Sound Speed Dispersion Research Articles

Low- to mid-frequency model of attenuation and dispersion.

A model of attenuation and sound speed in ocean sediments in the low- to mid-frequency range is presented. It is based on a combination of the Biot–Stoll and contact squirt and shear drag model [Chotiros and Isakson, J. Acoust. Soc. Am. 116, 2011–2022, (2004)] and the frame virtual mass model [Chotiros and Isakson, J. Acoust. Soc. Am. 121, EL70 (2007)]. This combination can match measured sound speeds below Wood’s equation lower bound and it addresses issues related to the Kramers–Kronig relationship. It is able to match both the sound speed dispersion and attenuation measurements from a large number of sites, including the sediment acoustics experiments (SAX99 and SAX04) in the Gulf of Mexico, the shallow water experiment on the Atlantic coast, and the Yellow Sea [Zhou, J. Acoust. Soc. Am. 78, 1003–1009 (1985)]. [Work supported by ONR, Ocean Acoustics.]

Sound attenuation coefficients in sandy and silty seabottoms from low‐ to mid‐frequency field measurements in shallow water.

The debate on the sound speed dispersion and the frequency dependence of sound attenuation in sediments has persisted for decades, mainly due to the lack of sufficient experimental data in the low‐ to mid‐frequency speed/attenuation transition band and the limitations of existing models. This paper analyzes and summarizes the LF measurements, conducted at 20 locations in different coastal zones around the world, that have resulted in the identification of nonlinear frequency dependence of sound attenuation in sand‐silt seabottoms for a frequency range of 50–2000 Hz [Zhou and Zhang, J. Acoust. Soc. Am. 117, 2494 (2005); 119, 3447 (2006)]. The resultant LF sound speed and attenuation can be described equally well by the Biot‐Stoll model, the Chotiros BICSQS model, and the Buckingham VGS model. However, a combination of the LF field‐inverted sound speeds and attenuations with data from the SAX99 and SAX04 measurements over a broadband of 50–400 000 Hz cannot simultaneously be matched by any of these models with one set of adjustable input parameters; these models either underestimate broadband dispersion or overestimate LF attenuation. Comments on the LF field‐derived data, such as “speed‐attenuation coupling,” are made. The possible reasons for the broadband data‐model mismatch are discussed. [Work supported by the ONR.]

Acoustical and optical measurements on a mixture of air microbubbles in water

An important challenge for current naval research is the modernization of battleships. Their target detection system must be increasingly efficient and they must be increasingly undetectable. Due to turbulent flows and bubbles, ship wakes are a detectable acoustic signature and ship bow waves disturb sonar detection. In this work, we study sound propagation through bubble clouds in water. We have developed an experimental set‐up which permits us to acquire, in synchronization, acoustical signals and optical images. The phenomenon of bubble monopole resonance in very low frequency, related to bubble size, provokes effects of strong sound damping and sound speed dispersion. These experimental results, related to theoretical results, permit to estimated sizes and concentrations of bubbles. The acquired bubble images permit to know the real bubble sizes and concentrations, in order to correlate with the experimental acoustical results. Air bubbles are generated with a high pressure water jet introduced into t...

Estimating the frequency dependent behavior of marine sediment sound speeds using low frequency aircraft sound

For investigating the dispersion behavior of sediment sound speeds, broadband sound speed measurements are required. Sediment sound speed dispersion models predict the largest sound speed variations typically at low frequencies. Aircraft fly-over noise acquired on receivers placed in sediment proved to be a promising approach towards broadband low-frequency measurements. Since the magnitude of the Doppler-shift depends on sound speed at the receiver position, the observed Doppler-shift can be used to derive the sound speed. We propose a new approach using the entire time series instead of employing only the two observed frequencies at approaching and departing. It is based on a model for received signals, accounting for the Doppler-shifted frequency. By maximizing the match between modeled and measured time series as a function of sound speed and frequency in a least-squares framework, estimates of the frequency-dependent sound speed are obtained. The method is applied to data acquired at receivers placed in air, water and sediment. Statistical tests indicate that the marine sediment sound speed depends indeed on frequency, i.e. sound speed decreases significantly below 300 Hz. A comparison is made with a modified viscous fluid model from which realistic values for the geotechnical parameters of the considered sediment were obtained.

Using buried vector sensors to examine seabed layering in sandy sediment

There is considerable interest within the underwater acoustics community in quantifying the sound-speed dispersion in sandy sediments at low kiloHertz frequencies. To address this, data were collected during the SAX04 experiment (a US Office of Naval Research Departmental Research Initiative) using projectors and directional (vector) receivers buried in the top 1 m of the seabed, in conjunction with a water-borne source directly above the buried sensor field. Although using buried sensors significantly increased the complexity of the experimental setup, it should enable a direct time-of-flight measurement of acoustic wave speed, which simplifies interpretation of the results. However, initial analysis of the time-of-flight results indicates the existence of a buried layer, which increases the complexity of the data. In this paper, the vector sensors are used to steer beams to confirm the existence of the layer and to isolate the direct and reflected arrivals to improve the estimate of sound speed dispersion. [Work partially funded by US Office of Naval Research.]

