Method for quickly calculating medium-high frequency sound field in ocean waveguide based on image source method

Abstract

The invention relates to the technical field of carrying out modeling calculation on a high-frequency sound field in an ocean waveguide environment by utilizing an image source method, in particular to a rapid calculation method for a high-frequency sound field in an ocean waveguide based on the image source method. The method solves the technical problem that in the prior art, an accurate and reliable rapid calculation method for the ocean waveguide medium-high frequency sound field under the scene of considering the piston sound source radiation diffraction beam characteristic is lacked, and specifically comprises the steps that a high-frequency sound field solution in a free field can be constructed into a Rayleigh integral, and a coordinate system is established based on setting of a rectangular piston sound source; constructing and forming the Rayleigh integral through a Helmholtz equation; on the basis of an image source method, components of a high-frequency sound field in the ocean waveguide are determined, and a formal solution of each part is given under the condition that waveguide boundary influence factors are considered; a non-paraxial approximate Gaussian beam expansion method is adopted to carry out numerical solution on the formal solution of each part, finally, distribution of a high-frequency sound field in the ocean waveguide is obtained through superposition, and the high-frequency sound field is simplified into a summation form from a Rayleigh integral.

Description

Technical Field

[0001] The present invention relates to the technical field of modeling and calculating high-frequency sound fields in an ocean waveguide environment using an image source method, and in particular to a fast calculation method for high-frequency sound fields in an ocean waveguide based on the image source method. Background Art

[0002] High frequency transducers are widely used. They are not only widely used in some traditional industrial and agricultural technologies, but also have penetrated into high-tech fields such as national defense, biology, medicine, and aerospace.

[0003] High-frequency transducers are also used in fields such as marine target detection due to their high directivity. However, in a complex marine waveguide environment, the propagation law of sound waves will inevitably be affected by the waveguide boundary. Therefore, it is necessary to study the characteristics of high-frequency sound fields in the marine waveguide environment, which will play a positive guiding role in the practical application of underwater high-frequency transducers.

[0004] The sound field radiated by a piston sound source in a free field can be expressed by Rayleigh integral (RI), but the computational time and memory required to solve the Rayleigh integral by direct numerical integration will increase significantly with the increase of frequency and solution area. Among them, the non-paraxial approximate Gaussian beam expansion method proposed by Zhao et al. has higher accuracy in calculating phased high-frequency sound fields (Zhao X, Gang T. Nonparaxial multi-Gaussian beam models and measurement models for phased array transducers [J]. Ultrasonics, 2009, 49 (1): 126-130.).

[0005] The existing research on the sound field radiated by a piston sound source in a waveguide has applied the simple normal wave theory for analysis (Zhang Renhe, Zhu Boxian. Simple normal wave sound field of a directional radiator [J]. Acta Physica Sinica, 1983, (04): 490-496.), but it still needs to introduce the far-field approximation in the derivation process, which will introduce errors in the calculation of the near-field distribution of the sound field. Summary of the invention

[0006] The present invention aims to solve the technical problem in the prior art of lacking a fast calculation method for the high-frequency sound field in an ocean waveguide with accurate and reliable results in the scenario of considering the diffraction beam characteristics of the piston sound source radiation, and provide a fast calculation method for the high-frequency sound field in an ocean waveguide based on the image source method, laying a foundation for the application of high-frequency transducers in actual ocean waveguide environments.

[0007] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0008] A fast calculation method for high-frequency sound field in ocean waveguide based on image source method, comprising:

[0009] Step S1: for a piston sound source, the high-frequency sound field solution in a free field can be constructed as a Rayleigh integral. The specific process is: a coordinate system is established based on the setting of a rectangular piston sound source, and the Rayleigh integral is constructed by the Helmholtz equation;

[0010] Step S2, based on the image source method, determine the components of the high-frequency sound field in the ocean waveguide, and give the formal solution of each part under the consideration of the influence of the waveguide boundary;

[0011] The formal solutions of the various parts include: the high-frequency sound field radiated by the rectangular piston sound source in the free field, the high-frequency sound field radiated by the image source on the upper interface of the waveguide, and the high-frequency sound field radiated by the image source on the lower interface of the waveguide;

[0012] Step S3, using the non-paraxial approximate Gaussian beam expansion method to numerically solve the formal solutions of each part, and finally obtain the distribution of the high-frequency sound field in the ocean waveguide through superposition, and simplify the high-frequency sound field from Rayleigh integral to the sum form.

