ZOU Dapeng ,YE Guican ,LIU Wei ,SUN Han,LI Jun,and XIAO Tibing

1) State Key Laboratory of Precision Electronic Manufacturing Technology and Equipment, Guangdong University of Technology,Guangzhou 510006,China

2) State Key Laboratory of Acoustics, Institute of Acoustics,Chinese Academy of Sciences, Beijing 100190,China

3) College of Engineering,South China Agricultural University,Guangzhou 510642,China

Abstract Because the sound speeds of seawater and seafloor sediment both increase with temperature,the influence of temperature on the bottom reflection characteristics of seafloor sediments needs to be investigated.Based on the calculation of the temperaturecontrolled experimental measurement data of typical seafloor surface sediment samples,the temperature-dependent acoustic characteristics,including acoustic impedance,acoustic impedance ratio between surface sediment and seawater,and reflection coefficient,were analyzed.The effective density fluid model was used to analyze and explain the reflection coefficient variation of surface sediments with temperature and predict the dispersion characteristics.Results show that the acoustic impedance of the seabed sediment increases with temperature,whereas the acoustic impedance ratio and acoustic reflection coefficient slightly decrease.The acoustic impedance,acoustic impedance ratio,and acoustic reflection coefficient of sandy,silty,and clayey sediments vary similarly with temperature variation.Moreover,the influence of temperature on these acoustic characteristics is independent of detection frequencies.

Key words reflection coefficient;seafloor sediment;temperature;acoustic impedance

1 Introduction

The interface between marine surface sediment and bottom water is one of the most crucial propagation interfaces of marine acoustics (Jackson and Richardson,2007;Yang and Ma,2009),and its reflection characteristics affect the precision,depth,and scope of marine acoustic detection.The reflectivity of seafloor surface sediments correlates with seafloor sediment types and directly with the acoustic impedance,acoustic detection frequency,and grazing angle.In acoustic field prediction (Lu and Ma,2014;Daet al.,2017;Yang,2019;Zhanget al.,2019) and acoustic parameter inversion (Sabraet al.,2005;Chenet al.,2018;Houet al.,2019;Liet al.,2019b),the seabed is usually regarded as an infinite half-space state,which is simplified to be equivalent to one layer or two layers.The seafloor temperature state,distribution,and gradient are generally ignored in the applications of the calculation and prediction of submarine propagation characteristics and the inversions of acoustic parameters and sediment types based on the reflection losses.Under the influence of the dual heat sources of bottom seawater and seabed geothermal gradients (Miet al.,2009;Yanget al.,2018),the temperature of seafloor surface sediments (within 3 m) is the same as that of bottom seawater (Rajan and Frisk,1992;Jackson and Richardson,2001;Zenget al.,2016).Thein situtypical temperature profile can vary from 1℃ to 30℃.Below the surface layer,the temperature of sediments gradually increases under the influence of geothermal activities.The geothermal gradient is usually within 29.4℃ km-1and 52.2℃ km-1(Miet al.,2009) and can even reach up to 58.5℃ km-1to 100.7℃ km-1(Liet al.,2010).The acoustic velocity profile (Jackson and Richardson,2007) generated by the influence of temperature on seawater has a notable acoustic velocity gradient,producing the acoustic velocity gradient on the seabed sediment layer.When acoustic propagation experiments are conducted in different seasons and sea areas,submarine acoustic wave propagation characteristics are generally affected by the differences or changes in seabed temperature (Rajan and Frisk,1992;Carbó and Molero,2000;Jackson and Richardson,2001).The differences in the geoacoustic inversion measurements at the same station in the Gulf of Mexico in two different seasons are closely correlated with the influence of water temperature on seafloor surface sediments (Rajan and Frisk,1992).The acoustic velocity gradient in seafloor sediments caused by seasonal temperature changes considerably influences sound waves below the 1 kHz frequency,and the scattering intensity and reflection loss of sound waves are significantly changed (Jackson and Richardson,2001).

The increase in temperature will cause the increase in the sound speed of both seawater (Jackson and Richardson,2007;Liet al.,2019a) and seafloor sediments (Kimet al.,2017;Kanet al.,2019),resulting in a decrease in the sound attenuation coefficient of seafloor sediments (Carbó and Molero,2002;Zouet al.,2015).Therefore,the change in seabed temperature will directly impact the reflection characteristics of the seafloor surface interface.At present,research on the effect of temperature on the reflection characteristics of seafloor surface sediments is limited.However,temperature has an undeniably significant influence on the acoustic characteristics of seawater and seabed sediments.

