A stable staggered-grid finite-difference scheme for acoustic modeling beyond conventional stability limit

Staggered-grid finite-difference(SGFD)schemes have been widely used in acoustic wave modeling for geophysical problems.Many improved methods are proposed to enhance the accuracy of numerical modeling.However,these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy(CFL)numbers,making them unstable when modeling with large time sampling intervals or small grid spacings.To solve this problem,we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers.First,to improve modeling stability,we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region,and make the FD dispersion approach a given function outside the given wave-number area,thus breaking the conventional limits of the maximum CFL number.Second,to obtain high modeling accuracy,we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients.In addition,the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme.Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber,indicating that the proposed scheme improves stability during the modeling.

Fine Sand and Clay Sediment Acoustic Properties of the Novel Sediment Sample from the Arabian Sea:Experimental Investigations and Biot−Stoll Model Validation

The present study explores the physical and acoustic characteristics of fine sand and clay in novel seabed marine sediments from of Pakistan coastline of the Arabian Sea.The measured physical parameters included mean grain size,mass density,bulk density,salinity,porosity,permeability,pore size and mineralogical composition.Acoustic properties,including sound speed and attenuation,in the high frequency range of 90-170 kHz were analyzed.A controlled laboratory setup with the acoustic transmission method and Fourier transform techniques was utilized to examine the sound propagation and absorption of novel seabed sediments.The standard deviation of mean sound speed in fresh water was 0.75 m/s,and attenuation was observed in the range of 0.43 to 0.61 dB/m.The mean sound velocity in sand and clay varied from 1706 to 1709 m/s and 1602 to 1608 m/s,respectively.Corresponding average attenuation was observed at 80 to 93 dB/m in sandy sediments and from 31.8 to 38.6 dB/m in clayey sediments.Sound velocity variation within sandy sediment is low,consistent with expected results,and smaller than the predicted uncertainty.However,clay sediment exhibited a positive linear correlation and low sound speed variation.Attenuation increased linearly with frequency for both sediments.Finally,the laboratory results were validated by using the Biot−Stoll model.The dispersion of sound speed in sandy and clayey sediments was consistent with the predictions of the Biot−Stoll model.Measured attenuation aligned more with Biot−Stoll model predictions due to improved permeability,tortuosity and pore size parameter fitting.

Numerical study of the acoustic spectrum of bubble clusters

This study delved into the acoustic spectrum of bubble clusters,each consisting of 352 vapor bubbles across volume fractions ranging from 0.005%to 40%.The clusters,organized in five distinct layers,were modeled using the volume of fluid(VOF)method to capture the bubble interfaces,and the Ffowcs Williams-Hawkings(FW-H)methodology to compute the far-field acoustic pressure from bubble collapse.Further analysis revealed distinct sound pressure behaviors across different volume fractions:For 25%–40%,time-domain analysis shows that the peak acoustic pressure pulses from the two innermost layers of bubbles are significantly higher than those from the outer layers.In the frequency domain,the octave decay rate of the acoustic pressure levels is relatively low,around−3dB/octave.For 0.5%–25%,four acoustic pressure pulses with similar widths and peak values were observed in the time domain.In the frequency domain,there are three distinct peaks in sound pressure levels(SPL),directly linked to the difference in collapse times of bubbles within the cluster,and the octave decay rate accelerates as the volume fraction decreases,stabilizing at−6dB/octave when the volume fraction is reduced to 17.5%.For 0.005%–0.5%,as the volume fraction decreases from 0.5%to 0.1%,the number of acoustic pressure pulses significantly reduces.Below 0.1%volume fraction,only a single wider pulse is observed.In the frequency domain,the octave decay rate gradually increases with decreasing volume fraction,significantly exceeding−10dB/octave when it drops below 0.1%,reaching up to−11.7dB/octave.

Microstructure Features and the Macroscopic Acoustic Behavior of Gassy Silt in the Yellow River Delta

The morphological changes in isolated bubbles in gassy silt play a critical role in the microscopic structures between soil particles and bubbles and macroscopic physical properties.Based on X-ray CT scanning experiments under various vertical loads(four levels),self-designed acoustic macro experiments,and a series of formula revisions to the macro-air-bearing silt sound-velocity prediction model,this paper discusses the macro-and micro-scale features of gassy silts from the Yellow River Delta.The samples consisted of different proportions of silt from the Yellow River Delta and porous media,and they were used to form two types of aerosol silts with initial gas contents of 4.23%and 7.67%.The results show that the air bubble content and external load considerably affect the microstructural parameters and acoustic behavior of gassy silt in the Yellow River Delta.The macroscopic sound velocity showed a linear positive correlation with vertical load and relation to microstructural parameters in varying manners and degrees.Based on the traditional Biot-Stoll acoustic model,the gas-phase medium coefficient was introduced for the proper calculation and prediction of the sound velocity of air-bearing silt.The errors of the overall prediction varied between 5.6%and 9.6%.

