Nicholas P. Chotiros

Biot model of sound propagation in water‐saturated sand

Elastic theory of wave propagation and the measured speed of sound in sandy ocean sediments indicate that such sediments are impenetrable to high‐frequency sound at shallow grazing angles. The speed of sound in water‐saturated, unconsolidated sand is in the region of 1700 m/s which, under the elastic theory of wave propagation, gives it a critical grazing angle in the region of 28°. At shallower grazing angles, refraction is not permitted, and total internal reflection is predicted. Recent experimental measurements contradict this view. Biot’s theory of acoustic propagation in porous sediments is the most likely explanation. Biot’s theory of acoustic propagation, as it applies to water‐saturated sand, is reviewed. The speed of the slow wave is found to be higher than previously predicted. New input parameter values are deduced.

A broadband model of sandy ocean sediments: Biot–Stoll with contact squirt flow and shear drag

Unlike the application of the Biot model for fused glass beads, which was conclusively demonstrated by Berryman [Appl. Phys. Lett. 37(4), 382–384 (1980)] using the experimental measurements by Plona [Appl. Phys. Lett. 36, 259–261 (1980)], the model for unconsolidated water-saturated sand has been more elusive. The difficulty is in the grain to grain contact physics. Unlike the fused glass beads, the connection between the unconsolidated sand grains is not easily modeled. Measurements 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 sound speed dispersion may be explainable in terms of the Biot plus squirt flow (BISQ) model of Dvorkin and Nur [Geophysics 58(4), 524–533 (1993)]. By using a similar approach that includes grain contact squirt flow and viscous drag (BICSQS), the observed diverse behavior of ...

An inversion for Biot parameters in water-saturated sand.

The discrepancy between acoustic measurements and the theoretical predictions was investigated in the case of water-saturated sand. Two theoretical models were considered: visco-elastic and poro-elastic solid models. The visco-elastic solid model could not be reconciled with reflection loss measurements and was rejected. The poro-elastic solid model using Biots theory [J. Acoust. Soc. Am. 103, 2723-2729 (1998)] as formulated by Stoll [J. Acoust. Soc. Am. 70, 149-156 (1981)] was an improvement. It was investigated using an inversion process. Operative values of grain bulk modulus and the frame bulk and shear moduli of water-saturated sand were inverted from simple measurements--reflection loss, compressional and shear wave speeds and attenuations. Although the inversion process is nonlinear, in practice, it is well behaved and converges quite rapidly to a unique solution. The issue of imprecisely known parameter values was handled in a probabilistic manner. The inversion results, using published laboratory and in situ measurements, showed that further improvement was needed. In an attempt to find a solution, two possible hypotheses are put forward. (1) Composite materials: The possibility that the frame may contain fluid and that the pore fluid may contain loose grains. (2) Independent coefficient of fluid content: The possibility that porosity may change with pore fluid pressure. Inversion results were encouraging for both hypotheses. It is difficult to say which of the two hypotheses is superior, and the two hypotheses are not mutually exclusive. The new hypotheses represent a significant advance because they have the potential to resolve the remaining discrepancies. At this stage, alternative interpretations of the data are possible.

A model for high‐frequency acoustic backscatter from gas bubbles in sandy sediments at shallow grazing angles

A model for acoustic backscatter from trapped bubbles in sandy sediments was developed. The model combines a Biot acoustic penetration model with a resonance scattering mechanism from trapped bubbles. The bubble size distribution is assumed to mirror the size distribution of the fluid pores that exist between sand grains. An estimate of the pore size distribution is constructed from the grain size distribution, based on the known pore structure between dense random packings of hard spheres. The principle of acoustic reciprocity is employed to compute backscattered acoustic pressure in terms of the incident pressure and the scattering cross section of a bubble distribution. The model is applied to data from experiments recently taken at sea. It is concluded that trapped gas is often a likely cause of observed backscatter from sandy sediments. Very small amounts of gas appear to be sufficient to produce significant backscatter.

REFLECTION AND REVERBERATION IN NORMAL INCIDENCE ECHO-SOUNDING

A mathematical model of normal incidence sediment backscatter, based on the Helmholtz integral and the Kirchhoff approximation, was developed. This model is different from existing models in that it is able to account for the effects of sonar beamwidth and wavefront curvature, including a first‐order correction for the effects of local slope. Bottom roughness was modeled as a spatial correlation function, constructed from a distribution of Gaussian functions. A probabilistic measure of the validity of the Kirchhoff approximation was also developed. Two bottom models, for a sand and a mud sediment, based on measured roughness spectra of real sediments in situ, were used to generate numerical results. The results confirm the ability of current narrow‐beam, high‐frequency systems to detect sub‐bottom interfaces in mud, and the ability of most systems to estimate the magnitude of the reflection coefficient of the sediment surface. They also predict that measurement of the phase of the reflection coefficient w...

