KAN Guangming ,MENG Xiangmei ,WANG Jingqiang ,CAO GuolinLI GuanbaoLIU Baohuaand ZHI Pengyao

1) Key Laboratory of Marine Geology and Metallogeny,First Institute of Oceanography,Ministry of Natural Resources,Qingdao 266061,China

2) Laboratory for Marine Geology,Pilot National Laboratory for Marine Science and Technology (Qingdao),Qingdao 266237,China

3) College of Earth Science and Engineering,Shandong University of Science and Technology,Qingdao 266590,China

Abstract To accurately characterize the shear wave speed dispersion of seafloor sediments in the northern South China Sea,five types of sediments including silty clay,clayey silt,sandy silt,silty sand,and clayey sand were selected,on which the measurements of the shear wave speed at 0.5– 2.0 kHz and related physical properties were performed.Results reveal that the shear wave speed of sediments increases as the frequency increases,and the dispersion enhanced in the sediments in the order of silty clay,clayey silt,sandy silt,silty sand,and clayey sand,at a linear change rate of 0.727,0.787,3.32,4.893,and 6.967 m s-1 kHz-1,respectively.Through regression analysis,linear and logarithmic regression equations for the correlation between shear wave speed and frequency were established for each sediment type and the determination coefficients of regression equations indicate that the correlation is closer to a logarithmic relationship.The Grain-Shearing (GS) and Biot-Stoll models were used to calculate the shear wave speed dispersion of the five sediment types,and the comparison between theoretical prediction and measured results of shear wave speeds shows that the GS model can more accurately describe the shear wave speed dispersion characteristics of these sediments in the frequency band of 0.5–2.0 kHz.In the same band,the predictions obtained by using the Biot-Stoll model are significantly different from the measured data.

Key words shear wave speed dispersion;seafloor sediments;Biot-Stoll model;Grain-Shearing model;South China Sea

1 Introduction

Shear wave speed is a critical parameter to characterize the acoustic properties of seafloor sediments.The measurement and analysis of the shear wave speed have important applications in ocean acoustic field predictions,seafloor geoacoustic model researches,as well as marine engineering surveys.In terms of the underwater acoustics research,the shear wave speed of shallow seafloor sediments is of great significance for the interpretation of experimental results of underwater acoustic propagation and acoustic field prediction (Luet al.,2004;Buckingham,2005).In studies of seafloor geoacoustic models,the shear wave speed of sediments is crucial in establishing a complete seafloor geoacoustic model.In marine engineering applications,the sediment shear modulus and shear wave speed are widely employed in the evaluation of seafloor bearing capacity,the identification of sand liquefaction caused by an earthquake,and the study of consolidation behavior(Gaoet al.,1998;Jackson and Richardson,2007;Liu and Zhang,2014).Studies on the relationship between the shear wave speed and physical and mechanical properties of the seafloor sediments have been extensively conducted in the literature.Luet al.(2004) conducted a preliminary analysis of the shear wave speed in typical offshore areas of China,and provided the regression relationship between the shear wave speed and two sediment parameters:density and liquid limit.Panet al.(2006) compared two shear wave test methods– the bender element and resonance column methods– and established the regression relationships between shear wave speed and sediment density,water content,porosity,liquid limit and plastic limit,and the compressional wave speed,based on the measured data.Kanet al.(2014) also established empirical regression equations for the correlation between shear wave speed and density,water content,void ratio,porosity,liquid limit,plastic limit,compressibility,and shear strength of the seafloor sediments in the South Yellow Sea.