Acoustic propagation uncertainty in internal wave environments using an ocean-acoustic joint model

An ocean-acoustic joint model is developed for research of acoustic propagation uncertainty in internal wave environments.The internal waves are numerically produced by tidal forcing over a continental slope using an ocean model.Three parameters(i.e.,internal wave,source depth,and water depth)contribute to the dynamic waveguide environments,and result in stochastic sound fields.The sensitivity of the transmission loss(TL)to environment parameters,statistical characteristics of the TL variation,and the associated physical mechanisms are investigated by the Sobol sensitivity analysis method,the Monte Carlo sampling,and the coupled normal mode theory,respectively.The results show that the TL is most sensitive to the source depth in the near field,resulted from the initial amplitudes of higher-order modes;while in middle and far fields,the internal waves are responsible for more than 80%of the total acoustic propagation contribution.In addition,the standard deviation of the TL in the near field and the shallow layer is smaller than those in the middle and far fields and the deep layer.

Model-constrained and data-driven double-supervision acoustic impedance inversion

Seismic impedance inversion is an important technique for structure identification and reservoir prediction.Model-based and data-driven impedance inversion are the commonly used inversion methods.In practice,the geophysical inversion problem is essentially an ill-posedness problem,which means that there are many solutions corresponding to the same seismic data.Therefore,regularization schemes,which can provide stable and unique inversion results to some extent,have been introduced into the objective function as constrain terms.Among them,given a low-frequency initial impedance model is the most commonly used regularization method,which can provide a smooth and stable solution.However,this model-based inversion method relies heavily on the initial model and the inversion result is band limited to the effective frequency bandwidth of seismic data,which cannot effectively improve the seismic vertical resolution and is difficult to be applied to complex structural regions.Therefore,we propose a data-driven approach for high-resolution impedance inversion based on the bidirectional long short-term memory recurrent neural network,which regards seismic data as time-series rather than image-like patches.Compared with the model-based inversion method,the data-driven approach provides higher resolution inversion results,which demonstrates the effectiveness of the data-driven method for recovering the high-frequency components.However,judging from the inversion results for characterization the spatial distribution of thin-layer sands,the accuracy of high-frequency components is difficult to guarantee.Therefore,we add the model constraint to the objective function to overcome the shortages of relying only on the data-driven schemes.First,constructing the supervisor1 based on the bidirectional long short-term memory recurrent neural network,which provides the predicted impedance with higher resolution.Then,convolution constraint as supervisor2 is introduced into the objective function to guarantee the reliability and accuracy of the inversion results,which makes the synthetic seismic data obtained from the inversion result consistent with the input data.Finally,we test the proposed scheme based on the synthetic and field seismic data.Compared to model-based and purely data-driven impedance inversion methods,the proposed approach provides more accurate and reliable inversion results while with higher vertical resolution and better spatial continuity.The inversion results accurately characterize the spatial distribution relationship of thin sands.The model tests demonstrate that the model-constrained and data-driven impedance inversion scheme can effectively improve the thin-layer structure characterization based on the seismic data.Moreover,tests on the oil field data indicate the practicality and adaptability of the proposed method.

Modeling cell contractility responses to acoustic tweezing cytometry

Acoustic tweezing cytometry(ATC)is a recently developed method for cell mechanics regulation.Tar-geted microbubbles,which are attached to integrins and subsequently the actin cytoskeleton,anchor,amplify and transmit the mechanical energy in an acoustic field inside the cells,eliciting prominent cy-toskeleton contractile force increases in various cell types.We propose that a mechanochemical con-version mechanism is critical for the high efficiency of ATC to activate cell contractility responses.Our models predict key experimental observations.Moreover,we study the influences of ATC parameters(ul-trasound center frequency,pulse repetition frequency,duty cycle,and acoustic pressure),cell areas,the number of ATC stimuli,and extracellular matrix rigidity on cell contractility responses to ATC.The simu-lation results suggest that it is large molecules,rather than small ions,that facilitate global responses to the local ATC stimulation,and the incorporation of visible stress fiber bundles improves the accuracy of modeling.

