Quantitative Analysis on the Influence of the Oceanic Front on Underwater Acoustic Detection with Investigated Marine Data

Abstract

At present, some shortcomings of the research on coupling modeling of the oceanic front–sound field may need attention: (1) Most of the acoustic propagation simulation is based on ideal front models, but the application of investigated marine data is lacking. (2) Most studies focus on the acoustic field characteristics, with the influence of fronts on acoustic propagation, but few studies aim at the direct quantitative analysis of the performance of underwater acoustic detection in oceanic fronts. To deal with the above problems, based on the measured data in the northwest Pacific Ocean, here, we first design different sound source layout schemes and calculate sound field characteristics in the sub-Arctic front using the ray theory. Then, the cumulative detection probability model is built based on the active sonar equation to evaluate the efficiency of underwater detection. Finally, the detection probability is calculated and expressed by regionalization, and the influence of the sub-Arctic front on underwater detection is quantitatively analyzed. The results show that the sub-Arctic front can significantly affect the underwater acoustic detection. The sound source located in the front in the cold-water mass has a better detection performance, especially detecting towards cold water (horizontal detection range > 60 km). In contrast, the sound source located in the warm-water mass has a poor detection performance (horizontal detection range in shallow sea < 10 km).

1. Introduction

The oceanic front is a special ocean structure formed by the intersection of different water masses with different properties. Within this narrow area, there are drastic changes in temperature, salinity, density, and other characteristics. These changes lead to significant variations in sound propagation, including shifting convergence zones, alteration in the order of multipath arrival, and horizontal refraction. The oceanic front is one of the most complex marine systems that significantly affects underwater acoustic signals, and this mesoscale structure widely exists. For example, due to the influence of unique topography and monsoons, the area near the Kuroshio Current is a high-frequency zone for oceanic fronts. Analyzing the impact of oceanic fronts on sound propagation and assessing the effects on underwater detection have great strategic value and practical significance.

Currently, the common approach to studying the influence of oceanic fronts on sound propagation is to combine front models with acoustic propagation models for coupling simulation [1]. Rousseau et al. [2] found that ocean temperature fronts could cause significant changes in sound speed profiles. The changing value ranges from 5 m/s to 30 m/s. Mellberg and Johannessen [3] studied the impact of oceanic fronts on sound propagation and found a strong correlation between the sound source depth and the effect of oceanic fronts on sound signal propagation. Carman and Robinson [4] conducted a study on sound propagation in the oceanic front between Iceland and the Faroe Islands, fully considering the changes in terrain and seabed geology. Heathershaw et al. [5] explored sound propagation through oceanic fronts using hydroacoustic environment data obtained from a 3D numerical ocean model. They found that the fronts caused a 10~20 dB change in propagation loss with different combinations of sound sources and receiver depths. Da et al. [6,7] used a simplified oceanic front model and a ray propagation model to study the impact of the oceanic front on propagation loss. They compared the position and depth of the convergence zone with/without the front. Nan et al. [8] analyzed the 3D sound ray trajectory in the oceanic front and found that sound rays bent under the influence of the front and the deflection angle increased with the increasing distance. Ma [9] simulated the underwater acoustic environment in the deep sea using the ray model. The results showed that the oceanic front weakens the efficiency of underwater communication and detection. However, the impact can be weakened if the sound source is located at the depth where the front is present. Liu [10] used the BELLHOPBellhop ray model to simulate and found that the oceanic front significantly changed the propagation loss and caused the convergence zone to shift.

Most of the oceanic front models adopted in the above studies are mathematical models based on spatial geometric structures, that are ideal characteristic models instead of real fronts. With the ocean observation capability enhancing, more and more navigational measured data, Argo buoy data, and satellite remote sensing data are being applied to the study of the impact of oceanic fronts on sound propagation. Compared with ideal front characteristic models, more detailed observations have been revealed with measured data.