[0013] Specifically, the piston sound source is set to a rectangular piston sound source, and the length and width of the radiation surface of the rectangular piston sound source are respectively 2l x and 2l y ;

[0014] A rectangular coordinate system O-xyz is established with the center of the rectangular piston sound source as the origin, and the z-axis is perpendicular to the surface of the sound source;

[0015] Assuming that the sound source radiates high-frequency waves with a frequency of f, the boundary condition of the sound source surface is expressed as formula (1)

[0016]

[0017] Where, j is the imaginary unit;

[0018] Among them, v z Indicates the vibration velocity perpendicular to the surface of the sound source;

[0019] in, is the coordinate of a point on the surface of the rectangular piston sound source;

[0020] in, For point The vibration speed at

[0021] Among them, ω = 2πf is the angular frequency of the high-frequency wave; is the site location;

[0022] Among them, e -jωt is the time factor;

[0023] The high-frequency sound field radiated by the rectangular piston sound source The following Helmholtz equation is satisfied, namely equation (2):

[0024]

[0025] Among them, p is the sound pressure, t is the time variable;

[0026] k=ω / c 0 +jα is the wave number of the high frequency wave with frequency f, c 0 is the adiabatic speed of sound at small signal;

[0027] α is the acoustic attenuation coefficient of high-frequency waves with a frequency of f;

[0028] For the rectangular piston sound source, the solution of formula (3) is It can be constructed as Rayleigh integral and expressed as:

[0029]

[0030] Among them, d s is a point on the sound source surface S To the space point The above formula can be used to calculate the sound field radiated by the sound source.

[0031] Specifically, a situation is set considering the horizontal incidence of the beam in the ocean waveguide;

[0032] A coordinate system considering the case of horizontal incident beam in the ocean waveguide is established, in which:

[0033] The xoz plane is the upper interface of the waveguide, and the x'o'z' plane is the lower interface;

[0034] The total depth of the waveguide is D 0 , the rectangular piston sound source is at depth H 0 Department;

[0035] Then in the observation area, the existence of the upper interface and the lower interface, that is, the two interfaces, will make the total high-frequency sound field It consists of three parts and can be expressed as formula (4)

[0036]

[0037] Among them, the first part is the high-frequency sound field radiated by a rectangular piston sound source in a free field;

[0038] Part 2 It is the high-frequency sound field radiated by the image source about the upper interface;

[0039] Part 3 It is the high-frequency sound field radiated by the image source on the lower interface;

[0040] The second part and the third part satisfy the boundary conditions of the sound wave on the reflecting surface;

[0041] By the depth H 0 The high-frequency sound field radiated by the rectangular piston sound source at can be expressed as formula (5):

[0042]

[0043] Among them, d s is a point on the sound source surface S To the space point distance.

[0044] Specifically, the preset is to meet the high-frequency wave At the boundary condition of the upper interface, the depth H 0 The image source of the rectangular piston sound source at the upper interface is located at a depth of -H 0 Department;

[0045] Define R(w) as the plane wave reflection coefficient at frequency w. For any impedance boundary, R(w) depends on the medium parameters and the angle of incidence. The high-frequency sound field radiated by the image source at the upper boundary can be expressed as formula (6):

[0046]

[0047] in, is the image source surface S u On a certain point To the space point The distance, R u (w) is the plane wave reflection coefficient about the upper interface.

[0048] Specifically, the high-frequency sound field radiated by the image source at the lower interface can be expressed as formula (7):

[0049]

[0050] Among them, the depth H 0 The image of the rectangular piston sound source about the lower interface is located at depth 2D 0 -H 0 Department, is the image source surface S d On a certain point To the space point The distance, R d (w) is the plane wave reflection coefficient about the lower interface.

[0051] Specifically, the three components of the high-frequency sound field in the waveguide are:

[0052] Similar form integral decomposition;

[0053] The similar form integral decomposition is obtained by calculating the high-frequency sound field solution of formula (3), and then all components in formula (4) are calculated based on the influence of the boundary. The specific process is:

[0054] Step S101, firstly decompose the surface vibration velocity of the piston sound source into formula (8):

[0055]

[0056] Among them, V 0 is the amplitude, A m , B m and A n , B m is the complex Gaussian coefficient;

[0057] Step S102, for distance d s The non-paraxial approximation process is expressed as formula (9):

[0058]

[0059] in,

[0060] Step S103, to simplify the expression, the following dimensionless variables are introduced, expressed as formula (10):

[0061]

[0062] In step S104, the high-frequency sound field p under the non-paraxial approximation can be obtained by derivation, which is expressed as formula (11):

[0063]

[0064] Among them, the function ζ, σ and γ are independent variables.