Mechanical responses and acoustic emission behaviors of coal under compressive differential cyclic loading(DCL):a numerical study via 3D heterogeneous particle model

The stability of coal walls(pillars)can be seriously undermined by diverse in-situ dynamic disturbances.Based on a 3D par-ticle model,this work strives to numerically replicate the major mechanical responses and acoustic emission(AE)behaviors of coal samples under multi-stage compressive cyclic loading with different loading and unloading rates,which is termed differential cyclic loading(DCL).A Weibull-distribution-based model with heterogeneous bond strengths is constructed by both considering the stress-strain relations and AE parameters.Six previously loaded samples were respectively grouped to indicate two DCL regimes,the damage mechanisms for the two groups are explicitly characterized via the time-stress-dependent variation of bond size multiplier,and it is found the two regimes correlate with distinct damage patterns,which involves the competition between stiffness hardening and softening.The numerical b-value is calculated based on the mag-nitudes of AE energy,the results show that both stress level and bond radius multiplier can impact the numerical b-value.The proposed numerical model succeeds in replicating the stress-strain relations of lab data as well as the elastic-after effect in DCL tests.The effect of damping on energy dissipation and phase shift in numerical model is summarized.

Three-dimensional acoustic wave equation modeling based on the optimal finite-difference scheme

Generally, FD coefficients can be obtained by using Taylor series expansion （TE） or optimization methods to minimize the dispersion error. However, the TE-based FD method only achieves high modeling precision over a limited range of wavenumbers, and produces large numerical dispersion beyond this range. The optimal FD scheme based on least squares （LS） can guarantee high precision over a larger range of wavenumbers and obtain the best optimization solution at small computational cost. We extend the LS-based optimal FD scheme from two-dimensional （2D） forward modeling to three-dimensional （3D） and develop a 3D acoustic optimal FD method with high efficiency, wide range of high accuracy and adaptability to parallel computing. Dispersion analysis and forward modeling demonstrate that the developed FD method suppresses numerical dispersion. Finally, we use the developed FD method to source wavefield extrapolation and receiver wavefield extrapolation in 3D RTM. To decrease the computation time and storage requirements, the 3D RTM is implemented by combining the efficient boundary storage with checkpointing strategies on GPU. 3D RTM imaging results suggest that the 3D optimal FD method has higher precision than conventional methods.

Long Short-Term Memory Recurrent Neural Network-Based Acoustic Model Using Connectionist Temporal Classification on a Large-Scale Training Corpus

A Long Short-Term Memory(LSTM) Recurrent Neural Network(RNN) has driven tremendous improvements on an acoustic model based on Gaussian Mixture Model(GMM). However, these models based on a hybrid method require a forced aligned Hidden Markov Model(HMM) state sequence obtained from the GMM-based acoustic model. Therefore, it requires a long computation time for training both the GMM-based acoustic model and a deep learning-based acoustic model. In order to solve this problem, an acoustic model using CTC algorithm is proposed. CTC algorithm does not require the GMM-based acoustic model because it does not use the forced aligned HMM state sequence. However, previous works on a LSTM RNN-based acoustic model using CTC used a small-scale training corpus. In this paper, the LSTM RNN-based acoustic model using CTC is trained on a large-scale training corpus and its performance is evaluated. The implemented acoustic model has a performance of 6.18% and 15.01% in terms of Word Error Rate(WER) for clean speech and noisy speech, respectively. This is similar to a performance of the acoustic model based on the hybrid method.

3-D acoustic wave equation forward modeling with topography

In order to model the seismic wave field with surface topography, we present a method of transforming curved grids into rectangular grids in two different coordinate systems. Then the 3D wave equation in the transformed coordinate system is derived. The wave field is modeled using the finite-difference method in the transformed coordinate system. The model calculation shows that this method is able to model the seismic wave field with fluctuating surface topography and achieve good results. Finally, the energy curves of the direct and reflected waves are analyzed to show that surface topography has a great influence on the seismic wave＇s dynamic properties.