The measurement frequency differs greatly for different shear wave measurement methods.However,compared with studies on the dispersion characteristics of the compressional wave speed and attenuation coefficient of sediments,there are relatively few studies on the characteristics of shear wave speed dispersion.The frequency used in the laboratory measurements for the shear wave speed in sediments based on the bender element method generally ranges from 2 kHz to 20 kHz (Panet al.,2006;Kanet al.,2014),the frequency used in the resonance column laboratory measurements for shear wave speed generally ranges from 5 Hz to 40 Hz (Panet al.,2006,2015),and the frequency used forin-situshear wave measurements based on the bender element method generally ranges from 100 Hz to 1 kHz (McNeeseet al.,2015;Leeet al.,2016;Ballardet al.,2020).Currently,no consensus exists regarding the frequency dependence of shear wave speed.Panet al.(2006) measured the shear wave speed in sediments in the frequency ranges of 3– 20 kHz and 5– 40 Hz using the bender element method and the resonance column method,respectively.Their results showed that the shear wave speed obtained by using these two methods appeared to have good consistency and no obvious frequency dispersion was detected within the range of a few hertz to tens of kilohertz (Panet al.,2006).However,according to the GS model,when the frequency increases from 100 Hz to 2 kHz,the shear wave speed increases by around 17%(Buckingham,2005).Zhenget al.(2015) discussed the dispersion characteristics of the shear wave speed of tidal flat sediments in Jiaozhou Bay and concluded that the shear wave speed logarithmically changed with frequency in the range of 0.2– 2.0 kHz,but the comparison with theoretical models was lacked.Herein,five types of sediment samples of silty clay (Type A),clayey silt (Type B),silty sand (Type C),sandy silt (Type D),and clayey sand(Type E) collected in the northern South China Sea were chosen to study the shear wave speed dispersion characteristics for the different types of sediments.Furthermore,the measured shear wave dispersion data were compared with predictions obtained from the GS model and the Boit-Stoll model.Finally,the differences in model prediction curves and input parameter values of models for different sediment types were discussed.

2 Materials and Methods

2.1 Overview of Study Area and Collection of Sediment Samples

The study area is located within 14?– 20?N,108?– 115? E in the northern South China Sea.The submarine geomorphology of the study area includes continental shelf and continental slope.The sediments in the continental shelf area are mainly composed of terrigenous clastic sediments,including clayey sand,silty sand,and sandy silt,with relatively high sand contents and relatively low clay contents;the sediments in the continental slope area are mainly composed of silty clay and clayey silt,with relatively high clay contents and relatively low sand contents (Yanet al.,2016;Zhaoet al.,2016).

Twenty-one sediment cores were collected by using a gravity corer in the study area.Five of them are located on the continental shelf area,and the other sixteen on the continental slope area.All sediment cores were transported to a special sample room with constant temperature and humidity after being collected from the bottom.Shear wave speed and related physical properties of the sediment samples such as wet bulk density,water content,mean grain size and porosity,were then measured in the laboratory.

2.2 Measurement of Shear Wave Speed

Using a bender element system manufactured by Global Digital Systems Ltd.located in UK,the shear wave speed of sediment samples was measured (see Fig.1).The bender element system primarily comprises two shear wave transducers,an integrated transmission and acquisition unit,and a monitoring software.To improve the accuracy and efficiency of measurements,a bracket for holding the shear wave transducer and sediment samples is customized for the experiment.The receiving and transmitting transducers were both fixed on the customized bracket platform with the former on the bottom of the bracket,and the latter on a vertically installed screw through a clamp.The height of the transmitting transducer can be adjusted by rolling the handle at the top of the bracket (Fig.1).There is a piezoelectric ceramic chip installed in each transducer.The piezoelectric ceramic chips in transmitting and receiving transducers must remain parallel to each other,rather than crossing or perpendicular to each other during the measurement.The shear wave measurement parameters were set as follows:sampling frequency:1000 kHz (i.e.,the sampling interval is 1 μs);excitation voltage:14 V;sampling points:10000.

Fig.1 Photo of the bending element test system for shear wave speed measurements.

After the sample is cut into 8-cm-long sections,the sediment section is placed between the two transducers,and the position of the transmitting transducer is adjusted by rolling the handle at the top of the bracket to ensure the efficient coupling between the bender stripes and the sediment samples.The equation for calculating shear wave speed is as follows:wherecsis the shear wave speed of sediments in meters per second andLis the length of the sample in meters,which can be measured by using a vernier caliper.The sample length was measured as follows.First,the distance between the transmitting and receiving transducer clamps (L1) is measured while it is ensured that the bender element stripes of the transmitting and receiving transducers were in direct contact with each other.Then,the distance between the transmitting and receiving transducer clamps (L2) was measured after the sample was placed.Finally,the sample length can be obtained byL=L2-L1.tis the first arrival of shear wave propagating in the sediment samples in seconds andt0is the time delay of the system in seconds,also known as the zero sonic time.Δtis the propagation time of the shear wave in the sediments in seconds.

