Effective Density Fluid Model Research Articles

Analysis of the variation of in situ seafloor sediments acoustic characteristics with porosity based EDFM

Numerous factors influence the acoustic characteristics of seafloor sediments, necessitating a comprehensive study that combines theoretical analysis, laboratory measurements and in situ measurements to support acoustic prediction and inversion. In this study, a porosity-based effective density fluid model (P-EDFM) is established to analyze the variation of acoustic properties with the porosity of seafloor sediments. On the biases of P-EDFM, the attribute of measured sound velocity and acoustic attenuation coefficient of seafloor sediment in Series 9B of the SAX99 was well interpreted within the frequency range of 25-100 kHz. The in situ measured sound velocity ratio was well predicated by the P-EDFM in the East China Sea and Yellow Sea. It reveals that the in situ sound velocity ratio decreases with increasing bulk porosity and with decreasing bulk density. The scattering and differences in the acoustic attenuation coefficient measured in situ in seafloor sediments are found to be greater than those observed for sound velocity. After considering the influence of temperature in the P-EDFM, the prediction of in situ sound velocity aligns well with the measured dataset. While, the acoustic attenuation coefficient exhibits an inflection point, increasing initially and then decreasing with changes in porosity, similar to the observed pattern in Hamilton’s observation and estimation. By incorporating temperature and frequency influences, the in situ measurements of sound velocity of seafloor sediments are corrected into laboratory sound velocities by using the P-EDFM. The result reveals the sediment samples’ sampling and transmitting process has a much greater impact on the sound velocity of sandy sediment in the East China Sea compared to muddy sediment. Overall, P-EDFM can predict the in situ sound velocity and sound attenuation coefficient under different temperatures and frequencies, with a lower prediction error for sound velocity compared to sound attenuation coefficient.

Integrating Multiple-Try DREAM(ZS) to Model-Based Bayesian Geoacoustic Inversion Applied to Seabed Backscattering Strength Measurements

The key to model-based Bayesian geoacoustic inversion is to solve the posterior probability distributions (PPDs) of parameters. In order to obtain PPDs more efficiently and accurately, the state-of-the-art Markov chain Monte Carlo (MCMC) method, multiple-try differential evolution adaptive Metropolis(ZS) (MT-DREAM(ZS)), is integrated to the inverse problem because of its excellent ability to fully explore the posterior space of parameters. The effective density fluid model (EDFM), which is derived from Biot–Stoll theory to approximate the poroelastic model, and the published field measurements of backscattering strength are adopted to implement the inversion. The results show that part of the parameters can be estimated close to the measured values, and the PPDs obtained by dual-frequency inversion are more concentrated than those of single-frequency inversion because of the use of more measured backscattering strength data. Otherwise, the comparison between the predicted backscattering strength of dual-frequency inversion results and Jackson’s prediction shows that the solutions of the inverse problem are not unique and may have multiple optimal values. Indeed, the difference between the two predictions is essentially the difference in the estimation of the contribution of volume scattering to the total scattering. Nevertheless, both results are reasonable due to the lack of measurement of volume scattering parameters, and the inversion results given by the posterior probabilities based on the limited measurements and the adopted model are still considered to be reliable.

An illustration of the effect of neglecting poroelastic physics of water-saturated glass beads in a laboratory phase speed inference process.

The sound speed of sand has been shown to vary with frequency, yet in many instances in geoacoustic inversions, sand is modeled as a frequency-independent effective fluid. This paper investigates the effect to which assuming a frequency-independent fluid model that neglects poroelasticity can skew parameter estimation in a laboratory layered waveguide consisting of 1-mm diameter water-saturated glass beads (WSGBs), suspended in a water-filled glass tube. The phase speed in the waveguide was measured from 1 to 7 kHz and compared with phase speeds predicted in a finite element simulation of the experiment, where the WSGBs were treated as either a fluid with constant bulk density and frequency-independent or frequency-dependent sound speed, or by an effective density fluid model (EDFM) that includes poroelasticity. Measurement-simulation agreement occurred when using the EDFM to model the WSGB, although neglecting poroelasticity in the simulation only led to a maximum phase speed discrepancy of 8 m/s. However, this effect was significant when an inference process was used to determine the effective fluid properties of the WSGBs. Finally, high-frequency (150 to 450 kHz) direct sound speed measurements of the WSGB were obtained, and best matched the mid-frequency inference results obtained using the EDFM.

