1 Introduction

Three main acoustic techniques are currently used to measure, invert, and forecast the acoustic properties of seafloor sediments under different environmental conditions. Geoacoustic inversion measurement methods (Li and Li, 2010; De and Chakraborty, 2011; Buckingham et al., 2012; Williams et al., 2015; Chapman, 2016) detect underwater and geoacoustic properties by the sound gradients of the seawater and sediment, which are affected by the spatial distributions of temperature and pressure in the propagation path. In-situ acoustic measurement methods (Richardson and Briggs, 1996; Buckingham and Richardson, 2002; Tao et al., 2009; Kan et al., 2013; Ballard et al., 2016) directly measure the acoustic properties of sediment in in-situ environmental conditions. In contrast, sampling acoustic measurement methods (Hamilton, 1971; Hoffman and Tobin, 2002; Richardson and Briggs, 2004; Lu et al., 2007; Meng et al., 2015; Wang et al., 2016) are applied to sediment core samples under laboratorial pressure and temperature conditions, which are quite different from those in the in-situ environment. Thus, environmental factor have the primary impact on the acoustical, physical, and mechanical properties of seawater and sediment by geoacoustic inversion measurement at different water surficial levels, in-situ acoustic measurements at different seafloor depths, and sampling acoustic measurements in different laboratory environments. The empirical equations of Hamilton (Hamilton, 1970, 1971; Hamilton and Bachman, 1982) are widely used and referenced by researchers in different marine regions using different measurement methods (Gorgas et al., 2002; Buckingham, 2005; Lu et al., 2006; Jackson and Richardson, 2007; Endler et al., 2015; Wang et al., 2016; Kan et al., 2019). Less consideration is given to the environmental influences on acoustic characteristics.

A solution to the abovementioned problems, which was proposed by Hamilton (1971), was to assume that the sound velocity ratio between the seafloor sediment and bottom seawater was constant. With the sound velocity ratio held constant, the sound speeds of sediments measured using different methods have been calculated and applied to correct or eliminate the influence of different temperatures and pressures (Hamilton and Bachman, 1982; Bachman, 1989; Wang et al., 2016). However, recent experimental results (Kim et al., 2018; Kan et al., 2019; Zou et al., 2019) have reported the influence of temperature and hydraulic pressure on both the sound speed of seafloor sediment and the sound velocity ratio, and that the sound velocity ratio can vary in different environmental conditions. However, the above research mostly focused on experimental analysis. Factors such as salinity, acoustic detection frequency, and sediment type must also be considered together. With the help of generally accepted theoretical models, further analysis and interpretation of experimental results is needed, along with exploration of the influence mechanisms of environmental factors.

In this study, we examine the influence of environmental conditions, including temperature, pressure, and salinity, on the sound velocity ratio of different types of seafloor surficial sediments (i.e., less than 3 m beneath the surface of the ocean bottom), analyze the relationship between the sound velocity ratio and the influence of environmental conditions using the effective density fluid model (EDFM), and describe the measurement results obtained in temperature- and pressure-controlled laboratory acoustic experiments to verify conclusions obtained by theoretical analysis.

2 Theoretical Analysis of the Environmental Influence on the Sound Velocity Ratio in Surficial Sediment 2.1 EDFM Considering the Influence of Environmental Factors

Widely employed theories, such as fluid, elastic, and poroelastic theories, focus on analysis of the influences of physical parameters of the seafloor sediment and acoustic frequency on the acoustic properties of sediment (Jackson and Richardson, 2007). These theories can also be used to analyze the influences of environmental factors. The EDFM (Williams, 2001) simplifies the parameters of the Biot–Stoll model for two-phase media at low frequencies and uses the effective bulk modulus K_eff and effective density ρ_eff to model a general expression for the properties of sound speed in sediment. The EDFM can explain the relationship between the compressional wave velocity and the detection frequency. With consideration of the effects of temperature, pressure, and salinity on the physical parameters, the sound speed c_p in the EDFM can be expressed as follows:

${c_p}(T, P, S) = \sqrt {{K_{{\rm{eff}}}}(T, P, S)/{\rho _{{\rm{eff}}}}(T, P, S)}, $

(1)

