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Sound multipath propagation is very important for target localization and identification in different acoustical zones of deep water. In order to distinguish the multipath characteristics in deep water, the Northwest Pacific Acoustic Experiment was conducted in 2015. A low-frequency horizontal line array towed at the depth of around 150 m on a receiving ship was used to receive the noise radiated by the source ship. During this experiment, a bearing-splitting phenomenon in the direct zone was observed through conventional beamforming of the horizontal line array within the frequency band 160 Hz–360 Hz. In this paper, this phenomenon is explained based on ray theory. In principle, the received signal in the direct zone of deep water arrives from two general paths including a direct one and bottom bounced one, which vary considerably in arrival angles. The split bearings correspond to the contributions of these two paths. The bearing-splitting phenomenon is demonstrated by numerical simulations of the bearing-time records and experimental results, and they are well consistent with each other. Then a near-surface source ranging approach based on the arrival angles of direct path and bottom bounced path in the direct zone is presented as an application of bearing splitting and is verified by experimental results. Finally, the applicability of the proposed ranging approach for an underwater source within several hundred meters in depth in the direct zone is also analyzed and demonstrated by simulations.
In the typical deep ocean, there generally exist the sound propagations of direct zone, shadow zones, and convergence zones for shallow source/receiver pairs. The range of direct zone (DZ) is always close, covering about several kilometers due to the water refraction depending on the gradient of the near-surface sound speed profile (SSP) and the source/receiver depths. In DZ, sound signals arrive at the receiver through direct and surface-reflected ray path propagation with small arrival angles (or launching angles) of several degrees. For low-frequency sound signals with less reflection loss than that for the high-frequency signals, bottom-reflected ray paths in DZ should also be taken into account, which arrive at the receiver with very large arrival angles. The sound field in shadow zones primarily comes from bottom-reflected ray paths with range-dependent arrival angles. The water-refracted ray paths far from the source interfere constructively without bottom interaction and contribute to the strong sound field in convergence zones. It is very important to understand the sound field for underwater acoustic applications in deep water.
In 2015, the Northwest Pacific Acoustic Experiment was conducted by the State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences. Passing of a source ship and a tow ship was involved during the experiment. The noise signals radiated from the source ship and were recorded on a low-frequency horizontal line array (HLA) towed by the receiving ship. During this experiment, broadband towed HLA measurements from the shadow zone to the closest point of approach (CPA) of two passing ships (source/receiver) were performed. A source bearing-splitting phenomenon in the direct zone was observed through low-frequency HLA’s conventional beamforming (CBF). In principle, the low-frequency sound field in the DZ of deep water is mainly contributed by direct-path (DP) rays (including surface reflected ones) and bottom bounced (BB) rays. There exists a very distinct difference between DP rays and BB rays in arrival angles, which causes source bearing splitting in DZ. The phenomenon was also observed in the North Pacific Acoustic Laboratory Philippine Sea 2009 experiment.[1] In Ref. [1], Heaney et al. analyzed the experimental data and focused on the variance of bottom bounce energy due to the scattering effects of rough seafloor and sea surface. Actually, beam-spreading of HLA is common in the underwater waveguide due to multipath propagation, which degrades the resolution and array gain of the formed beams, especially in the endfire direction of the array. Buckingham[2] presented a theoretical analysis of the response of a towed array to the acoustic field in isovelocity shallow water, revealing that when the source is endfire-on to the array, beam broadening or, in the extreme cases, beam splitting due to a different angular response to each of the modes may exist. Yang[3] indicated that for a near endfire source in shallow water, signal-arrival angles were associated with different modes. Each mode led to its own bearing and thus beam broadened. Ma et al.[4] gave the simulated CBF results of the tow ship’s noise. The results showed that the maximum output of the towed line array was widely spread and away from the endfire as a result of near-field multipath propagation, which influenced strongly the target detection near the endfire of the horizontal array. However, serious bearing-splitting is less common due to a little difference of multipath arrival angles.
Source ranging has always been a hot topic in underwater acoustics, and a variety of approaches have been developed.[5–7] One of the most common methods is based on time delay of multiple paths. Evan and David[8] made a source track localization via cross correlating the received signals at horizontally separated receivers and matching the measured and simulated correlation time delay in shallow water. Duan et al.[9] localized a moving source by tracking the time delay of the direct and surface-reflected arrivals in the reliable acoustic path in deep water. Wu et al.[10] achieved the near-surface source ranging by extracting time delay between bottom-reflected and bottom-surface-reflected arrivals from the interference pattern of sound intensity in frequency and time domain in the first shadow zone of deep water. For a shallow source–receiver pair in DZ, however, a time delay of several seconds between DP path and BB path can hardly be extracted in practical applications. Moreover, the amplitudes of the two paths differ evidently and their correlation coefficient is too small to be identified. In this paper, a near-surface source ranging approach is presented by avoiding the calculation of time delay and taking full advantage of the split bearings of DP and BB paths in DZ. The approach is demonstrated by experimental data. As an extension, the applicability of the proposed approach in DZ for an underwater source within several hundred meters deep is also analyzed and demonstrated by simulations.