Acoustic emission activity in directly tensile test on marble specimens and its tensile damage constitutive model

For understanding acoustic emission （AE） activity and accumulation of micro-damage inside rock under pure tensile state, the AE signals has been monitored on the test of directly tension on two kinds of marble specimens. A tensile constitutive model was proposed with the damage factor calculated by AE energy rate. The tensile strength of marble was discrete obviously and was sensitive to the inside microdefects and grain composition. With increasing of loading, the tensile stress-strain curve obviously showed nonlinear with the tensile tangent modulus decreasing. In repeated loading cycle, the tensile elastic modulus was less than that in the previous loading cycle because of the generation of micro damage during the prior loading. It means the linear weakening occurring in the specimens. The AE activity was corresponding with occurrence of nonlinear deformation. In the initial loading stage which only elastic deformation happened on the specimens, there were few AE events occurred; while when the nonlinear deformation happened with increasing of loading, lots of AE events were generated. The quantity and energy of AE events were proportionally related to the variation of tensile tangent modulus. The Kaiser effect of AE activity could be clearly observed in tensile cycle loading. Based on the theory of damage mechanics, the damage factor was defined by AE energy rate and the tensile damage constitutive model was proposed which only needed two property constants. The theoretical stress-strain curve was well fitted with the curve plotted with tested datum and the two property constants were easily gotten by the laboratory testing.

Study of A Geo-Acoustic Model of Gas-Bearing Sediment and Its Application in Sediment with Low Acoustic Veloctiy

A new geo-acoustic model for gas-bearing sediment is proposed based on the work of Dvorkin and Prasad, and Biot theory. Only five geophysical parameters： sediment mineral composition, free gas saturation, tortuosity （also known as the structure factor）, permeability, and porosity, are considered in the model. A benefit of this model is that we need only five parameters instead of ten parameters in the Blot＇ s formulas for acoustic velocity and attenuation calculation. Here the model is demonstrated with the in-situ experimental data collected from the Hangzhou Bay, China. The results of this study suggest that free gas content in sediment is the most critical condition resulting in a low acoustic velocity （compressional wave）. The respective contributions of the other four parameters in the model are also discussed.

Discrete element modeling of acoustic emission in rock fracture

The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.

Effect of Methane Gas on Acoustic Characteristics of Hydrate-Bearing Sediment–Model Analysis and Experimental Verification

Gas leakage is an important consideration in natural systems that experience gas hydrate accumulation.A number of velocity models have been created to study hydrate-bearing sediments,including the BGTL theory,the weighted equation,the Wood equation,the K-T equation,and the effective medium theory.In previous work,we regarded water as the pore fluid,which meant its density and bulk modulus values were those of water.This approach ignores the presence of gas,which results in a biased calculation of the pore fluid's bulk modulus and density.To take into account the effect of gas on the elastic wave velocity,it is necessary to recalculate the bulk modulus and density of an equivalent medium.Thus,a high-pressure reactor device for simulating leakage systems was developed to establish the relationship between wave velocity and hydrate saturation in methane-flux mode.A comparison of the values calculated by the velocity model with the experimental data obtained in this study indicates that the effective medium theory(EMT,which considers gas effects)is more applicable than other models.For hydrate saturations of 10%–30%,the result ranges between EMT-B(homogenous gas distribution)and EMT-B(patchy gas distribution).For hydrate saturations of 30%–60%,the results are similar to those of the EMT-B(homogenous gas distribution)mode,whereas hydrate saturations of 60%–70%yield results similar to those of the EMT-A mode.For hydrate saturations greater than 80%,the experimental results are similar to those of the EMT-B mode.These results have significance for hydrate exploitation in the South China Sea.

Theoretical modeling of the effects of temperature and moisture content on the acoustic velocity of Pinus resinosa wood

To investigate the effects of temperature and moisture content(MC) on acoustic wave velocity(AWV)in wood,the relationships between wood temperature,MC,and AWV were theoretically analyzed.According to the theoretical propagation characteristics of the acoustic waves in the wood mixture and the differences in velocity among various media(including ice,water,pure wood or oven-dried wood),theoretical relationships of temperature,MC,and AWV were established,assuming that the samples in question were composed of a simple mixture of wood and water or of wood and ice.Using the theoretical model,the phase transition of AWV in green wood near the freezing point(as derived from previous experimental results) was plausibly described.By comparative analysis between theoretical and experimental models for American red pine(Pinus resinosa) samples,it was established that the theoretically predicted AWV values matched the experiment results when the temperature of the wood was below the freezing point of water,with an averageprediction error of 1.66%.The theoretically predicted AWV increased quickly in green wood as temperature decreased and changed suddenly near 0 °C,consistent with the experimental observations.The prediction error of the model was relatively large when the temperature of the wood was above the freezing point,probably due to an overestimation of the effect of the liquid water content on the acoustic velocity and the limited variables of the model.The high correlation between the predicted and measured acoustic velocity values in frozen wood samples revealed the mechanisms of temperature,MC,and water status and how these affected the wood(particularly its acoustic velocity below freezing point of water).This result also verified the reliability of a previous experimental model used to adjust for the effect of temperature during field testing of trees.