Ramp [11] used the data from the 2001 Asia Experimental Acoustics Experiment (ASIAEX) and discovered that sound lines are refracted downward and quickly attenuate after being refracted through the shelf slope due to the oceanic front of Kuroshio. They also discussed the impact of the ocean environmental uncertainty on sound propagation. Lin [12] discovered the echo-reverberation effect using data from the Shallow Water 2006 (SW06) experiment conducted by the Woods Hole Oceanographic Institution (WHOI). Jian et al. [13] used measured data of oceanic fronts to determine the front parameters, including width, steepness, and position, and established a theoretical model for calculating sound speeds suitable for oceanic fronts. They used a 2D PE model to study the effect of the oceanic front on sound propagation and compared the differences in propagation loss at different receiver depths. Wang et al. [14] conducted an acoustic fluctuation experiment in the Yellow Sea (AEYFI05), which confirmed that strong hydrological environmental changes could lead to coupling between normal modes. Guo [15] used Kraken software and fused Argo data to establish a numerical prediction system for ocean acoustic fields, simulating sound path and propagation loss for typical sound fields.

The above researchers have studied the impact of oceanic fronts on acoustic propagation based on numerical propagation models and analyzed acoustic field characteristics such as acoustic propagation loss and convergence area distance in oceanic fronts in detail. However, we think the following shortcomings exist. On the one hand, the oceanic front models adopted in most studies are mathematical models, which are constructed based on a spatial geometry structure. The marine environmental field of fronts for sound propagation is relatively ideal, and the acoustic simulation experiment with measured data is very rare. There is a lack of understanding of the influence mechanism of real oceanic fronts on acoustic propagation.

On the other hand, the above studies focus on the analysis of the influence of fronts on acoustic propagation, mainly analyzing the characteristics of acoustic transmission loss in fronts. It is well-known that the ultimate purpose of studying acoustic propagation in marine mesoscale systems is to carry out underwater detection more effectively. It should be noted that underwater acoustic detection performance is not only dependent on acoustic propagation characteristics, but also closely related to background interference, target characteristics, and other parameters. Unfortunately, in the existing studies, the efficiency analysis of underwater acoustic detection is limited to the macro-analysis based on acoustic propagation characteristics, and few studies directly evaluate and analyze the influence of oceanic fronts on the underwater detection efficiency. The analysis of sound propagation characteristics remains at the theoretical level, while the quantitative analysis of underwater detection efficiency is of great practical meaning, which could directly guide the application of detection equipment.

Some scholars have constructed evaluation indicators for detection efficiency by means of mathematical modeling to analyze the performance of underwater detection equipment, such as sonars. Cong [16] established a calculation model for the search performance of the sonar buoy array through geometric analysis and mathematical deduction methods. Hou [17] improved the signal allowance equation based on the working principle of active sonar and established a probability calculation model for the airborne active sonar. Wan [18] and Fan [19] adopted operational research methods such as grey hierarchy analysis and fuzzy comprehensive evaluation to construct the relationships between environmental factors and the effective detection range of sonars, so as to evaluate the underwater detection performance. Liu [20] analyzed the scattering law of targets and established an efficiency assessment model for submarine search, under the condition that the approximate initial position of the target is known, but the speed and heading are unknown. The model could provide the submarine search probability using the deployed sonar in an extended square search method. Ju [21] established a ship motion model and an array of sonar models, including circular, square, and triangular buoys, then used the Monte Carlo method to analyze the impact of different initial conditions on the submarine search probability.

The above studies provided the mathematical derivation and calculation methods for detection evaluation indicators such as detection distance and detection probability, achieving the quantitative expression of detection efficiency and construction of the assessment model. However, most of the evaluation models are based on a virtual or simulated ocean environment. Some studies even fail to consider the impact of the ocean environment. Therefore, there is a lack of analysis on the impact of oceanic fronts in the real ocean environment on underwater detection performance.