A Comparison of Three Sediment Acoustic Models Using Bayesian Inversion and Model Selection Techniques

Many geoacoustic models are used to establish the relationship between the physical and acoustic properties of sediments. In this work, Bayesian inversion and model selection techniques are applied to compare combinations of three geoacoustic models and corresponding scattering models—the fluid model with the effective density fluid model (EDFM), the grain-shearing elastic model with the viscosity grain-shearing (VGS(λ)) model, and the poroelastic model with the corrected and reparametrized extended Biot–Stoll (CREB) model. First, the resolution and correlation of parameters for the three models are compared based on estimates of the posterior probability distributions (PPDs), which are obtained by Bayesian inversion using the backscattering strength data. Then, model comparison and selection techniques are utilized to assess the matching degree of model predictions and measurements qualitatively and to ascertain the Bayes factors in favor of each quantitatively. These studies indicate that the fluid and poroelastic models outperform the grain-shearing elastic model, in terms of both parameter resolution and the ability to produce predictions in agreement with measurements for sandy sediments. The poroelastic model is considered to be the best, as the inversion based on it can provide more highly resolved information of sandy sediments. Finally, the attempt to implement geoacoustic inversion with different models provides a relatively feasible remote sensing scheme for various types of sediments under unknown conditions, which needs further validation.

Comparison of sound speed and attenuation measurements to the corrected effective density fluid model for gassy sediments.

To validate the corrected effective density fluid model for gassy sediments, an acoustic experiment was undertaken to measure the sound speed and attenuation in the frequency band of 10 to 120 kHz in a laboratory tank. Sound speed and attenuation each have four peaks, with a one-to-one correspondence between them. The optimal bubble size distribution modeled by five continuous modified Gaussian functions is obtained from inversion of sound speed and attenuation data. The measured sound speed and attenuation are in good agreement with the predicted results.

Comparison of velocity and attenuation measurements to the corrected effective density fluid model for gassy sediments

To validate the corrected effective density fluid model for gassy sediments, an acoustic experiment was undertaken to measure the velocity and attenuation over the frequency range of 8 and 120 kHz in an indoor water tank. The velocity and attenuation obtained by different estimation methods have good consistency respectively. Both of them have four distinct peaks and there is one-to-one correspondence between velocity peaks and attenuation peaks. Through numerical simulation of the acoustic characteristics attributed to the resonance of gas bubbles with different radii, the existence of small bubbles causes the velocity to decrease in the vicinity of resonance frequency of large bubbles. Five modified Gaussian functions are introduced to model the bubble size distribution inside the gassy sediment. A best bubble size distribution is obtained by inversion of the velocity and attenuation data simultaneously, and the predictions of the corrected model are broadly in good agreement with the measurements.

Frequency dependence of sound speed and attenuation in fine-grained sediments from 25 to 250 kHz based on a probe method

The frequency dependence of the sound speed and attenuation in seafloor sediments was measured in a laboratory by using a probe method at the frequency range of 25–250 kHz. The standard deviation of repeated sound speed measurement in fresh water is about 2.82 m/s. Repeated measurement of attenuation shows a minimum standard deviation of 0.58 dB at 25 kHz and a maximum standard deviation of 3.06 dB/m at 250 kHz. The measurement results indicate that the sound speeds vary from 1638 to 1658 m/s in sandy silt sediments and from 1548 to 1571 m/s in clayey silt sediments. The attenuation increases from 14.2 to 51.9 dB/m in sandy silt sediments and from 7.8 to 31.7 dB/m in clayey silt sediments. The measured sound speed dispersion in sandy silt sediment agrees reasonably with the predictions of the Biot-Stoll model, the Grain-Shearing model, and the Effective Density Fluid model (EDFM). The measured sound speed in clayey silt sediment agrees better with the predictions of the GS model than that of the Biot-Stoll model and the EDFM. The measured attenuation is more consistent with f1/2 dependence than the f1 dependence, and is similar to the predictions of Biot-Stoll model and the EDFM.

