A method for fast estimation of the depth of the arctic underwater low-frequency remote sound source matching the upper limit of the normal wave frequency

Abstract

The application relates to underwater acoustic positioning and relates to a method for rapidly estimating the depth of a low-frequency remote sound source in the Arctic ocean, which matches the upper limit of the normal mode frequency. The sound speed profile in the deep sea of the Arctic results in the vertical coverage range of the normal mode eigenfunction decreasing with the increase of the frequency. When the sound source depth is greater than the vertical coverage range of the eigenfunction, the normal mode cannot be excited, which leads to the normal mode having an upper limit of the frequency under the condition of the sound speed profile in the deep sea of the Arctic. The upper limit of the frequency is directly related to the sound source depth. Therefore, the sound source depth can be estimated by matching the upper limit of the frequency of each normal mode in the received sound signal and the upper limit of the frequency obtained through model simulation. The measured upper limit of the frequency is estimated according to a time-frequency analysis diagram. The relationship between the upper limit of the frequency of the normal mode and the sound source depth is calculated according to the measured environment by using a model. The sound source depth estimation can be obtained by comparison and matching. The above method for rapidly estimating the depth of a low-frequency remote sound source in the Arctic ocean can be realized by using a single hydrophone.

Description

Technical Field

[0001] This invention relates to underwater acoustic localization methods, and more particularly to a method for rapid depth estimation of low-frequency long-range underwater sound sources applicable to the Arctic. Background Technology

[0002] In recent decades, with the gradual reduction of Arctic sea ice, the Arctic marine environment has undergone drastic changes. Previous studies on underwater sound propagation and the applicability of underwater acoustic applications in the new environment require further in-depth research. The Arctic deep sea has a unique deep-sea sound velocity profile, divided into two sections with approximately linearly increasing sound velocity. The upper section has a water thickness varying from hundreds to tens of meters, while the lower section's sound velocity variation is mainly caused by increased seawater hydrostatic pressure. Underwater sound propagation in the Arctic has been studied for decades, focusing primarily on sub-ice sound field modeling and sub-ice sound source localization. Sound source localization research mainly utilizes vertical arrays to obtain the vertical spatial distribution of the sound field, and then uses a matching field to estimate the sound source distance and depth, or uses a vertical array to separate normal modes before source localization. Due to the unique sea ice environment of the Arctic Ocean, conducting experiments using large-aperture vertical arrays is challenging and costly.

[0003] In recent years, some international scholars have used single hydrophones to obtain the fine dispersion structure of underwater acoustic signals in the Arctic and to locate the sound source. However, these studies mainly focus on seabed reflection normal modes in shallow Arctic waveguides. For deep Arctic waters, the water within the top 400-500 meters can form water refraction normal mode waveguides due to the approximately monotonically increasing sound velocity profile. The vertical distribution of its eigenfunctions has different characteristics from those of shallow waveguides. However, there is currently almost no research on single hydrophone depth estimation for refraction normal modes in typical deep Arctic waveguides. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned problems in existing technologies by utilizing the vertical distribution variation characteristics of the eigenfunctions of surface waveguide refraction-like normal modes in the Arctic deep sea. This invention proposes a rapid method for estimating the depth of low-frequency long-range underwater sound sources in the Arctic by matching the upper limit of the normal mode frequency. This method can be implemented with a single hydrophone, resulting in low experimental costs and fast processing speed.

[0005] Based on the characteristics of the approximate upper and lower linear positive gradient sound velocity profiles of typical deep-sea sound velocity profiles in the central Arctic ice region, the eigenfunctions of normal modes under the Arctic deep-sea sound velocity profile are analyzed. Through simulation calculation of the normal mode sound field model, the characteristics of the normal mode eigenfunctions changing with frequency are obtained. Specifically, the vertical coverage of the eigenfunctions gradually decreases with increasing frequency. When the sound source depth is greater than the eigenfunction coverage, the normal mode cannot be excited. Therefore, there is a clear upper frequency limit for normal modes in the refractive normal waveguides of the Arctic deep-sea surface, and this upper limit is directly related to the sound source depth. Based on this principle, the received sound signal is obtained through experimental measurement, and the sound signal is then subjected to time-varying analysis. Frequency analysis is used to determine whether the refracted normal modes exhibit a rising dispersion structure that increases with time and frequency. Once determined, the upper frequency limit of each normal mode is obtained based on time-frequency analysis. Simultaneously, based on the sound velocity profile and sea depth of the Arctic deep sea in the experimental area, the vertical distribution of the eigenfunctions of each normal mode at various frequencies can be calculated using the normal mode model. Based on the vertical distribution, the upper frequency limit of each normal mode at different sound source depths can be obtained. Combining the two-dimensional relationship between the measured upper frequency limit of each normal mode and the simulated upper frequency limit and sound source depth, the sound source depth can be quickly estimated by matching the upper frequency limit of the normal modes, ultimately achieving rapid depth estimation of low-frequency long-range underwater sound sources in the Arctic.