To address the problems of existing studies, this paper establishes the cumulative detection probability model using measured data from a navigational marine survey, so as to evaluate the impact of oceanic fronts on the underwater acoustic detection. Based on the ocean environment–sound field coupling investigation data in the Kuroshio extension area, we use the ray theory model to calculate the sound field characteristics of the sub-Arctic front under different sound source deployment schemes. Further, based on the active sonar equation, we establish the probability calculation model for underwater detection and evaluate the detection performance through zoning assessment. The influence of the sub-Arctic front on the underwater detection efficiency is quantitatively analyzed.

The paper is structured as follows: Section 2 briefly introduces the sub-Arctic front characteristics, the acoustic propagation model, and the detection probability calculation model. Section 3 provides a detailed elaboration of the marine survey data used in our experiment and the scheme designation of the oceanic front–acoustic coupling modeling. Section 4 analyzes the influence of the sub-Arctic front on the underwater detection performance based on the experimental results, in detail. Finally, Section 5 concludes the paper.

2. Introduction of the Theory and Model

2.1. Sub-Arctic Front

The Kuroshio-Oyashio Confluence Region (KOCR; 142°~152° E, 35°~40° N), located in the sea east of Japan, is where the Kuroshio Extension Northern Branch (KENB) and the cold current of the Aleutian Islands (also known as Oyashio, or OY) converge. A cyclonic eddy located on the southern side of the confluence zone carries warm and salty water from the KENB northwards, while a cyclonic eddy situated on the northern side mixes in colder, less salty water from the Oyashio, resulting in an oceanic front with a significant temperature and salinity gradient.

The sub-Arctic front (143°~171° E, 37°~43° N) includes the western sub-Arctic front and the eastern sub-Arctic front. Among them, the western sub-Arctic front has a larger temperature and salinity gradient, which is mainly manifested as a strong and steady sea surface temperature gradient (0.03 °C/km) and salinity gradient (5 PSU/km) located near 40° N throughout the year, as shown in Figure 1 [22]. In this paper, we will focus on analyzing the impact of the western sub-Arctic front on the underwater acoustic detection based on the measured data from a marine survey conducted by our team.

2.2. Ray Theory Model

The acoustic propagation models suitable for horizontally nonuniform conditions mainly include ray models, adiabatic normal mode models, coupled normal mode models, and parabolic equations. The ray theory model is the earliest and most widely used modeling theory for acoustic propagation. The classic ray acoustic theory assumes that the energy of the sound field is transmitted by sound rays. Sound rays originating from the sound source take a certain path to reach the receiver, and the received sound energy is the superposition of all the arriving sound rays, also known as the intrinsic sound rays. The path of the sound ray represents the path of sound wave propagation, the time taken by the sound ray represents the time taken by the sound wave to propagate, and the energy carried by the sound ray represents the acoustic energy of sound propagation.

However, the traditional ray models are limited by the high-frequency approximation and cannot effectively calculate the propagation loss near the caustic line. The BELLHOP model based on the Gaussian beam ray tracing algorithm is proposed [23], which associates each sound ray in the sound beam with a Gaussian-type intensity profile perpendicular to the ray. This model effectively improves the traditional ray theory and solves the calculation difficulties of the sound propagation in the shadow zone and the caustic zone. Due to its advantages such as a clear physical image, fast calculation speed, and broad applicability, the BELLHOP model has been widely used in underwater sound propagation. We will use this model for acoustic propagation calculation in the oceanic front.

2.3. Detection Probability Calculation

The detection probability is a crucial indicator for evaluating the performance of underwater acoustic detection. Sonar is the primary sensor employed for underwater target detection, especially active sonar, which can accurately detect and locate targets through ranging and direction finding.

Active sonars are widely used in underwater detection and target identification. In this paper, we developed a probability calculation model for underwater detection based on the active sonar equation and the signal allowance equation.

