Frequency dependencies of phase velocity and attenuation coefficient in a water-saturated sandy sediment from 0.3 to 1.0 MHz

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.

On acoustic reflection from sand-sized water-saturated granular media at MHz frequencies: Measurements, models and the role of speckle

Acoustic reflection coefficients are reported for water-saturated granular media at frequencies from 1.2 to 2.0 MHz using a narrow-beam broadband transducer in a monostatic geometry at near-normal incidence. Natural sand and glass beads with median grain diameters ranging from 0.22 to 0.40 mm were used. For each granular medium, bed elevation and root-mean-square roughness were measured using side-on photographs of the sediment-water interface. The probability density distributions of the bed elevations are Gaussian. The roughness parameter is close to 1, indicating that the reflected pressure field is mainly due to coherent scattering. The probability distribution of the observed reflection coefficients is nearly Gaussian, consistent with the predictions from a coherent single-scattering model. The horizontal decorrelation length of the observed reflection coefficients is ∼4 mm, with no consistent dependence on either frequency or grain size, and approximately equal to 20% of the transducer diameter. This behaviour, which is reproduced by the single-scattering model, is due to speckle. The size/frequency-dependence of the reflection coefficients are well described by Eckart's [(1953). J. Acoust. Soc. Am. 25(3), 566-570] prediction for a rough surface with Gaussian-distributed surface elevations. Comparisons are made to previously reported reflection coefficient measurements.

Phase speed in water-saturated sand and glass beads at MHz frequencies

Measurements of the phase velocity of compressional sound waves in water-saturated granular materials are reported for the 1.0-2.0 MHz frequency range. The sound speed estimates are based on travel times through granular layer thicknesses ranging from 8 to 17 mm. Three types of granular media were used: 336 μm median diameter glass beads and two natural sands with median diameters of 219 and 406 μm. These grain sizes and frequency range correspond to 0.5<ka<1.2, where k is the wavenumber and a the grain radius. To remove trapped air, the samples were boiled under pressure before transfer to the measurement tank. The results are compared to previously reported experimental results and to the Schwartz and Plona [J. Appl. Phys. 55(11), 3971-3977 (1984)] multiple scattering prediction, confirming negative dispersion for ka > 0.5. Scaling the data by a factor depending on porosity and grain density reduces the spread among the available phase speed estimates by nearly a factor of 2, from 12.5% to 6.9%.

Attenuation and group speed in water-saturated granular materials at MHz frequencies

Attenuation and group speed measurements are reported for water-saturated granular materials (natural sand and glass beads) at frequencies of 1.0 to 1.8 MHz. Median grain diameters were 219 to 497 μm, corresponding to kd≳1, i.e., the scattering regime. The measurements were made for different thicknesses of sediment resting on a reflective surface using a monostatic geometry. The attenuation estimates compare well with previously reported experimental results and to the predictions of multiple scattering theory, confirming in particular the tendency toward f ⁴ dependence for kd≳1. Group speed estimates exhibit the negative dispersion predicted by theory and are comparable in magnitude to previously reported measurements made using transmission geometries. It is found that the available data exhibit a O(10)% spread among the sound speed measurements at a given kd value, and that this spread is reduced to 2.2% when the data are scaled by a factor dependent on porosity and grain density, and that essentially all of the reduction can be attributed to differences in porosity.

High frequency compressional wave speed and attenuation measurements in water-saturated granular media with unimodal and bimodal grain size distributions

Compressional wave speed and attenuation were measured for water-saturated granular media employing five kinds of glass beads having unimodal and bimodal grain size distributions. Glass beads with grain sizes ranging from 250 to 850  μm were used for the acoustic measurements at a frequency range from 350 kHz to 1.1 MHz, which includes the transition range where scattering and non-scattering losses co-exist. The compressional wave speed and attenuation data are presented as a function of frequency and grain size distribution. The compressional wave speed and attenuation data show a variety of frequency dependencies for varying grain size distribution. The observed acoustic properties are investigated for the volume ratio of larger and smaller sized grains in the mixed bimodal media. Also, the measured results are compared with the empirical multiple scattering formula as a function of Rayleigh parameter  kd (product of wavenumber in the water k and mean grain diameter of the glass beads d) using weighted mean grain size. The measured results are also discussed, focusing on the geophysical difference between unimodal and bimodal mixed grains.