Frequency dependences of absorption and scattering components of attenuation for water‐saturated sands

Frequency dependences of attenuation of sound waves in water‐saturated marine sands are discussed. Measured attenuation includes a scattering component, and this makes it difficult to understand the frequency dependences of attenuation. By removing the scattering component from the measured attenuation, the Kramers‐Kronig (K‐K) relationship gives the correct sound speed dispersion. Consequently, the intrinsic attenuation extracted from the data collected during SAX99 experiments follows the Biot theory for overall frequencies. This suggests that the attenuation coefficient of sound waves for water‐saturated sands is not linear in f. The sound speeds recalculated via the K‐K relationship are also in excellent agreement with the Biot theory at high frequencies.

Frequency dependence of sound speed and attenuation in marine sediments

Zhou and Zhang [J. Acoust. Soc. Am. (2005) (2006)] have reviewed diverse data for propagation in sandy sediments. Attenuation for frequencies below 1 kHz corresponds roughly to α=0.34(f/fo)2 dB/m with the reference frequency being 1 kHz. The best‐fit exponent is slightly less than 2. Their review of results for frequencies above 10 kHz suggests a substantially different frequency dependence. They considered two explicit models, the Biot model as parametrized and extended by Stoll and the BICSQS model of Chotiros and Isakson [J. Acoust. Soc. Am. (2004)]. In either case the fit of parameters to match sound speed dispersion resulted in an unsatisfactory fit of attenuation versus frequency, and conversely. The present paper reexamines this and contends that, while Biot’s formulation is intrinsically correct at low frequencies, Stoll’s parametrization is noncausal: Chotiros’ model more nearly captures the correct physics in that it is intrinsically causal and includes relaxation processes. A considered extensi...

Sediment sound speed measurements using buried vector sensors

As part of the SAX04 sediment acoustics experiment conducted off the coast of Florida in the Gulf of Mexico, vector sensors containing three-axis accelerometers and pressure sensors were buried in the seabed. These sensors were used as the receivers to measure sediment sound speed dispersion from 300 to 3000 Hz a band in which it has been particularly difficult to make these measurements. The acoustic intensity measured by the vector sensors was combined with the experimental geometry and propagation conditions, to relate the angle of arrival to sediment sound speed as a function of frequency. Lower frequency measurements, 300 to 1200 Hz, used noise radiated from a moored research vessel as the acoustic source. Higher frequency measurements, 800 to 3000 Hz, used transmissions from an acoustic projector in a three-point mooring in the water column that could be adjusted to change the angle of ensonification. Results from the two techniques are compared with each other and previous measurements of dispersion in sandy sediments. [Work performed under ONR Grants N00014-04-1-0013 and N00014-03-1-0883.]

Inferences on Seabed Acoustics in the East China Sea From Distributed Acoustic Measurements

Low-frequency acoustic data acquired in the central East China Sea basin at two locations are analyzed for the purpose of making inferences on seabed acoustics. Previous geophysical studies indicate that the first sediment layer is composed of a fine to medium sand. The current analysis employs octave-averaged transmission loss (TL) versus range data and pressure time series generated from explosive sources. The TL and time series data were collected in locations separated by about 65 km during the same month of the year. Both locations are near the same longitude, with water depths of 100-120 m. A linear frequency dependence of the attenuation in the 25-800 Hz band, with or without sound speed dispersion, leads to a geoacoustic solution using the TL data consistent with a soft clay, and thus inconsistent with the existing geophysical data. However, seabed representations that allow for a nonlinear frequency dependence of the attenuation, such as a Kramers-Kronig dispersion relationship, a simplified six-parameter Biot description, and an empirical frequency power law of the attenuation, all give similar values of the attenuation as a function of frequency and sediment sound speeds that are consistent with the previous geophysical studies in the area. Geoacoustic solutions obtained with the TL inversions produce reasonably good fits to the measured time series data. Inversions of the time series indicate that the sound speed at the top of the sediment is lower as compared to the values estimated from the location where the TL data were acquired. While the data have significant limitations as to the information they contain on the properties of the seabed, the analysis aids in quantifying the sensitivity of geoacoustic inversion of acoustic data in shallow water littoral regions to assumptions about the frequency dependence of attenuation and sound speed

