Sediment Acoustics Research Articles

An explicit granular-mechanics approach to marine sediment acoustics.

Here, we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms, which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features.

Biogeoacoustic variability in muddy ocean bottom sediment

Both physical and biological benthic processes can influence seabed heterogeneity and contribute to spatiotemporal variability in geoacoustic properties. In particular, how biological processes affect both sediment acoustic properties and their variability is poorly understood. To address this deficiency, recent measurements investigated spatial variability in the upper few decimeters of sediment near the water-seabed interface within a fine-grained sediment deposit on the New England shelf. At each measurement location, acoustic probes were inserted into the sediment to collect direct in situ measurements of sediment sound speed and attenuation at near-ambient conditions, after which cores were collected from the inter-probe propagation paths for ex situ analysis of sediment physical, biological, and acoustic properties. Relationships among sediment properties, such as bulk density, porosity, grain size distribution, organic matter composition, infaunal community composition, and acoustic measurements spanning several frequency decades (10–1000 kHz) will be explored in this paper. Frequency dependence of sediment acoustic properties will also be discussed in the context of sediment acoustics models for mud based on the viscous grain shearing and extended Biot theories. [Sponsored by ONR.]

The crucial role of granular packing structure in marine sediment acoustics

Motivated by the acoustic properties of marine sediments, we study via discrete-element method simulations the frequency dependence of dispersion and attenuation in model marine sediments. By numerically solving for the motion of each grain in a packing, rather than solving a continuum wave equation, we find that the granular packing structure, which is not explicitly considered in existing sediment-acoustics models, plays a crucial role in determining how attenuation and wave speed vary with frequency. Prior work has typically postulated a wave equation that is motivated by grain- scale forces, including viscous effects from the interstitial fluid, without explicitly considering the disordered packing structure of the grains. However, the packing structure is known to produce complex, nonlinear behavior (e.g., during shear or quasistatic compression), and how it affects dispersion and attenuation is not known. We consider linearized forces between particles (i.e., springs and dashpots), and demonstrate that the disordered packing structure leads to emergent scaling laws that do not agree with PDE-based approaches. Our results demonstrate that the granular packing structure must be explicitly considered when constructing theories for the acoustic properties of marine sediments.

Physical properties and in situ geoacoustic properties of seafloor surface sediments in the East China Sea

Seafloor sediment acoustics is a burgeoning field of marine scientific research. In situ measurement technique is a key technique for investigating sediment acoustic properties. Establishing a correlation between in situ acoustic parameters and physical parameters is of great scientific significance for advancing the theory of seafloor acoustics. This study employed an in situ sediment acoustic measurement system to measure the sound speed and attenuation of various types of sediment, such as sand, silty sand, silty clay, and clayey silt. The results showed that in situ sound speed and attenuation were strongly curvilinear correlated with physical properties, such as wet bulk density, porosity, and mean grain size. Empirical regression relationships between in situ acoustic properties and physical properties were derived. These findings supplement the in situ measurement data of acoustic properties of seafloor sediments, compensate for the lack of an empirical relationship of in situ attenuation in previous studies, and broaden the predicting theory and method of the acoustic properties of seafloor sediments.

Unraveling the link between sediment acoustics and organic carbon

The top meter of marine sediments is estimated to store a total of 2322 Pg of carbon [Atwood et al., 2020. Front. Mar. Sci., vol. 7 p.165], which is twice that of terrestrial soils. Physical disturbance and remineralization of these carbon stocks could further accelerate climate change. Rapid and accurate quantification of sediment carbon stocks can (1) better inform carbon budgets and management of human activities in the ocean to minimize carbon remineralization and (2) monitor changes in sediment carbon stocks due to anthropogenic and natural disturbances. Sediment acoustics, which have been linked with sediment total organic carbon/content in mud banks, seagrass beds, and estuarine environments, can be measured in situ and offer a scalable solution toward rapid estimation of carbon stocks. However, before this modality can be applied broadly, a fundamental understanding between sediment acoustic properties and sediment organic/inorganic constituents must be realized. Here, direct ex situ measurements of sediment acoustic properties, sediment organic carbon, and grain size distribution will be compiled and compared across a variety of sediment types and locations from our own measurements and from published datasets. The development of a non-site-specific constitutive-based relationship will be discussed. [Work supported in part by ONR.]