To elucidate the effect of temperature on the acoustic propagation impedance and reflection coefficient of seafloor sediments,we conducted the present study.Based on the measured data of typical seafloor surface sediments,the effect of temperature on the acoustic impedance of seafloor surface sediments was calculated and analyzed.Based on the analysis of the relationship between temperature and acoustic impedance ratio of seafloor sediment and bottom seawater,the reflection coefficient characteristics with the temperature change were calculated.The effective density fluid model (EDFM) model was used to analyze and explain the variation of the reflectance of seabed sediment with temperature.The reflection coefficient and the characteristics of low-frequency submarine sediments were predicted.This study provides the basis for analyzing the effect of temperature change on the acoustic propagation and reflection characteristics of the seabed under the actual in situ situations for underwater detection and geoacoustic inversion.

2 Relationship Between Acoustic Impedance and Temperature of Seafloor Surface Sediments

Seafloor surface sediment samples were mainly collected in the South China Sea and the Yellow Sea by gravity samplers.The sections were stored in a polyvinyl chloride tube and cut into sections 0.3– 0.5 m in length.For each section of the samples,the acoustic and physical properties were measured.The physical parameters,namely,porosity,density,and sediment type,of the representative seafloor surface sediment samples are shown in Table 1.The sound speeds of the samples were measured at ultrasonic bands by the temperature-controlled experiments,and the detection frequency was selected differently to determine the universal trend considering the actual measurement frequencies.The temperature of the sediment samples was controlled within 30℃ at 1 atm,with increments of 1℃.The measurement accuracy of sound speed is more than±1.8 m s-1.The detailed experimental measurement and theoretical analysis of the influence of temperature on the sound speed of the representative samples,including the acoustic measurement method and experimental principle under temperature control and the measurement method of the physical characteristics of sediments,were conducted in the early stage (Kanet al.,2019;Zouet al.,2021b).A sample of Carbó’s sand (Carbó and Molero,2002) was selected as a comparison.

Table 1 Properties of the representative samples

By controlling the temperature variation of sediment samples in the laboratory,the sound speed of surface sediments in the possible temperature variation range on the seafloor surface could be obtained.The controlled experiment could solve the problem that neither thein situmeasurement nor the acoustic telemetry can obtain any possible temperature change even through long-term observation.Based on the temperature-controlled acoustic measurements,the acoustic characteristics of seafloor surface sediments in various possible existing temperature states caused by diurnal,seasonal,and other abnormal changes were systematically and continuously simulated and measured.

The agreement between experimental results and theoretical analysis revealed that the sound speed of seafloor surface sediments increased with temperature,whereas the sound speed ratio decreased.Moreover,the acoustic characteristics of sediments were mainly caused by the variation of the physical properties of pore water with temperature change (Carbó and Molero,2002;Zouet al.,2015,2021a,2021b;Kimet al.,2017;Kanet al.,2019).Therefore,considering the influence of temperature,the acoustic impedances of seafloor sedimentZs(T) and bottom seawaterZw(T) can be written as follows:

whereTis the temperature,ρs(T) is the density of the sediment,cps(T) is the sound speed of the sediment,n(T) is the porosity of the seafloor sediment,ρw(T) is the density of pore water (which is also expressed as the density of bottom seawater),andρg(T) is the density of solid particles in sediments.The parameters of porosityn(T) and solid particle densityρg(T) in the investigated temperature range(i.e.,1℃ to 30℃) vary slightly and are regarded as constants when compared with those of pore water (Zouet al.,2021a);thus,they can be used asnandρgwithout considering the temperature variation.The changes in the density and sound speed of pore water (or bottom seawater) can be calculated using the seawater state equations (Jackson and Richardson,2007;Zouet al.,2015).Then,the acoustic impedance of seawater can be calculated for comparison and used to calculate the acoustic impedance ratio.

As the temperature increases,the acoustic impedance of the representative samples increases significantly and is similar to the seawater acoustic impedance,as shown in Fig.1.The change rateRAIof the increase used to represent the change degree is defined as follows:

Fig.1 Changes in sediment acoustic impedance under the influence of temperature.

where MaxAI,MinAI,and AveAIare the maximum,minimum,and average values of acoustic impedance,respectively.