A hybrid model of sound propagation in unconsolidated sediments

Efforts to model sound speed and attenuation in sandy sediments have centered on the use of theories for which either the relative motion of the pore fluid is the dominant attenuation mechanism, such as Biot theory, or the dominant loss mechanism is grain-to-grain friction. A recent model which attempts to incorporate grain-to-grain loss mechanisms into a model of sandy sediments was proposed by Buckingham. This model can fit the frequency dependence of the attenuation measured in ocean sediments and laboratory glass bead sediments, but it does not capture the sound speed dispersion as effectively as Biot theory. The relative success of each model suggests that both attenuation mechanisms may play important roles in sediment acoustics. In order to explore this possibility, a hybrid model has been developed which incorporates Buckingham’s grain-to-grain shearing mechanisms into the frame moduli used in Biot theory. In the hybrid model, the grain-to-grain losses dominate at high and very low frequencies while pore fluid attenuation dominates at mid-frequencies where the sound speed dispersion is the most pronounced. As a consequence, the hybrid model is able to describe both the measured sound speed and attenuation in ocean and laboratory sediments. [Work supported by ONR.]

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 the attenuation was successfully modeled.

A broadband ocean sediment acoustics model for signal processing applications

It has been shown that fluid and viscoelastic solid approximations cannot accommodate the observed sound speed dispersion and enhanced reflection loss over sandy shallow water sediments. A plausible poroelastic model has been developed for the high frequency band (>50 kHz) using measurements from several sources. This model, with constant coefficients, is unable to track the observed sound speed dispersion at lower frequencies. It is hypothesized that one parameter, the frame bulk modulus, varies with frequency in a relaxation process associated with squirt flow at the grain–grain contact. This hypothesis has the potential to be a critical component in broadband acoustic models of granular ocean sediments. It will link measurements at high frequencies to propagation modeling at low frequencies, provide accurate, physics based, models of propagation loss, and a means to invert for bottom properties over a broad range of frequencies. [Work supported by ONR, Undersea Signal Processing.]

Comparison of sound speed and attenuation measured in a sandy sediment to predictions based on the Biot theory of porous media

During the sediment acoustics experiment in 1999 (SAX99), several researchers measured sound speed and attenuation. Together, the measurements span the frequency range of about 125 Hz-400 kHz. The data are unique both for the frequency range spanned at a common location, and for the extensive environmental characterization that was carried out as part of SAX99. Environmental measurements were sufficient to determine or bound the values of almost all the sediment and pore water physical property input parameters of the Biot poroelastic model for sediment. However, the measurement uncertainties for some of the parameters result in significant uncertainties for Biot-model predictions. Here, measured sound-speed and attenuation results are compared to the frequency dependence predicted by Biot theory and a simpler "effective density" fluid model derived from Biot theory. Model/data comparisons are shown where the uncertainty in Biot predictions due to the measurement uncertainties for values of each input parameter are quantified. A final set of parameter values, for use in other modeling applications e.g., in modeling backscattering (Williams et al., 2002) are given, that optimize the fit of the Biot and effective density fluid models to the sound-speed dispersion and attenuation measured during SAX99. The results indicate that the variation of sound speed with frequency is fairly well modeled by Biot theory but the variation of attenuation with frequency deviates from Biot theory predictions for homogeneous sediment as frequency increases. This deviation may be due to scattering from volume heterogeneity. Another possibility for this deviation is shearing at grain contacts hypothesized by Buckingham; comparisons are also made with this model.

The joint analysis of general aspects of the phenomenological thermodynamics and the kinetic Boltzmann theory

The question of agreement of the kinetic moment theory with the first principle continuum thermodynamics is considered. The characteristics of distribution function describing local non-equilibrium state of monatomic gases are analyzed. In the first approach on non-equilibrium variables the equations making more exact the results of Chapman and Enskog are received. The paradox of heat conduction is eliminated and the coincidence of theoretical and experimental data on dispersion of sound speed in inert gases is improved.

An approach to acoustic properties of biological tissues using acoustic micrographs of attenuation constant and sound speed.

To develop a method for two-dimensional measurement of acoustic properties of biological tissue elements at the microscopic level for specimens with a thickness of approximately 10 microm. The procedure was developed on the basis of mechanically scanned acoustic microscopic techniques in the frequency range of 100 to 200 MHz and the theory of interference phenomena. Various tissues and samples were prepared to evaluate the method and to interpret sound propagation properties. Tissues with high protein content, low water content, or both had a high attenuation constant and sound speed. The exponent n of attenuation against frequency was almost unity at the microscopic level, whereas it was greater than unity when the specimen thickness was greater. Sound speed dispersion was not observed. The method was shown to be reproducible, and the data were interpreted acoustically and pathologically with reference to tissue type and specimen thickness.