${K_{{\rm{eff}}}}(T, P, S) = \frac{{{K_g}}}{{1 + n({K_g}/{K_f} - 1)}}, $

(2)

${\rho _{{\rm{eff}}}}(T, P, S) = \\ \;\;\;\;\;\;{\rho _f}(\frac{{\alpha (1 - n){\rho _g} + n(\alpha - 1){\rho _f} + i(n{\rho _s}F\eta /{\rho _f}\omega k)}}{{n(1 - n){\rho _g} + (\alpha - 2n + {n^2}){\rho _f} + i(nF\eta /\omega k)}}), $

(3)

${\rho _s}(T, P, S) = n \cdot {\rho _f} + (1 - n) \cdot {\rho _g}, $

(4)

where T, P, and S are the temperature, pressure, and salinity, respectively. K_g and K_f are the bulk modulus of solid grains and the bulk modulus of pore water, respectively, and n is the porosity of the sediment. ρ_f, ρ_g, and ρ_s are the bulk densities of the pore water, solid grains, and sediment, respectively. η is the viscosity of the pore water and k is its permeability. F is a dynamic viscosity correction factor, ω is the detected angular frequency, and α is the tortuosity. Generally speaking, the above parameters all vary with changes in temperature and pressure, albeit with different scales.

With consideration of the environmental influence on the bottom seawater (equal to the pore water in the sediment), the sound velocity ratio R of the surficial sediment to the bottom seawater can be written as:

$R = {c_p}/{c_w} = \sqrt {{K_{{\rm{eff}}}}(T, P, S)/{K_f}(T, P, S)} \cdot \\ \;\;\;\;\;\;\;\sqrt {{\rho _f}(T, P, S)/{\rho _{{\rm{eff}}}}(T, P, S)}, $

(5)

where the K_f (T, P, S) and ρ_f (T, P, S) can be calculated using the seawater state equation (Jackson and Richardson, 2007).

Eqs. (1) and (5) can be used to study both the sound speed c_p in sediment and the sound velocity ratio R of the surficial sediment to the bottom seawater in different environmental conditions. These applications may lead to the discovery of the mechanism underlying the influence of temperature and pressure on the acoustic properties of sediment.

According to Eq. (1), even if the texture and grain composition of sediment do not change, the sound speed in the sediment will change due to the influence of different salinities, temperatures, and pressures on the sediment's physical parameters. This mechanism can be described as the influence of salinity, temperature, and pressure on the effective elastic modulus and effective density of the sediment. For surficial sediment, analysis based on a general model of the sound velocity ratio indicates that the series texture is dominant in two-phase structures of unconsolidated sediments (Zou, 2018). In other words, most solid particles are suspended in pore water or separated by a liquid film, with the solid and liquid phases subject to equal stress. Therefore, filling with seawater weakens the effect of the shear modulus of the solid grains. Thus, to study compressional waves with the EDFM, we use the Wood equation, as shown in Eq. (2), to express the effective bulk modulus. Changes in the environmental factors will result in variations in both the seawater and sediment, and thus the sound velocity ratio according to Eq. (5).

The equivalent bulk modulus and equivalent density of solid grains are expected to be influenced much less by environmental factors compared to their effect on those of pore water. Therefore, variations in the acoustic properties of surficial sediment can mainly be attributed to changes in the acoustic properties of pore water. This assumption has been verified and elucidated by experimental and theoretical analyses of the influence of temperature on sediment (Shumway, 1958; Rajan and Frisk, 1992; Eastwood, 1993; Zou et al., 2015). That is, changes in the bulk modulus and density of pore water with changing environmental factors determine the variations in the effective bulk modulus and effective density of the sediment. This determination, in turn, affects the trend and extent of the acoustic variation.

2.2 Analysis of the Environmental Influence on the Sound Velocity Ratio of Surficial Sediment Based on EDFM

Typical sandy sediment was selected for this study, the representative physical parameters of which are listed in Table 1. The changes in the bulk modulus, bulk density, and viscosity of seawater can be calculated using the seawater state equation with temperature, pressure, and salinity (Jackson and Richardson, 2007).