The rest of this paper is organized as follows. In Section 2, the Northwest Pacific Acoustic Experiment is briefly reviewed, and the bearing splitting in DZ through the broadband CBF is presented. In Section 3, the bearing-splitting phenomenon is explained by using ray theory and comparing the simulated CBF results with experimental ones. Near-surface source ranging based on the split bearings in DZ is analyzed in Section 4, and the applicability of the proposed approach is analyzed in Section 5. A summary is presented in Section 6.
In 2015, an acoustic experiment was done in the Northwest Pacific, with a towed HLA deployed on the receiving ship with a towed depth of around 150 m. The voyage speed was 4 knots. During the experiment, a source ship with a draft of around 6 m sailed close to the receiving ship, passed across the DZ, and then moved away. The array recorded the noise radiated from the source ship. The water depth was about 5200 m. The GPS positions, distances and relative bearings of the receiving ship and source ship during the passing period are shown in Fig.
![]() | Fig. 1. (a) Source and receiving ship’s GPS positions during the experiment. The black circle is the schematic DZ of the receiving ship. (b) Source–receiver distances. (c) Relative bearings. |
Figure
The cross bearing-time record in Fig.
In terms of ray theory, a formal solution of the acoustic wave equation in a range-independent environment can be obtained from the transport equation and the eikonal equation.[12] The solution of the sound pressure field to the wave equation for a receiver at range r and depth z follows the form
By solving the eikonal equation, we can obtain the eikonal[13]
![](cpb_25_12_124311/cpb160957ieqn1.gif)
Eigenrays’ arrival structure from a 6-m deep source to a 150-m deep receiver located 3 km away, calculated by the Bellhop program[14] is shown in Fig.
For the direct sound field, equation (
Then we analyze the conventional beamforming outputs of a towed horizontal line array. Again, we employ a ray representation of the direct sound field
when the source is in the broadside direction, cos θT = 0, both groups of arrivals appear in one beam with θ = θT = 90°, so there will be neither bearing splitting nor bearing deviation;
for a nonbroadside source, cos θT ≠ 0, the arrivals split into two beams with the angles determined by
As for the endfire case, θ1 is also offset from θT and spreads a lot. This is similar to the phenomenon in shallow water, which has been explained by Yang.[3]
For numerical simulations of the beam pattern, we shall use the same acoustic environment as that shown in Fig.
It can be seen that in DZ, BTR is classified into two groups as predicted by the theoretical analysis. The first one corresponds to DP, which has a higher bearing rate, peaks at CPA, and approaches to the real bearing. This group of energy falls off with range as the source moves out of the direct zone. The second one arrives within the whole time. It has a lower bearing rate, and is closer to the broadside. This group corresponds to BB paths. Experimental bearings of DP (blue dashed line) and BB paths (blue dot dashed line) extracted from Fig.
Based on the split bearings, near-surface source ranges can be estimated in DZ. By using the ray theory, the relationship between range and depth can be described as[13]
Applying Snell’s Law, equation (
As can be seen in Eq. (
Recalling the analysis in Section 3, the bearing of DP is approximately equal to the real target bearing. Then the bearing of the BB path in Eq. (
Now we apply this method to the experimental data which have been analyzed in Section 2. Before calculating the arrival angles, the preprocessing of sliding linear fitting for the experimental estimated bearings every 10 s is needed in order to reduce the bearing fluctuation. Then the arrival angles are estimated and plotted in Fig.
Taking the differential on both sides of Eq. (
During the above analysis, source depth is assumed to be a surface source (set to be 6-m deep). In practice, however, it is necessary to discuss the applicability of Eq. (
Then taking the differential of Eq. (
Equation (
From Eq. (
In the following simulations, we consider the source range estimation with the source depth changing from 10 m to 300 m. The source–receiver range is 3 km, HLA depth is 150 m, and the target bearing is 60 °. By conventional beamforming, the beam intensity output with a 0.1° sampling interval is shown in Fig.
In this paper, low-frequency towed horizontal line array recordings are presented at a close range (< 18 km). Passing of a source ship and a tow ship is involved during the Northwest Pacific Acoustic Experiment in 2015. Broadband conventional beamforming is performed to the ship noise recorded on the array. A bearing-splitting phenomenon in the direct zone is observed, which might be misjudged as two different targets easily.
To explain the phenomenon, the ray theory is introduced. In terms of ray theory, sound field in the direct zone is mainly contributed by direct and bottom bounced paths. From the beam intensity equation, the bearing splitting is caused by the two groups of rays with significantly different arrival angles. Numerical simulations are performed and compared with experimental results. In both cases the bearings split into two parts. The one corresponding to the direct path is clearly visible within 3 km. It has a higher bearing-rate and is almost equal to the true bearing. The other one corresponding to the bottom bounced paths is evident during the observed voyage. It has a lower bearing-rate and is biased toward the broadside.
Finally, near-surface source ranges are estimated as an application of the split bearings in DZ. In deep water, the estimated near-surface source ranges are related to source/receiver depths and arrival angles. For the near-surface source, as the depths of a surface ship and a towed horizontal line array are always known and the arrival angles could be obtained by the split bearings, source ranges can be estimated within an acceptable error. For the underwater source within several hundred meters in depth, the ranges could also be estimated by the split bearings even though the source depth is unknown, which is based on the poor sensitivity between range and source depth. Therefore, the source–receiver range could be estimated with an average error of less than 3% by taking an underwater source as a near-surface source.
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