2.3 Determination of the Zero Sonic Time and Shear Wave Propagation Time

Because the responding time of shear wave measurement system at different frequencies is different,in order to measure the shear wave speed more accurately,the zero sonic time corresponding to each target frequency was measured.The measurement method is as follows.Firstly,the transmitting transducer was placed onto the receiving transducer directly to ensure that the bender element stripes of the transmitting and receiving transducers were in direct contact with each other.Then,the shear wave was transmitted from the transmitting transducer and received and collected by the receiving transducer and acquisition unit.The transmitted and received shear waveforms are shown in Fig.2.The time delay for each frequency (namely zero sonic time) was obtained when the cross-correlation values between the transmitted and received waveforms reached to the maximum.Similarly,the propagation time of the shear wave in the sediments was determined through the cross-correlation analysis of the transmitted waveforms from the transmitting transducer and the received waveforms after propagating through the sediment samples.This method greatly reduced the error of traditional method to manually select the jump point of the first arrival of shear waves.

Fig.2 Transmitted waveforms and received waveforms at different frequencies during zero sonic time measurement.

2.4 Measurement of Physical Properties

Following the shear wave speed measurement,the physical properties of the sediment samples were measured in the laboratory,including the wet bulk density,water content,mean grain size,and porosity.The wet bulk density of samples was measured by using the ring knife method,and the water content was measured by using the drying method.The particle composition of samples was measured by combining sieving and density meter analysis.The porosity of the samples was calculated based on parameters such as particle density and water content.

3 Results

3.1 Results of Physical Property Measurement

Table 1 shows the physical property measurement results for each type of sediment.Overall,the wet density of sediments ranges from 1.30 to 1.96 g cm-3,the porosity ranges from 42.4% to 82.4%,the water content ranges from 26.1% to 173.0%,and the mean grain size ranges from 4.18 to 9.07 φ.The sediments were classified mainly based on the standard of specifications for oceanographic survey-Part 8:Marine geology and geophysics survey (GB/T 12763.8-2007) and the grain size compositions combined with the sand content,silt content and clay content were involved.There are differences in the porosity,wet density,water content,and mean grain size for different types of sediments.Silty sand,sandy silt,and clayey sand have relatively high wet density,relatively low porosity and water content,and relatively large mean grain size.Silty clay and clayey silt have relatively low wet density,relatively high porosity and water content,and relatively small mean grain size.According to the measurements of Panet al.(2006) in the northern South China Sea,sediments include silt,clayey silt,silty sand,and the density ranged from 1.43 to 2.06 g cm-3,the porosity ranged from 38.7%to 76.3%,and the water content ranged from 24.1% to 120.0%.In another measurement in the northern South China Sea (Zouet al.,2018),sediments include clayey silt,silty sand,and the density ranged from 1.35 to 1.97 g cm-3,the porosity ranged from 49.1% to 79.6%,and the water content ranged from 34.4% to 149.0%.The physical properties of sediments such as density,porosity,and water content obtained in this study are consistent with the above-mentioned results.

Table 1 Measurement results of physical properties for different types of sediments

3.2 Results of Shear Wave Speed at Different Frequencies

Results of shear wave speed measurement for the five types of sediments at different frequencies are shown in Table 2,wherein the shear wave speed ranges from 25.64 to 70.76 m s-1.The sediment types corresponding to the maximum and minimum shear wave speed are sandy silt and silty clay,respectively.The shear wave speed differs for different types of sediments.The shear wave speeds of silty sand,sandy silt,and clayey sand sediments with high wet density,low porosity,low water content,and large grain size are significantly higher than those of silty clay and clayey silt sediments with low wet density,high porosity,high water content,and small grain size.The shear wave speed of sediments in the central area of the South Yellow Sea ranges from 12.05 to 74.55 m s-1(Kanet al.,2014),and the shear wave speed of tidal flat sediments at Jiaozhou Bay ranges from 26.5 to 103.5 m s-1(Zhenget al.,2015).The range of the shear wave speed of sediments in the northern South China Sea is 29.2 -128.3 m s-1(Panet al.,2006),and the range of the shear wave speed of sediments of the Lower Florida Keys is 40.0 -150.0 m s-1(Richardsonet al.,1997).The shear wave speeds herein are consistent with above results.In the measurement frequency range of 0.5 -2 kHz,the shear wave speeds of different types of sediments all show an increasing trend with increasing frequency,but have different gradients.The average change rate (ACR) of shear wave speed of silty clay is the smallest,0.727 m s-1kHz-1,followed by clayey silt,with an ACR of 0.787 m s-1kHz-1.The ACR of shear wave speed of clayey sand is the largest,6.967 m s-1kHz-1,followed by sandy silt,with an ACR of 4.893 m s-1kHz-1.The ACR of shear wave speed of silty sand is 3.32 m s-1kHz-1.