Application of Sub-Bottom Profiler to Study Riverbed Structure and Sediment Density

In this pater, we present a study on the riverbed structure and sediment density in-situ test by using sub-bottom profiler. Compared with traditional direct observation methods, the sub-bottom profiler method based on sonar technology is non-contact, low-disturbance and high-efficient. We finish the investigation of several sections in Sanmenxia and Xiaolangdi reservoirs, which located on the main channel of lower reaches of Yellow River. Collected data show a detailed layered structure of the riverbed sediment which believed caused by sedimentary processes in different periods. Further more, we analyse the reflection coefficient of water-sediment interface and inverse the sediment density data from the raw wave record. The inversion method is based on the effective density fluid model and Kozeny-Carman formula. The comparison of the inversion results and sample tests shows that the in-situ test is reliable and useable.

Propagation of elastic waves in saturated porous medium containing a small amount of bubbly fluid

It is very important to understand the acoustical properties of porous medium. To study the relationship between acoustical and other physical properties of porous medium will help us to use acoustical tools for determining the physical properties of porous medium. Many researchers have paid much attention to the properties of acoustic wave propagation in the gassy marine sediments based on the Biot model which is popularly used to predict the dispersion and attenuation of sound in saturated porous medium. The patchy model which contains gas inside the spherical water predicts that the existence of gas just has little effect on the propagation of acoustic wave in porous medium when the gas content is very small. However, the presence of a small number of bubbles in a fluid saturated sediment will lead to different acoustic responses. As is well known, the bubble vibration theory proposed by Keller and Miksis shows that a small number of bubbles existing in the liquid will have a great influence on sound velocity and attenuation. Therefore, in order to study the effect of a small amount of gas existing in fluid saturated porous medium on the property of acoustic wave propagation, we investigate a bubbly liquid saturated porous medium and consider the case of the bubbles vibrating linearly under the action of sound waves. First, we derive the continuity equation of the seepage according to the mass conservation of the pore fluid and the relationship between porosity differentiation and pore fluid pressure differentiation. Then, the bubble linear vibration theory given by Commander is used to deal with the time derivative of gas volume fraction in the continuity equation of the seepage, The bubble linear vibration theory gives the relationship between instantaneous bubble radius and background pressure of the medium. Through this relationship, we obtain the equation of time derivative of gas volume fraction and time derivative of pore fluid pressure. Then, we combine the obtained equation with the continuity equation of seepage, and obtain the modified continuity equation of seepage whose form is similar to that of Biot model. Finally, the modified Biot's equations for fluid saturated porous medium containing a small amount of bubbly fluid is obtained. As is well known, an effective density fluid model for acoustic propagation in sediments, derived from Biot theory, just can predict the acoustic properties of the fast compressional waves. However, the present model can predict the acoustic properties of fast, slow compressional waves and shear waves propagating in sediments. Through numerically calculating the dispersion, attenuation, amplitude ratios of pore fluid displacement to solid displacement for fast and slow compressional waves, it is found that the existence of a small number of bubbles has an influence on the acoustic properties of both the fast compressional waves and the slow compressional waves, especially the velocity of the fast compressional wave. In addition, the low-frequency speed approximation formula for the fast compressional wave is also presented. The approximate formula directly indicates the relationship between the velocity of fast compressional wave and the parameters of porous medium such as the gas volume fraction and the bubble radius. This study shows that the influence of a small number of bubbles in fluid saturated on acoustic wave propagation is noticeable. The modified Biot model presented in this paper provides one model to study the properties of acoustic waves in fluid saturated porous medium with a small number of bubbles.

Acoustic inversion method for parameters of sediments based on adaptive predatory genetic algorithm.