Nonlinear wave propagation in porous materials based on the Biot theory

Nonlinearity must be considered with some porous granular media because of the large deformation under seismic waves. In this study, the propagation of nonlinear waves in porous media is studied based on the Biot theory and the governing equations are obtained by the Lagrangian formulation. Three new nonlinear parameters are introduced to consider the coupled nonlinearity between the solid and fluid components in porous media. It is shown that an additional nonlinear wave with a double frequency is generated by the coupling effect of linear fast and slow waves. When only a shear wave is applied at the source, no double-frequency nonlinear wave is predicted and three nonlinear longitudinal waves are generated. On the basis of the practical case studies, the effect of strong nonlinearity is computed under the influence of a one-dimensional single longitudinal wave source and a single shear wave source.

Velocity dispersion and attenuation in granular marine sediments: comparison of measurements with predictions using acoustic models

The large velocity dispersion recently reported could be explained by a gap stiffness model incorporated into the Biot model (the BIMGS model) proposed by the author. However, at high frequencies, some measured results have been reported for negative velocity dispersion and attenuation proportional to the first to fourth power of frequency. In this study, first, it is shown that the results of velocity dispersion and attenuation calculated using the BIMGS model are consistent with the results measured in two kinds of water-saturated sands with different grain sizes, except in the high-frequency range. Then, the velocity dispersion and attenuation in six kinds of water-saturated glass beads and four kinds of water-saturated silica sands with different grain sizes are measured in the frequency ranges of 80-140 and 300-700 kHz. The measured results are compared with those calculated using the BIMGS model plus some acoustic models. It is shown that the velocity dispersion and attenuation are well predicted by using the BIMGS model in the range of kd ≤ 0.5 (k: wavenumber in water, d: grain diameter) and by using the BIMGS model plus multiple scattering effects in the range of kd ≥ 0.5 in which negative velocity dispersion appears.

Sound speed in water-saturated glass beads as a function of frequency and porosity

Sound propagation in water-saturated granular sediments is known to depend on the sediment porosity, but few data in the literature address both the frequency and porosity dependency. To begin to address this deficiency, a fluidized bed technique was used to control the porosity of an artificial sediment composed of glass spheres of 265 μm diameter. Time-of-flight measurements and the Fourier phase technique were utilized to determine the sound speed for frequencies from 300 to 800 kHz and porosities from 0.37 to 0.43. A Biot-based model qualitatively describes the porosity dependence.

Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads

Dynamic acoustoelastic testing is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound (US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60-530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate US attenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.

High frequency measurements of sound speed and attenuation in water-saturated glass-beads of varying size

Acoustic measurements of p-wave speed and attenuation were made for water-saturated granular medium, consisting of six kinds of glass-beads with mean grain size ranging from 90 to 875 microm, at frequency range between 400 kHz and 1.1 MHz. Sound speed and attenuation were obtained using the inter-receiver broadband estimation technique. The measured data exhibit various frequency dependencies for the different mean grain sizes, consistent with earlier measurements from other researches. These results reveal that the trend of dispersion relation for the sound speed and attenuation, in the high frequency region, is strongly dependent on the range of Rayleigh parameter kd.

Sensing a buried resonant object by single-channel time reversal

Scaled laboratory experiments are conducted to assess the efficacy of iterative, single-channel time reversal for enhancement of monostatic returns from resonant spheres in the free field and buried in a sediment phantom. Experiments are performed in a water tank using a broad-band piston transducer operating between 0.4 and 1.5 MHz and calibrated using free surface reflections. Solid and hollow metallic spheres, 6.35 mm in diameter, are buried in a consolidation of 128-microm-mean- diameter spherical glass beads. The procedure consists of exciting the target object with a broadband pulse, sampling the return using a finite time window, reversing the signal in time, and using this reversed signal as the source waveform for the next interrogation. Results indicate that the spectrum of the returns rapidly converges to the dominant mode in the backscattering response of the target. Signal-to-noise enhancement of the target echo is demonstrated for a target at several burial depths. Images generated by scanning the transducer over the location of multiple buried targets demonstrate the ability of the technique to distinguish between targets of differing type and to yield an enhancement of different modes within the response of a single target as a function of transducer position and processing bandwidth.

High-frequency dispersion from viscous drag at the grain-grain contact in water-saturated sand

Shear viscous drag within the thin fluid film at the contact between grains in water-saturated sand is an important loss mechanism for high-frequency sound in the Biot-Stoll plus contact squirt flow and shear viscous drag (BICSQS) model [J. Acoust. Soc. Am. 116, 2011-2022 (2004)]. Couette flow was assumed for the shear drag but it breaks down when inertial effects within the film become significant. Using Biot's method, a correction is derived for the shear drag and inserted into the BICSQS model. The result is a prediction of negative sound speed dispersion, consistent with dynamic theories of fluid-filled poroelastic bodies.