[0006] This invention includes the following steps:

[0007] 1) Measuring the sound velocity profile and depth of seawater in the deep Arctic sea area. Due to the spatiotemporal variation of the sound velocity profile in the Arctic Ocean and its complex seabed topography, it is necessary to measure the sound velocity profile and depth of seawater in advance before deploying equipment and estimating the depth of the sound source. The measurement range of the seawater sound velocity profile is the entire ocean depth. When the working depth of the measuring equipment is limited, it is necessary to measure the range of more than 1000m. The sound velocity values ​​at deeper depths are extended by empirical formulas. This sound source depth estimation method is applicable to the deep Arctic sea conditions, and the seawater depth is preferably above 1000m.

[0008] 2) After determining the working sea area of ​​the equipment, measuring the sound velocity profile of the seawater and the sea depth, the underwater acoustic signal acquisition equipment is deployed. This sound source depth estimation method only requires a single hydrophone. According to the normal wave characteristics under the Arctic deep-sea conditions, the deployment depth of the hydrophone needs to be set to be less than the sound source depth. Considering the depth range of the underwater sound source of main concern, the hydrophone depth is set to within 50m. The entire system can be deployed using submersible mooring, buoy, or shipboard hoisting methods.

[0009] 3) Based on the underwater acoustic signals collected by the system, the presence of acoustic signals rather than noise signals is first determined by the time-domain waveform. The presence of signals and the signal-to-noise ratio can be determined by the low-frequency bandwidth. For confirmed obvious low-frequency broadband acoustic signals, their dispersion structure is analyzed by time-frequency analysis. If there are multiple normal modes with dispersion curves that increase with time and frequency, they are confirmed as typical refraction normal modes in the Arctic deep sea surface. In this case, the sound source depth estimation method is applicable. Furthermore, the highest frequency of each normal mode is estimated based on the time-frequency analysis diagram, i.e., the upper frequency limit.

[0010] 4) In order to further match the upper limit of the normal mode frequency, it is necessary to conduct simulation calculations using the normal mode sound propagation model based on the measured sound speed profile and seawater depth in the Arctic deep sea. The vertical distribution of the eigenfunctions of each normal mode in the signal frequency band is obtained by the model calculation. The maximum coverage depth of the eigenfunctions of each normal mode at each frequency point is obtained by setting threshold conditions. This result is the relationship between the upper limit frequency of each normal mode and the sound source depth.

[0011] 5) Compare the measured upper limit frequency of each normal mode with the relationship curve between the upper limit frequency and the sound source depth obtained by simulation. The sound source depth can be estimated by matching the upper limit frequency of a single normal mode. The depth estimation error can be reduced by averaging the sound source depths estimated by multiple normal modes. After the above five steps, the rapid estimation of the depth of a low-frequency long-range sound source underwater in the Arctic can be realized.

[0012] This invention includes a fast depth estimation method for low-frequency long-range underwater sound sources in the Arctic by matching the upper limit of the normal mode frequency; compared with existing methods, this invention has the following advantages:

[0013] 1) Based on the unique deep-sea sound velocity profile of the Arctic deep sea area, the vertical distribution of the eigenfunctions of the surface refractive normal modes as a function of frequency was calculated using a sound field model. It was found that the surface refractive normal modes in the Arctic deep sea have an upper frequency limit, and this upper frequency limit is directly related to the sound source depth. Therefore, only a single hydrophone is needed to collect the sound signal, and time-frequency analysis is performed on the received sound signal to obtain the upper frequency limit of the refractive normal modes, so as to estimate the sound source depth. That is, this invention only needs to use a single hydrophone to realize the sound source depth estimation in the Arctic deep sea area. Compared with the previous method of using a large aperture vertical array of nearly 1000m to achieve mode separation of refractive normal modes in the Arctic, the present invention has the advantage of low requirements for sound signal receiving equipment.