Table 2 Shear wave speeds of different types of sediments at different frequencies

4 Discussion

4.1 Correlation Between the Shear Wave Speed and Frequency

Linear fitting and logarithmic fitting were used to perform regression analysis to get the correlation between shear wave speed and frequency,for the five types of sediments.The results are shown in Table 3 and Fig.3.In Table 3,csis the shear wave speed in meters per second,fis the shear wave frequency in kilohertz,andR2is the coefficient determination of regression equation.As shown in Table 3,the determination coefficient obtained by logarithmic fitting is slightly larger than that by linear fitting,indicating that the shear wave speed and frequency is closer to logarithmic correlation for the five types of sediments selected herein,which is consistent with the result of Buckingham(1997,2001) that the shear wave speed of unconsolidated sediments on the seafloor exhibits logarithmic dispersion(Buckingham,1997,2001).The regression equations in Table 3 reveal that among the five types of sediments,the linear fitting and logarithmic fitting results of silty clay both have the smallest slopes,which are 0.6989 and 1.8564,respectively,indicating that the shear wave speed dispersion of silty clay has the smallest gradient,followed by clayey silt.In contrast,the linear and logarithmic fit slope of clayey sand are the largest,6.9039 and 17.8601,respectively,indicating that the shear wave speed dispersion gradient of clayey sand is the largest.The shear wave speed dispersion gradients of sandy silt and silty sand are slightly smaller than those of clayey sand.Based on the physical property measurement results of the sediments in Table 1,clayey sand has the largest mean grain size,whereas that of silty clay is the smallest.Therefore,the shear wave speed dispersion gradient of the sediment appears to increase with the increasing of sediment grain size.The coarser sediments may exhibit more obvious translational shearing.According to the GS model,translational shear is an important factor which causes the dependence of shear wave speed on frequency,and makes the shear wave speed show stronger dispersion characteristics.

Fig.3 The correlation diagrams between the shear wave speed and frequency for the five types of sediments.(a),linear fitting;(b),logarithmic fitting.

Table 3 Regression equations and correlation coefficient of determination (R2) between the shear wave speed and frequency for the five types of sediments

4.2 Comparison of Shear Wave Speed Dispersion Obtained from Measured Data and Model Prediction

Herein,two models for seafloor sediment acoustic properties,Biot-Stoll and grain shearing (GS),are used to compare the shear wave speed of different types of sediments obtained from measured data with the model predictions.The two models differ in both the model input parameters and the mechanism of sound wave propagation in sediments.To better understand the comparison between the measured data and the model predictions,the equation for shear wave speed calculation and input parameter selection method for each of the two models are briefly explained below.

4.2.1 Biot-Stoll model

The Biot-Stoll model considers seafloor sediments as a two-phase medium composed of the solid frame and pore fluid.The Biot-Stoll model concluded that the relative movement between the pore fluid with dynamic viscosity and the sediment frame under acoustic excitation is the main mechanism that causes sound speed dispersion and sound wave attenuation (Biot,1962;Stoll and Bryan,1970;Stoll,1995;Williamset al.,2002;Kimura,2013).

In Eqs.(2) and (3),csis the shear wave speed of sediments,ωis the angular frequency (ω=2πf),ρis sediment density (ρ=(1-β)ρs+βρf),ρsis the particle density of sediments,andρfis the pore fluid density.κandηare the sediment permeability and fluid dynamic viscosity respectively,μbis the complex shear modulus of the sediment,Fandmare the viscosity correction factor and effective fluid density,respectively.

In Eqs.(4) to (8),KbandKgare the frame and grain bulk moduli,respectively.J1andJ0are the first and zero order Bessel functions,respectively.ris the pore radius of the sediment.