Investigation of surficial sediment acoustic, physical, and biological properties in the New England Mud Patch

Measurements of surficial sediment properties at five locations in the New England Mud Patch (NEMP) were conducted during a coring survey in April 2022. At each location the Acoustic-Multi-Corer (AMC) sampled the upper few decimeters of sediment near the water-seabed interface. The AMC inserted acoustic probes into the sediment to collect in situ measurements of compressional waves (30–140 kHz) and shear waves (0.8–1.2 kHz) at near ambient conditions, after which cores were collected from the inter-probe propagation paths for ex situ analysis of the sediment properties. Onboard the ship, the cores were scanned with a Core and Resonance Logger (CARL), which provided high-frequency sound speed and attenuation measurements (100–1000 kHz) along the lengths of the cores, as well as resonance-based measurements of sound speed at 12–16 kHz. A subset of cores was sieved for infauna onboard the vessel, and the remaining cores were later analyzed in an onshore laboratory for porosity, bulk density, mineral and organic matter composition, and grain size. The frequency dependence of the surficial sediment acoustic properties will be discussed in the context of the mud’s physical and biological properties as well as sediment acoustics models. [Work sponsored by ONR.]

Direct measurements of acoustic and physical properties in mud and comparison to sediment acoustics models

Sediment acoustics models relate seabed physical properties to acoustic wave speed and attenuation, and direct measurements of sediment acoustic and physical properties provide a means to test such models. We examine direct measurements from two field experiment sites with muddy sediments that contain different ratios of clay, silt, sand, and organic components, comparing the acoustic data with sediment acoustic model predictions using parameters obtained from cores as model inputs. In the New England Mud Patch, sediment sound speed profiles up to several meters below the seabed surface were measured using in situ acoustic probes mounted to a gravity corer. At a second site near Mobile Bay, in situ probe measurements of sound speed, attenuation, and shear speed were obtained in the upper 20 cm of sediment, and diver cores were collected and scanned with an acoustic core logger. Sediments from both sites were analyzed for porosity and grain size distribution. The applicability of various models to the mud found at each site will be discussed, as well as effects of infauna and organic matter, which were also measured, but are not explicitly included in the models. [Work sponsored by ONR.]

Broadband core and resonance logger measurements of sound speed and attenuation in the New England mud patch

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.]

High-resolution transdimensional geoacoustic inversion using autonomous underwater vehicle data

We invert reflection coefficient measurements of muddy sediment layers along a 12-km seabed transect on the Malta Plateau in the Mediterranean Sea using 1711 source transmissions recorded on a 32-element linear hydrophone array with both source and array towed by an autonomous underwater vehicle. Trans-dimensional Bayesian inference using reversible jump Markov chain Monte Carlo sampling is applied to obtain posterior probability densities of the number of homogeneous sediment layers, their depths, and their geoacoustic parameters. The forward sediment acoustics model is based on the grain-shearing model which obeys physical causality and provides correlation between important geoacoustic properties. Each dataset was treated as one-dimensional seabed structure inversion carried out on high performance clusters, and inversion results for multiple data sets were combined to yield a two-dimensional subsurface profile including full uncertainty analysis. Comparisons of inversion results to piston and gravity core estimates show agreement in both geoacoustic parameter values and depths of discontinuities. In the range-dependent model constructed from inverting the entire data set, dipping and terminating layers are observed along the track with high vertical resolution on the order of 10 cm.

