Relationships between the sound speed ratio and physical properties of surface sediments in the South Yellow Sea
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Abstract: Building empirical equations is an effective way to link the acoustic and physical properties of sediments. These equations play an important role in the prediction of sediments sound speeds required in underwater acoustics. Although many empirical equations coupling acoustic and physical properties have been developed over the past few decades, further confirmation of their applicability by obtaining large amounts of data, especially for equations based on in situ acoustic measurement techniques, is required. A sediment acoustic survey in the South Yellow Sea from 2009 to 2010 revealed statistical relationships between the in situ sound speed and sediment physical properties. To improve the comparability of these relationships with existing empirical equations, the present study calculated the ratio of the in situ sediment sound speed to the bottom seawater sound speed, and established the relationships between the sound speed ratio and the mean grain size, density and porosity of the sediment. The sound speed of seawater at in situ measurement stations was calculated using a perennially averaged seawater sound speed map by an interpolation method. Moreover, empirical relations between the index of impedance and the sound speed and the physical properties were established. The results confirmed that the existing empirical equations between the in situ sound speed ratio and the density and porosity have general suitability for application. This study also considered that a multiple-parameter equation coupling the sound speed ratio to both the porosity and the mean grain size may be more useful for predicting the sound speed than an equation coupling the sound speed ratio to the mean grain size.
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Figure 1. The location of the study area (a, red shaded area), contour map of the bottom seawater temperature (°C) in the study area in June (b, from Editorial Board for Marine Atlas, 1993), and contour map of the bottom seawater sound speed (m/s) in the study area in June (c, from Editorial Board for Marine Atlas, 1993). In a, the black shaded area shows the study area of Kim et al. (2011) and Bae et al. (2014), whose data were used for comparison. BS: Bohai Sea, NYS: North Yellow Sea, SYS: South Yellow Sea, ECS: East China Sea, KWC: Kuroshio Warm Current, YSWC: Yellow Sea Warm Current, YSCC: Yellow Sea Coastal Current, and KCC: Korea Coastal Current.
Figure 2. Comparison of the bottom seawater sound speed interpolated from the hydrology atlas to that measured by CTD during the cruises. The 1:1 dashed line represents that the sound speed is equal, and the solid line is the fitting curve.
Figure 3. Shepard ternary diagram of sediment types in the study area. The black points represent the data used in this paper and the red points represent the collected data from Bae et al. (2014).
Figure 4. Relationship between the sound speed ratio and the three physical properties of mean grain size (a), bulk density (b), and porosity (c). Black points represent our data, and black solid lines represent their fitted curves, corresponding to equations listed in Table 1. Also plotted are the curves of the H&B model (blue lines), the J&R model (pink lines) as listed in Appendix, and data from Kim et al. (2011) (green diamonds) and Bae et al. (2014) (red triangles).
Figure 5. Relationship between the porosity and the mean grain size (a), and double-parameters relationship of sound speed ratio with both porosity and mean grain size (b). In a, black points represent our data; also plotted are the H&B model (blue lines), the J&R model (pink lines), and data from Bae et al. (2014) (red triangles).
Figure 6. Relationship between the IOI and the geoacoustical and physical properties and comparison with equations from Jackson and Richardson (2007). a. Sound speed ratio against the IOI, b. mean grain size against the IOI, c. density against the IOI, d. porosity against the IOI, and e. sand content and clay content against the IOI (the pink line represents the regression for IOI against sand and gravel content in J&R model).
Table 1. Empirical relationships of the sediment sound speed ratio with physical properties
Physical properties Regression equation for VpR Correlation coefficient (R2) Mean grain size (Mz)$/\phi$ $V_{p} R\!=\!1.151\;3\!-\!3.292\;3 {\rm{e}}^{-2} M_{z}\!+\!1.421\;3 {\rm{e}}^{-3} M_{z}^{2}$ 0.687 8 Density (ρ)/(kg·m–3) ${V_p}R \!=\! 1.373\;4 \!-\! 5.793\;5{{\rm{e}}^{ - 4} } \rho \!+\! 2.081\;9{{\rm{e}}^{ - 7} } {\rho ^2}$ 0.878 5 Porosity (η)/% $V_{p} R\!=\!1.378\;8\!-\!1.067\;1 {\rm{e} }^{-2} \eta\!+\!6.986\;0 {\rm{e} }^{-5} \eta^{2}$ 0.877 4 Porosity and mean grain size$/\phi$ $V_{p} R\!=\!0.998\;8\!-\!0.005\;2 \eta\!-\!0.025\;0 M_z\!+\!0.009\;5 \eta^{2}\!-\!0.013\;0 \eta M_z\!+\!0.013\;1 M_z^{2}$ 0.876 5 
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Table 2. Empirical relationships between the index of impedance (IOI) and geoacoustical and physical properties
Parameters Regression equation for the IOI Correlation coefficient (R2) Sound speed ratio (VpR) $\normalsize{V_{p} R\!=\!1.161\;0\!-\!0.321\;4 ({\rm{IOI}})\!+\!0.134\;4 ({\rm{IOI}})^{2}}$ 0.938 3 Mean grain size (Mz)/ϕ $\normalsize{M_{z}\!=\!15.607\;6\!-\!4.957\;3 ({\rm{IOI}})\!-\!0.405\;8 ({\rm{IOI}})^{2}}$ 0.832 1 Bulk density (ρ)/(g·cm–3) $\normalsize{\rho\!=\!-0.508\;4\!+\!1.828\;8 ({\rm{IOI}})\!-\!0.313\;5 ({\rm{IOI}})^{2}}$ 0.995 7 Porosity (η)/% $\normalsize{\eta\!=\!187.42\!-\!105.24 ({\rm{IOI}})\!+\!18.04 ({\rm{IOI}})^{2}}$ 0.995 2 Sand content (SC)/% $\normalsize{{\rm{SC}}\!=\!196.07\!-\!287.15 ({\rm{IOI}})\!+\!106.63 ({\rm{IOI}})^{2}}$ 0.595 5 Clay content (CC)/% $\normalsize{{\rm{CC}}\!=\!399.23\!-\!376.47 ({\rm{IOI}})\!+\!91.86 ({\rm{IOI}})^{2})$ 0.775 9
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