[0065] The present invention has the following beneficial effects:

[0066] First, the image source method is used to model the high-frequency acoustic field in the ocean waveguide, and the non-paraxial approximate Gaussian beam expansion method with higher accuracy is used for numerical calculation, so as to obtain the high-frequency acoustic field solution in the ocean waveguide more efficiently.

[0067] Secondly, the characteristics of the diffraction beam radiated by the actual piston sound source are taken into account, which has strong applicability;

[0068] Thirdly, the calculation process is in the form of summation, the result is accurate and reliable, and the calculation method is simple and easy. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0070] Figure 1 Flowchart of calculation method;

[0071] Figure 2 It is a schematic diagram of the sound field radiated by a rectangular piston sound source in a free field of the present invention;

[0072] Figure 3 It is a geometrical schematic diagram of the sound field radiated by a rectangular piston sound source in the ocean waveguide of the present invention;

[0073] Figure 4 Sound pressure level distribution of high frequency sound field radiated by rectangular piston sound source in free field;

[0074] Figure 5 The phase distribution of the high-frequency sound field radiated by a rectangular piston sound source in a free field;

[0075] Figure 6 Sound pressure level distribution of high frequency sound field radiated by rectangular piston sound source in ocean waveguide;

[0076] Figure 7 The phase distribution of the high-frequency sound field radiated by a rectangular piston sound source in an ocean waveguide;

[0077] Figure 8 High-frequency sound wave distribution on the acoustic axis in comparison between free field and ocean waveguide;

[0078] Fig. 9 Comparison of high-frequency sound field distribution in free field and ocean waveguide. High-frequency sound wave directivity at a distance of 30m. DETAILED DESCRIPTION

[0079] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention; it should be noted that in this application, for the convenience of description, the "left side" in the current view is the "first end", the "right side" is the "second end", the "upper side" is the "first end", and the "lower side" is the "second end". The purpose of such description is to clearly express the technical solution, and it should not be understood as an improper limitation on the technical solution of this application.

[0080] The present invention relates to the technical field of modeling and calculating high-frequency sound fields in ocean waveguide environments using an image source method, and specifically relates to

[0081] A fast calculation method for high-frequency sound fields in ocean waveguides based on the image source method. The image source method is used to model the high-frequency sound field in the ocean waveguide environment, and the non-paraxial approximate Gaussian beam expansion method is used to solve the high-frequency sound field in the free field. Then, the influence of the waveguide boundary conditions is considered, and finally the distribution of the high-frequency sound field in the waveguide is obtained. This method takes into account the characteristics of the diffraction beam radiated by the piston sound source, has strong applicability, accurate and reliable calculation results, and a simple and easy calculation method.

[0082] Based on the previous theories, the present invention proposes a method for calculating the high-frequency sound field in the ocean waveguide based on the image source method. First, the components of the sound field are analyzed, and then the sound field is numerically solved using the non-paraxial approximate Gaussian beam expansion method with high accuracy, which is conducive to further research on the distribution characteristics of the high-frequency sound field in the ocean waveguide. The method is simple to calculate and the calculation results are accurate and reliable.

[0083] A fast calculation method for high-frequency sound field in ocean waveguide based on image source method, comprising:

[0084] Step S1: for a piston sound source, the high-frequency sound field solution in a free field can be constructed as a Rayleigh integral. The specific process is: a coordinate system is established based on the setting of a rectangular piston sound source, and the Rayleigh integral is constructed by the Helmholtz equation;

[0085] Step S2, based on the image source method, determine the components of the high-frequency sound field in the ocean waveguide, and give the formal solution of each part under the consideration of the influence of the waveguide boundary;

[0086] The formal solutions of the various parts include: the high-frequency sound field radiated by the rectangular piston sound source in the free field, the high-frequency sound field radiated by the image source on the upper interface of the waveguide, and the high-frequency sound field radiated by the image source on the lower interface of the waveguide;

[0087] Step S3, using the non-paraxial approximate Gaussian beam expansion method to numerically solve the formal solutions of each part, and finally obtain the distribution of the high-frequency sound field in the ocean waveguide through superposition, and simplify the high-frequency sound field from Rayleigh integral to the sum form.