Bayesian geoacoustic inversion of 1-2 kHz seabed reflection data for layered muddy sediments

This paper presents trans-dimensional Bayesian geoacoustic inversion of seabed reflection data for sub-bottom geoacoustic profiles and associated uncertainty estimation at the New England Mud Patch. The data considered here are wide-angle seabed reflection coefficients as a function of grazing angle and frequency measured during the 2017 Seabed Characterization Experiment. Chirp pulses over a frequency band of 1–6 kHz were transmitted by an omnidirectional acoustic source towed by a research vessel at a speed of about 4 knots and recorded at a bottom-moored hydrophone. High signal-to-noise-ratio reflection coefficients from 1–2 kHz and angular coverage of ∼15–25° are considered here for geoacoustic inversion. This frequency range is higher than for previous reflection-coefficient data sets on the Mud Patch. The angular range, although relatively narrow, includes strong Bragg resonances which provide information on the sediment layering properties. The inversion applies the viscous grain-shearing sediment acoustics model, which provides dispersive (frequency-dependent) results for sound speeds and attenuations. The seabed structure estimated here is compared to previous inversion results and to core measurements in the vicinity. [Work supported by the Office of Naval Research.]

Development and Experimental Validation of Endfire Synthetic Aperture Sonar for Sediment Acoustics Studies

Seafloor sediment acoustic returns are comprised of scattering from both the sediment-water interface and the sediment volume. For low frequencies, volume scattering is often the dominant mechanism; however, direct measurements of this component have rarely been made, owing to the large beamwidths typically associated with low-frequency echosounder systems. When beamwidths are large, the sediment interface and volume returns arrive at the same time, causing estimates of volume scattering to become biased by the interface scattering. Endfire synthetic aperture sonar (EF-SAS) can achieve narrower beamwidths by coherently combining multiple acoustic returns as a vertically oriented transmitter and/or receiver is moved toward the seafloor. This article will present a proof of concept for EF-SAS, which will include an analysis of EF-SAS processing methods and an experimental verification of EF-SAS beamwidth improvements. Results from a motion-controlled EF-SAS experiment indicate that EF-SAS gains can be accurately predicted and that these gains are significant enough to remove the interface scattering bias.

Estimating geoacoustic properties of sediments with a wide grain-size distribution using sediment organic content and the viscous grain shearing model

Interstitial organic matter (OM) is a ubiquitous constituent of marine sediment, particularly prevalent in sediments with significant silt/clay fractions, and is often quantified across a wide range of disciplines. OM suspends silt and clay particles in the sediment matrix, adsorbs onto mineral surfaces, and resides primarily between mineral contacts, all of which are hypothesized to alter geoacoustic properties, yet OM has not been included in sediment acoustics models. Recent studies have shown that OM content (OC) correlates well with sediment geoacoustic properties, such as porosity and index of impedance, from sediments found in the Baltic Sea to seagrass-bearing sediments in Texas to mud banks in Brazil. In Mobile Bay, Alabama, OC correlated well not only with porosity and index of impedance, but also with grain-shearing coefficients described by the viscous grain shearing (VGS) model. Using empirical regressions derived from a subset of the Mobile Bay biogeoacoustic data and VGS, OC will be used to estimate geoacoustic properties of Mobile Bay sediments with a wide grain-size distribution. The efficacy and potential of using OC to predict sediment geoacoustic properties (and vice versa) in Mobile Bay and in other sediments with similar composition will be discussed. [Work supported by ONR.]

Biogeoacoustic sediment properties along a horizontal sand-mud gradient

Whether deposited from the water column or generated by benthic infauna, interstitial organic matter is a ubiquitous constituent of marine sediment and is particularly prevalent in sediments with significant silt/clay fractions. Interstitial organic matter suspends silt and clay particles in the sediment matrix, adsorbs onto mineral surfaces, and resides between mineral contacts, all of which are hypothesized to alter geoacoustic properties. However, the extent to which interstitial organics alter geoacoustic properties is understudied and warrants further investigation. To address this, diver cores were collected along a horizontal sand-mud gradient in Mobile Bay, Alabama. The sediment was subsequently processed in the laboratory, where compressional wave speed (10 kHz to 1 MHz), compressional wave attenuation (100 kHz to 1 MHz), density, porosity, grain-size distribution, and organic carbon and nitrogen content were measured. In addition, physics-based geoacoustic models, such as VGS(λ) and mCREB, were fit to the wide range of sediment types. Measured geoacoustic properties and fit parameters inherent to each sediment acoustics model are compared with organic sediment properties. The extent to which organics control sediment geoacoustic properties and considerations to include organics in future modeling efforts will be discussed. [Work sponsored by ONR.]