Acoustic inversion for the physical parameters of seafloor sediments is an important and difficult aspect of sediment acoustic research. Submarine surface sediments are typical porous media, which involve many parameters. Thus, the optimization of high-dimensional inversion represents one of the difficulties. An acoustic inversion method to obtain the physical parameters of seafloor sediments is constructed based on the adaptive predatory genetic algorithm and effective density fluid model derived from Biot theory. The method introduces the adaptive process and predatory strategy into the genetic algorithm and uses the norm of the relative difference between the predicted wave number and the measured wave number as the objective function. The method is confirmed to be stable and efficient by simulated data and is also applied to invert porosity, tortuosity, and permeability of the sediments in Hangzhou Bay of China using acoustic data measured by an in situ acoustic measurement system.

Gas-bubble inversion in marine sediments

The acoustic properties of marine sediments can dramatically change because of the presence of gas-bubbles. Many applications require the detailed information of gas-bubbles, such as gas void fraction and gas-bubble size distribution. It is possible to relate the acoustic transmission measurements with bubble sizes. This study aims toward the development of an acoustic method able to both detect and quantify the gas present in marine sediments. This acoustic method adapts the effective density fluid model corrected by gas-bubble pulsations as a forward model and expands the unknown gas-bubble size distribution by a finite sum of cubit B-splines. The inverse problem can be transformed into solving the equation groups involving the coefficients of cubit B-splines. This method can be verified by testing analytical results and then applied to measurement sound speed and attenuation data which were acquired via transmission experiments.The acoustic properties of marine sediments can dramatically change because of the presence of gas-bubbles. Many applications require the detailed information of gas-bubbles, such as gas void fraction and gas-bubble size distribution. It is possible to relate the acoustic transmission measurements with bubble sizes. This study aims toward the development of an acoustic method able to both detect and quantify the gas present in marine sediments. This acoustic method adapts the effective density fluid model corrected by gas-bubble pulsations as a forward model and expands the unknown gas-bubble size distribution by a finite sum of cubit B-splines. The inverse problem can be transformed into solving the equation groups involving the coefficients of cubit B-splines. This method can be verified by testing analytical results and then applied to measurement sound speed and attenuation data which were acquired via transmission experiments.

Geoacoustic sediment model discrimination using acoustic color comparison

Many competing geoacoustic models exist to represent sandy sediments. These models can be fluid, elastic, or poroelastic, depending on the number and types of waves the sediment is assumed to support. In this talk, a fully scattered field finite element approach is utilized to construct acoustic color templates for a buried spherical aluminum shell and a spherical bubble. The simulated results are then used to assess the ability of target strength measurements to discriminate between the predictions of the competing sediment models. Such discrimination may help determine the physical validity of a given geoacoustic model and aid in model selection. Five geoacoustic sediment models are considered: a simple fluid, constant-Q fluid model, the effective density fluid model of Williams, the viscous grain shearing model of Buckingham, the Biot-Stoll poroelastic model, and the extended Biot model of Chotiros. [Work supported by ONR, Ocean Acoustics.]

Inversion of river-bottom sediment parameters using mechanically sampled specimens and subbottom profiling data

The study of river dynamics requires knowledge of physical parameters, such as porosity, permeability, and wave propagation velocity, of river-bottom sediments. To do so, sediment properties are determined on mechanically sampled specimens and from subbottom profiling. However, mechanical sampling introduces disturbances that affect test results, with the exception of grain-size distribution. In this study, we perform inversion of acoustic data using the grain-size distribution of mechanically sampled specimens and the relation between porosity and permeability from the Kozeny–Carman equation as prior information. The wave reflection coefficient of the water–silt interface is extracted from the raw subbottom profile. Based on the effective density fluid model, we combine the Kozeny–Carman equation and the wave reflection coefficient. We use experimental data from two Yellow River reservoirs to obtain the wave velocity and density of multiple sections and their spatial variations, and find that the inversion and testing results are in good agreement.

