Deep sea convergence area characteristic forecasting method and system based on normal wave theory

Abstract

The invention provides a deep sea convergence area characteristic forecasting method and system based on a normal wave theory. The method comprises the following steps: determining a normal wave eigenvalue equation; solving a normal wave eigenequation, and calculating a normal wave eigenvalue of each order from the first order to a set normal wave order upper limit; calculating a normal wave eigenfunction value according to the sound source and the receiving depth; superposing and synthesizing a sound field by using the normal wave eigenvalue and the normal wave eigenfunction value; and calculating the sound propagation loss of the convergence area by using the synthesized sound field so as to obtain the energy and position of the deep sea convergence area. Compared with the prior art, the method has the advantages that the analytical solution form of the normal wave eigenequation is obtained in advance, compared with pure numerical calculation, certain calculation time can be saved, in addition, some function expansion and frequency interpolation technologies can be conveniently combined, a basis is provided for broadband sound propagation and signal waveform forecasting of the deep sea convergence area, and the method has a wide application prospect. The sound field calculation speed of the convergence area is greatly improved, and the method has good calculation precision.

Description

Technical Field

[0001] This application belongs to the field of underwater acoustics physics, and particularly relates to a method and system for predicting the characteristics of deep - sea convergence zones based on the normal - mode theory. Background Art

[0002] In the deep - sea environment, when the sound source is near the sea surface, the sound field shows a "bright - dark - bright - dark" distribution with distance. The bright regions are areas of high sound intensity and are called sound - field convergence zones. In practical applications, the convergence - zone effect of the deep - sea sound field can be used to achieve remote detection and communication. Therefore, it is necessary to accurately predict the distribution of the deep - sea sound - field convergence zones so as to quickly extract the characteristic information of the convergence zones.

[0003] Common sound - field prediction models are constructed based on ray theory, normal - mode theory, and parabolic equation theory. Among them, the ray - acoustic algorithm model approximately assumes that in the convergence zone, the cross - sectional area of the sound - beam tube approaches zero and the sound intensity tends to infinity, and in the shadow zone, the sound rays cannot reach and the sound intensity is zero. It is difficult to accurately describe the sound - field distribution near the shadow zone and the convergence zone in the deep - sea sound channel, such as the BELLHOP ray - algorithm program. However, the actual sound - propagation situation is not like this. In terms of the shadow zone, due to sound diffraction, the sound field in the shadow zone is not completely zero. At the same time, the reflected sound from the sea - surface or seabed interface will also fill into the shadow zone. Only because of the existence of reflection loss and scattering loss, the intensity is much lower compared with the sound propagation along the refraction path, resulting in inaccurate calculations in the ray model. From the perspective of normal modes, within a certain horizontal - distance range, the difference between adjacent normal - mode eigenvalues can always remain a relatively stable constant, that is, some normal modes are in - phase superposed and the sound - field intensity interference is enhanced, thus the phenomenon of deep - sea sound - field convergence zones appears. The main work of the normal - mode sound - field algorithm model is to solve the differential equations of normal - mode eigenvalues and eigenfunctions to obtain the required normal - mode parameters, mainly including normal - mode eigenvalues, eigenfunctions, normalization constants, attenuation coefficients, group velocities, etc. For the sound - speed profile in the actual ocean environment, the normal - mode eigenvalue equation generally does not have an analytical solution and needs to be solved numerically, such as the commonly used KRAKEN algorithm program. However, for numerical calculation to ensure sufficient accuracy, a relatively fine spatial - grid division is required, which has the problems of large computational amount and long time, especially for broadband sound - propagation loss and signal - waveform prediction, the computational amount is even larger and the time is even longer. Summary of the Invention

[0004] The purpose of this application is to overcome the defects of the existing methods with large computational amount and long calculation time.