[0014] 2) Based on the unique sound velocity profile of the deep Arctic sea area, the two-dimensional relationship curve between the upper frequency limit of the refracted normal mode and the sound source depth is calculated in advance based on the normal mode sound field model. After obtaining the upper frequency limit of the normal mode of the measured sound signal, the sound source depth can be quickly estimated by comparing the curve. Compared with the previous sound source depth estimation method that requires complex calculation, this invention has the advantage of obtaining results quickly.

[0015] 3) Based on the variation law of the vertical distribution of the eigenfunctions of the refracted normal modes under the unique sound speed profile of the Arctic deep sea with frequency, the depth of the sound source can be estimated by matching the upper frequency limit of a single normal mode. Compared with the previous method that requires amplitude information of at least three normal modes to estimate the depth of the sound source, the present invention has the advantages of requiring less information and requiring fewer normal mode numbers in the sound signal. Attached Figure Description

[0016] Figure 1 This is the Arctic deep-sea sound velocity profile in this invention.

[0017] Figure 2 These are the normal mode eigenfunctions of the Arctic deep-sea waveguide in this invention. They are the first five normal mode eigenfunctions at frequencies of 11Hz, 40Hz, 70Hz, and 100Hz.

[0018] Figure 3 This is a time-frequency analysis diagram of the received acoustic signal under different sound source depth conditions in this invention. The depths are 100m, 152m, 200m, 252m, 300m, 352m, and 400m.

[0019] Figure 4 This is a curve showing the upper frequency of different normal modes as a function of sound source depth. It includes the calculation results for the first 5 normal modes from 20Hz to 100Hz.

[0020] Figure 5 This is a flowchart of a method for estimating the depth of a low-frequency long-range sound source under Arctic ice by matching the upper limit frequency of the normal mode, which is included in this invention. Detailed Implementation

[0021] The following embodiments will further illustrate the present invention with reference to the accompanying drawings.

[0022] Figure 1This invention relates to the Arctic deep-sea sound velocity profile. A typical Arctic deep-sea sound velocity profile consists of two linearly increasing sound velocity profiles, with the sound velocity gradient in the surface section being significantly greater than that in the deep section. The water thickness in the surface section gradually decreases from the Pacific side to the Atlantic side. Under such sound velocity profile conditions, a low-frequency sound field dispersion structure similar to that in a shallow sea environment can be formed within the surface sound propagation channel. The influence of the sound source depth on the sound signal dispersion structure can be analyzed based on the vertical distribution of the eigenfunctions of the normal modes, thereby further obtaining a sound source depth estimation method.

[0023] Figure 2 This invention relates to the eigenfunctions of the Arctic deep-sea waveguide. Based on the measured sound velocity profile of the central Arctic ice zone, the vertical distribution of the eigenfunctions is calculated using the eigenfunction model. The figure shows the typical vertical distribution of the eigenfunctions of the lower-order eigenmodes in the low-frequency band, which are the eigenfunctions of the first to fifth eigenmodes at frequencies of 11Hz, 40Hz, 70Hz, and 100Hz. As can be seen from the figure, the vertical distribution range of the eigenfunctions of each eigenmode gradually decreases with increasing frequency. For example, the vertical coverage range of the eigenfunctions of the first eigenmode decreases from over 500m to about 150m in the range of 11Hz to 100Hz. Because when the sound source depth is greater than the eigenfunction coverage range of a certain eigenmode at a certain frequency, the sound source cannot excite that eigenmode at that frequency, that is, the amplitude of that eigenmode at that frequency is zero. Therefore, the size of the sound source depth limits the highest frequency that each eigenmode can excite, and thus the sound source depth can be deduced from the highest frequency of each eigenmode.

[0024] Figure 3 This is a time-frequency analysis diagram of the received acoustic signal under different sound source depth conditions in this invention. Due to the characteristic of the vertical distribution of eigenfunctions with frequency variation under the typical deep-sea sound velocity profile in the Arctic, the normal modes have different upper limit frequencies at different sound source depths. Of course, this is on the premise that the receiving depth is less than the sound source depth; otherwise, the upper limit frequency of the normal modes is determined by the receiving depth. The figure gives a simulation example with a seawater depth of 3800m, a receiving depth of 50m, a propagation distance of 200km, and a sound source frequency of 10Hz to 100Hz. Using a typical sound velocity profile from the central Arctic ice region, time-frequency analysis diagrams of received sound signals at different source depths (100m, 152m, 200m, 252m, 300m, 352m, 400m) were simulated. It can be clearly seen from the diagrams that each normal mode has a distinct upper limit frequency, and the upper limit frequency gradually decreases as the source depth increases. Taking the first normal mode as an example, as the source depth changes from 200m to 400m, the upper limit frequency of the normal mode changes from 75Hz to 30Hz.