The change rate of acoustic impedance ranges from 3.28% to 4.79%,as shown in Table 2.The results show that the acoustic impedance of sediments varies significantly within the conventional range,i.e.,from 2℃ to 27℃,and positively correlates with temperature.The change rate of sediments is similar to that of seawater (4.77%).

Table 2 Properties of the acoustic impedance and its ratio from 2℃ to 27℃

The seafloor reflection characteristics are considered to correlate with the relative acoustic characteristics of bottom seawater and seafloor sediments.The acoustic impedance ratio of seafloor sediment and bottom seawaterRZ(T)represents the relative acoustic impedance characteristics against temperature and is expressed as follows:

The acoustic impedance ratio slightly decreases with the increase in temperature,as shown in Fig.2,which shows a different trend compared with the variation trend of acoustic impedance shown in Fig.1.The main reason is that,with the increase in temperature,the sound velocity ratio of seafloor sediment to bottom seawater decreases,whereas the density ratio increases.The decrease in sound velocity ratio is slightly greater than the increase in density ratio.Hence,the acoustic impedance ratio shows an overall slight decrease.Using Eq.(4),the change rate of acoustic impedance ratioRrowas calculated to range from 0.41%to 1.79%.As shown in Table 2,compared with the change rate of seafloor sediment acoustic impedance,the change rate of acoustic impedance ratio is minimal.This comparison result further indicates that the seafloor sediment acoustic impedance variation is mainly influenced by the effect of temperature on bottom seawater.Because the variation of the sound speed and density of seafloor sediment is similar to that of bottom seawater against the effect of temperature,the ratio of the two can weaken the notable effect of temperature on the acoustic impedances of both seafloor sediments and seawater.

Fig.2 Relationship between acoustic impedance ratio and temperature.

The acoustic impedance of the five samples has an excellent linear positive correlation with temperature,as shown in Table 3.However,the acoustic impedance ratio of three samples,namely,TS1,TS4,and Carbó’s sand,has a negative correlation with temperature;thus,the coefficients of their regression equations are small and can be omitted.The comparison between Tables 3 and 4 shows that the acoustic impedance is positively correlated with temperature,whereas the acoustic impedance ratio has a weak negative correlation with temperature and is similar to some constants to a certain degre.

Table 3 Regression equations of acoustic impedance(AI) and the ratio of acoustic impedance (RZ)with temperature

Table 4 Change rate of the sound reflection coefficient

3 Relationship Between Acoustic Reflection Coefficient and Temperature

When the acoustic wave on the seabed has an incident angleθiand a refraction angleθt,the reflection coefficient can be calculated as follows:

At normal incidence,both incident and refraction angles are 0?.Considering the effect of temperature,the reflection coefficient can be expressed as the function of the acoustic impedance ratio,as follows:

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In general,the higher the acoustic impedance of sediments is,the higher the seafloor interfacial reflection coefficient.Therefore,sediments with high sand content and low porosity have high reflection coefficients,whereas those with high clay content and high porosity have low reflection coefficients.The actual seafloor acoustic inversion measurements (Camin and Isakson,2006;Chenet al.,2016;Zhouet al.,2020) are consistent with the phenomenon of high reflection coefficients for coarse particles and low reflection coefficients for fine particles.As shown in Table 4,the mean values of the reflection coefficients of the five typical samples are consistent with the aforementioned trend.The reflection coefficient of clayey sample TS4 is <0.2.By contrast,the reflection coefficients of sandy samples TS1,STX1204,and Carbó’s sand are >0.3.Meanwhile,the reflection coefficient of silty sample STX1205 is between 0.2 and 0.3.These values are consistent with the average measurement values of bottom sediments in different sea areas (Liu and Lei,1993;Liu and Guang,2004).

The EDFM (Williams,2001) could well explain both the sound speed dispersion (Brianet al.,2009) and the relationship between sound speed of seafloor sediment and temperature change (Zouet al.,2021a,2021b).Considering the effect of temperature,the EDFM was applied to theoretically analyze the sound reflection coefficient and expressed as follows (Zouet al.,2015):

whereηis the viscosity of pore water,kis the permeability,Fis the dynamic viscosity correction factor,ωis the angular frequency,Ksis the bulk modulus of solid grains,Kfis the bulk modulus of pore water,andαis the tortuosity.