[0005] To achieve the above purpose, this application proposes a method for predicting the characteristics of deep - sea convergence zones based on the normal - mode theory, including:

[0006] Determine the normal - mode eigenvalue equation;

[0007] Solve the simple normal wave eigenvalue equation, starting from the first order to the set upper limit of the simple normal wave order, and calculate the simple normal wave eigenvalue of each order; calculate the simple normal wave eigenfunction value according to the sound source and receiving depth;

[0008] The sound field is synthesized by superimposing the eigenvalue of the simple normal wave and the eigenfunction value of the simple normal wave;

[0009] The synthesized sound field is used to calculate the sound field propagation loss in the converging area.

[0010] As an improvement to the above method, the method further comprises:

[0011] After the sound field propagation loss is calculated, the position, width and intensity characteristic information of the convergence zone are read according to the obtained sound field propagation loss distribution graph.

[0012] As an improvement to the above method, the simple normal wave eigenvalue equation is:

[0013]

[0014] Where k(z) represents the wave number of the layered medium, z represents the depth; ξ m Represents the horizontal wave number of each order simple normal wave; η m and ζ m Indicates the depth of the up and down reversal points, corresponding to represents the phase shift of reflection or inversion near the sea surface; m represents the order of the eigenvalue of the simple normal wave.

[0015] As an improvement to the above method, the calculation of the normal wave eigenvalue of each order includes:

[0016] The iterative root-finding method is used to calculate the eigenvalue of each order of the simple normal wave. The iterative formula is:

[0017]

[0018] in, Indicates the horizontal wave number of iteration j Substitute the value obtained into the simple normal wave eigenvalue equation;

[0019] When calculating the first-order normal wave eigenvalue, the initial value of the iteration of the normal wave eigenvalue is set to the maximum wave number k in the water layer. max 85%-95%; k max =ω / c min , ω represents the angular frequency of the sound source, c min represents the minimum sound speed in deep-sea waveguide;

[0020] When calculating the eigenvalues of the second-order and higher normal waves, the initial value of the iteration of the eigenvalues of the normal wave is set to 85%-95% of the eigenvalue of the previous order normal wave;

[0021] When the maximum set number of iterations is reached, the calculation is completed.

[0022] As an improvement of the above method, the formula for the superimposed synthetic sound field is:

[0023]

[0024] where p(r,z s ,z|ω) represents the superimposed synthetic sound field; r represents the horizontal propagation distance; ρ(z) represents the medium density; N represents the maximum order of the calculated normal mode series solution; i represents the imaginary number; p n represents the normal mode series solution of each order of the sound field; δ n represents the normal mode attenuation coefficient; ξ n represents the eigenvalue of the nth normal mode; ψ n (z) represents the normal mode eigenfunction value, ψ n (z s ) represents the normal mode eigenfunction value at the sound source depth z s ;

[0025] As an improvement of the above method, when the sound source frequency is greater than 1 kHz, the normal mode attenuation coefficient δ n takes the value of:

[0026]

[0027] where f represents the sound source frequency, with the unit of kHz; the attenuation coefficient δ n has the unit of dB / km;

[0028] When the sound source frequency is less than or equal to 1 kHz, the normal mode attenuation coefficient δ n takes the value of 0.

[0029] As an improvement of the above method, the formula for calculating the sound field propagation loss is:

[0030] TL C (r|z s ,z) = 10 log |p(r,z s ,z|ω)| 2

[0031] where TL C (r|z s ,z) represents the sound field propagation loss.

[0032] This application also provides a deep - sea convergence zone characteristic prediction system based on the normal mode theory, which is implemented based on the above method. The system includes:

[0033] The normal mode eigen - equation solving module is used to solve the normal mode eigen - equation, starting from the first order up to the set upper limit of the normal mode order, and calculate the normal mode eigenvalues of each order; according to the source and receiver depths, calculate the normal mode eigen - function values;

[0034] The superposition and synthesis of the sound field module is used to superpose and synthesize the sound field by using the normal mode eigenvalues and normal mode eigen - function values; and

[0035] The sound propagation loss calculation module is used to calculate the sound field propagation loss in the convergence zone by using the synthesized sound field.