[0088] like Figure 2 As shown, the piston sound source is set to a rectangular piston sound source, and the length and width of the radiation surface of the rectangular piston sound source are respectively 2l x and 2l y ;

[0089] A rectangular coordinate system O-xyz is established with the center of the rectangular piston sound source as the origin, and the z-axis is perpendicular to the surface of the sound source;

[0090] Assuming that the sound source radiates high-frequency waves with a frequency of f, the boundary condition of the sound source surface is expressed as formula (1)

[0091]

[0092] Where, j is the imaginary unit;

[0093] Among them, v z Indicates the vibration velocity perpendicular to the surface of the sound source;

[0094] in, is the coordinate of a point on the surface of the rectangular piston sound source;

[0095] in, For point The vibration speed at

[0096] Among them, ω = 2πf is the angular frequency of the high-frequency wave; is the site location;

[0097] Among them, e -jωt is the time factor.

[0098] The high-frequency sound field radiated by the rectangular piston sound source The following Helmholtz equation is satisfied, namely equation (2):

[0099]

[0100] Among them, p is the sound pressure, t is the time variable;

[0101] k=ω / c 0 +jα is the wave number of the high frequency wave with frequency f, c 0 is the adiabatic speed of sound at small signal;

[0102] α is the acoustic attenuation coefficient of high-frequency waves with a frequency of f;

[0103] For the rectangular piston sound source, the solution of formula (3) is It can be constructed as Rayleigh integral and expressed as:

[0104]

[0105] Among them, d s is a point on the sound source surface S To the space point The above formula can be used to calculate the sound field radiated by the sound source.

[0106] like Figure 3 As shown, a situation is assumed in which the beam is horizontally incident in the ocean waveguide;

[0107] A coordinate system considering the case of horizontal incident beam in the ocean waveguide is established, in which:

[0108] The xoz plane is the upper interface of the waveguide, and the x'o'z' plane is the lower interface;

[0109] The total depth of the waveguide is D 0 , the rectangular piston sound source is at depth H 0 Department;

[0110] Then in the observation area, the existence of the upper interface and the lower interface, that is, the two interfaces, will make the total high-frequency sound field It consists of three parts and can be expressed as formula (4)

[0111]

[0112] Among them, the first part is the high-frequency sound field radiated by a rectangular piston sound source in a free field;

[0113] Part 2 It is the high-frequency sound field radiated by the image source about the upper interface;

[0114] Part 3 It is the high-frequency sound field radiated by the image source on the lower interface;

[0115] The second part and the third part satisfy the boundary conditions of the sound wave on the reflecting surface;

[0116] By the depth H 0 The high-frequency sound field radiated by the rectangular piston sound source at can be expressed as formula (5):

[0117]

[0118] Among them, d s is a point on the sound source surface S To the space point distance.

[0119] Preset to meet high frequency wave At the boundary condition of the upper interface, the depth H 0 The image source of the rectangular piston sound source at the upper interface is located at a depth of -H 0 Department;

[0120] Define R(w) as the plane wave reflection coefficient at frequency w. For any impedance boundary, R(w) depends on the medium parameters and the angle of incidence. The high-frequency sound field radiated by the image source at the upper boundary can be expressed as formula (6):

[0121]

[0122] in, is the image source surface S u On a certain point To the space point The distance, R u (w) is the plane wave reflection coefficient about the upper interface.

[0123] The high-frequency sound field radiated by the image source at the lower interface can be expressed as formula (7):

[0124]

[0125] Among them, the depth H 0 The image of the rectangular piston sound source about the lower interface is located at depth 2D 0 -H 0 Department, is the image source surface S d On a certain point To the space point The distance, R d (w) is the plane wave reflection coefficient about the lower interface.

[0126] The three components of the high frequency sound field in the waveguide are:

[0127] Similar form integral decomposition;

[0128] The similar form integral decomposition is obtained by calculating the high-frequency sound field solution of formula (3), and then all components in formula (4) are calculated based on the influence of the boundary. The specific process is:

[0129] Step S101, firstly decompose the surface vibration velocity of the piston sound source into formula (8):

[0130]

[0131] Among them, V 0 is the amplitude, A m , B m and A n , B m is the complex Gaussian coefficient;

[0132] Step S102, for distance d s The non-paraxial approximation process is expressed as formula (9):

[0133]

[0134] in,

[0135] Step S103, to simplify the expression, the following dimensionless variables are introduced, expressed as formula (10):

[0136]

[0137] In step S104, the high-frequency sound field p under the non-paraxial approximation can be obtained by derivation, which is expressed as formula (11):

[0138]

[0139] Among them, the function ζ, σ and γ are independent variables.

