incidence data.- SedimentQpfrom spectral ratios of converted shear reflections.- Constraints on shear velocities in deep-ocean sediments as determined from deep-tow multichannel seismic data.- Changes inPandSvelocities caused by subduction related sediment accretion off Washington/Oregon.- Compressional and shear wave velocities in the upper crust.- Sedimentary shear modulus and shear speed profiles from a gravity wave inversion.- Measurements of compressional wave and shear wave speeds, attenuation, permeability, and porosity in marine sediments.- Sea-bed shear moduli from measurements of tidally induced pore pressures.- Section 3 Modelling and inversion techniques.- Excess attenuation in low-frequency shallow-water acoustics: a shear wave effect? (Invited).- Sensitivity of bottom loss to attenuation and shear conversion.- The effect of shear wave attenuation on acoustic bottom loss resonance in marine sediments.- The influence of sediment rigidity on the plane-wave reflection coefficient.- Shear wave conversion due to subbottom facets.- A seismo-acoustic finite element model for underwater acoustic propagation.- Finite difference modelling of shear waves.- A stable higher-order elastic parabolic equation with application to Scholte wave propagation.- ELASTIC PE: a parabolic approximation for propagation modelling of shear wave effects in sediment layers.- Computation of shear waves by integral equations methods in stratified media.- Normal modes identification in shallow water using spectral analysis: theory and experiments.- Estimation of geoacoustic properties by inversion of acoustic field data (Invited).- A fast simulated annealing algorithm for the inversion of marine sediment seismo-acoustic parameters.- Determination of the sediment shear speed profiles from phase and group velocity dispersion data of SH wave.- Measurement of the elastic properties of the ocean bottom by inversion of reflection amplitude data.- Surface wave inversion for shear wave velocity (Invited).- Determination of shear velocity profiles by inversion of interface wave data.- Using synthetic seismograms to determine shear wave velocities in sediments from ocean bottom seismometer refraction observations.- Analytical investigation of seismic surface waves in the seafloor.- List of Participants.- Author Index.

The frequency dependence, or dispersion, of sound speed in marine sediments has been a topic of considerable interest and remains a research topic. While experiments on well-sorted sediments (having a narrow range of grain sizes) show promising concordance with theory, the more typical continental shelf sediments exhibit a rather wide range of grain sizes. A major experimental challenge is to measure in-situ sound speed over a sufficiently wide frequency range, such that the underlying mechanisms (e.g., viscous or friction) that control intrinsic dispersion can be isolated. Broadband 1.8-10 kHz seabed reflection measurements in the TREX13 experiment show a critical angle that is very nearly frequency independent. When effects of wavefront curvature, sound speed gradients, layering, and roughness are taken into account, this observation indicates that sediment sound speed must also be nearly independent of frequency. [Research supported by the ONR Ocean Acoustics Program.]

Extensive measurements of sound speed and attenuation have been performed on sandy sediments over the last few decades, which have motivated a variety of physical sediment acoustics models. Recently, the seabed characterization experiment (SBCEX) was performed in 2015–2017, in part, to quantify the geoacoustic properties of a clayey-silt accumulation, known as the New England Mud Patch (NEMP). Due to the variability and frequency range reported by the various direct measurements and geoacoustic inversions, the sound speed measured in the NEMP lacked any noticeable frequency dependence. In 2022, an additional coring cruise was completed in the NEMP area and included shipboard core and resonance logger (CARL) measurements, expanding upper limit of the band to 1 MHz. CARL measured sound speed and attenuation as a function of depth from 100 kHz to 1 MHz using a time-of-flight technique, and sound speed along the entire core length from 12 kHz to 16 kHz using a resonance technique. Positive dispersion and depth dependance was observed in the 200 kHz to 1 MHz band. The frequency and depth dependence of the CARL measurements will be presented and compared with previously published model fits to the 2015–2017 SBCEX dataset. [Work sponsored by ONR.]

Low-frequency acoustic data acquired in the central East China Sea basin at two locations are analyzed for the purpose of making inferences on seabed acoustics. Previous geophysical studies indicate that the first sediment layer is composed of a fine to medium sand. The current analysis employs octave-averaged transmission loss (TL) versus range data and pressure time series generated from explosive sources. The TL and time series data were collected in locations separated by about 65 km during the same month of the year. Both locations are near the same longitude, with water depths of 100-120 m. A linear frequency dependence of the attenuation in the 25-800 Hz band, with or without sound speed dispersion, leads to a geoacoustic solution using the TL data consistent with a soft clay, and thus inconsistent with the existing geophysical data. However, seabed representations that allow for a nonlinear frequency dependence of the attenuation, such as a Kramers-Kronig dispersion relationship, a simplified six-parameter Biot description, and an empirical frequency power law of the attenuation, all give similar values of the attenuation as a function of frequency and sediment sound speeds that are consistent with the previous geophysical studies in the area. Geoacoustic solutions obtained with the TL inversions produce reasonably good fits to the measured time series data. Inversions of the time series indicate that the sound speed at the top of the sediment is lower as compared to the values estimated from the location where the TL data were acquired. While the data have significant limitations as to the information they contain on the properties of the seabed, the analysis aids in quantifying the sensitivity of geoacoustic inversion of acoustic data in shallow water littoral regions to assumptions about the frequency dependence of attenuation and sound speed. © 2006 IEEE.