[0036] As an improvement of the above - mentioned system, the system further includes:

[0037] The prediction of the characteristics of the sound field in the convergence zone module is used to read the position, width and intensity characteristic information of the convergence zone by using the sound field propagation loss distribution graph.

[0038] Compared with the prior art, the advantages of the present application are as follows:

[0039] 1. The method of the present invention pre - obtains the analytical solution form of the normal mode eigen - equation. Compared with pure numerical calculations, it can save a certain amount of calculation time. In addition, it can conveniently combine some function expansion and frequency interpolation techniques, providing a basis for broadband sound propagation and signal waveform prediction, and greatly improving the sound field calculation speed;

[0040] 2. The method for predicting the characteristics of the deep - sea convergence zone of the present invention is based on the normal mode theory. It limits the order of the normal mode summation and is mainly used for predicting the characteristics of typical deep - sea convergence zones. It can quickly give the corresponding sound propagation loss and has good calculation accuracy. Furthermore, the characteristic information such as "position, width, intensity" of the convergence zone can be read according to the obtained sound propagation loss distribution graph. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The figure shows the flow chart of the method for predicting the characteristics of the deep - sea convergence zone based on the normal mode theory;

[0042] Figure 2 The figure shows the verified input MUNK sound speed profile;

[0043] Figure 3 The figure shows the plane distribution of the propagation loss calculated by KRAKEN for comparison with the method of the present invention;

[0044] Figure 4 The figure shows the comparison diagram of the sound propagation loss curves of the two algorithms with a receiver depth of 200m;

[0045] Figure 5 The figure shows the comparison diagram of the sound propagation loss curves of the two algorithms with a receiver depth of 500m. DETAILED DESCRIPTION OF THE INVENTION

[0046] The technical solution of the present application will be described in detail below with reference to the accompanying drawings.

[0047] Considering that if the analytical solution form of the normal mode eigen - equation can be obtained in advance, compared with pure numerical calculations, a certain amount of calculation time can be saved. In addition, some function expansion and frequency interpolation techniques can be combined to provide a basis for predicting signal waveforms and broadband acoustic propagation. In view of this, the present invention proposes a method and system for predicting the characteristics of deep - sea convergence zones based on the normal mode theory.

[0048] As Figure 1 shown, the method for predicting the characteristics of deep - sea convergence zones based on the normal mode theory of the present invention includes the following steps:

[0049] Step 1: Solve the normal mode eigen - equation and calculate the first - order normal mode eigenvalue ξ m , m = 1;

[0050] Considering the characteristics of deep - sea acoustic propagation, in order to improve the calculation efficiency, during the numerical implementation of the algorithm, the phase - integral approximation normal mode eigenvalue equation is adopted:

[0051]

[0052] where k(z) is the wave number of the stratified medium, z is the depth, ξ m is the horizontal wave number of each order of normal mode, η m and ζ m are the depths of the upper and lower turning points, corresponding to is the phase shift of reflection or inversion near the sea surface;

[0053] Set the initial iteration value of the normal mode eigenvalue slightly less than the maximum wave number k max = ω / c min (85% - 95% of the maximum wave number k max ), ω is the angular frequency of the sound source, and c min is the minimum sound speed in the deep - sea waveguide.

[0054] Perform iterative root - finding calculations, and the iterative formula is:

[0055]

[0056]

[0057] where is the horizontal wave number at the j - th iteration is the value obtained by substituting into the normal mode eigenvalue equation.

[0058] Calculate the normal mode eigen - function value ψ according to the sound source and receiving depthm (z s ) and ψ m (z r ), where z s and z r are the source depth and the receiving depth, respectively.