Changes in the sound velocity ratio were calculated by the EDFM using Eqs. (1) to (5) at 200 Hz, 40 kHz, and 1 MHz in different environmental conditions. These three typical frequencies were chosen for comparison to represent different acoustic measurement methods. The calculations were performed using Matlab software and the results are shown in Fig. 1 and Table 2. Although different detection frequencies show a notable influence on the sound velocity ratio, the changes in the sound velocity ratio were found to be similar to the changes in the environmental factors. Table 2 presents the mean value of each factor's influence on the sound velocity ratio. The difference between the maximum and minimum values (Vd_max−min) and its division by the mean value (R_Vd/mean), which is referred to as the relative rate, are used to observe the change in the sound velocity ratio and the change rate. An absolute change rate (V_abs) is obtained to represent the change in the sound velocity ratio with respect to the range of a given factor. This parameter provides a reference value for changes in the sound velocity ratio for different environmental factors. In Fig. 1 and Table 2, it is evident that the influence of salinity is obviously less than that of the other two factors. Considering the fact that the variation range in the salinity of seawater is small and the absolute and relative change rates are also small, the influence of salinity is ignored in the following analysis.

Fig. 2 shows a three-dimensional profile of the changes in the sound velocity ratio with temperature and hydrostatic pressure, which indicates the acoustic attributes of seafloor surficial sediment for most in-situ and laboratorial environmental conditions. The theoretical calculations show that the sound velocity ratio decreases with increases in both temperature and hydrostatic pressure. With variations in the temperature and hydrostatic pressure, the sound velocity ratio does not remain constant. As salinity has only a slight impact on the velocity ratio, its effect is omitted. The theoretical analysis indicates that the sound velocity ratio of surficial sandy sediment changes by up to 0.0006 per ℃ when the temperature ranges from 1℃ to 30℃, and by up to 0.00054 MPa⁻¹ when the hydrostatic pressure ranges from 0 to 40 MPa, which is equal to that of the sea bottom at 4 km depth, in both in-situ and laboratory distributions.

3 Experimental Relationships Between the Sound Velocity Ratio and the Temperature and Hydrostatic Pressure

Due to the minor effect of salinity, as determined by theoretical analysis, experiments were conducted to determine only the influences of temperature and hydrostatic pressure. Changes in the sound velocity ratio of the seafloor sediment were systematically investigated in experiments with respect to the actual sediment distribution in any possible environmental state.

Table 3 and Fig. 3 show the representative relationships between the physical properties and the depth of seawater in the Yellow Sea and the South China Sea, respectively. The seawater temperature and sound-speed profile were measured using SBE-9 CTD probes. The Yellow Sea is shallow, with an average depth of about 40 m, which means its temperature changes significantly and has a strong influence on the sound speed of the seawater. As a result, the sound speed of the seafloor sediment is apt to be affected by seasonal variations in temperature. The South China Sea is much deeper, with an average depth of about 1200 m, and its temperature decreases with increasing water depth as the hydrostatic pressure increases. Initially, the seawater temperature decreases rapidly and then slows, whereas the pressure continues to increase linearly. Therefore, the sound speed of seawater first decreases with decreasing temperature, and then increases at depths exceeding approximately 1000 m due to the effect of the continuous increase in hydrostatic pressure (Fig. 3).

3.1 Sample Attributes and Experimental Processes

The sediments were sampled using the gravity sampling method at different sites and times from the Yellow Sea (YS) and South China Sea (SCS). These samples were stored in a PVC tube to protect their structures and maintain their seawater contents. Most of the samples utilized in these experiments were surficial sections approximately 300 mm in length. Table 4 lists the properties of the representative samples.

Using laboratory equipment, experiments were conducted to examine the change in the sound speed while controlling for temperature and pressure, respectively. In the experiments, the environmental conditions were recreated to reflect the most likely state of the seafloor surficial sediment. The experimental system mainly consisted of a measurement bench, a digital sonic meter (WSD-3 or DB4), and a pair of planar transducers. The experimental principles and equipment are described in greater detail in Kan et al. (2019). In the temperature-controlled experiments, the equipment was filled with air at 1 atm, and the temperature of the sediment sample was controlled at increments of 1℃. In the pressure-controlled experiments, the pressure chamber was filled with seawater, and the hydrostatic pressure of the sediment sample was controlled at increments of 2 MPa. The temperature during the pressure measurement process was 25.6℃ ± 0.5℃. At each controlled temperature or pressure, the sound speed of the sediment was measured using an acoustic pulse detection technique and the time-of-flight method. To compare the in-situ and laboratory acoustic detection approaches used in different methods and by different researchers, several representative detection frequencies, as shown in Table 4, were chosen in the ultrasonic range. The degree of uncertainty of the sample length measurement was approximately 0.5 mm. The total uncertainty of the sound velocity measurements was approximately ±1.8 m s⁻¹.