Study on sound-speed dispersion in a sandy sediment at frequency ranges of 0.5–3 kHz and 90–170 kHz

In order to study the properties of sound-speed dispersion in a sandy sediment, the sound speed was measured both at high frequency (90–170 kHz) and low frequency (0.5–3 kHz) in laboratory environments. At high frequency, a sampling measurement was conducted with boiled and uncooked sand samples collected from the bottom of a large water tank. The sound speed was directly obtained through transmission measurement using single source and single hydrophone. At low frequency, an in situ measurement was conducted in the water tank, where the sandy sediment had been homogeneously paved at the bottom for a long time. The sound speed was indirectly inverted according to the traveling time of signals received by three buried hydrophones in the sandy sediment and the geometry in experiment. The results show that the mean sound speed is approximate 1710–1713 m/s with a weak positive gradient in the sand sample after being boiled (as a method to eliminate bubbles as much as possible) at high frequency, which agrees well with the predictions of Biot theory, the effective density fluid model (EDFM) and Buckingham’s theory. However, the sound speed in the uncooked sandy sediment obviously decreases (about 80%) both at high frequency and low frequency due to plenty of bubbles in existence. And the sound-speed dispersion performs a weak negative gradient at high frequency. Finally, a water-unsaturated Biot model is presented for trying to explain the decrease of sound speed in the sandy sediment with plenty of bubbles.

Effect of gas bubble volume fraction on low-frequency acoustic characteristic of sandy sediment

Owing to the decomposition of organic material and other reasons, the actual marine sediment contains gas bubbles, and the existence of gas bubbles will significantly affect the low-frequency acoustic characteristics of sediment. Therefore, it is significant to investigate the effect of gas bubbles on the low-frequency sound velocity in the sediment. Considering the uncontrollable environmental factors of field experiment, an experiment platform for obtaining acoustic characteristics of a large-scale gas-bearing unsaturated sandy sediment is constructed in the indoor water tank. Considering the long wavelength of low-frequency acoustic wave and the multipath interference in water tank, the transmitted acoustic signals are received by hydrophones which are buried in the unsaturated sediment. The sound velocity data (79-142 m/s) in the gas-bearing unsaturated sediment are acquired by using a multi-hydrophone inversion method in the bounded space for the first time in a 300-3000 Hz range, and the sound velocity data (112-121 m/s) are also acquired by using a double-hydrophone method in the same frequency range. The refraction experiments at different horizontal distances between the source and the hydrophones are conducted, which verifies the reliability of sound velocity data acquired by using the multi-hydrophone inversion method and the double-hydrophone method. At the acoustic frequency well below the resonance frequency of the largest bubble in the sediment, the pore water and the gas bubbles are regarded as an effective uniform fluid based on effective medium theory. On this basis, the density and the bulk elastic modulus of pore water in the effective density fluid model are replaced by the effective density and the effective bulk modulus of the effective uniform fluid, then a corrected effective density fluid model is proposed in gas-bearing unsaturated sediment. The numerical analysis indicates that when the gas bubble volume fraction is small (1%), a small increase in the gas bubble will cause a significant decrease in the effective bulk elastic modulus of sediment, but the density of pore water is much greater than the density of gas bubbles, the presence of a small number of gas bubbles hardly changes the density of pore fluid and certainly does not change the density of sediment, which results in a significant decrease at a low-frequency sound velocity in the gas-bearing unsaturated sediment. Furthermore, with the increase of gas bubble volume fraction, the sound velocity predicted by the corrected model gradually decreases, and the decreasing trend gradually becomes gentle. The corrected model reveals the effect of gas bubbles on the low-frequency acoustic characteristic of sediment. By analyzing the sensitivity of the predicted sound velocity to parameters of the model, the gas bubble volume fractions (1.07%-2.81%) of different areas are acquired by inversion according to the measured sound velocity distribution and the corrected model. In the future, it will provide a new method of obtaining the volume fraction and the distribution of gas bubbles in the sediment.

A corrected effective density fluid model for gassy sediments.