[0059] Step 2: m = m + 1, calculate the eigenvalue ξ of the next-order normal mode until the upper limit of the set normal mode order; m

[0060] Set the initial iteration value of the normal mode eigenvalue slightly less than the eigenvalue ξ of the previous-order normal mode m-1 (85% - 95% of the eigenvalue of the previous-order normal mode);

[0061] Repeatedly perform iterative root finding to calculate the normal mode eigenvalue;

[0062] Calculate the normal mode eigenfunction value ψ m (z s ), ψ m (z r );

[0063] Step 3: After obtaining the normal mode parameters, superpose and synthesize the sound field p(r, z s , z|ω):

[0064]

[0065] where r is the horizontal propagation distance, ρ(z) is the medium density, N is the maximum order of the calculated normal mode series solution, i is the imaginary number, p n is the series solution of each order of the normal mode of the sound field, δ n is the normal mode attenuation coefficient; ψ n (z) represents the normal mode eigenfunction value, ψ n (z s ) represents the normal mode eigenfunction value at the source depth z s .

[0066] Step 4: Calculate the sound propagation loss TL C (r|z s , z), since the sound field description in the deep-sea convergence zone is suitable for the coherent sound propagation loss, then:

[0067] TL C (r|z s , z) = 10 log |p(r, z s , z|ω)| 2

[0068] After calculating the sound propagation loss, the characteristic information such as "position, width, intensity" of the convergence zone can be read from the obtained sound propagation loss distribution graph, and then the sound field characteristics of the convergence zone can be predicted.

[0069] After programming the method of the present invention into a source program using FORTRAN language, the calculation process of sound wave propagation loss includes:

[0070] The first step is to write the parameters to be set into the input file INPUT.ENV, with a total of six BLOCKs:

[0071] The first line: the title name TITLE, not exceeding 80 characters;

[0072] The second line: the sound source frequency FREQ, in Hz; the farthest distance RMKM for sound field calculation and the distance interval DRKM, in km. The number of receiving distance points to be calculated is obtained by converting them, and it is required not to exceed 3001; the number of sound sources NSD, the sound source depths ZSD(1:NSD);

[0073] The third line: the number of sound sources NSD, the corresponding sound source depths ZSD(1:NSD), in m. The program currently allows 1 sound source, otherwise the calculation result is meaningless. Note that the final " / " is required.

[0074] The fourth line: the number of receivers NRD, the corresponding receiver depths ZRD(1:NRD), in m. The receiver depths can be input one by one. When the number of receiver depths is greater than 2 and they are evenly arranged, only the starting and ending depth values can also be input, and the program will automatically calculate and obtain them. The number of receiver depths is less than 301. Note that the final " / " is required for NRD.

[0075] The distance range RANGE, in km, must be greater than or equal to the farthest distance to be calculated; the ocean depth DEPTH, in meters, needs to be consistent with the last depth input in the sound speed profile of the "sixth line";

[0076] Input the sound speed profile of the water layer, which is two columns of data: depth and sound speed, not exceeding 101 data. The first one corresponds to the sea surface, and the last data must correspond to the depth set in the "fifth line", otherwise the program execution will go wrong;

[0077] The second step is to determine the position of the sound channel axis ZMIN and the corresponding minimum sound speed CMIN;

[0078] The third step is to solve the normal mode eigen - equation and calculate the first - order normal mode eigenvalue ξ m , m = 1;

[0079] Considering the characteristics of deep - sea sound propagation, in order to improve the calculation efficiency, in the numerical implementation of the algorithm, the normal mode eigenvalue equation approximated by phase integration is adopted:

[0080]

[0081] where k(z) is the wavenumber of the stratified medium, and ξ m is the horizontal wavenumber of each normal mode, and η m and ζ m are the depths of the upper and lower turning points, corresponding to the phase shift of reflection or inversion near the sea surface;

[0082] Set the initial iteration value of the normal mode eigenvalue slightly less than the maximum wavenumber k max = ω / c min , where ω is the angular frequency of the sound source and c min is the minimum sound speed in the deep - sea waveguide.

[0083] Perform iterative root - finding calculations. The iterative formula is

[0084]

[0085] f′(ξ) = df(ξ) / dξ,

[0086] where is the horizontal wavenumber at the i - th iteration substituted into the normal mode eigenvalue equation.

[0087] According to the input sound source ZSD(1:NSD) and receiving depth ZRD(1:NRD), calculate the normal mode eigenfunction values ψ m (z s ) and ψ m (z r ), where z s and z r are the sound source depth and receiving depth respectively.