[0140] Calculation Example

[0141] The example parameter settings are as follows: Consider the ocean waveguide boundary as an ideal boundary, and the seawater sound speed c 1 =1482m / s, seawater density ρ 1 =998kg / m 3 , the attenuation is calculated according to the empirical formula of seawater absorption. The reflection coefficient of the upper interface of the ocean waveguide is -1, and the reflection coefficient of the lower interface is 1. The surface sound pressure of the rectangular piston sound source is 100kPa, 2l x =0.072m,2l y =0.10m. The frequency of the radiated high frequency wave is f=40kHz;

[0142] As attached Figure 3 As shown, in the spatial rectangular coordinate system O-xyz, the coordinates of the rectangular piston sound source are (0m, 30m, 0m), and the sound field observation space range is: x∈[-50m, 50m], y∈[0m, 100m], z∈[0m, 100m]. The implementation of the fast calculation method of the high-frequency sound field in the ocean waveguide based on the image source method can be based on a computing platform, and the computing platform configuration includes AMD Ryzen 77840HS with Radeon 780M Graphics 3.80GHz and 32GB of machine RAM.

[0143] In the three-dimensional sound field results obtained by simulation, the yoz section is taken for observation.

[0144] Figure 4 The sound pressure level distribution of the high-frequency sound field radiated by a rectangular piston sound source in a free field is given.

[0145] Figure 5 The phase distribution of the high-frequency sound field radiated by a rectangular piston sound source in a free field is given.

[0146] Figure 6 The sound pressure level distribution of the high-frequency sound field radiated by a rectangular piston sound source in an ocean waveguide is given.

[0147] Figure 7 The phase distribution of high-frequency acoustic field radiated by a rectangular piston sound source in an ocean waveguide is given.

[0148] Figure 8 A comparison of the high-frequency sound wave distribution on the acoustic axis of the sound source in the free field and in the ocean waveguide is given.

[0149] Fig. 9 A comparison of the directivity of high-frequency sound waves in the free field and in the ocean waveguide at a distance of 30 m from the sound source is given.

[0150] It can be seen from the embodiments that the high-frequency acoustic field characteristics in the ocean waveguide environment are significantly different from those in the free field, because the waveguide boundary will act on the high-frequency beam, thereby affecting the distribution of the high-frequency acoustic field. This method can quickly obtain the high-frequency wave field solution in the ocean waveguide in combination with a high-precision numerical method, taking into account the diffraction characteristic beam radiated by the actual sound source. It has a wide range of applications and lays the foundation for the calculation of high-frequency acoustic fields in more complex ocean waveguides in the future. It has positive guiding significance for the practical application of high-frequency transducers in actual ocean waveguide environments.

[0151] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the invention.

Claims

1. A fast calculation method for high-frequency sound field in ocean waveguide based on image source method, characterized in that: include: Step S1: for a piston sound source, the high-frequency sound field solution in a free field can be constructed as a Rayleigh integral. The specific process is: a coordinate system is established based on the setting of a rectangular piston sound source, and the Rayleigh integral is constructed by the Helmholtz equation; Step S2, based on the image source method, determine the components of the high-frequency sound field in the ocean waveguide, and give the formal solution of each part under the consideration of the influence of the waveguide boundary; The formal solutions of the various parts include: the high-frequency sound field radiated by the rectangular piston sound source in the free field, the high-frequency sound field radiated by the image source on the upper interface of the waveguide, and the high-frequency sound field radiated by the image source on the lower interface of the waveguide; Step S3, using the non-paraxial approximate Gaussian beam expansion method to numerically solve the formal solutions of each part, and finally obtain the distribution of the high-frequency sound field in the ocean waveguide through superposition, and simplify the high-frequency sound field from Rayleigh integral to the sum form.

