Acoustics of the Seabed as a Poroelastic Medium

Building upon the advances made by Biot-Stoll and by Jackson and Richardson, this book advances the modeling by extending the Biot model to include the physics of the grain-grain contact and other anomalies observed in the practical measurements. In addition, an attempt is made to cover a wide range of sediment types, which have different frequency dependencies of wave speeds and attenuation. Finally, the number of independent input parameters is reduced to a manageable number in an effort to render the model accessible to a wider community.

Sediment classification is based on grain size. The Wentworth 1922 scale is one of the more popular ones, and it is the one adopted here. Rather than having one characteristic grain size, natural sediment tends to have a distribution of grain sizes. A truly comprehensive map of all the possible mixtures of grain sizes would be too cumbersome. Consequently, the geophysical classification of sediments remains an imprecise science. Similarly, the prediction of acoustic properties from a sediment class, or the inversion for sediment class from acoustic properties, is equally inexact. Nevertheless, the mean grain size remains a very useful metric.

Neither the fluid nor the solid model is capable of representing the acoustic properties of the seabed, particularly where the reflection coefficient is concerned. The Rayleigh reflection equation, which applies to both fluid and solid models at normal incidence, gives inaccurate results when applied to the seabed. Consequently, there is a need for the poroelastic model. It is shown that the both the solid and fluid models are contained within the Biot poroelastic model. One can smoothly transition from a fluid model, through a range of poroelastic models, and arrive at a solid model.

In the baseline Biot model, both shear and compressional wave absorption is dominated by the viscous loss due to relative motion between the pore fluid and the solid particles. For the compressional wave, frequency dependence is close to the second power of frequency below the characteristic frequency. At higher frequencies, the attenuation follows the half-power of frequency. In practice, other factors, such as squirt flow at the grain contacts, combined with the unavoidable distribution in pore sizes, can produce a range of frequency dependencies. Compressional wave absorption is most sensitive to the presence of small amounts of gas. Most of the laboratory measurements are suspected of being biased by the presence of minute concentrations of gas of the order of 1–10 parts per million by volume. At even higher frequencies, when the grains and pores are no longer small compared to the wavelength, the effective medium assumption that underlies the Biot model breaks down. Multiple scattering dominates and absorption increases as the fourth power of frequency. The shear wave speed is controlled by the frame shear modulus. There is an increase in the shear speed at the contact squirt-flow relaxation frequency. The Biot slow wave, being highly attenuated, is difficult to detect. Its speed is a function of the frame bulk modulus. It is easily detected in water-saturated sintered glass beads, in which the frame moduli are high, but more difficult to detect in unconsolidated sand, which, in the absence of any confining pressure, has low frame moduli. Nevertheless, it cannot be ignored because it makes its presence felt as a significant loss mechanism in the reflection process.

The Extended Biot (EB) model for sandy seabeds is improved with the aid of the Revil, Glover, Pezard, and Zamora (RGPZ) model. The RGPZ model provides a direct link between the mean grain diameter and porosity, which is the primary means of sediment classification, and the input parameters of the EB model. The difficult-to-measure parameters, such as permeability, pore size, and tortuosity, are replaced by relationships based on mean grain size, porosity, and a couple of well-bounded dimensionless parameters: cementation exponent and pore shape parameter. The combined RGPZ and EB (REB) model is extended to silts and clays. Regarding the frame moduli, one modification to the model was necessary. In the EB model, the relationship between grain-contact stiffnesses at the microscopic scale and the macroscopic frame moduli was based on a model of randomly packed spheres. A heuristic correction, based on porosity, was necessary to fit the observed relationships in silts and clays, which tend to have a flocculated structure, which is very different from randomly packed spheres. The corrected REB model (CREB) is able to model the wave speeds and absorptions of mono-sized, unconsolidated, and uncompacted sediments across the Wentworth scale, from pebbles through various grades of sands and silts to clays.

A set of parameter values was constructed to represent each of the sediment types in the Wentworth scale using the CREB model. It is shown that the wave speeds and attenuations and reflection coefficients of each sediment type compared favorably with known measurements in the open literature. The coarsest grains need to be measured at frequencies below 1 kHz to avoid multiple scattering effects. Sands and silts exhibit the typical sound speed dispersion and frequency dependence of absorption predicted by the Biot theory. The clays exhibit wave speeds that are very nearly independent of frequency, absorption that is nearly constant-Q, and creep with a long relaxation time constant. The reflection loss is consistent with known measurements, across all sediment types. These results suggest that the CREB model contains the physical processes underlying the acoustic properties of the full range of sediment types. By simply adjusting 5 input parameter values, it is possible to transition from one sediment type to another.