4.2.2 Grain-Shearing (GS) model

The GS model suggests that there is relative movement among particles of an unconsolidated seafloor sediment under acoustic excitation.There are two types of shear motion at the contact point of particles,namely translational shear and torsional shear,which is a stick-slip mechanism according to Buckingham’s point (Buckingham,2000).The stiffness of the sediment is caused by mutual sliding between particles,and the stiffness supports the existence of the shear wave in the sediment (Buckingham,2000,2005;Leeet al.,2016).The prediction equation of the shear wave speed based on the GS model is as follows:

In Eq.(9),ωis the angular frequency andρis sediment density.Tis a random time variable,which can be set to 1 s.nis the strain hardening index,which characterizes the degree of strain hardening of contact among particles when they slide.γsis the shear stiffness coefficient,which represents the influence of the interaction between particles on the shear wave speed and attenuation of sediments.The calculation equation ofγsis as follows:

In Eq.(10),β,ug,anddare the measured fractional porosity,sediment grain size,and sediment burial depth,whereasβ0,ug0,andd0are the reference values of fractional porosity,sediment grain size,and sediment burial depth.The actual values ofβ0,ug0,andd0were assigned to 0.377,1000 μm and 0.3 m respectively,in shear wave speed prediction of GS model.γs0can be considered as the initial value ofγs.

4.2.3 Calculation method and values of model parameters

The input parameters of the Biot-Stoll model can be divided into three categories:solid particle parameters,pore fluid parameters,and solid frame parameters.The accurate acquisition of these parameter values is a problem that needs to be solved in order to effectively employ the model.Measuring the particle bulk modulus of seafloor sediments is difficult,and the value of this parameter is usually inferred on the basis of related papers.Williamset al.(2002) and Buckingham (2005) used a particle bulk modulus (Kg) of 3.2 × 1010Pa when using the Biot-Stoll model and the GS model respectively to study the relationship between sound speed of sandy sediments and frequency in the SAX99 seafloor acoustic experiment.The same value is used in the model calculation herein.Particle density (ρs),fluid density (ρf),fluid dynamic viscosity (η),and permeability (κ) are assigned the values recommended by Williamset al.(2002).Porosity (expressed as fractional porosity herein) and grain size (φ) are assigned the values from the actual measurement.Frame shear modulus (μb)is the assumed values,which the model whose results can fit the measured values best is based on.The calculation equations of fluid bulk modulus (Kf),pore size (r),tortuosity (α),and frame bulk modulus (Kb) are as follows.

In the equation for fluid bulk modulus (Kf),cfis the sound speed in the pore fluid (sea water) and can be obtained through measurement.K'in the equation for pore size (r) is an empirical constant,usually is set to 5 (Hovem and Ingram,1979;Schock,2004).In the equation of tortuosityα,φis the grain size,expressed as

whereugis the grain size in micrometers.In the equation of frame bulk modulus (Kb),σis Poisson’s ratio,in the range of 0.15 -0.35,determined as follows.

Here,φis the grain size,which is calculated by Eq.(15).

For the input parameters of the GS model,the reference particle size (u0),reference sediment burial depth (d0),and reference fractional porosity (β0) values are adopted from recommendations in the literature (Buckingham,2005).Particle size (ug),reference sediment burial depth value(d),and fractional porosity (β) are assigned actual measured values,and the frame bulk modulus (Kb) and frame shear modulus (μb) are the values which make the predicted curves of the shear wave speed fit the measured values best.

4.2.4 Sediment Sound Speed Dispersion Characteristics and Model Prediction Results

To more accurately understand the shear wave speed dispersion of seafloor sediments,and to ensure that the input parameters of the Biot-Stoll and the GS models were set reasonably,the measured shear wave speeds at different frequencies of the five types of sediments were compared with the model prediction results,as shown in Fig.4.The input parameter values of the GS model were listed in Table 4 and the prediction curves of shear wave dispersion obtained were shown in Fig.4.The values of shear stiffness coefficient and strain hardening index in Table 4 were obtained through the best fit curve,determined by comparing the theoretical prediction values of the GS model with the measured shear wave speed values at 1 kHz,as shown in Fig.4.In Table 5,the model input parameter values of the Biot-Stoll model were listed and the shear wave dispersion prediction curves obtained were shown in Fig.4.The bulk modulus values of sediment frame was obtained through the best fit curve,which is determined by comparing the theoretical prediction value of the Biot-Stoll model with the measured shear wave speed at 1 kHz,as shown in Fig.4.

Table 4 Input parameter values for the five types of sediments in the GS model

Table 5 Input parameter values for the five types of sediments in the Biot-Stoll model

Fig.4 Comparison of the measured shear wave speed data (blue dot) with the prediction curves of two models for the five types of sediments.(a),silty clay (Type A);(b),clayey silt (Type B);(c),sandy silt (Type C);(d),clayey sand (Type D);(e),silty sand (Type E).