Justification for power laws and fractional models

Wave equations with non-integer derivative operators describe attenuation which increases with frequency with other powers than two, unlike ordinary wave equations. It is desirable to try to understand what properties of, e.g., biological tissue that give rise to this behavior. The main attenuation mechanisms of standard acoustics are heat conduction and relaxation, as well as structural and chemical relaxation. They have fractional parallels and the first one is heat relaxation described by fractional Newton cooling due to anomalous diffusion. The most important mechanism is however the fractional parallel to structural relaxation. Instead of one there are multiple relaxation processes with a distribution of relaxation times that follows a power-law distribution, possibly indicating fractal properties. The distribution also has a relationship to the Arrhenius equation, indicating a link to chemical relaxation, albeit a quite speculative one. The multiple relaxation model may also be formulated as a hierarchical polymer model. Time-varying non-Newtonian viscosity and a medium with a fractal distribution of scatterers can also give rise to power law behavior. Existing models in sediment acoustics such as the grain shearing model and the Biot poroelastic model can also be reformulated with fractional operators. These approaches are presented in the hope of progressing towards an understanding of whether fractional wave equations give clues to some deeper reality, or if they are just a compact phenomenological description.

Acoustic measurements of marine sediments with pebbles and cobbles

ABSTRACTThe majority of sediment acoustics research has focused to date on sediments with sand‐sized particles or smaller; measurements for sediments containing cobbles (6–26 cm) are rare. This paper presents the first measurements (to the authors’ knowledge) over a wide frequency range of compressional‐wave velocity and bulk density for a sediment with cobbles. The in situ velocity from inversion from wide‐angle reflection‐coefficient data at 0.4–2 kHz for cobbles suspended in sand is found here to be 1800 m/s with 95% credibility interval bounds of [1787–1828] m/s and for cobbles suspended in clay 1532 [1528–1536] m/s. Measured core velocities at 50 kHz and 200 kHz are lower for each sediment due to multiple scattering. The in situ bulk density for cobbles suspended in sand is 2.25 [2.21–2.28] g/cm3 and for cobbles suspended in clay 1.83 [1.78–1.87] g/cm3. Though cobbles in the upper few metres of sediment may be considered unusual on the mid‐shelf at mid‐latitudes, they appear to be present over tens of square kilometres on the Malta Plateau in a several metre thick layer starting at about 1 m below seafloor. In fact, geologic process considerations suggest that cobbles may be generally more common in mid to outer shelf environments than the paucity of measurements would suggest. Increased interest in the Arctic continental shelf environment, where pebbles and cobbles are expected to be prevalent, provides an additional motivation for this work.

Measurement and Modeling of High‐Frequency Acoustic Properties in Fine Sandy Sediments

AbstractThe object of this study was to obtain the acoustic properties of fine sandy sediments with approximately 22% clay content from the East China Sea Shelf. This study conducted the in situ acoustic measurement to measure the sound speed and attenuation, and eight sediment cores were collected and measured the wet bulk density, porosity, and mean grain size in laboratory environment. The correlations between in situ sound speed ratio and physical properties show good accordance with two empirical equations, while the in situ attenuation factor deviated the regression curves. Both the sound speed ratio and the attenuation data show the obvious change against the measurement frequency. The comparisons of the measured sound speed ratio and attenuation to the Biot‐Stoll model predictions were performed. The sound speed ratio dispersion agrees well with the model prediction, when the permeability and pore size were calculated using the extended Kozeny‐Carman's equation and the extended Hovem's equation. The attenuation data in this study accords better with the prediction curves reported for fine sediments than that for coarse sediments from the 1999 Sediment Acoustics Experiment.