Normal incidence reflection loss from a sandy sediment

Acoustic reflection loss at normal incidence from a sandy sediment, in the Biodola Gulf on the north side of the island of Elba, Italy, was measured in the frequency band 8-17 kHz, using a self-calibrating method. The water depth was approximately 11 m. The mean and standard deviation of the sand grain diameter were 2.25 (0.21 mm) and 0.6 phi, respectively. The reflection loss was measured using an acoustic intensity integral method, which is insensitive to roughness effects within the selected frequency band. The measured value of reflection loss was 11 dB, +/- 2 dB. The result is consistent with previous measurements in the published literature. The computed reflection loss for a flat interface between water and a uniform fluid or visco-elastic medium with the same properties is 8 dB, +/- 1 dB. The theoretical and experimental values do not significantly overlap, which leads to the conclusion that the visco-elastic model is inappropriate. The Biot model is suggested as a better alternative but more work is needed to ascertain the appropriate parameter values.

Shallow-water bottom reverberation measurements

High-frequency bottom reverberation measurements were made at an experimental site in the Gulf of Mexico. The acoustic data were taken as a function of frequency (40-180 kHz) and grazing angle (40-33/spl deg/). The measured acoustic reverberation results are compared to predictions made by models developed by Jackson et al. (1986, 1996) and Boyle and Chotiros (1995). The models used inputs from the analysis of sediment cores and stereophotography. The model predictions show differences from each other and from the data. The results show reverberation-level variabilities as a function of frequency that cannot be accurately predicted by these models.

Nonlinear acoustic scattering from a gassy poroelastic seabed

A model for difference frequency backscatter from trapped bubbles in sandy sediments was developed. A nonlinear volume scattering coefficient was computed via a technique similar to that of Ostrovsky and Sutin [“Nonlinear sound scattering from subsurface bubble layers,” in Natural Physical Sources of Underwater Sound, edited by B. R. Kerman (Kluwer, Dordrecht, 1993), pp. 363–373], which treats the case of bubbles surrounded by water. Biot’s poroelastic theory is incorporated to model the acoustics of the sediment. Biot fast and slow waves are included by modeling the pore fluid as a superposition of two acoustic fluids with effective densities that differ from the pore fluid’s actual density and account for its confinement within sediment pores. The principle of acoustic reciprocity is employed to develop an expression for the backscattering strength. Model behavior is consistent with expectations, based on the known behavior of bubbles in simpler fluid media.

Acoustic penetration of a silty sand sediment in the 1-10-kHz band

An experiment was performed to measure sediment penetrating acoustic waves to test a model of acoustic propagation, which is based on Biots theory. Independent geophysical measurements provided model input parameters. A parametric sound source was used to project a narrow beam pulse into a silty sand sediment at a shallow grazing angle. The sediment acoustic waves were measured by an array of buried sensors and processed to measure wave directions and speeds. Two acoustic waves were observed, corresponding to the fast and slow waves predicted by Biots theory. Discrepancies between model predictions and measured acoustic waves were examined, deficiencies in the model identified, and strategies for improvement postulated. The permeability and bulk modulus of the solid frame were of particular interest.

A model for acoustic backscatter from muddy sediments

It is well known that muddy sediments often contain significant amounts of gas of biological origin. Since the scattering cross section of a gas bubble in water is typically 1000 times its geometric cross section, it is reasonable that an acoustic backscatter model intended to work over muddy sediment should contain a bubble resonance scattering component. In this paper a heuristic model is presented, based on scattering from a distribution of suspended bubbles in mud. For acoustic propagation purposes, the mud is treated as a viscous fluid. Since estimates of bubble size distributions in mud are currently unavailable, a bubble distribution similar in shape to that observed in the water column is assumed. The model’s only free parameter is the gas fraction, which can be varied to fit the model to observed data. Small amounts of gas appear to be sufficient to produce observed levels of backscatter. For a homogeneous bubble distribution, the model can be inverted to give an estimate of the gas bubble size d...