As shown in Fig.3,the measurement results of the sound reflection coefficient are consistent with the theoretical calculation curves of the five typical samples.They both show that the sound reflection coefficient has a slow downward trend with temperature.Although the sand samples STX1204 and Carbó’s sand are taken from different sea areas,their physical properties are similar.Hence,their reflection coefficients should be similar.However,a significant difference is detected,as shown in Fig.3 and Table 4,which can be correlated with different sedimentary structures caused by the sedimentary history of two different sea areas and mainly by the dispersion effect caused by different detection frequencies.

Fig.3 Relationship between acoustic reflection coefficient and temperature,the curve is calculated based on the EDFM model.

These two samples’ actual measured physical parameters were used to analyze the differences in the reflection coefficients caused by the dispersion phenomenon using the EDFM.Based on the CTD measurements,thein situtemperatures at 10 and 50 m in the Yellow Sea in June are 20.62℃ and 10.26℃,respectively.The corresponding relationship of reflection coefficients at different frequencies and temperatures is calculated,as shown in Fig.4.

Fig.4 Calculated correlation between reflection coefficient and detection frequency of the two sandy samples using the EDFM.

First,the 23.8 kHz frequency was selected and investigated according to the actual detection frequency of sample STX1204.At 10.26℃,the reflection coefficient of the sample of Carbó’s sand was 0.3457,which was 0.0183 larger than that of sand sample STX1204,with a difference rate of 5.29%.At 20.62℃,the reflection coefficient of the sample of Carbó’s sand was 0.3449,which was 0.0162 larger than that of sand sample STX1204,with a difference rate of 4.70%.Second,the 1 MHz frequency was selected and investigated according to the actual detection frequency of the sample of Carbó’s sand.At 10.26℃,the reflection coefficient of the sample of Carbó’s sand was 0.3712,which was 0.0316 greater than that of sand sample STX1204,with a difference rate of 8.51%.At 20.62℃,the reflection coefficient of the sample of Carbó’s sand was 0.3702,which was 0.0319 larger than that of sand sample STX1204,with a difference rate of 8.62%.Notably,at the same frequency,the difference rate of the reflection coefficient slightly changes at different temperatures.This finding indicates that temperature has a similar influence on the two sandy samples even though dispersion has a significant influence on specific reflection coefficient values.

If different detection frequencies are compared at the same temperature,then the reflection coefficients of the two sandy sediments significantly differ in terms of dispersion characteristics,as shown in Fig.4.The reflection coefficient of the low-frequency band was further calculated to predict the acoustic properties using geoacoustic inversion methods.When the detection frequency was 100 Hz (at 20.62℃),the reflection coefficient of the sample of Carbó’s sand was 0.3421 and that of sand sample STX-1204 was 0.3096.The difference was 0.0325 and the difference rate was 9.50%.The difference rate of the reflection coefficient at low frequency (100 Hz) was higher than that at medium frequency (23.8 kHz,5.29%) and high frequency (1 MHz,8.62%).The main reason is the difference in the texture and composition of the two sandy samples.The main physical properties of the two samples were similar,as shown in Table 1.However,the relative difference rate of porosity was approximately 15% because the two samples were from different sea areas that had different sedimentary histories,pore channels,particle accumulation structures,and salinities.Although the acoustic and dispersion characteristics were similar,they had different characteristic frequencies according to Biot’s theory(Biot,1956).The different characteristic frequencies resulted in significant differences in the reflection coefficients at different frequencies but had only a slight influence on the change trend with temperature.

As a result,the significant differences in the reflection coefficients of the two samples at low frequency (<1 kHz)and high frequency (≥ 10 kHz) were not caused by the temperature change but by the dispersion characteristics of the sediments.The variation of the reflection coefficient of these two sediments was still slightly affected by temperature.The comparison indicates that the EDFM can be used as a tool to predict the sound reflection coefficient of seafloor sediments when the actual measurement values at certain temperatures are lacking.