Grain shearing models and relevance beyond sediment acoustics

The grain shearing (GS) and viscous grain shearing (VGS) models for saturated, unconsolidated marine sediments fit well to real data. But the models have much further relevance. The inherent convolution is in fact the definition of a non-integer derivative. Therefore, the GS theory is exactly described by the fractional diffusion-wave equation for shear waves and the fractional Kelvin-Voigt wave equation for the compressional mode. Both have been studied extensively in fractional calculus [Pandey and Holm, “Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations,” JASA (2016)]. The GS theory demonstrates that fractional derivatives arise naturally from physical processes and thus are more than just clever mathematics. These derivatives appear in the relaxation modulus, the stress response to a strain step, of the GS process. The variation in time of the viscosity makes it a time variant non-Newtonian process. But when strain and stress change roles, a surprising result appears. The creep response is the Lomnitz law, an empirically defined logarithmic relationship for such diverse materials as igneous rocks and wood [Pandey and Holm, “Linking the fractional derivative and the Lomnitz…,” Phys. Rev. E (2016)]. In the VGS model, the power-law response is exponentially tempered. The relaxation modulus is then that of the Cole-Davidson model, known from dielectric materials. This relationship has yet to be explored [Holm, Waves with Power-Law Attenuation (Springer, 2019), Chap. 8].

Some reflections on Buckingham’s viscous grain shearing model

Sediment geoacoustic properties are of considerable interest for commercial, industrial, and naval applications. In order to make geoacoustic inferences from acoustic data, the practitioner must choose a sediment acoustics model. The ‘Hamilton model’ is the most common, which assumes a frequency-independent sound speed, density, and an attenuation varying linearly with frequency, f1. Buckingham’s Viscous Grain Shearing (VGS) model offers a practical alternative with important benefits. For example, since it obeys causality, it provides fundamental bounds to the parameter space that the Hamilton model does not. Furthermore, if the acoustic data are sufficiently informative, the model provides insight into the frequency dependence of sound speed and attenuation. The central physics in VGS are expressed in high-level (material impulse response) functions, which consider both viscous and friction loss mechanisms and lead to attenuation varying between f1/2 to f1 to f2. Geoacoustic inference from seabed reflection measurements using the VGS model provides insight into the frequency dependence of naturally occurring marine sediments, i.e., admixtures of clay, silt, sand. At present, the VGS model is likely the most general (causal) sediment acoustics model, i.e., can reasonably treat the broadest range of sediment fabrics. [Research supported by the ONR Ocean Acoustics Program.]

Variability of the geoacoustic properties of infauna-bearing marine sediments

Infauna influence sediment physical parameters, such as porosity, grain size, and pore fluid properties, through bioturbation and other biological processes. To investigate the effects of the resulting sediment inhomogeneity, in situ measurements of compressional and shear wave propagation were acquired in Petit Bois Pass, west of Dauphin Island, Alabama, USA. After completion of the acoustic measurements, diver core samples were collected from between the sources and receivers to characterize the physical properties of the seabed along the acoustic propagation paths. The collected sediments were analyzed for infauna biomass and geotechnical properties to support acoustic propagation modeling. The acoustic data are analyzed in the context of infaunal functional groups, which are based on acoustically significant traits such as body type (hard/soft and large/small) and infaunal activity (sediment mixing or tube building). While existing sediment acoustics models do not explicitly account for effects of biology, they do allow for parameterization of various physical properties, which can be modified by the presence of biological organisms and bioturbation. Results from the in situ acoustic measurements and core analysis will be compared with such models to gain insight into the acoustical effects of infauna. [Work supported by ONR.]

Power law attenuation modeled as multiple relaxation

Wave equations with non-integer order derivatives may model power law behavior in medical and sediment acoustics. As experiments only support a finite bandwidth, there is a limit to how much physical insight that can be gained from such models. Other ways to model a power law are with a fractional heat law, hierarchical ladder models for polymer chains, and the non-Newtonian rheology of grain shearing. Multiple relaxation processes may be motivated by a hierarchy of substructures at different scales. It is also inherent in soft glassy materials, such as cells, with disordering and metastability. Even the Biot model with contact squirt flow and shear drag (BICSQS) may be interpreted as a multiple relaxation model. A weighted sum of relaxation processes will approximate a power law over a limited band, and an even distribution of relaxation frequencies on a logarithmic frequency axis, and with equal relaxation strengths, will give a power law attenuation with unit power, y = 1. This can be generalized to other power laws if the contribution from each relaxation process varies in proportion to the relaxation frequency to the power of y - 1. This scale-invariant distribution may hint at some fractal medium properties.