
In general, sea surface scattering is comprised of rough surface scattering and bubbles scattering. Consequently, the total scattering cross section σ_{tot} is given by:
Where σ_{r} and σ_{b} denotes rough surface and bubbles components respectively. The complete model for scattering strength is 10log_{10}σ_{tot}.
In this paper, the experimental results are compared with second order perturbation theory with “PiersonMoskowitz” (PM) roughness spectrum and nearsurface bubbles model follows Dahl et al. (1997). The results shows that the measured seasurface backscattering strengths at grazing angles of 40°–80° are consistent with the prediction results of the small roughness perturbation theory, and the backscattering strengths at lower grazing angles are dominated by bubbles scattering.
For 1D rough surface backscattering, k_{ix}=–k_{sx}and k_{iz}=k_{sz}, where k_{i} and k_{s} are the incident and scattered wave numbers, respectively. The components are indicated by subscript. Then the second order perturbation backscattering cross section is given by:
With the PM roughness spectrum
where U_{19.5} is wind speed at a height of 19.5 m, and α=8.1×10^{–3}, β=0.74, g_{c} is gravitational acceleration. Note that the measured backscattering strengths are from 2D surfaces in our experiment. In general, there are intrinsic differences between scattering from 1D and 2D surfaces. However, Thorsos (1990). found the accurate relationship between scattering from 1D and 2D surfaces for second order perturbation theory expressions
where Φ(K, ϕ) describes the azimuthal dependence of roughness spectrum, ϕ is azimuthal angle. In our case, scattering is from all the azimuthal angles. So, the averaged Φ(K, ϕ) is
It then follows from Eqs (22)–(25) that the 2D surface second order perturbation backscattering cross section
where μ_{p}=1.61×10^{–4}, σ=1.01×10^{6} m^{4}·s^{–6}, f is the acoustic frequency in hertz, and θ is the grazing angle. The scattering cross section σ_{2D}^{(2)} in Eq. (26) was affected very little by variation in wind speed and frequency but was strongly dependent on the grazing angle; in particular, at small grazing angles, it sharply declined as the grazing angle decreased.
The bubbles scattering model used here is based on Dahl’s research, which summarized researchers’ works (Clay and Medwin, 1977; Crowther, 1980; Sakar and Prosperetti, 1994) with some simplifications. The bubbles scattering cross section is:
where γ=γ_{g}/sinθ, δ_{r}=0.013 6 is the radiation damping constant at resonance, δ is the total damping coefficient at resonance, which is related to frequency by δ=2.55×10^{–3}f^{1/3}, and γ_{g} describes the concentration of bubbles in seawater and is defined as the depthintegrated extinction cross section per unit volume. Generally, γ_{g} varies with seawater environment. Based on a large amount of experimental data, Dahl developed the following empirical formula for γ_{g} as a function of wind speed and frequency:
where U_{10} is the wind speed at 10 m height above sea surface, and f is the resonance frequency.
The comparisons of the measured backscattering strengths with second order perturbation theory and bubbles model are presented in Fig. 4 and Fig. 5. The red circle with error bar represents the measured backscattering strength, and the soild black line and dotted line indicate second order perturbation theory and bubbles model respectively. The total backscattering strengths are represented by dashed line. As shown in Fig. 4 and Fig. 5, the measured backscattering strengths agree well with the predictions of perturbation theory at mid to high grazing angles (30°–85°). While at low grazing angles, the measurement scattering strengths exceeded the prediction of the small roughness perturbation approximation. The contribution of bubble scattering at frequencies of 6–25 kHz ranged from −52 to −49 dB at a wind speed of 3 m/s and from −45 to −42 dB at a wind speed of 4.5 m/s; these values are slightly smaller than the total backscattering strength computed at grazing angles of <30°. Dahl et al. believed that nearsurface bubbles have a crucial effect on seasurface scattering mainly at low grazing angles (<30°) and high wind speeds (wind speeds > 3 m/s as generally considered). This assumption is supported by the results of our experiment. In summary, the seasurface backscattering strengths at intermediate to high grazing angles were primarily affected by the rough sea surface, and the contribution of nearsurface bubbles generated by breaking waves to the total backscattering strengths was inconsiderable. Whereas the bubbles scattering is dominated at low grazing angles.
Figure 4. Comparisons of the measured backscattering strengths with second order perturbation theory and bubbles model at wind speeds of 3 m/s. The frequencies are 9 kHz (a), 11 kHz (b), 13 kHz (c), 15 kHz (d), 17 kHz( e),18 kHz (f), 21 kHz (g),25 kHz (h),respectively.
Figure 5. Comparisons of the measured backscattering strengths with second order perturbation theory and bubbles model at wind speeds of 4.5 m/s. The frequencies are 6 kHz (a), 9 kHz (b), 11 kHz (c), 15 kHz (d),17 kHz (e), 19 kHz (f), 21 kHz, (g),25 kHz (h), respectively.