Study of acoustic bubble cluster dynamics using a lattice Boltzmann model

The search for the development of a reliable mathematical model for understanding bubble dynamics behavior is an ongoing endeavor.A long list of complex phenomena underlies the physics of this problem.In the past decades,the lattice Boltzmann method has emerged as a promising tool to address such complexities.In this regard,we have applied a 121-velocity multiphase lattice Boltzmann model to an asymmetric cluster of bubbles in an acoustic field.A problem as a benchmark is studied to check the consistency and applicability of the model.The problem of interest is to study the deformation and coalescence phenomena in bubble cluster dynamics,as well as the screening effect on an acoustic multibubble medium.It has been observed that the LB model is able to simulate the combination of the three aforementioned phenomena for a bubble cluster as a whole and for every individual bubble in the cluster.

Cross-Ice Acoustic Communication:Cascade Acoustic Channel Model and Experimental Results

Cross-ice acoustic information transmission is an effective means of communication in polar sea areas covered by ice.However,the channel is extremely complicated because of the combined influence of water,ice,and air.Based on the normalmode theory,this paper establishes a cascade acoustic channel(CAC)model for the transmission of underwater acoustic waves across ice layer.The model can calculate the displacement response of the ice layer’s upper surface by separating the upward waves from normal modes in the water and multiplying it by a transmission coefficient matrix.The relationship between the displacement response of the upper surface of ice layer and the acoustic frequency is calculated by the finite-element method,and the calculation result was consistent with that of the CAC model.To verify the applicability of the model,a cross-ice acoustic communication experiment was conducted in Songhua River in January 2019.Experimental results show the energy of the acoustic signals received by geophones is closely related to sound frequency and crossice acoustic communication is feasible.The result of present research is important for understanding crossice acoustic channel characteristics and developing future cross-ice acoustic communication in polar sea areas.

Numerical analysis of the resonance mechanism of the lumped parameter system model for acoustic mine detection

The method of numerical analysis is employed to study the resonance mechanism of the lumped parameter system model for acoustic mine detection. Based on the basic principle of the acoustic resonance technique for mine detection and the characteristics of low-frequency acoustics, the “soil-mine” system could be equivalent to a damping “mass-spring” resonance model with a lumped parameter analysis method. The dynamic simulation software, Adams, is adopted to analyze the lumped parameter system model numerically. The simulated resonance frequency and anti-resonance frequency are 151 Hz and 512 Hz respectively, basically in agreement with the published resonance frequency of 155 Hz and anti-resonance frequency of 513 Hz, which were measured in the experiment. Therefore, the technique of numerical simulation is validated to have the potential for analyzing the acoustic mine detection model quantitatively. The influences of the soil and mine parameters on the resonance characteristics of the soil–mine system could be investigated by changing the parameter setup in a flexible manner.

A Modified Monte Carlo Model of Speckle Tracking of Shear Wave Induced by Acoustic Radiation Force for Acousto-Optic Elasticity Imaging

A modified Monte Carlo model of speckle tracking of shear wave propagation in scattering media is proposed. The established Monte Carlo model mainly concerns the variations of optical electric field and speckle. The two- dimensional intensity distribution and the time evolution of speckles in different probe locations are obtained. The fluctuation of speckle intensity tracks the acoustic-radiation-force shear wave propagation, and especially the reduction of speckle intensity implies attenuation of shear wave. Then, the shear wave velocity is estimated quantitatively on the basis of the time-to-peak algorithm and linear regression processing. The results reveal that a smaller sampling interval yields higher estimation precision and the shear wave velocity is estimated more efficiently by using speckle intensity difference than by using speckle contrast difference according to the estimation error. Hence, the shear wave velocity is estimated to be 2.25 m/s with relatively high accuracy for the estimation error reaches the minimum （0.071）.