The signal allowance equation of active sonar is:

$$SE=SL-2TL+TS-NL+DI-DT$$

(1)

where SL is the transmitting sound source level, NL is the background noise level of the receiver, DI is the receiving array directivity index, TS is the target strength, TL is the transmission loss, and DT is the detection threshold of the receiver. In general, the signal allowance follows a normal distribution:

$$P_d=1-\underset{-\infty }{\overset{-\frac{SE}{\sigma }}{{\displaystyle \int }}}\frac{1}{\sqrt{2\pi }}exp\left(\frac{-t^2}{2{\sigma }^2}\right)dt$$

(2)

where $P_d$ represents the detection probability, which is the instantaneous detection probability, and $\sigma$ represents the variance of the signal allowance. If each variable in the signal allowance equation follows a normal distribution and is independent of the others, then:

$${\sigma }^2={\sigma }_{SL}^2-2{\sigma }_{TL}^2+{\sigma }_{TS}^2-{\sigma }_{NL}^2+{\sigma }_{DI}^2-{\sigma }_{DT}^2$$

(3)

The above instantaneous detection probability is the likelihood of locating the target when the active sonar detects it once, also known as the glance probability. In reality, active sonar carries out multiple detections; thus, a complete representation of the detection process requires calculation of the cumulative detection probability.

If each detection performed by the active sonar is independent, then the detection process can be understood as a series of discrete, independent detections that accumulate over time. The simplest way to calculate the cumulative detection probability is to assume that the sonar only needs to detect the target in one of n detections. In such a scenario, the cumulative detection probability can be calculated as follows:

$$P_n=1-{\displaystyle \prod }_{i=1}^n\left(1-P_i\right)$$

(4)

The detection method that accords with the actual observation process is the “double bright spot model”: in n detections, the target signal is detected for at least two consecutive detections; thus, the target is considered found.

The first observation of the target signal functions as an alert, and the second occurrence confirms the detection. If the target signal is not continuously observed the second time, the target is assumed to have been forgotten. As a result, the probability of detecting the target for the $i$th time can be expressed as:

$$g_i=P_{i-1}·P_i$$

(5)

where $P_{i-1}$ and $P_i$ are the instantaneous detection probability of the ($i-1)$th and the $i$th detection of the target, respectively, and then the cumulative detection probability of $n$ detections is shown in Equation (6). In this paper, the cumulative detection probability calculated based on the “double bright spot model” was used as a detection efficiency evaluation indicator to analyze the impact of the oceanic front on underwater detection.

$$P_n=1-{\displaystyle \prod }_{i=1}^n\left(1-g_i\right)$$

(6)

To sum up, we proposed the modeling technology of underwater acoustic detection efficiency based on the measured data and the above theory. The technical route is shown in Figure 2. In the next section, we will adopt this modeling flow to analyze the influence of the real sub-Arctic front on the underwater acoustic detection.

3. Overall Design of Modeling Experiment

3.1. Data Introduction

In 2020, our team conducted a detailed oceanographic environmental survey of the 3D oceanic front structure in the Kuroshio extension area of the Northwest Pacific Ocean. All the investigated devices, such as CTD, MVP, sound source, hydrophone, and so on, were calibrated in order to obtain reliable data. We completed the investigation of 27 transects in 5 areas (A, B, C, D, E) within the survey area (145°~156° E, 36°~42° N).

In the modeling experiment of this paper, measured data of section A18 in area D, which includes 5 investigated sections (A15~A19) as shown in Figure 3, were used to analyze the influence of the sub-Arctic front on underwater acoustic detection. Since the measured depth of CTD cannot reach the seabed during the survey of the sub-Arctic front, HYCOM datasets were used to supplement the thermohaline profile to the seabed for 1250~5000 m, in order to meet the need of the acoustic model to simulate the real marine environment.

We used the ETOP1 dataset (1′ Gridded Global Relief Data) from the National Oceanic and Atmospheric Administration (NOAA) as the seafloor topographic data. The resolution of the ETOP1 terrain data is $1^{\prime }\times 1^{\prime }$ (https://www.ncei.noaa.gov/products/etopo-global-relief-model) (accessed on 12 March 2023).

3.2. Experimental Scheme Designation

To comprehensively study the impact of the sub-Arctic front on the underwater sound propagation and the detection performance, we designed various experimental schemes for comparative analysis. Various layouts of sound sources with different horizontal distances and vertical depths were conducted within the characteristic scale of the sub-Arctic front, as illustrated in Figure 4.