Measurements in sandy ocean sediments over a broad range of frequencies show that the sound speed dispersion is significantly greater than that predicted by the Biot‐Stoll model with constant coefficients, and the observed sound attenuation does not seem to follow a consistent power law. The observations may be explained in terms of the Biot‐Stoll model with frequency‐dependent complex frame bulk and shear moduli that are governed by the grain‐grain contact physics, and random motion at the grain level. In the case of water‐saturated sands, the contact stiffness is dominated by squirt flow and viscous drag of a thin fluid film that permeates the contact area. Using this approach, the observed sound and shear wave speeds and attenuations may be modeled over a broad band of frequencies.

The evaluation of many high-frequency bottom-interaction models requires as inputs sound speed and attenuation in marine sediment. A bottom probe system mounted on the underside of a cable-controlled underwater vehicle was used to make measurements at 15, 30, and 60 kHz, and at probe depth positions of 17, 42, and 67 cm. Sound-speed ratios are determined in-situ to 0.1% and attenuation to 0.2 dB/m. Measurements made in a 1 km by 1 km area of Puget Sound indicated small but significant spatial distributions of acoustic properties in a nominally uniform area. Attenuation coefficients were determined using the empirical relation K times frequency to the nth power. Exponent n was approximately 0.70. Past data in a Santa Barbara area indicated an n value of 1.19. These results indicate that for different sediments, exponent n is distributed about one with significant deviations. [Work supported by Naval Sea Systems Command.]

Using data from the Yellow Sea, arrival times of the direct wave and surface/bottom reflections from explosive sources to a vertical hydrophone array are used to precisely determine each explosive source’s location, the source energy spectral density (SESD), and the water depth. Long-range propagation waveforms reveal modal dispersion: the ground wave, water wave, Airy phase, etc. There are two high-frequency (HF) groups of water waves. One propagates with the sound speed in the water below the thermocline, the other with a speed close to the sound speed in the water above the thermocline. The HF group arrival times offer a time reference for dispersion analyses, including the ground wave speed at the cutoff frequency and the group velocity at Airy frequency. Associated with a top layer oflow-velocity sediments (LVS), seafloor reflections have two pulses: one from the water-sediment interface, one from the sediment-basement interface; Long-range transmission loss (TL) exhibits abnormal peaks at selected frequencies. Above-mentioned physics characteristics and the SESD-normalized TL(r) and TL(f) in 50–5000 Hz range up to 27.6 km are used for observationally driven inferences of seafloor geo-acoustic parameters, such as the sound velocity and attenuation in the LVS layer, its thickness, the sound velocity in the basement, etc.

Sharing the same experimental apparatus, two complementary techniques were developed to measure the frequency‐dependent speed of sound in marine sediments during the SAX04 sea‐trial. The first technique enabled direct time‐of‐flight measurements of acoustic wave speed along all three Cartesian axes. The second technique determined the acoustic wave speed based on the arrival angle of pulses generated in the water column and refracted upon entry into the seabed. None of the results could be modeled or explained when the seabed was parametrized as a sand half‐space. However, both techniques suggested the presence of a thin muddy layer, 0.05–0.2 m thick within the top 1 m of the sediment. For the time‐of‐flight technique, in the vertical direction, the interference from the layer created considerable apparent variability in sound speed measurements. In the horizontal direction, the layer caused the measured sound speeds to be lower than what a simplified poro‐elastic model would predict, unless one accounts ...

Sound speed criterion for two-phase critical flow

Echo sounding and acoustic propagation in the hadal zone (depths below 6 km) rely on models of sound speed that suffer from uncertainty due to a paucity of measurements at those depths. In order to assess models of sound speed in deep water, and to provide additional measurements, the Deep Acoustic Lander, a passive acoustic profiler, was deployed into the Mariana Trench from the RV Pressure Drop in April 2021. The Deep Acoustic Lander houses an array of hydrophones along with an AML Scientific CTD and AML MinosX sound speed meter. Pressure, temperature and salinity data measured by the CTD were used to inform some of the most commonly used sound speed models. The modeled sound speed was then compared with direct measurements of the speed of sound in the hadal zone to depths beyond 10 000 m. The goodness of fit between each model and the direct measurements was then compared to assess the performance of each model in deep water.

Cohesive or muddy sediments have received relatively sparse attention in the ocean acoustics community—this despite the fact that they form a non-negligible fraction of the sediments found in shallow water (roughly 25%) and by far the major sediment type in the deep ocean. Seabed reflection measurements have provided some understanding about the frequency dependence of the sound speed and attenuation in muddy sediments. The evidence is for weak dispersion from 300–200,000 Hz and an approximately linear dependence of attenuation on frequency from 300–3000 Hz. In addition, the measurements have yielded information on gradients. Surprisingly large near-surface density gradients exist that vary across the shelf. Given the large density gradients, the gradients in sound speed are curiously small, suggesting that the bulk modulus is nearly proportional to the density, at least in depth. Dispersion and gradient results are discussed for muddy sediments in various mid to outer shelf regions.

This paper presents a Moving long baseline (MLBL) positioning algorithm for the underwater target considering the uncertain underwater sound speed. First, the positioning and the sound speed models are established. To tackle the uncertain sound speed, a Uncertain least squares (ULS) positioning algorithm is applied to estimate the target position and the sound speed. Then it is essentially shown that four mobile buoys are necessarily (at least) required to locate the target. Further, it is found that under a singularity scenario in which the ranges between the target and each of the mobile buoys are equal, there is no solution to the positioning according to the classical geometrical equations. In order to solve this singularity problem, an ULS-based Unscented Kalman filter (UKF) algorithm is proposed to obtain the estimated solution. Simulation results illustrate the effectiveness of proposed methods.