[0025] Figure 4This invention presents curves showing the variation of the upper cutoff frequencies of different normal modes with the source depth. Based on the analysis of the vertical distribution characteristics of the normal mode eigenfunctions and the simulation of broadband low-frequency long-range acoustic signals, after analyzing the received acoustic signals to obtain the upper cutoff frequencies of each normal mode, it is necessary to know the source depth corresponding to the upper cutoff frequencies of each normal mode. Therefore, based on the normal mode sound field model and combined with hydrological condition simulation, the normal mode eigenfunctions at different frequencies are obtained. A threshold is set to define the maximum depth of the vertical distribution of the eigenfunctions, and finally, the curves showing the correspondence between the upper cutoff frequencies of different normal modes and the source depth are obtained, as shown in the figure. It can be seen from the figure that the upper cutoff frequencies of each normal mode decrease as the source depth increases, while the upper cutoff frequencies of different normal modes increase as the number of modes increases under the same source depth. This result is consistent with the dispersion structure in the time-frequency analysis of the simulated acoustic signals at different source depths.

[0026] Figure 5 This invention includes a flowchart of a method for estimating the depth of a low-frequency long-range sound source under Arctic ice by matching the upper limit frequency of normal modes. The process mainly includes five steps: measuring the sound velocity profile and depth of the seawater in the working area; deploying receiving equipment to collect sound signals; performing data analysis on the received sound signals to obtain the measured upper limit information of each normal mode; using the normal mode sound propagation model based on the measured sound velocity profile and sea depth to calculate the curves of the upper limit frequency of different normal modes as a function of the sound source depth; and obtaining the sound source depth estimate by matching the upper limit frequency of each normal mode.

[0027] This invention discloses a rapid depth estimation method for low-frequency long-range underwater sound sources in the Arctic by matching the upper limit of the normal mode frequency. The basic principle of this method is as follows:

[0028] For the low-frequency sound propagation field in the ocean, the received sound field can be represented as the effect of a series of superimposed normal modes. Each normal mode has a different group velocity at different frequencies. Therefore, the dispersion structure of normal modes can be observed in the broadband received sound signal, and the dispersion structure usually carries a large amount of sound source information. For the typical deep-sea sound velocity profile in the Arctic, that is, the approximately two-segment linear positive gradient sound velocity profile, a refractive normal mode waveguide can be formed on its surface. The sound signal dispersion structure in this waveguide has the characteristic that the dispersion curve increases with time and frequency.

[0029] Based on the characteristics of the approximate upper and lower linear positive gradient sound velocity profiles of typical deep-sea sound velocity profiles in the central Arctic ice zone, the eigenfunctions of normal modes under the Arctic deep-sea sound velocity profile are analyzed. The eigenfunctions are calculated through simulation using a normal mode sound field model, revealing the characteristics of the eigenfunctions changing with frequency. Specifically, the vertical coverage of the eigenfunctions gradually decreases with increasing frequency. When the sound source depth exceeds the coverage of the eigenfunctions, the normal mode cannot be excited. Therefore, there is a clear upper frequency limit for normal modes within the refractive normal mode waveguides of the Arctic deep-sea surface, and this upper limit is directly related to the sound source depth. Based on this principle, by matching the measured upper frequency limit of the normal mode with the pre-calculated curve of the relationship between the upper frequency limit and the sound source depth, the sound source depth can be quickly estimated. This is a sound source depth estimation method based on the characteristics of the normal mode eigenfunctions under the unique deep-sea sound velocity profile environment of the Arctic. The following section details how to estimate the depth of low-frequency long-range underwater sound sources in the Arctic by matching the upper frequency limit of the normal mode, using formulas and accompanying figures.

[0030] In the environment of a typical deep-sea sound velocity profile in the Arctic, such as Figure 1 The red line shown is a typical measured deep-sea sound velocity profile in the Arctic. The sound velocity in the surface water about 400 meters increases approximately linearly with depth, forming a waveguide for refracted normal modes in the surface water. When the energy of the refracted normal modes is mainly concentrated in the surface, an approximate expression for the horizontal wavenumber of the normal modes can be derived. The sound velocity profile in the surface water about 400 meters can be approximated as a linearly increasing sound velocity profile as shown in equation (1).