4 Discussion

The acoustic impedances,acoustic impedance ratios,and acoustic reflection coefficients of sandy,silty,and clayey sediments exhibited a similar variation trend with temperature.The experimental results were consistent with the theoretical analysis based on the EDFM,which further confirmed that the primary influencing mechanism of pore water on the acoustic characteristics of seafloor surface sediments (Zouet al.,2015,2021b).Seafloor surface sediments are composed of pore water and solid particles in a loosely packed skeleton.Pore water is seawater stored in the pores of sediments and exchanged with bottom seawater.Within the in situ normal temperature range of 1℃to 30℃ on the seabed,the physical and mechanical properties of pore water are more affected by temperature than those of solid particles.Hence,the acoustic and physical parameters of seafloor sediments are mainly affected by the change of pore water and are similar to those of bottom seawater.As a result,the acoustic impedance variation of seafloor sediments is consistent with that of bottom seawater,and the acoustic reflection parameters (i.e.,acoustic impedance ratio and reflection coefficient) slightly change because of the ratio of seafloor sediment to bottom water.The difference between fine and coarse sediments in the pore channel leads to the differences in the amplitude and magnitude of the relative motion between solid and liquid phases during the acoustic wave propagation process,but does not affect the law and trend of the influence of temperature.

For different detection frequencies,the acoustic impedances,acoustic impedance ratios,and acoustic reflection coefficients of different sediments exhibited a similar variation trend with temperature.The sound speed dispersion only leads to differences in the specific values of these parameters.The dispersion characteristics measured in Jiaozhou Bay,China (Wanget al.,2018),the Gulf of Mexico(Buckingham and Richardson,2002),and the Yellow Sea in China (Kanet al.,2018) were analyzed and compared.They showed that the variation of sound speed was generally no more than 20 m s-1from 25 kHz to 100 kHz.Because the water is nondispersive,the acoustic impedance ratio and reflection coefficient depend on the sound speed difference and different dispersion characteristics of various seafloor sediments.For example,the difference rates of sound impedance and sound speed of sand sample STX-1204 are both 4.35%,and the difference rate of the reflection coefficient varies 6.17% from 0.3096 (at 100 Hz,20.62℃) to 0.3287 (at 23.8 kHz,20.62℃).

Because temperature had a similar influence on seafloor sediment and bottom seawater,it has only a slight influence on the reflection coefficient and sound impedance ratio.However,the reflection coefficient is not constant and is negatively correlated with temperature variation.At the same temperature,the reflection coefficient is correlated with the frequency.When the detention frequency is the same,the reflection coefficient is related to temperature.When the reflection coefficients from different sea areas with different sediment types are compared,the reflection coefficient difference is correlated with the texture and composition of the sediments,the detection frequency,and the environmental conditions (we focus on temperature here).

5 Conclusions

The influences of seafloor temperature on thein situsurface sediments include diurnal variation,seasonal variation,bottom flow movement,and geological variation.Based on the previously presented analysis and calculation of acoustic reflection parameters,the following valuable conclusions about the acoustic characteristics of seafloor surface sediments can be drawn:

1) The sound speed and acoustic impedance of seafloor sediment positively correlate with temperature,and the temperature variation trend of seafloor sediment is similar to that of bottom seawater.

2) The acoustic impedance ratio and acoustic reflection coefficient of seafloor sediment against seawater are not constant and slightly decrease with temperature.

3) The acoustic reflection characteristics (i.e.,acoustic impedance,acoustic impedance ratio,and acoustic reflection coefficient) of sandy,silty,and clayey sediments vary similarly with temperature variation.

4) The influence of temperature on the acoustic reflection characteristics (i.e.,acoustic impedance,acoustic impedance ratio,and acoustic reflection coefficient) of the seafloor surface sediment is independent of detection frequencies.

Thus,the acoustic impedance ratio and acoustic reflection coefficient under different temperatures can be used as constants with a small error and can simplify the complexities of underwater acoustic propagation analysis and geoacoustic inversion research.At the same time,further study andin situobservation of acoustic reflection coefficient under different marine seafloor environments can precisely explain the differences in the sound propagation characteristics in different seasons.Meanwhile,by monitoring the changes of the reflection characteristics in the same sea area,the temperature changes of thein situseafloor surface sedimentary environment could be predicted or inversed.

Acknowledgements

The authors are grateful for the invaluable support and assistance of the members of the EHIMCE Research Group,Guangdong University of Technology,and would like to especially thank Prof.Guangming Kan from the First Institute of Oceanography of Ministry of Natural Resources for his help and advice throughout the project.This study is supported by the National Natural Science Foundation of China (No.41776043),the Natural Science Foundation of Guangdong Province (No.2019A1515011055),the Opening Fund of the State Key Laboratory of Acoustics,Chinese Academy of Sciences (No.SKLA202105),and the Opening Fund of Qingdao National Laboratory for Marine Science and Technology (No.MGQNLM-KF201805).