The theoretical model prediction curves of the five different types of sediments based on the GS and Biot-Stoll models,shown in Fig.4,are significantly different.The prediction curves of the GS model reveal that the shear wave speed of sediments linearly increases with logarithmic frequency,i.e.,the shear wave speed of sediments exhibits logarithmic dispersion characteristics.The prediction curves of the Biot-Stoll model show that at the low frequency (<1 kHz) and high frequency (>10 kHz) bands,the shear wave speed dispersion of sediments are not obvious,and the shear wave speed tends to slowly increase with frequency.However,at the medium frequency band (1– 10 kHz),the shear wave speed dispersion of sediments is significant and the speed rapidly increases with frequency.

As shown in Fig.4,by using the parameter values listed in Table 4,the predictions of the shear wave speed dispersion for the five types of seafloor sediments obtained based on the GS model fit relatively well with measured data at the frequency band of 0.5– 2.0 kHz.At the same band,the predictions obtained by using the Biot-Stoll model are markedly different from the measured data.For silty clay and clayey silt samples,the measured data are lower than the prediction curves of the Biot-Stoll model at the 0.5– 2.0 kHz frequency band.For sandy silt,clayey sand,and silty sand samples,the measured data are higher than the prediction curves at the frequencies higher than 1 kHz,and lower than the prediction curves at the frequencies lower than 1 kHz.

As shown in Fig.4,for the five types of sediments in this paper,the fit to measured data for the prediction curves obtained by the GS model is generally superior to that obtained by using the Biot-Stoll model.For the Biot-Stoll model,viscous loss associated with the relative motion between the pore fluid and the skeletal frame is the main mechanism of the dispersion,and the non-zero skeletal shear modulus supports the existence of shear waves in sediments.However,for unconsolidated sediments,the particles are not fully bonded and the shear modulus of the skeleton frame is very small.It is likely the inter-particle interactions,including translational and radial shearing,under the excitation of shear wave propagation that the GS model takes into account that accounts for the dispersion of shear wave for the five types of sediments discussed in this paper.In addition,according to the predictions of the GS model,the silty clay and clayey silt with low shear wave speed have smaller shear stiffness coefficient and strain hardening index,while sandy silt and clayey sand with high shear wave speed have larger shear stiffness coefficient and strain hardening index.For the five types of sediments considered herein,as the shear wave speed increases,the shear stiffness coefficient and strain hardening index both exhibit the increasing trends.

5 Conclusions

1) The shear wave speed of the five types of sediments in the northern South China Sea all show dispersion characteristics,but their shear wave speed and dispersion gradient are different.The dispersion gradient exhibits the correlation with sediment grain size:the larger the grain size is,the greater the dispersion gradient of the shear wave is.The dispersion is weaker for silty clay and clayey silt,which are finer in grain size;and their average change rate of shear wave speed is 0.727 and 0.787 m s-1kHz-1,respectively.The dispersion is stronger for sandy silt and clayey sand,which are coarser in grain size.The clayey sand has the most prominent shear wave speed dispersion,with an average change rate of 6.967 m s-1kHz-1,followed by sandy silt,whose shear wave speed has an average change rate of 4.893 m s-1kHz-1.Silty sand has a moderate shear wave speed dispersion,with an average change rate of 3.32 m s-1kHz-1.

2) The shear wave speed of the five types of sediments has a strong correlation with frequency,with the coefficient of determination of regression equation all greater than 0.87.The coefficient of determination obtained through logarithmic fitting is slightly larger than that obtained through linear fitting,indicating that the correlation is closer to a logarithmic one.

3) In the frequency range of 0.5– 2.0 kHz,the prediction curves of the GS model fit the measured data of shear wave speed dispersion better than those of the Biot-Stoll model.The result indicates that the GS model which takes into account inter-particle interactions under the excitation of shear wave propagation,including translational and radial shearing,can better account for the shear wave speed dispersion characteristics of the five types of sediments discussed in this paper.

Acknowledgements

We would like to thank Dr.Zhengyu Hou from the South China Sea Institute of Oceanology,Chinese Academy of Science and the crew of theR/V Shiyan 1for their assistance of sampling the sediments.This study was supported by the Basic Scientific Fund for National Public Research Institutes of China (No.GY0220Q09),the National Natural Science Foundation of China (Nos.41676055,41527809,42176191,and 41330965),the Opening Fund of Qingdao National Laboratory for Marine Science and Technology(No.QNLM2016ORP0209),and the Taishan Scholar Project Funding (No.tspd20161007).