[0031] (1)

[0032] in, The speed of sound at the sea surface. Let be the slope of the sound speed as it increases with depth. , Seawater depth The range is limited to 0m to 400m. For depth The speed of sound of the seawater.

[0033] The vertical distribution of eigenfunctions of low-frequency, low-sign normal modes under a typical deep-sea sound velocity profile in the Arctic was calculated using a normal mode acoustic field model. Figure 2 The vertical distribution of the eigenfunctions of the first five normal modes at four typical low-frequency points (11Hz, 40Hz, 70Hz, and 100Hz) is given; from Figure 2 As can be seen, the vertical distribution range of the eigenfunctions of each normal mode decreases with increasing frequency. When the sound source depth exceeds the vertical coverage range of the eigenfunctions, the normal mode cannot be excited. Therefore, there is an upper frequency limit for normal modes at a given sound source depth. Taking the first normal mode as an example, when the sound source depth is 300m, according to... Figure 2The upper frequency limit of the first normal mode is approximately 40Hz; taking the second normal mode as an example, when the sound source depth is 300m, according to Figure 2 The upper frequency limit of the second normal mode is approximately 70 Hz.

[0034] In summary, therefore, for the deep-sea environment under a typical deep-sea sound velocity profile in the Arctic, for low-frequency, long-range acoustic signals, by analyzing the time-frequency structure of the acoustic signals, such as... Figure 3 The above describes the estimation of the upper frequency limit of each normal mode in the sound signal, followed by the calculation of the relationship curve between the upper frequency limit of each normal mode and the sound source depth using a normal mode sound field model. Figure 4 As shown, the depth of the sound source can be quickly estimated by matching the two.

[0035] This invention provides a fast method for estimating the depth of low-frequency long-range sound sources under Arctic ice by matching the upper limit of the normal mode frequency. Based on the above principle, it is implemented according to the following steps:

[0036] Step 1: Measure the sound velocity profile and depth of the seawater in the deep Arctic sea area. Due to the spatiotemporal variations in the sound velocity profile within the Arctic Ocean and its complex seabed topography, it is necessary to measure the sound velocity profile and depth of the seawater before deploying equipment and estimating the sound source depth. The measurement range of the seawater sound velocity profile is the entire ocean depth. If the working depth of the measuring equipment is limited, it is necessary to measure a range exceeding 1000m. The sound velocity values ​​at deeper depths are extended using empirical formulas. This sound source depth estimation method is applicable to the deep Arctic sea conditions, and the seawater depth is best above 1000m.

[0037] Step 2: After determining the working sea area of ​​the equipment, measuring the sound velocity profile of the seawater and the sea depth, deploy the underwater acoustic signal acquisition equipment. This sound source depth estimation method only requires a single hydrophone. According to the normal wave characteristics under the conditions of the Arctic deep sea, the deployment depth of the hydrophone needs to be set to be less than the sound source depth. Considering the depth range of the underwater sound source of main concern, the hydrophone depth is set to within 50m. The entire system can be deployed using methods such as submersible mooring, buoy, or shipboard hoisting.

[0038] Step 3: Based on the underwater acoustic signals collected by the system, first determine whether there is an acoustic signal rather than a noise signal based on the time-domain waveform. The presence of the signal and the signal-to-noise ratio can be determined by the low-frequency bandwidth. For the confirmed obvious low-frequency broadband acoustic signal, its dispersion structure is analyzed by time-frequency analysis. If there are multiple normal modes with dispersion curves that increase with time and frequency, it is confirmed as a typical refraction normal mode in the Arctic deep sea surface. That is, the sound source depth estimation method is applicable. Furthermore, the highest frequency of each normal mode is estimated based on the time-frequency analysis diagram, i.e., the upper frequency limit.

[0039] Step 4: In order to further match the upper limit of the normal mode frequency, it is necessary to conduct simulation calculations using the normal mode sound propagation model based on the measured sound speed profile and seawater depth in the Arctic deep sea. The vertical distribution of the eigenfunctions of each normal mode in the signal frequency band is obtained by the model calculation. The maximum coverage depth of the eigenfunctions of each normal mode at each frequency point is obtained by setting threshold conditions. This result is the relationship between the upper limit frequency of each normal mode and the sound source depth.

[0040] Step 5: Compare the measured upper limit frequency of each normal mode with the relationship curve between the upper limit frequency and the sound source depth obtained from the simulation. The sound source depth can be estimated by matching the upper limit frequency of a single normal mode. The sound source depth estimated by multiple normal modes can be averaged to reduce the depth estimation error.