For the horizontal positioning, we selected six sound source locations in both the cold and warm-water masses of the front, denoted as A (120 km from “N”), B (95 km from “N”), C (58 km from “N”), D (47 km from “S”), E (70 km from “S”), and F (78 km from “S”). In the vertical direction, four sound source depths (50 m, 100 m, 200 m, and 300 m) were selected, which lay within the depth range of 0~300 m, an active area for underwater target activity. The propagation direction was classified into four categories: “warm-water mass → warm-water mass”, “warm-water mass → cold-water mass”, “cold-water mass → warm-water mass”, and “cold-water mass → cold-water mass”. The above experimental plans were compared with the underwater target detection in the standard ocean environment (without fronts).

3.3. Model Parameter Settings

The parameter settings for the acoustic propagation calculation using the BELLHOP model were as follows: the source frequency was 200 Hz, the water depth was 5000 m, and the horizontal range was 150 km. The nautical chart for the sea area east of Japan indicates that the seabed sediment primarily consists of clay. We set the sediment parameters according to the seafloor acoustic experience parameter table in [9]: the density was 1.421 g/cm³ and the attenuation coefficient was 0.12 dB/λ. The number of sound lines was set to 300, with grazing angles ranging from −20° to 20°.

According to [24], the parameters for the signal allowance equation were set as follows: the transmission source level was 210 dB, the ambient noise was 50 dB, the receiving directionality was 18 dB, the detection threshold was 9 dB, the target intensity was 15 dB, and the mean square error of the signal allowance was 3.5 dB. Thus, the sound propagation loss was calculated with the BELLHOP model.

4. Result Analysis

For the different layout schemes of the sound source presented above, the modeling process was as follows: Firstly, we used the measured data including temperature and salinity to calculate the sound speed; then, we input the sound speed and the sound propagation loss across the sub-Arctic front, which can be obtained with the Bellhop model. Finally, we estimated the cumulative detection probability of underwater targets across water depths ranging from 0 to 800 m. To better visualize the detection efficiency, we divided the results into two zones according to the detection probability. The target was considered detected if the probability was greater than 0.7, and it was defined as the detection blind zones when the probability was less than 0.7. It should be noted that this standard can be adjusted according to different scenarios. Finally, we obtained the detection probability distribution map to evaluate the detection efficiency and directly analyze the effect of the sub-Arctic front on the underwater detection.

4.1. Underwater Acoustic Detection in Standard Marine Environment

Under standard marine environmental conditions (uniform temperature and salinity distribution without oceanic fronts), we used the “Chen-Millero” empirical formula to calculate the sound speed, and the overall sound speed is shown in Figure 5. Based on the above modeling process, the detection probability of different sound source layout schemes could be obtained, as illustrated in Figure 6. Specifically, we defined that the yellow area in this map represents the targets that could be detected (probability greater than 0.7), while the green area represents the targets that could not be detected (probability less than 0.7).

(1)

When the sound source was located 50 m beneath the surface (Figure 6a), a notable detection blind zone existed within the region shallower than 40 m. In the depth range of 50~200 m, an excellent detection performance was observed with a detection probability exceeding 0.7. Within this range, the horizontally effective detection distance could reach up to 100 km. However, beyond the depth range of 300 m, the detection performance demonstrated a significant decline, with the detection probability exceeding 0.7 only within a limited horizontal range (0~17 km).

(2)

When the depth of the sound source was 100 m (Figure 6b), the spatial distribution of the detection efficiency was essentially similar to that observed at a depth of 50 m. A considerable detection blind zone persisted in the shallower depth range (0~40 m). The detection performance remained relatively satisfactory within the depth range of 50~200 m, although the blind zone range slightly extended. Nevertheless, the target detection performance beyond a depth of 300 m remained inadequate.