Figure 6 shows the comparisons of measured backscattering strengths at different wind speeds and at the same frequencies. It is evident that, within the frequency range from 6 to 21 kHz, the backscattering strengths increased as the grazing angle increased. Moreover, At grazing angles in the range of 40°–80°, the backscattering strengths are on average 5–10 dB higher at a wind speed of 4.5 m/s than at a wind speed of 3 m/s, in which the roughness scattering is dominated Noted that the scattering strengths near the grazing angle of 50 at a wind speed of 3 m/s and frequencies of 12–14 kHz is abnormally stronger than that of adjacent grazing angles. Some kind of fixed interference of observation system may account for the phenomenon. The backscattering strengths essentially remained constant at grazing angles from 16° to 35° owing to the effect of scattering from bubbles. At a wind speed of 4.5 m/s, the bubbles scattering strengths are approximately –40 dB which are almost 10 dB higher than those at a wind speed of 3 m/s. As we can see in Fig. 4 and Fig. 5, there are some discrepancies between the data and bubbles model. The reason for these discrepancies may be related to variability in the wind speed. Actually, γ_{g} in Eq. (22) is related to the depthintegrated distribution of resonantsized bubbles, which is dependent on local environment generally. Therefore, it is very difficult to accurately predict the bubbles scattering, and this may be another reason for the discrepancies.
As shown in Fig. 7, at a wind speed of 4.5 m/s and at all frequencies between 6 and 24 kHz, the backscattering strengths at grazing angles between 40° and 80° differ slightly, and at the same grazing angles, the maximum difference in the backscattering strengths at different frequencies does not exceed 6 dB, which means that rough surface scattering is not sensitive to the frequency. However, the maximum discrepancy of backscattering strength at low grazing angles is more than 10 dB. Furthermore, the backscattering strengths show little frequency dependence, which is consistent with the studies of reverberation at frequencies of 15–60 kHz in open ocean (Lilly and McConnell, 1978). In fact, considering the uncertainty of measured backscattering strength which incorporates the statistical error and the systematic error, it is difficult to conclude the frequency dependence. The systematic error of this experiment is about ±2 dB, which mainly included source level error and sensitivity error. The statistical error is ±2 dB. Hence, the total uncertainty of this experiment is approximately ±3 dB. Meanwhile wind speeds during the experiment fluctuated between a minimum value of 3.5 m/s and a maximum value of 5.5 m/s, so the fluctuation in wind speeds might be the primary cause for the fluctuation in backscattering strengths at different frequencies. Consequently, measurement errors and variation in environmental conditions would mask the influence of frequencies on seasurface backscattering.
Figure 7. Backscattering strength at a wind speed of 4.5 m/s and in the frequency range of 6–24 kHz.
Though it appears to be impossible to obtain the accurate frequency dependence, we can conclude the influence trend of frequency. As listed in Table 1, the slopes of linear regression between backscattering strength and the frequency in the range of 6–25 kHz at different grazing angles are computed. It can be seen that the slopes at low grazing angles are positive, and the slopes at high grazing angles are negative, which indicates that the scattering strengths increase at low grazing angles as the grazing angle increased but decrease at high grazing angles. The results at low grazing angles are not difficult to understand from Eq. (24). As for the results at high grazing angles, it may be the influence of bubbles. Because resonant bubbles scatter as well as absorb acoustic energy. The higher that frequency is, the stronger that the resonant bubbles scattering and attenuation is.
Garzing angle/(°) Slope/dB·kHz^{–1} 20 0.203 0 24 0.142 6 30 0.496 5 34 0.401 9 40 0.203 7 50 −0.050 0 60 −0.170 4 70 −0.140 4 80 −0.111 2 Table 1. Slopes of linear regression between backscattering and frequency at a wind speed of 4.5 m/s
Seasurface acoustic backscattering measurement at 6–25 kHz in the Yellow Sea
doi: 10.1007/s1313102015397
 Received Date: 20181029
 Available Online: 20200421
 Publish Date: 20200301

Key words:
 seasurface acoustic scattering /
 moderate frequency /
 scattering model /
 bistatic backscattering /
 frequency dependence
Abstract: Seasurface acoustic backscattering measurements at moderate to high frequencies were performed in the shallow water of the south Yellow Sea, using omnidirectional spherical sources and omnidirectional hydrophones. Seasurface backscattering data for frequencies in the 6–25 kHz range and wind speeds of (3.0±0.5) and (4.5±1.0) m/s were obtained from two adjacent experimental sites, respectively. Computation of seasurface backscattering strength using bistatic transducer is described. Finally, we calculated seasurface backscattering strengths at grazing angles in the range of 16°–85°. We find that the measured backscattering strengths agree reasonably well with those predicted by using second order smallroughness perturbation approximation method with “PM” roughness spectrum for all frequencies at grazing angles ranged from 40° to 80°. The backscattering strengths varied slightly at grazing angles of 16°–40°, and were much stronger than roughness scattering. It is speculated that scattering from bubbles dominates the backscattering strengths at high wind speeds and small grazing angles. At the same frequencies and moderate to high grazing angles, the results show that the backscattering strengths at a wind speed of (4.5±1.0) m/s were approximately 5 dB higher than those at a wind speed of (3.0±0.5) m/s. However, the discrepancies of backscattering strength at low grazing angles were more than 10 dB. Furthermore the backscattering strengths exhibited no significant frequency dependence at 3 m/s wind speed. At a wind speed of 4.5 m/s, the scattering strengths increased at low grazing angles but decreased at high grazing angles with increasing grazing angle.
Citation:  Lehua Qi, Guangming Kan, Baohua Liu, Yanliang Pei, Zhiguo Yang, Shengqi Yu. Seasurface acoustic backscattering measurement at 6–25 kHz in the Yellow Sea[J]. Acta Oceanologica Sinica, 2020, 39(3): 113122. doi: 10.1007/s1313102015397 