[0088] Step 4, m = m + 1, calculate the eigenvalue ξ of the next - order normal mode m , until the upper limit of the normal mode order set by the program;

[0089] Set the initial iteration value of the normal mode eigenvalue slightly less than the eigenvalue ξ m-1 of the previous - order normal mode;

[0090] Repeat the iterative root - finding calculation;

[0091] According to the input sound source ZSD(1:NSD) and receiving depth ZRD(1:NRD), calculate the normal mode eigenfunction values ψ m (z s ), ψ m (z r );

[0092] Step 5: After obtaining the normal mode parameters, superpose and synthesize the acoustic field P(r,z s ,z r ),

[0093]

[0094] where r is the horizontal propagation distance, z is the depth, ρ(z) is the medium density, N is the maximum order of the normal mode series solution, i is the imaginary number, and p n is the normal mode series solution of each order of the acoustic field.

[0095] Step 6: Calculate the acoustic propagation loss TL C (r|z s ,z), Since the description of the acoustic field in the deep - sea convergence zone is suitable for using the coherent acoustic propagation loss, then

[0096] TL C (r|z s ,z) = 10log|p(r,z s ,z)| 2 dB (4)

[0097] Step 7: Output the data file OUTPUT.DAT, which is divided into 4 BLOCKs:

[0098] The first line: The number of receiving points NRD;

[0099] The second line: The depths of the receiving points ZRD(1:NRD);

[0100] The third line: The number of receiving distance points NR;

[0101] The fourth line: The acoustic propagation loss data, R(n), (TL(n,k), k = 1:NRD), where n = 1:NR, and there are a total of NR data, corresponding to NR receiving distance points;

[0102] Step 8: The above prediction algorithm is compiled in FORTRAN language, and the source program is CZTL.FOR. After compilation and linking, an executable file CZTL.EXE is formed for fast calculation; running the executable file CZTL.EXE, the program automatically reads the calculation parameters and environmental parameters of the input file INPUT.ENV, and the data output file OUTPUT.DAT can be obtained, which is divided into two cases: single - transmitter and single - receiver, and multiple - transmitter and multiple - receivers.

[0103] The applicable conditions and limitations of the method of the present invention include:

[0104] (1) The position and intensity prediction of the deep - sea convergence zone are given by the sound propagation loss curve (single receiver) or the planar distribution (multiple receivers) graph obtained by this method;

[0105] (2) In principle, this method is not suitable for the numerical prediction of sound fields for other purposes. Considering the necessary conditions for the obvious appearance of the deep - sea convergence zone: the sound speed c rs at the position of the transmitter - receiver is less than the sound speed c H in the water layer near the seabed. The summation of normal modes set in the program is limited to the part of "normal modes without seabed reflection". If the influence of seabed reflection is obvious, there will be errors in the sound field calculation. However, at this time, the "convergence zone" phenomenon in the deep sea is not obvious;

[0106] (3) This method only answers the question of "if the convergence zone exists, the position where it should appear and the convergence zone gain it has", without discussing the question of "under what circumstances the convergence zone will definitely appear", except for a "necessary condition" given;

[0107] (4) In principle, this method has no frequency limit. However, considering high - frequency sound absorption and the concern about the prediction of the convergence zone, it is recommended that the calculation frequency be limited to below 5 kHz;

[0108] (5) The number of sound sources is limited to 1; the number of receiving depth points is less than 301; the number of receiving distance points is less than 3001. These limitations mainly stem from the limitations of the array dimensions in the program code;

[0109] (6) It cannot handle the problem of two - channel sound, that is, the case where there are multiple sound - speed minima. It is necessary to perform "polishing" pre - processing on the actually measured sound - speed profile to eliminate the "false sound channels" so that it has a typical distribution form with one deep - sea sound - channel axis;