2. The method for rapidly calculating the high-frequency sound field in an ocean waveguide based on the image source method according to claim 1, characterized in that: The piston sound source is set as a rectangular piston sound source, and the length and width of the radiation surface of the rectangular piston sound source are 2l respectively. x and 2l y ; A rectangular coordinate system O-xyz is established with the center of the rectangular piston sound source as the origin, and the z-axis is perpendicular to the surface of the sound source; Assuming that the sound source radiates high-frequency waves with a frequency of f, the boundary condition of the sound source surface is expressed as formula (1) Where, j is the imaginary unit; Among them, v z Indicates the vibration velocity perpendicular to the surface of the sound source; in, is the coordinate of a point on the surface of the rectangular piston sound source; in, For point The vibration speed at Among them, ω = 2πf is the angular frequency of the high-frequency wave; is the site location; Among them, e -jωt is the time factor; The high-frequency sound field radiated by the rectangular piston sound source The following Helmholtz equation is satisfied, namely equation (2): Among them, p is the sound pressure, t is the time variable; k = ω / c0 + jα is the wave number of the high-frequency wave with frequency f, c0 is the adiabatic sound speed under small signal; α is the acoustic attenuation coefficient of high-frequency waves with a frequency of f; For the rectangular piston sound source, the solution of formula (3) is It can be constructed as Rayleigh integral and expressed as: Among them, d s is a point on the sound source surface S To the space point The above formula can be used to calculate the sound field radiated by the sound source.

3. The method for rapidly calculating the high-frequency sound field in an ocean waveguide based on the image source method as claimed in claim 2, characterized in that: A situation is set up considering horizontal incidence of the beam in the ocean waveguide; A coordinate system considering the case of horizontal incident beam in the ocean waveguide is established, in which: The xoz plane is the upper interface of the waveguide, and the x'o'z' plane is the lower interface; The total depth of the waveguide is D0, and the rectangular piston sound source is at a depth of H0; Then in the observation area, the existence of the upper interface and the lower interface, that is, the two interfaces, will make the total high-frequency sound field It consists of three parts and can be expressed as formula (4) Among them, the first part is the high-frequency sound field radiated by a rectangular piston sound source in a free field; Part 2 It is the high-frequency sound field radiated by the image source about the upper interface; Part 3 It is the high-frequency sound field radiated by the image source on the lower interface; The second part and the third part satisfy the boundary conditions of the sound wave on the reflecting surface; The high-frequency sound field radiated by the rectangular piston sound source located at the depth H0 can be expressed as formula (5): Among them, d s is a point on the sound source surface S To the space point distance.

4. The method for rapidly calculating the high-frequency sound field in an ocean waveguide based on the image source method as claimed in claim 3, characterized in that: Preset to meet high frequency wave Under the boundary condition of the upper interface, the image source of the rectangular piston sound source at the depth H0 with respect to the upper interface is located at the depth -H0; Define R(w) as the plane wave reflection coefficient at frequency w. For any impedance boundary, R(w) depends on the medium parameters and the angle of incidence. The high-frequency sound field radiated by the image source at the upper boundary can be expressed as formula (6): Among them, d su is the image source surface S u On a certain point To the space point The distance, R u (w) is the plane wave reflection coefficient about the upper interface.

5. The method for rapidly calculating the high-frequency sound field in an ocean waveguide based on the image source method as claimed in claim 4, characterized in that: The high-frequency sound field radiated by the image source at the lower interface can be expressed as formula (7): Among them, the image of the rectangular piston sound source at depth H0 about the lower interface is located at the depth 2D0-H0, is the image source surface S d On a certain point To the space point The distance, R d (w) is the plane wave reflection coefficient about the lower interface.

6. The method for rapidly calculating the high-frequency sound field in an ocean waveguide based on the image source method as claimed in claim 5, characterized in that: The three components of the high frequency sound field in the waveguide are: Similar form integral decomposition; The similar form integral decomposition is obtained by calculating the high-frequency sound field solution of formula (3), and then all components in formula (4) are calculated based on the influence of the boundary. The specific process is: Step S101, firstly decompose the surface vibration velocity of the piston sound source into formula (8): Where V0 is the amplitude, A m , B m and A n , B m is the complex Gaussian coefficient; Step S102, for distance d s The non-paraxial approximation process is expressed as formula (9): in, Step S103, to simplify the expression, the following dimensionless variables are introduced, expressed as formula (10): In step S104, the high-frequency sound field p under the non-paraxial approximation can be obtained by derivation, which is expressed as formula (11): Among them, the function ζ, σ and γ are independent variables.

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