Elisabeth M. Brown

Analytical discussion of past measurements of acoustic attenuation in mud sediments and of possible future experimental approaches

Attenuation of compressional waves in mud is higher than in sea water, and less than in sandy/silty sediments. For experiments reported in 1964 (Acustica) by Wood and Weston, the Inferred circumstances are a 1 m thick mud slab overlying a gravel bottom, with air above (low tide), and with source and receiver either at the mud-gravel interface or slightly above it. Frequencies from 4 kHz to 72 kHz were transmitted, with signals received at a succession of horizontal distances of up to 50 m. Reported data in decibels versus range show considerable erratic behavior. Attempt is made to explain this behavior using a full-wave analysis of a Pekeris waveguide, with a fluid layer (the mud slab) overlying a (fluid or elastic) half-space, with a series of plausible guesses concerning the properties of the half-space. The conclusion is that the data and the circumstances allowed considerable variability in the attenuation estimates, but those made by Wood and Weston were about as good as could be expected. it is arg...

Viscosity-based theory of phase velocity and attenuation of sound in mud consisting of water and flocculated clay particles

Recent theory of authors ascribes attenuation in typical marine mud sediments to be caused by viscous interaction of sea water with embedded silt particles. Influence of underlying clay matrix is regarded as passive and of minor importance. Present paper considers silt-less mud where clay particles are flocculated to a card-house structure, with the flocculation hypothesis yielding a porosity of 90%. During the passage of a sound wave, Van-der-Waals forces between platelets cause the matrix to move to-and-fro as a unit; viscous forces are insufficient to cause the matrix to move perfectly with the water. The silt-less theory assumes that the local force on the matrix is the sum of the viscous forces on the platelets in the matrix. Forces on clay particles, which are thin platelets, are given by a low-Reynolds flow theory initiated by Stokes, and further developed by Oberbeck, Lamb, and Brenner. For each particle there is a characteristic frequency inversely proportional to the platelet thickness, which turns out to be extremely high for clay. Consequently, at acoustic frequencies, the clay matrix moves nearly in lock-step with the fluid motion associated with the sound wave. The inevitable very-small slip leads to an attenuation that is proportional to the square of the frequency, but which is very small compared with that of mud with embedded silt-particles. Current idealized theory results in prediction of attenuation inversely proportional to viscosity and of nearly constant phase velocity. [Work supported by ONR.]

Implications from a clay/silt suspension model of mud for data from the Seabed Characterization Experiment

Mud-like marine sediments may be modeled as a suspension of flocculated clay particles in water, in which silt particles are embedded in the clay flocs. Recent calculations based on this model [Pierce et al., New Orleans ASA] produced new predictions for the frequency-dependent phase speed and attenuation of compressional waves. For phase speed, very good comparisons between model predictions and archival data were found. Comparisons will be presented using geoacoustic data from sediment cores extracted from the New England Mud Patch. For attenuation, predictions using Gaussian distributions of silt particle radius were calculated. An approach will be described for producing a frequency-dependent effective particle radius to account for size-distribution effects using single-particle attenuation expressions. The influence of non-Gaussian size distributions on the effective radius and on the frequency intervals of near-linear attenuation behavior will be shown. An environmental model for a WHOI AUV track d...

Distinctions among physical types of marine sediments, especially mud, and their possible fundamentals-based and heuristic models

Marine sediments at different locations and depths are not necessarily similar. Distinctions are (1) sandy/silty sediments, when most particles have settled and almost every particle touches other particles, and (2) mud sediments, where the majority in a layer are suspended so that they do not touch other particles. Most theoretical and analytical modeling over the years has largely been confined to sandy/silty sediments, and some successful models, although arguably heuristic and with adjustable parameters, have emerged. There is also some speculation that such models might apply equally well for mud sediments. The present authors in recent years have concentrated on the development of a fundamentals-based model for mud sediments, although there is as yet insufficient data to adequately test its validity. The present paper speculates on what this model may have in common with models for sandy/silty sediments. There are expectations that the Mallock-Wood model may approximately apply for sound speed predi...

Geoacoustic parameter variations and inversion estimates with a silt-suspension theory of mud

Marine mud sediments can be modeled by a recent silt-suspension theory [Pierce, et al., JASA, 142, 2591 (2017) (A)], in which silt particles are embedded in a suspension of flocculated clay particles. This presentation investigates the influence on attenuation predictions from uncertainties in parameters such as the effective grain density and the distribution of grain sizes. For example, the matrix of clay flocs may effectively lower the density of silt grains and cause decreased attenuation. Effects from such parameters are determined on the regime where attenuation is nearly linear with frequency. The value of porosity is critical for specifying sound speed and attenuation in the mud layer. Porosity measurements from sediment cores can have significant uncertainty, particularly in the upper region, from the core extraction process. Inversions for porosity and other physical parameters of the silt-suspension theory are performed along a WHOI AUV track from the 2017 Seabed Characterization Experiment. Characteristics of cores guide parameter modeling and ranges for the inversions. This approach produces estimates of sound speed, attenuation, and density that are related by physical constraints. In addition, the approach allows for validity assessment of current geoacoustic mud models using measured data. [Work supported by ONR.]Marine mud sediments can be modeled by a recent silt-suspension theory [Pierce, et al., JASA, 142, 2591 (2017) (A)], in which silt particles are embedded in a suspension of flocculated clay particles. This presentation investigates the influence on attenuation predictions from uncertainties in parameters such as the effective grain density and the distribution of grain sizes. For example, the matrix of clay flocs may effectively lower the density of silt grains and cause decreased attenuation. Effects from such parameters are determined on the regime where attenuation is nearly linear with frequency. The value of porosity is critical for specifying sound speed and attenuation in the mud layer. Porosity measurements from sediment cores can have significant uncertainty, particularly in the upper region, from the core extraction process. Inversions for porosity and other physical parameters of the silt-suspension theory are performed along a WHOI AUV track from the 2017 Seabed Characterization Experiment. Ch...