(3)

When the depth of the sound source was 200 m (Figure 6c), the range of the surface detection blind zone was reduced to only 30 m. The detection efficiency was relatively high within the depth range of 30~300 m; however, the blind zone in this range was significantly larger than that of the sound source at the depths of 50 and 100 m. As the sound source depth decreased, the detection performance beyond a depth of 300 m slightly improved, and the detection performance remained strong within a horizontal distance range of 0~20 km.

(4)

When the depth of the sound source was 300 m (Figure 6d), the surface detection blind zone ranged from 0 to 30 m. In the depth range of 30~300 m, the detection probability showed a significant “Λ”-shaped distribution pattern, with blind zones between the convergence areas. These blind zones exhibited a clear increase in the range. Compared with the sound source at a depth of 200 m, the detection performance beyond a depth of 300 m slightly improved.

To sum up, under the standard marine environment, the horizontal distance of the underwater acoustic detection could reach more than 100 km. With the increase of the sound source depth, the depth of the surface detection blind zone became shallower, and the detection blind zone in the whole domain gradually increased. The detection probability distribution was in the form of skipping convergence regions, and there were detection blind areas between the convergence regions.

4.2. Sound Source at Location A (Warm-Water Mass), Detecting towards Warm Water

Figure 7 depicts the sound speed distribution in the sub-Arctic front. By varying the depth of the sound source in the warm-water mass of the front, we could calculate the corresponding detection probability. Comparatively, the underwater detection efficiency in this environment significantly varied from that of the standard ocean environment.

(1)

When the depth of the sound source was 50 m and 100 m (Figure 8a,b), the detection efficiency in the depth range of 0~800 m was poor, with a large detection blind zone. The detection probability was higher only within the horizontal distance of 0~5 km, and the detection range was significantly reduced. It can be seen that the temperature and salinity inhomogeneity caused by the sub-Arctic front significantly reduced the underwater detection performance.

(2)

When the depth of the sound source was 200 m (Figure 8c), there still existed a large detection blind zone. The detection efficiency was higher within the horizontal distance range of 0~5 km. In the range with a horizontal distance of 20~35 km from the sound source and a depth greater than 200 m, there was a “Λ”-shaped, easily detectable area, which may correspond to the sound convergence zone.

(3)

When the depth of the sound source was 300 m (Figure 8d), the detection performance significantly improved. The detection performance was higher within the horizontal distance range of 0~10 km, there existed a detection blind zone within the depth range of 0~200 m, the detection performance was relatively high within the depth range of 200~300 m, and the horizontal effective detection range was over 30 km.

To sum up, when the sound source was located in the warm-water mass of the sub-Arctic front and the sound propagated towards the warm water, a large detection blind zone was formed due to the nonuniform distribution of the warm-water mass caused by the front mixing, which seriously affected the detection performance. With the increase of the sound source depth, the detection blind zone gradually decreased, and the detection range increased, by more than 30 km.

4.3. Sound Source at Location B (Front), Detecting towards Warm Water

As shown in Figure 9, the sound source was placed in the oceanic front and the sound propagated toward the warm-water mass. The underwater detection performance of this scheme significantly changed again.

(1)

When the depth of the sound source was 50 m (Figure 10a), the detection probability in the depth range of 0~800 m was mostly less than 0.7, especially in the shallower areas within 200 m, where there were large detection blind areas with poor detection performance. Only within the horizontal distance of 0~10 km was the detection efficiency relatively high. There existed a “Λ”-shaped, easily detectable area within the horizontal distance of 20~35 km, and at the depth greater than 200 m.

(2)

When the depth of the sound source was 100 m (Figure 10b), the detection efficiency improved, and there existed an easily detectable area within the depth range of 150~250 m, whose horizontal detection range was about 30 km. When the depth of the sound source was 200 m (Figure 10c), the detection efficiency distribution was basically the same as that at a depth of 100 m.

(3)

When the depth of the sound source was 300 m (Figure 10d), the detection probability was almost less than 0.7 in the area within a 500 m depth, and there existed a large detection blind zone. In the depth range of 500~700 m, a “Λ”-shaped, easily detectable area was formed, with a horizontal detection distance of up to 60 km.