3.2 Experimental Results of the Temperature-Dependent Sound Velocity Ratio

For comparison, a sandy sample measured at 1 MHz was provided (Carbó and Molero, 2000), which consisted of fine sand with a porosity of 42% and a density of 1.97 g cm⁻³. Its sound velocity ratio was found to decrease with increases in temperature. The sound velocity ratios of samples TS1, TS2, STX1204, and STX1205 in Fig. 4 show a similar decreasing trend even with different sediment types, different acoustic detection frequencies, and sediments from different sea areas. The uneven variation in the sound velocity ratio indicates the anisotropy and non-uniformity of the sediment. Table 5 lists the relative and absolute change rates of the sound velocity ratio with temperature.

The theoretical EDFM calculation can explain the decreasing trend of the sound velocity ratio (Fig. 4), verifying that the temperature mainly affects the acoustic properties of the seafloor sediment via changes in the elastic modulus, density, and viscosity of the pore water. The decreasing trend and fluctuation of the sound velocity ratio in this experiment imply that the sound velocity ratio should not be regarded as a constant when the temperature changes.

3.3 Experimental Results of the Hydrostatic-Pressure-Dependent Sound Velocity Ratio

As shown in Fig. 5, the sound velocity ratios of sandy samples SPE1404 and SPE1901 decreased with the hydrostatic pressure, and those of samples SPE1402, SPE1403, and SPE1405 also showed a decreasing trend. Table 5 lists the relative and absolute change rates of the sound velocity ratio with hydrostatic pressure. The decreasing trend and fluctuation in the sound velocity ratio with hydrostatic pressure in this experiment imply that the sound velocity ratio must not be regarded as a constant.

The theoretical EDFM calculation can explain the decreasing trend of the sound velocity ratio. The hydrostatic pressure was found to mainly affect the acoustic properties of the seafloor sediment via changes in the elastic modulus, density, and viscosity of the pore seawater. This well explains the influence of hydrostatic pressure on the sound velocity of sandy sediment, with slight deviations for silty and clayed sediments, as shown in Fig. 5.

4 Discussion

Sandy sediments have good porous connections, with the inside pore water being well-connected and easily balancing changes in temperature and pressure. The physical state of pore water rapidly changes and evenly affects the solid grains of the sediment due to the good porous connections. Because of the relatively minor changes in the solid grains within the experimental temperature and pressure ranges, changes in the physical properties of the pore water was determined to dominate changes in the acoustic properties of the sediments. This finding was verified in both the temperature experiment (Carbó's sand sample, STX1204, and TS1 in Fig. 4) and pressure experiment (SPE1404 and SPE1901 in Fig. 5), and shows good agreement with the theoretical analysis. However, the porous connections are complex. In sediments with more clay and silt, the pores are smaller and the pore channels are narrower, although the pore water retained its dominant role in the experiments. However, reconstruction of tortuous pore channels by changes in the environmental conditions becomes increasingly complex, due to the enhanced capillary action and blockage effect of more finely grained particles. Fluctuations occur with changes in the physical properties of the sediment, followed by changes in the sound speed of the sediment. Due to heat conduction, the silty sample STX1205 and the clayey sample TS4 in the temperature experiment showed the same change phenomenon as the sandy samples. However, in the hydrostatic pressure experiment, effects such as capillary action and the blockage effect lead to more complex influences on the sediment. These effects may increase the non-uniformity and weaken the effect of the pore water, which was found in the clayey sample SPE1202 and the silty samples SPE1203 and SPE1205 at high pressure. The sound velocity ratios of the silty and clayey samples seemed to first rapidly and then slowly decrease, whereas the sound velocity of the sandy sample decreased almost immediately. This phenomenon merits further study.