Inelastic X-ray scattering determination of the dynamic structure factor of liquid lithium

Abstract We present new inelastic X-ray scattering data for the dynamic structure factor S(Q, ω) of liquid lithium collected at two different temperatures (T = 475K and T = 600K) and in a wide range of exchanged wave-vectors (Q = 1 nm−1 to Q=110nm−1). The analysed Q range covers the transition from collective to single-particle regimes. The spectra have been put on an absolute scale using its first sum rules, and the result obtained has been tested on diffraction data and novel molecular dynamie results. A relaxation fingerprint is observed at low wave-vectors (the so-called positive dispersion of the apparent sound speed), while at higher Q the single particle behaviour gradually emerges.

Acoustic propagation in gassy sediments

Measurements of values of sediment physical properties, bubble volume, and bubble size distribution are used to predict sound speed and attenuation in the fine-grained, gassy sediments of Eckernförde Bay, Baltic Sea. The predicted results are compared to in situ and laboratory measurements of sound speed and attenuation over the frequency range of 5–400 kHz. Dispersion of sound speed is used to determine the upper limit of methane bubble resonance near 20 kHz. These data combined with bubble size distribution measured using CT scans of sediments held under ambient conditions yield an estimate of effective bubble size of 0.3–5.0-mm equivalent radii. Histograms of bubble size distribution are then used to predict frequency-dependent sound speed and attenuation based on the model of Anderson and Hampton [J. Acoust. Soc. Am. 67, 1865–1903 (1980)]. Given the highly variable spatial distribution of bubble volume and size, the agreement between theory and measurement is remarkably good.

Brillouin light scattering of a fragile glass former: O-terphenyl

Abstract We report Brillouin scattering measurements of the fragile glass former o-terphenyl over a wide temperature range covering the normal and the supercooled liquid phase down to the glass temperature. The velocity dispersion and the absorption of the longitudinal sound waves are reported and compared with literature data. The presence of both a residual sound speed dispersion in the hot liquid phase and a strongly asymmetric shape of the Brillouin line width curve in the high-temperature region indicates the existence of two relaxation phenomena: a structural and a fast secondary relaxation. This picture is consistent with the classication of o-terphenyl as a non-associated liquid, as emerges from the analysis of the temperature behaviour of the ratio of the experimental to the classically calculated sound wave absorption.

Measurements of passive and active microbubbles in the sea

Around 1960 an oceanographer at the Navy Electronics Laboratory dared to question physics laboratory measurements when he wrote an internal memo titled ‘‘Do Invisible Microbubbles Exist at Sea?.’’ Indeed they do! From 1964 to 1974 a series of M.S. students at the Naval Postgraduate School published the first microbubble density distributions at sea. These were measured by several in-situ ocean techniques including: change of transducer impedance; photography; excess attenuation, backscatter and sound-speed dispersion in a small pulse-echo system: Fourier transform of a sawtooth signal propagating between two separated hydrophones. An ‘‘unbelievable’’ immense number of coastal bubbles of radius 15 to 300 μm were found. The 1990s have seen a renaissance in the field. The spatial and temporal variation of bubble numbers have been studied, and acoustical oceanographers now use bubbles as tracers to determine ocean processes near the ocean surface. Sea state noise and rain noise have both been definitively ascribed to the radiation from huge numbers of infant microbubbles. Indeed, the ‘‘noises’’ have now become ‘‘signals.’’ The underwater sound of breaking waves has been inverted to yield the spectrum of ocean wave height and recently the underwater sound of rainfall has been inverted to reveal the real-time rainfall drop size distribution. The distinctive spectrum of underwater sound during rainfall even allows one to describe the clouds from which the rain has fallen. [Work supported by ONR.]

Detonation in a relaxing gas

One-dimensional steady-state detonation has been theoretically investigated in a gas with internal degrees of freedom (not directly related to irreversible energy release) characterized by a finite relaxation time τ. Relaxing gas is a variant of a system with sound speed dispersion. Detonation in such a system has been studied in detail by Kirkwood and Wood, who have pointed out the difficulties in formulating the Chapman-Jouguet (C-J) condition in such a medium. Self-sustaining (normal) and strong detonations for an arbitrary α  τ τ Q (where τ Q is the characteristic heat release time) have been determined, using an ideal gas with relaxing vibrational energy of molecules. The “topology” of continuous (in α) evolution of normal and strong detonations in the p- ν (pressure and specific volume of gas) plane has been determined with varying α. For normal detonations two values α ∗ and α ∗∗ < α ∗ , both of the order of unity, have been found to exist such that for the equilibrium C f and frozen cf sound speeds and for gas velocity u relative to the detonation wave at the Jouguet point, we have u = c f if c f > α ∗, c f > u > c e if α ∗ > α > α ∗∗, and u c e if α < α ∗∗ . The steady detonation wave zone has been matched with the rarefaction wave. The C-J condition has been generalized and a procedure has been described for calculating the parameters at the Jouguet point and the normal detonation velocity in a real gas mixture with relaxation.