In conclusion, when the sound propagates from the oceanic front towards the warm water, if the sound source is at a shallow depth, it will be significantly affected by the front. There were larger-area blind zones within a depth of less than 800 m, and the horizontal detection distance was less than 10 km. With the increase of the sound source depth, the influence of the front decreased, and the detection range increased. However, the area within a depth of less than 100 m remained a detection blind zone.

4.4. Sound Source at Location C (Cold-Water Mass), Detecting towards Warm Water

As shown in Figure 11, the sound source was placed in the cold-water mass of the oceanic front, and the sound propagated toward the warm-water mass. The sound passed through the front, and the underwater detection performance of this scheme significantly changed again.

(1)

When the depth of the sound source was 50 m (Figure 12a), in the depth range of 0~30 m, the detection probability was less than 0.7, and there existed a detection blind zone. In the depth range of 30~300 m, there existed a significant, easily detectable area within a horizontal distance of 0~60 km from the sound source. When the depth of the sound source was 100 m and 200 m (Figure 12a,b), the detection efficiency distribution was in accordance with that at a depth of 50 m. The difference is, with increasing sound source depth, the horizontal effective detection range gradually decreased.

(2)

When the depth of the sound source was 300 m (Figure 12d), there was still a detection blind zone within the depth range of 0~30 m, but the significant, easily detectable area disappeared. The detection performance was relatively high only within the depth range of 250~350 m and the horizontal distance of 0~40 km.

All in all, when the sound passed through the front from the cold-water mass, the detection efficiency was acceptable within a horizontal distance of 0~50 km, and the detection performance significantly decreased after passing through the front. As the depth of the sound source increased, the area of the detection blind zone increased.

4.5. Sound Source at Location D (Warm-Water Mass), Detecting towards Cold Water

As shown in Figure 13, the sound source was placed in the warm-water mass of the oceanic front and sound propagated toward the cold-water mass. The sound passed through the front, and the underwater detection performance of this scheme significantly changed again.

(1)

When the depth of the sound source was 50 m and 100 m (Figure 14a,b), the detection probability was almost less than 0.7 within the depth range of 0~800 m, resulting in a large detection blind zone and poor detection performance. Only within the horizontal range of 0~10 km was the detection performance relatively high. It can be seen that when the sound passed through the front from the warm-water mass, the detection performance significantly decreased.

(2)

When the depth of the sound source was 200 m (Figure 14c), the sound did not fully pass through the front, resulting in a detection blind zone within the depth range of 0~100 m and the horizontal distance range of 10~35 km. The impact of the front was relatively small within the depth range of 100~200 m, and the detection performance was higher, with a horizontal detection distance of about 70 km.

(3)

When the depth of the sound source was 300 m (Figure 14d), the detection performance decreased, especially for long-range detection. The detection performance was relatively high only within the horizontal range of 0~20 km.

In summary, when sound propagated from the warm water through the front to the cold water, the horizontal inhomogeneity caused by the oceanic front severely reduced the detection performance. With the depth of the sound source increasing, the detection performance improved. Overall, the area of the detection blind zone was still relatively large.

4.6. Sound Source at Location E (Front), Detecting towards Cold Water

As shown in Figure 15, the sound source was placed within the oceanic front and sound propagated towards the cold-water mass. In this scheme, the sound did not fully pass through the front.

(1)

When the depth of the sound source was 50 m and 100 m (Figure 16a,b), the detection efficiency distribution was relatively similar. A detection blind zone existed in the surface layer depth range of 0~30 m. There was an easily detectable zone within the depth range of 30~300 m. When the sound source was at a depth of 100 m, the horizontal detection distance was farther than when it was at a depth of 50 m (60 km > 35 km).

(2)

When the depth of the sound source was 200 m (Figure 16c), there was still a detection blind zone in the depth range of 0~30 m. The coverage depth range of the easily detected zone increased, up to 30~400 m, but the horizontal detection distance was shortened (0~30 km).

