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. 1. Figure 1(a) shows the GPS positions during the experiment. Figures 1(b) and 1(c) show the source–receiver distances and their relative bearings, respectively. The CPA was at about 29 min and the closest distance was about 2 km.

Fig. 1.

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	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 2 shows the bearing-time record (BTR) calculated by the broadband (160 Hz–360 Hz) CBF during the crossing. It includes closing from a range of 18 km, the CPA and moving away. The black line represents the true source bearing. The strong energy at 10° near the endfire comes from the noise radiated by the tow ship, which is similar to that in shallow water.^[4] From Fig. 2, an interesting and important phenomenon can be seen that the source’s bearing splits into two different parts from 25 min to 34 min. One is close to the real bearing and has a higher bearing-rate and less beam-spreading, corresponding to the direct path. The other is deviated from the real bearing and has a lower bearing-rate and strong beam-spreading, which comes from the BB path propagation and extends to the shadow zone outside the time window 25 min–34 min. The bearing deviation in the shadow zone has been discussed in Ref. [11].

Fig. 2.

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	Fig. 2. Bearing time record during the crossing. The black line represents the true source bearing.

The cross bearing-time record in Fig. 2 actually shows the same target ship. It is easy to be misjudged as two different targets. This paper focuses on explaining this bearing-splitting phenomenon in DZ theoretically and numerically, and then applying it for the near-surface source ranging.

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]

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. 3.^[14] Figure 3(a) shows the measured SSP from the at-sea Northwest Pacific experiment with a 50-m-deep surface channel. Figure 3(b) shows the eigenrays including the DP and BB paths. As shown intuitively in Fig. 3(c), the DZ sound field is mostly contributed by DP and BB paths. Other paths with twice or more bottom bounces can be neglected due to serious sound attenuation. Figure 3(d) shows the arrival angles versus arrival time of DP and BB paths. It shows that arrival angles of DP are around 10°, while those of BB path are more than 70°.

Fig. 3.

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	Fig. 3. Eigenrays’ arrival structure at the 3-km range for the shallow source and receiver pair in the direct zone. (a) Measured SSP from the Northwest Pacific. (b) Eigenrays. (c) Normalized amplitude. (d) Arrival angles.

For the direct sound field, equation (3) can be simplified into the summation of DP and BB paths:

Then we analyze the conventional beamforming outputs of a towed horizontal line array. Again, we employ a ray representation of the direct sound field

Fig. 4.

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	Fig. 4. Arrival angles of DP and BB paths for a source within a range of 10 km.

For numerical simulations of the beam pattern, we shall use the same acoustic environment as that shown in Fig. 3(a). The bottom is a flat homogeneous half-space with sound speed 1600 m/s, the density 1.6 g/cm³ and the attenuation coefficient 0.2 dB/λ. The source is 6-m deep, while the HLA receiver is 150-m deep, with 160 elements in which the spacing between two elements is 2 m. Simulated results of BTR by the broadband (160 Hz–360 Hz) CBF are shown in Fig. 5, and for comparison, the same ranges and bearings (shown as the black dotted line) as experimental data are used.

Fig. 5.

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	Fig. 5. Simulated BTR results by using the same ranges and bearings as experimental data. Black dotted line: Target bearing. Blue dot dashed line: experimental bearing of BB path. Blue dash line: experimental bearing of DP.

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. 2 are also indicated in Fig. 5. They are similar to the simulated bearings.

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]

Fig. 6.

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	Fig. 6. Schematic diagram of BB path simplified in a straight line.

Applying Snell’s Law, equation (11) can be transformed into

As can be seen in Eq. (12), the source–receiver range is related to SSP, water depth, source/receiver depths and arrival angle α₀₂ of BB ray paths. Usually, SSP and water depth can be measured, and HLA depth is known. Thus the range is correlated with source depth and arrival angle. For a near-surface source, the depth can be considered to be about 6 m. Then the range is only dependent on the arrival angle of the BB path.

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. (9) can be written as

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. 7. The black dots indicate α₀₂ calculated by Eq. (14), which is abnormal near the broadside of HLA. The red stars within 5° of the broadside indicate α₀₂ calculated by Eq. (16). Then the arrival angles along with time could be modified by replacing the abnormal points with the red stars. Substituting the arrival angles into Eq. (12), source–receiver ranges could be obtained. Figure 8 shows the estimated ranges and the real ranges (black line) as the source ship passes across DZ of the receiver. It can be seen that the estimated ranges fit well with the real one. The error near the broadside is larger than the others: the error comes from an estimation error of arrival angle α₀₂. As the beam with respect to the BB path is broadened, the errors of extracted bearings from BTR are inevitable.

Fig. 7.

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	Fig. 7. Arrival angles calculated by Eq. (14) and Eq. (16), respectively.

Fig. 8.

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	Fig. 8. Ranges estimated by the split bearings.

Taking the differential on both sides of Eq. (14) yields

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. (12) for an underwater source (with unknown depth) when the BB path of the sound field is strong enough to be detected. In this section, the performance of the ranging approach for an underwater source within 300-m deep is analyzed. For convenience of analysis, it is reasonable to simplify the BB path into a straight line, shown in Fig. 6 schematically. Through the geometric relationship in Fig. 6, we have

Then taking the differential of Eq. (18) yields

Equation (19) shows that arrival angle α₀₂ of the BB path decreases with increasing source depth z_s. Generally, with α₀₂ being more than 70° and r on the order of 10³ m, α₀₂ varies slightly when dz_s is within several hundred meters. Figure 9 gives the arrival angles at different source depths for a receiver depth of 150 m located 3 km away. It shows that for all source depths from 10 m to 300 m, the arrival angles of DP are small, while those of the BB path are large and fluctuate less than 1°.

Fig. 9.

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	Fig. 9. Arrival angles at different source depths for a receiver depth of 150 m located 3 km away.

From Eq. (20), assuming that α₀₂ = 70°, dz_s = 300 m, then dr = 109 m. It means that the estimation error of the range is theoretically less than 109 m for an underwater source within 300 m in depth, which is acceptable in practical application.

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. 10. It shows that the detected bearings corresponding to the DP beam and BB beam are weakly dependent on source depth. Extracting the two bearings, arrival angles can be estimated by Eq. (14). Then the source range can be estimated by substituting them into Eq. (12). Figure 11(a) gives the estimated range, where red circles indicate the ranges estimated with a supposed source depth of 6 m, which means the depth of a near-surface source. The relative estimation error is shown in Fig. 11(b). It reveals that when taking an underwater source as a near-surface source, the estimated range values are larger than the real values with an average error of less than 3%. It means that equation (12) is also suitable for estimating the range of underwater source within a several hundred meters’s depth in DZ if the underwater source depth is unknown and the bottom bounced energy can be detected.

Fig. 10.

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	Fig. 10. Beam output of HLA at 150 m in depth with a source bearing of 60° located 3 km away.

Fig. 11.

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	Fig. 11. (a) Ranges estimated and (b) relative estimation error versus source depth.

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.