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The Acoustics of Marine Sediments
to frequencies below 500 Hz. It is believed that slower wave speeds and higher shear-wave attenuation at the deeper site were caused by the presence of vascular plants or algae, in- fauna, and their organic and inorganic byproducts that have the potential to alter the physical properties of the sediment (e.g., density, porosity, or shear strength) and pore fluid (e.g., viscosity) and thereby modify the acoustic properties. The potential of biological activity to affect the geoacoustic pro- prieties of the seabed is discussed below.
Sediment Acoustic Models
Theoretical models describing wave propagation in marine sediment properties can be used to predict the compres- sional- and shear-wave speed and attenuation of a given sediment from measurements of physical properties. Mod- els of varying complexity (e.g., treating the sediment as a fluid, elastic, or poroelastic medium) have been developed to describe the acoustic behavior of marine sediments. Dif- ferent models have been applied to predict measured data from various laboratory and field experiments with varying degrees of success; however, there is no general consensus on whether any of the models fully describe the physical mechanisms governing the acoustics in even the most ho- mogeneous granular sediment. The inhomogeneity found in naturally occurring sediments further confounds the pre- dictive capability of the models.
Fluid models are the simplest descriptions of sound propa- gation in sediment. A well-known example of such a model is the Mallock-Wood equation, which employs mixture rules to predict the sound speed in an effective medium com- posed of two or more constituent materials (e.g., water/gas, water/mineral, or water/gas/mineral; Mallock, 1910; Wood, 1946). The fluid description of marine sediments inherently includes no rigidity, treating the sediment as a suspension of its various components. According to this formulation, each constituent material contributes to the bulk compressibility and bulk density of the suspension in proportion to its vol- ume concentration. Notably, the resulting sound speed cal- culated from the Mallock-Wood equation can be lower than that of either of the components.
For sediments possessing rigidity, the Mallock-Wood equa- tion will underpredict the compressional-wave speed. To more accurately model the acoustic properties of marine sediments, more complex models that include the propaga- tion of shear waves in sediment have been developed. Two types of models widely used within the underwater acous- tics research community today are viscoelastic models such
as Buckingham’s grain-shearing (GS) theory (2014) and poroelastic models based on Biot’s theory (1956a,b). Both types of models predict the frequency dependence of all four acoustic parameters (compressional- and shear-wave speeds and attenuations) but differ both in their description of the physical mechanisms contributing to the wave dispersion relationships and in their application through the number and type of input parameters.
A recent example of an elastic-sediment model, Bucking- ham’s GS theory (2014), treats unconsolidated marine sedi- ment as a two-phase medium, with internal losses arising at grain-to-grain contacts from shearing and stress relaxation. The wave speeds and the associated attenuations are deter- mined from the compressional- and shear-wave equations, which are developed from a generalized Navier-Stokes equa- tion that takes into account the stresses that are present at the intergranular contacts. It has been shown that the effects of viscosity are important for calculating compressional-wave properties but can be neglected for calculating shear-wave properties. The relative importance of viscosity and its de- pendence on the type of propagating wave is accounted for in a slightly modified form of the model designated VGS(λ).
An alternative family of sediment acoustic models is based on Biot’s theory of wave propagation in poroelastic media, which considers a consolidated elastic frame filled with a viscous pore fluid (Biot, 1956a,b). In the Biot theory, dis- sipation arises solely from the viscosity of the pore fluid. Stoll (1977) later modified the Biot theory to allow for em- pirically determined complex frame moduli in an attempt to account for losses in an unconsolidated frame, and he ap- plied the model to wave propagation in marine sediments. Other models seeked to extend the Biot-Stoll formalism by incorporating frequency-dependent losses. In a recent mod- el (Chotiros and Isakson, 2014), these losses arise from the inclusion of grain-contact squirt flow and viscous shear drag into frequency-dependent complex frame moduli, designat- ed as the extended Biot (EB) model.
Fits of the Mallock-Wood equation, VGS(λ) theory, and EB model to the shallow-site data from the Currituck Sound experiment (Lee et al., 2016a) are shown in Figure 4. The Mallock-Wood equation, which acts a low-frequency limit to the VGS(λ) model, is frequency independent and hence is not capable of describing the sound-speed dispersion ob- served at higher frequencies. The VGS(λ) model was fit to the data using measured values of shear-wave speed and attenu- ation at 500 Hz and compressional-wave speed at 70 kHz.
14 | Acoustics Today | Fall 2017
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