(3)

When the depth of the sound source was 300 m (Figure 16d), the center depth of the easily detectable zone continued to increase, while its coverage area became smaller. The easily detectable zone was at the depth range of 300~400 m, with a horizontal detection distance up to 40 km.

When the sound source was located within the front, compared to the situation where the sound propagated to the warm-water mass (as mentioned in Section 4.3), the detection performance within the depth range of 0~400 m was significantly better if the sound propagated towards the cold-water mass, but the detection performance was worse below the 500 m depth.

4.7. Sound Source at Location F (Cold-Water Mass), Detecting towards Cold Water

As shown in Figure 17, the sound source was placed within the cold-water mass of the front and propagated towards the cold-water mass. In this scheme, the sound did not pass through the front.

(1)

Overall, the horizontal detection distance was small for different sound source depths, limited to a range of 40 km. When the depth of the sound source was 50 m (Figure 18a), there was a detection blind zone at the depth range of 0~40 m. There were two easily detectable zones within the depth ranges of 30~300 m and 600~700 m.

(2)

When the depth of the sound source was 100 m, 200 m, and 300 m (Figure 18b–d), the overall distribution of the detection performance was relatively similar, and there was no significant easily detectable zone. The detection performance was higher only within a horizontal distance of 0~10 km. With the increase of the sound source depth, the area of the detection blind zone increased, and the detection performance decreased.

It should be pointed out that the detection probability is hard to obtain in real experiments, making the direct verification difficult. However, the detection probability is calculated based on acoustic transmission loss, and our team verified the sound propagation simulation with the BELLHOP model in the oceanic front based on the measured data from our 2020 Oceanographic Environmental Survey. The calculation of acoustic transmission loss was consistent with the reality [25,26]. Therefore, the results of the detection probability and corresponding analysis are credible.

5. Conclusions

In this paper, we established the cumulative detection probability model using measured data from the navigational marine survey, so as to evaluate the impact of oceanic fronts on the underwater acoustic detection. Based on the ocean environment–sound field coupling investigation data in the Kuroshio extension area, we used the ray theory model to calculate the sound field characteristics of the sub-Arctic front under different sound source deployment schemes. Further, based on the active sonar equation, we established the probability calculation model for underwater detection and evaluated the detection performance through zoning assessment. The influence of the sub-Arctic front on the underwater detection efficiency was quantitatively analyzed. Compared to underwater acoustic detection in an ocean environment without fronts, the oceanic front can significantly impact the detection efficiency, and we drew the following conclusions by comparing the experimental results:

(1)

When detecting towards the warm-water mass and when the sound source was sequentially placed in the warm-water mass (position A), front (position B), and cold-water mass (position C), the detection efficiency gradually improved. When detecting towards the cold-water mass and when the sound source was sequentially placed in the cold-water mass (position D), front (position E), and warm-water mass (position F), the detection efficiency first improved and then slightly decreased. Overall, the detection performance towards the cold-water mass was better than that towards the warm-water mass.

(2)

When the sound source was located in the warm-water mass of the oceanic front, the detection performance was significantly lower whether the sound propagated to the cold water or the warm water. The detection performance towards the cold-water side was slightly better than that towards the warm-water side. When the sound source was located in the front, the detection performance towards the cold-water side was significantly better than that towards the warm-water side. When the sound source was located within the cold-water mass of the oceanic front, the detection performance towards both the cold- and warm-water masses was similar.

(3)

When the sound source was located in the front and in the cold-water mass, the detection performance was good. Especially, when the sound source was located in the front and detected towards the cold-water mass, the detection performance was the best (horizontal detection range > 60 km). The detection performance was poor when the sound source was located within the warm-water mass (horizontal detection range in shallow sea < 10 km).

Compared with the previous studies, we used the investigated data of the oceanic front in the real marine environment, instead of the ideal front model, for the acoustic propagation simulation, which is closer to reality. Besides, we analyzed the influence of the oceanic front on underwater acoustic detection and quantificationally evaluated the efficiency of underwater acoustic detection, which will directly guide the application of sonar detection and covert navigation of underwater vehicles in the complicated environment of the ocean.