[0110] (7) In the calculation, the highest phase velocity of the normal mode is limited to the sound speed in the water layer near the seabed, without considering the contribution of the seabed - reflected normal mode: This has no impact on the position prediction of the convergence zone, but it will have a certain impact on the sound - field intensity, especially in the shadow zone, because the interface - reflected sound mainly contributes to the sound - shadow zone;

[0111] (8) When the sound - source frequency is high, greater than 1 kHz, seawater absorption needs to be considered. The seawater absorption coefficient α adopts the calculation formula of dB / km, where f is the sound - source frequency, and approximately the normal - mode attenuation coefficient δ n =α, and the corresponding additional sound - propagation loss is 20log[exp(-αr)] decibels, where α is the seawater absorption coefficient in nepers per meter, and r is the horizontal propagation distance; when the sound - source frequency is less than or equal to 1 kHz, seawater absorption does not need to be considered, and the normal - mode attenuation coefficient takes a value of 0;

[0112] (9) This method does not directly give the gain in the convergence zone but only the sound propagation loss defined in the usual way. If needed, it can be obtained by conversion according to the "difference in spherical spreading loss" or other definitions.

[0113] To verify the calculation accuracy of the algorithm model of this inventive method, for a typical MUNK sound speed profile (as Figure 2 shown), comparative calculations were carried out using the KRAKEN normal mode algorithm program, where the source depth is 200 m and the source frequency is taken as 1 kHz. Figure 3 is the planar distribution of the calculated sound propagation loss. Figure 4 and Figure 5 are the sound propagation loss curves at two selected receiving depths of 200 m and 500 m for comparison (CZTL represents the calculation result of the method of this application). It can be seen from Figure 4 and Figure 5 that the positions of the convergence zones and the predictions of the sound field intensities are basically consistent, but there are still certain errors in the predictions of the sound field intensities in the shadow zones. Considering that the main purpose of this algorithm is to predict the positions of the convergence zones, and for practical applications, the prediction of the sound field intensities in the convergence zones is more important. The sound field intensities in the shadow zones are easily affected by the reflected sound from the seabed, and their predictions are not the main consideration of this algorithm program because the contributions of the seabed-reflected normal modes have been ignored.

[0114] Regarding the calculation time of the algorithm, corresponding estimates are given. For a frequency of 1 kHz, the time for calculating 301×2001 planar distributions of sound propagation loss does not exceed 3 minutes. For the prediction of the usual propagation loss curves, it does not exceed a few seconds.

[0115] This application also provides a deep-sea convergence zone characteristic prediction system based on the normal mode theory, which is implemented based on the above method. The system includes:

[0116] A module for solving the normal mode eigen-equation, which is used to solve the normal mode eigen-equation, calculate the eigen-values of each order of the normal mode from the first order to the set upper limit of the normal mode order, and calculate the eigen-function values of the normal mode according to the source and receiving depths.

[0117] A module for superposing and synthesizing the sound field, which is used to superpose and synthesize the sound field using the normal mode eigen-values and eigen-function values.

[0118] A module for calculating the sound propagation loss, which is used to quickly calculate the sound propagation loss in the convergence zone sound field using the synthesized sound field.

[0119] A module for predicting the characteristics of the convergence zone sound field, which is used to read the position, width, and intensity characteristic information of the convergence zone using the distribution graph of the sound field propagation loss.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit them. Although the present application has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present application does not depart from the spirit and scope of the technical solutions of the present application, and they should all be covered by the scope of the claims of the present application.

Claims

1. A method for predicting the characteristics of deep - sea convergence zones based on the normal - mode theory, comprising: Determining the normal - mode eigenvalue equation; Solving the normal - mode eigen - equation, starting from the first order up to the set upper limit of the normal - mode order, calculating the normal - mode eigenvalues of each order; calculating the normal - mode eigen - function values according to the sound - source and receiving depths; Using the normal - mode eigenvalues and normal - mode eigen - function values to superpose and synthesize the sound field; Using the synthesized sound field to calculate the sound - field propagation loss in the convergence zone.