Characterization of mud sediments using the frequency dependence of phase velocity and attenuation of compressional waves

The present paper’s theory predicts phase velocity and attenuation for mud sediments that contain silt particles, and is based on the model of a suspension consisting of solid particles dispersed in a viscous liquid; the attenuation expression dates back to Lambs Hydrodynamics and to Urick (JASA, 1948), clarified and rederived by Pierce, Siegmann, and Brown (POMA, 2017). The application to mud is based on the premise that silt particles are held in suspension by the loosely connected matrix of clay particles and that their natural oscillation frequencies are significantly less than the frequencies used in underwater acoustics. The present paper extends that theory with a fresh derivation based on concepts of matched asymptotic expansions and results in an expression for the complex wave number k as a function of the angular frequency. The results for phase velocity disagree with results published in the past by Ahuja (JASA, 1972) and Temkin (JASA, 2000). The assertion is made that the use of the theoreti...

Role of clay particle electrostatics and the dielectric permittivity of suspended silt particles in sound attenuation in mud

Sound attenuation in marine mud sediments is partly caused by viscous dissipation of acoustically induced flow past suspended silt particles. Clay particles in the surrounding lattice carry electrostatic charges, causing high porosity, so one asks why silt particles do not settle because of gravity to the bottom of the mud layer. Explanation of the suspension and the associated attenuation of sound proceeds from consideration of a quartz sphere immersed in mud. The somewhat-random electric field created by the clay particles causes an electric dipole moment to arise in the sphere because of its dielectric permittivity. This is proportional to the electric field and varies with position, and the result is an electrostatic force on the sphere, the force being proportional to the gradient of the electric field. In equilibrium, this force is balanced by a gravity force. There is a natural spring constant associated with deviations from equilibrium, and the resulting dynamical model is a fixed-mass sphere subj...

Influence of sand/silt particle size distributions on compressional wave attenuation in marine mud sediments

High porosity marine mud from different sites typically contains different amounts of clay, sand, and silt particles, along with other material. A recent talk [Pierce et al., ASA Honolulu, 5aAO1 (2016)] explored a mechanism for why sand and silt particles in suspension can provide the dominant contributions to the frequency dependence of compressional wave attenuation. The card-house structure of the clay is critical in supporting the particles and keeping them separated. Example calculations for spherical particles of the same size showed physically reasonable attenuation behavior at low and high frequencies. This presentation considers extensions of the approach, particularly accounting for distributions of particle sizes, and emphasizes comparisons of attenuation predictions with available field data. Using reasonable assumptions about the clay volume and the sand and silt distributions, it is possible to estimate the numbers of sand and silt particles, and consequently the attenuation, from the sedime...

Applications of a suspension theory of silt particles in mud to frequency and other parameter dependencies of geoacoustic quantities

A recent suspension theory of marine mud [Pierce, et al., POMA 29, accepted] hypothesizes that embedded silt particles are the dominant contributors to compressional wave attenuation. The approach predicts frequency intervals within which attenuation increases roughly linearly with frequency, as often assumed. These intervals depend on the measured (or assumed) mean silt particle size. This presentation investigates the influence of distributions of silt particle sizes on attenuation, including the distribution shapes obtained from data, and the intervals of linear frequency with multiple particle sizes. In addition to attenuation, the theory also provides compressional sound speed predictions. Their sensitivity to changes in measured physical parameters and frequency will be determined, and the results compared with archival data and recently analyzed SBCEXP core data along a range-dependent experimental track. Another consequence of the theory is how porosity is affected by the minimum separation distan...

Effect of sand and silt particles on the attenuation of compressional waves in marine mud sediments

Mud in marine sediments is a mixture of clay, sand, and silt particles. Present paper follows up on a suggestion by Holland and Dosso (JASA, 2013) that the variability of the measured frequency-dependent compressional wave attenuation may be caused by the variability of the amounts of sand and silt particles. The premise is that the porosity for the mud is high and that the sand and silt particles are in suspension. They do not settle out to the bottom of the layer because the card-house fabric of the clay particles tends to hold them in place. This supposition leads to a theory where the clay configuration gives a base-line attenuation, and the contribution from the individual sand and silt particles is additive. The estimation of the latter is distinguished from the existing theories of attenuation of sound in sandy/silty sediments in that the particles are presumed not to touch each other. Particles are assumed to be spherical and there is no slip between particle surfaces and the surrounding water. Ea...