In Table 5, the uneven variation in the sound velocity ratio indicates anisotropy and non-uniformity in the sediment. The inhomogeneous distribution of the sedimentgrain composition and the loosely packed pore structure can lead to a micro-reconstruction of the texture under the action of thermal or hydrostatic stress, which then causes a slight fluctuation in the sound speed of the sediment (Zou et al., 2015, 2019).

The sound-speed dispersion in samples SPE1402 and SPE1403 slightly increased in by approximately 10 m s⁻¹, whereas the acoustic frequency increased from 25 kHz to 250 kHz (Kan et al., 2018). This dispersion is smaller than the result obtained by Buckingham and Richardson (2002) of approximately 17 m s⁻¹, with the acoustic frequency increasing from 25 kHz to 100 kHz. The difference may be due to the different types of seafloor sediment in the two studies. It indicates that the dispersion of seafloor sediments had no significant effect on the detection frequency in this experiment (in Table 4). Although the acoustic detection frequencies were different and dispersion was evident in the datasets, the experimental results showed that the influence of environmental factors on the sound velocity ratio resulted in almost the same change trend at different detection frequencies. As shown in Fig. 4, the sound velocity ratios changed similarly with increases in temperature at 1 MHz, 23.8 kHz, and 35 kHz, which agrees with the EDFM analysis shown in Fig. 1a. As depicted in Fig. 5, the sound velocity ratios changed similarly with increases in the hydrostatic pressure at 33 kHz and 100 kHz, which substantially agrees with the EDFM analysis shown in Fig. 1b.

The experimental results showed that the sound velocity ratio decreased with increases in both temperature and hydrostatic pressure. Compared with the theoretical calculations, the experimental results showed fluctuations in the decreasing trend due to the complex texture and composition of the actual samples. The experimental analysis showed that the sound velocity ratio changed up to 0.0008 per ℃ when the temperature ranged from 2℃ to 25℃ and up to 0.0064 MPa⁻¹ when the hydrostatic pressure ranged from 0 to 40 MPa. The experimental results were slightly larger than those obtained by theoretical analysis. The change rate of the sound velocity due to changes in hydrostatic pressure was slightly higher than that due to changes in temperature for the examined environmental conditions.

Therefore, use of the sound velocity ratio method (Hamilton, 1971), wherein the sound velocity ratio is considered to be constant, can incur errors when it is applied to correct the variation in sound speed caused by variations in temperature and hydrostatic pressure under different environmental conditions (e.g., in-situ, laboratory, and different depths below the seafloor). The expected errors can be estimated, as shown in Table 5.

5 Conclusions

Various compositions and textures are major factors that determine the acoustic properties of seafloor sediments. However, temperature and hydrostatic pressure are also key factors that impact the acoustic properties of seafloor surficial sediments in different sedimentary environmental conditions. By comparing the results obtained by experimental measurements and theoretical calculations, the relationship between the sound velocity ratio and environmental factors was investigated with consideration of both the sediment types and different detection frequencies. These analyses yielded some meaningful results, from which the following conclusions can be drawn:

1) Among the three environmental factors considered, the sound velocity ratio is sensitive to temperature and pressure but not to salinity.

2) In surficial sediments, pore water plays a key role in the sound velocity ratio of sediment influenced by environmental factors.

3) The sound velocities of different types of sediments (sandy, silty, and clayey sediments) change in similar ways with temperature, but change slightly differently with hydrostatic pressure.

4) The influence of environmental factors on the sound velocity ratio of seafloor sediments is independent of different detection frequencies.

5) The sound velocity ratio decreases with both temperature and hydrostatic pressure.

6) The results obtained by experimental measurements regarding the influence of temperature and hydrostatic pressure on the sound velocity ratio agree with those obtained by the EDFM.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Nos. 41676055 and 41776043), the Natural Science Foundation of Guangdong Province (No. 2019A1515011055), and the Foundation of Qingdao National Laboratory for Marine Science and Technology (No. MGQNLM-KF201805). The authors wish to thank the staff at Guangdong University of Technology, the First Institute of Oceanography of Ministry of Natural Resources, and the South China Sea Institute of Oceanology of Chinese Academy of Sciences for performing measurements, conducting experiments, analyzing the datasets, and discussing the findings for this research. The authors also wish to thank the reviewers and Pro. Guoliang Ye for providing so much valuable advice regarding this paper.