2. The method for predicting the characteristics of deep-sea convergence zones based on the normal mode theory according to claim 1, characterized in that, The method further comprises: After calculating the sound - field propagation loss, reading the position, width, and intensity characteristic information of the convergence zone according to the obtained sound - field propagation loss distribution graph.

3. The method for predicting the characteristics of deep-sea convergence zones based on the normal mode theory according to claim 1, wherein The normal - mode eigenvalue equation is: where k(z) represents the wavenumber of the stratified medium, z represents the depth; ξ m represents the horizontal wavenumber of each normal mode; η m and ζ m represent the depths of the upper and lower turning points, corresponding to represents the phase shift of reflection or inversion near the sea surface; m represents the order of the normal mode eigenvalue.

4. The method for predicting deep-sea convergence zone characteristics based on the normal mode theory according to claim 3, wherein The calculating the normal - mode eigenvalues of each order includes: Using iterative root - finding to calculate the normal - mode eigenvalues of each order, and the iterative formula is: Among them, represents the horizontal wavenumber at the j-th iteration the value obtained by substituting into the normal mode eigenvalue equation; When calculating the eigenvalue of the first-order normal mode, the initial iteration value of the normal mode eigenvalue is set to 85%-95% of the maximum wavenumber k in the water layer; k max ; k max = ω / c min , where ω represents the angular frequency of the sound source, and c min represents the minimum sound speed in the deep ocean waveguide; When calculating the normal - mode eigenvalues of the second order and above, the initial iterative value of the normal - mode eigenvalue is set to 85% - 95% of the normal - mode eigenvalue of the previous order; When the maximum set number of iterative times is reached, the calculation is completed.

5. The method for predicting the characteristics of deep-sea convergence zones based on the normal mode theory according to claim 4, characterized in that, The formula for superposing and synthesizing the sound field is: where p(r,z s ,z|ω) represents the superimposed and synthesized sound field; r represents the horizontal propagation distance; ρ(z) represents the medium density; N represents the maximum order of the normal mode series solution; i represents the imaginary number; p n represents the normal mode series solution of each order of the sound field; δ n represents the normal mode attenuation coefficient; ξ n represents the eigenvalue of the nth order normal mode; ψ n (z) represents the normal mode eigenfunction value, ψ n (z s ) represents the normal mode eigenfunction value at the sound source depth z s .

6. The method for predicting the characteristics of deep - sea convergence zones based on the normal mode theory according to claim 5, characterized in that, When the source frequency is greater than 1 kHz, the normal mode attenuation coefficient δ n takes the value of: where f represents the sound source frequency, with the unit of kHz; the attenuation coefficient δ n has the unit of dB / km; When the sound source frequency is less than or equal to 1 kHz, the normal mode attenuation coefficient δ n takes a value of 0.

7. The method for predicting deep-sea convergence zone characteristics based on the normal mode theory according to claim 5, characterized in that The formula for calculating the sound - field propagation loss is: TL C (r|z s ,z) = 10 log|p(r,z s ,z|ω)| 2 Among them, TL C (r|z s , z) represents the sound field propagation loss.

8. A deep - sea convergence zone characteristic prediction system based on the normal mode theory, implemented based on any of the methods described in claims 1 - 7, characterized in that, The system includes: A normal - mode eigen - equation solving module, used to solve the normal - mode eigen - equation, starting from the first order up to the set upper limit of the normal - mode order, calculating the normal - mode eigenvalues of each order; calculating the normal - mode eigen - function values according to the sound - source and receiving depths; A sound - field superposition and synthesis module, used to superpose and synthesize the sound field using the normal - mode eigenvalues and normal - mode eigen - function values; and A sound - propagation loss calculation module, used to calculate the sound - field propagation loss in the convergence zone using the synthesized sound field.

9. The deep-sea convergence zone characteristic prediction system based on the normal mode theory according to claim 8, characterized in that The system further includes: A module for predicting the characteristics of the sound field in the convergence zone, used to read the position, width, and intensity characteristic information of the convergence zone according to the sound - field propagation loss distribution graph.

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