A corrected effective density fluid model is developed for predicting sound speed dispersion and attenuation coefficient in gassy sediments. An acoustic experiment was undertaken to measure the attenuation coefficient in a frequency band of 600 to 3000 Hz in gassy unsaturated sand. The measured frequency spectra of the attenuation coefficient show four peaks due to bubble resonance. Then a method of using several modified Gaussian functions to model bubble size distribution is proposed to fit measured attenuation data, which shows that the magnitudes of the fitted model attenuation coefficients are broadly in agreement with those measured attenuation data.

Erratum: On the validity of the effective density fluid model as an approximation of a poroelastic sediment layer [J. Acoust. Soc. Am. 138, 748-757 (2015)

Erratum: On the validity of the effective density fluid model as an approximation of a poroelastic sediment layer [J. Acoust. Soc. Am. 138, 748-757 (2015)

Acoustic Velocity and Attenuation in Magnetorhelogical fluids based on an effective density fluid model

Magnetrohelogical fluids (MRFs) represent a class of smart materials whose rheological properties change in response to the magnetic field, which resulting in the drastic change of the acoustic impedance. This paper presents an acoustic propagation model that approximates a fluid-saturated porous medium as a fluid with a bulk modulus and effective density (EDFM) to study the acoustic propagation in the MRF materials under magnetic field. The effective density fluid model derived from the Biot’s theory. Some minor changes to the theory had to be applied, modeling both fluid-like and solid-like state of the MRF material. The attenuation and velocity variation of the MRF are numerical calculated. The calculated results show that for the MRF material the attenuation and velocity predicted with this effective density fluid model are close agreement with the previous predictions by Biot’s theory. We demonstrate that for the MRF material acoustic prediction the effective density fluid model is an accurate alternative to full Biot’s theory and is much simpler to implement.

First arrival cycle-based calculation methods of in situ sound speed and attenuation in sediments

ABSTRACTThe acoustic properties of seafloor sediments are of great importance in geoacoustic modeling, detecting, and oceanic engineering. The methods based on the first arrival cycle are investigated to calculate sound speed and attenuation of sediment more precisely in in situ measurements. The comparison of different data analysis methods based on the first arrival cycle approach for in situ measurement results in the following conclusions: (1) the calculated methods can help find the effective cycles and reduce the errors in calculating sound speed and attenuation; (2) using this approach, the point judgment method-based data analysis has the same effectiveness as the cross-correlation method-based data analysis in calculating group sound speed and has the same effectiveness in calculating attenuation in the time domain as the spectrum analysis method-based data analysis has in calculating attenuation in frequency domain; and (3) measurement in water can help not only calibrate the transmitting distance but also can calculate the time delay for the sound speed and the attenuation loss in the transmitting process. Finally, theoretical calculation was used to calculate the measured results, indicating a good agreement, which supports that first arrival cycle-based calculated methods can be used to analyze the measured data and the effective density fluid model can be used to analyze more acoustic properties and invert several physical properties in this experiment.

Influence of Temperature on Acoustic Sound Speed and Attenuation of Seafloor Sand Sediment

The temperature dependence of the parameters within an effective density fluid model that incorporates the effects of granularity is used to examine sound speed and attenuation of sand within the temperature range of 1 $^{\circ}$ C–30 $^{\circ}$ C. Analysis of the behavior of attenuation as a function of frequency and permeability over the above temperature range give some new insights. In particular, the attenuation coefficient can either increase or decrease with temperature depending on the physical parameters and the frequency range being examined. A relaxation frequency is defined that separates frequency ranges where attenuation temperature dependence changes. Below the relaxation frequency, attenuation increases with temperature, and above this frequency, attenuation decreases with temperature. The analysis of the effect of sand sediment physical parameters on acoustic properties versus temperature also reveals the unique role of permeability. An “attenuation transition permeability” is also defined. As temperature increases, attenuation increases if the static permeability is less than the attenuation transition permeability and decreases if the static permeability is greater than the attenuation transition permeability. The comparison of experimental data sets with calculations using the temperature-dependent effective density fluid model indicates the dominant role of pore water both on the temperature-dependent sound speed and attenuation of sand sediment and gives support to use of an effective-density-based model.