[0041] By following the above five steps, we can achieve rapid depth estimation of low-frequency long-range sound sources underwater in the Arctic.

[0042] This embodiment analyzes the characteristics of the vertical distribution of eigenfunctions of low-frequency, low-sign normal modes under typical sound velocity profiles in the Arctic deep sea, revealing that normal modes under typical sound velocity profiles in the Arctic deep sea have an upper frequency limit. This upper frequency limit is directly related to the sound source depth. Therefore, the sound source depth can be quickly estimated by matching the upper frequency limit of the normal modes. Compared with existing methods for estimating sound source depth in the Arctic deep sea, this invention only requires a single hydrophone to achieve sound source depth estimation, only requires matching the highest frequency to estimate the sound source depth without complex calculations, and only requires a single normal mode to achieve sound source depth estimation without needing multiple normal mode information. The method of this invention has the advantages of low experimental cost, low experimental difficulty, and low requirements for acoustic signals, which is beneficial for conducting sound source localization research based on a single hydrophone in the Arctic deep sea.

[0043] This invention utilizes a single hydrophone acoustic signal acquisition system deployed in the deep Arctic sea area, based on buoys, submersibles, or shipboard-mounted methods. By performing time-frequency analysis on the received acoustic signals and estimating the upper frequency limit of each normal mode, the system simultaneously measures the sound velocity profile and depth of the experimental sea area. Using a normal mode sound field model, the system calculates the relationship curve between the upper frequency limit of the normal mode and the sound source depth. Then, by matching this curve with the measured upper frequency limit of the normal mode, the system obtains an estimate of the sound source depth.

[0044] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A fast method for estimating the depth of a low-frequency long-range underwater sound source in the Arctic by matching the upper limit of the normal mode frequency, characterized in that, The typical deep-sea sound velocity profile in the Arctic causes the eigenfunction coverage range to gradually decrease with increasing frequency. When the underwater sound source depth exceeds the vertical coverage range of the normal mode eigenfunction, the sound source cannot excite that normal mode. Under the condition of sound source depth, the low-frequency, low-signature normal mode in Arctic underwater has a frequency upper limit, and this frequency upper limit decreases with increasing sound source depth. In the typical deep-sea environment of the Arctic, shallow underwater acoustic signal acquisition equipment is set up, and time-frequency analysis is performed on the received signal to obtain the frequency upper limits of multiple normal modes. Combining the relationship curves between the upper limit frequency of each normal mode and the sound source depth calculated based on the model, the sound source depth is estimated by matching the upper limit frequency of the normal mode. The estimation method specifically includes the following steps: 1) Measure the sound velocity profile and depth of seawater in the deep Arctic sea area; 2) Deploy underwater acoustic signal acquisition equipment. This sound source depth estimation method only requires a single hydrophone. Based on the normal wave characteristics under Arctic deep-sea conditions, the deployment depth of the hydrophone needs to be set to be less than the sound source depth. Considering the main focus on the underwater sound source depth range, the hydrophone depth is set to within 50m. 3) For the underwater acoustic signals collected by the system, for the confirmed obvious low-frequency broadband acoustic signals, the dispersion structure is analyzed by time and frequency. If there are multiple normal modes with dispersion curves that increase with time and frequency, they are confirmed as typical refraction normal modes in the Arctic deep sea surface. That is, the sound source depth estimation method is applicable. The highest frequency of each normal mode is estimated based on the time and frequency analysis diagram, i.e., the upper frequency limit. 4) In order to further match the upper limit of the normal mode frequency, simulation calculations were carried out using the normal mode sound propagation model based on the measured sound speed profile and seawater depth in the Arctic deep sea. The vertical distribution of the eigenfunctions of each normal mode in the signal frequency band was obtained by the model calculation. The maximum coverage depth of the eigenfunctions of each normal mode at each frequency point was obtained by setting threshold conditions. The result is the relationship between the upper limit frequency of each normal mode and the sound source depth. 5) Compare the measured upper limit frequency of each normal mode with the relationship curve between the upper limit frequency and the sound source depth obtained by simulation. The sound source depth can be estimated by matching the upper limit frequency of a single normal mode. The depth estimation error can be reduced by averaging the sound source depths estimated by multiple normal modes. This enables rapid estimation of the depth of low-frequency long-range sound sources underwater in the Arctic.

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