An underwater acoustic field calculation method and system based on wave number integration theory

Abstract

The application discloses a kind of underwater sound field calculation methods based on wave number integral theory, comprising the following steps: step S1, wave equation is solved by wave number integral theory, and the displacement potential function that needs to be solved is obtained by decomposition;The displacement potential function contains depth Green function;Step S2, based on the linear layered modeling of sound velocity profile, the underwater waveguide structure is divided into uniform layer, multiple negative gradient layer, multiple positive gradient layer and uniform liquid half-space seabed from top to bottom;Step S3, the numerical value of depth Green function in linear layered waveguide environment is solved;Step S4, according to depth Green function, the sound field displacement potential is calculated;Step S5, according to the sound field displacement potential, the propagation loss of underwater sound field is calculated.The present application can process and realize the efficient and stable solution of depth Green function in the waveguide with obvious linear characteristics of sound velocity profile, and the strategy of FFP+ is adopted to calculate the sound field potential function, so as to realize the high-precision and high-efficiency calculation simulation of underwater sound field.

Description

Technical Field

[0001] This invention relates to the field of underwater sound field calculation technology, and in particular to an underwater sound field calculation method and system based on wavenumber integral theory. Background Technology

[0002] Underwater acoustic experiments are highly specialized and complex systems engineering projects, facing challenges and difficulties in many aspects. Among these, the high cost is a significant obstacle limiting the conduct of underwater acoustic experiments. First, specialized instruments and equipment are required, and the procurement and maintenance of these instruments alone place a heavy burden on the experimental budget. Second, conducting experiments at sea requires renting specialized research vessels and a well-trained professional team for operation and data collection. Finally, a specialized team is also needed for data processing and analysis. Considering equipment, facilities, and manpower, underwater acoustic experiments are extremely costly. Therefore, the field of underwater acoustics typically conducts preliminary research on underwater acoustic physics and signal processing using numerical simulations of underwater sound fields.

[0003] Numerical calculation of underwater sound fields is a core foundation for underwater target detection, localization, and marine environmental parameter inversion. After decades of development, sound field modeling has formed a relatively mature theoretical system, mainly including: normal mode models, ray models, wavenumber integral models, parabolic equation models, finite difference models, and finite element models. Existing models, due to their different theoretical foundations and solution strategies, each have their own advantages in applicable scenarios and computational performance, while also possessing corresponding limitations.

[0004] Traditional ray theory, based on high-frequency approximations, has clear physical meaning, but its accuracy is limited in low-frequency problems and complex regions such as shadow zones and caustics. Normal mode methods perform excellently in far-field calculations and are one of the classic methods for sound field modeling. However, this method may become numerically unstable when eigenvalues ​​approach the secant and often neglects leakage modes, affecting near-field accuracy. Parabolic equation methods are widely used to handle waveguide problems that vary with distance, but their computational efficiency is relatively low when dealing with high-frequency, ocean-deep, horizontally invariant waveguide problems. While the finite element method can accurately handle complex media and boundaries, its computational resource requirements increase dramatically with the problem scale, making it difficult to handle large-scale underwater sound propagation problems.

[0005] The wavenumber integral method was first introduced to the field of underwater acoustics by Pekeris in his paper "Theory of propagation of explosive sound in shallow water," and subsequently, scholars both domestically and internationally have conducted extensive research on this method. Among them, SAFARI, OASES, and SCOOTER are currently the most widely used wavenumber integral models. Compared to the normal mode method, which has a similar mathematical foundation, it solves the sound field through direct numerical integration, offering advantages in near-field calculation and numerical stability. DiNapoli et al. proposed the efficient Fast Field Program (FFP) in their paper "Theoretical and numerical Green's functionfield solution in a plane multilayered medium" to calculate the Green's function of the sound field. Building on this, Liu Wei et al. developed the FFP+ and FFP++ models in their paper "Improved Fast Field Model for Marine Acoustics to Enhance Near-Field Accuracy," significantly improving near-field accuracy while maintaining efficiency by processing the Bessel function in different regions. In their papers "A Wavenumber Integration Method for Stable Calculation of Sound Field in Pekeris Waveguide" and "A Wavenumber Integration Method for Stable Calculation of Sound Field in Shallow Sea Environment with Negative Gradient Layer," Luo Wenyu et al. proposed a series of stable wavenumber integration algorithms that provide effective solutions for sound field calculation in specific waveguide environments. However, the depth Green's function represented by these methods is at risk of numerical overflow under positive gradient sound velocity profile conditions, which limits its applicability in a wider range of scenarios. Summary of the Invention

[0006] This invention aims to address the limitations and low computational efficiency of traditional wavenumber integration methods in numerical calculations of underwater sound fields in marine waveguide scenarios, and to provide an unconditionally stable, accurate, and efficient method and system for calculating underwater sound fields.

[0007] To solve the above-mentioned technical problems, this application provides a method for calculating underwater acoustic fields based on wavenumber integral theory, characterized by the following steps: Step S1: Solve the wave equation using wavenumber integral theory to obtain the displacement potential function to be solved; the displacement potential function includes the depth Green's function.

[0008] Step S2: Based on linear layered modeling of the sound velocity profile, the underwater waveguide structure is divided from top to bottom into a uniform layer, multiple negative gradient layers, multiple positive gradient layers, and a uniform liquid half-space seabed. Step S3: Solve for the numerical value of the depth Green's function in a linear layered waveguide environment; Step S4: Calculate the acoustic field displacement potential based on the depth Green's function; Step S5: Calculate the propagation loss of the underwater sound field based on the sound field displacement potential.

[0009] As one aspect of the above method, characterized in that, in step S1, the point sound source has a depth of [missing information] in cylindrical coordinates. At that time, displacement potential The Helmholtz equation is: (1) in: For the intensity of the sound source, Wavenumber; using Hankel transform: (2) (3) in For horizontal wavenumber, Given a zero-order Bessel function, we obtain the wave equation with distance and depth separation: (4) in ; The depth Green's function is obtained by solving the wave equation based on the separation of distance and depth. Then, substitute it into equation (3) to obtain the acoustic field displacement potential in the spatial domain.

[0010] As another aspect of the above method, the characteristic is that, in step S2, the sound velocity-depth relationship in each water layer can be uniformly expressed as: (5) Where c j (z) represents the speed of sound at depth z of the j-th layer, a j For the j-th layer Linear gradient in a linear layer, b j The constant for the j-th layer is calculated based on the depth and sound speed.

[0011] As another embodiment of the above method, the feature is that step S3 specifically includes the following steps: Step S3-1, the steps for solving the numerically stable depth Green's function under the negative gradient condition are as follows: In equation (4) for: (6) By introducing variable substitution: (7) Will Substituting into equation (4) yields information about The equation: (8) From equation (8), the homogeneous solution of the depth Green's function that is numerically stable under the negative gradient condition is: (9) in , For the Airy function, For the normalized Airy function, , The subscripts u and d represent the values ​​of the variable at the upper and lower boundaries of the linear layer, respectively; Step S3-2, the homogeneous solution of the depth Green's function under the positive gradient condition is expressed as: (10) Among them, When, the exponential factor in equation (10) and All are negative values; Step S3-3: Process the sound velocity distribution of the uniform layer to maintain a set difference in sound velocity between the upper and lower interfaces, so that the uniform layer is regarded as a positive gradient layer with minimal gradient. Step S3-4, calculate the depth Green's function for the uniform liquid half-space seabed as follows: use Expression (8) in the first Numerically stable homogeneous solutions in layered seawater, using The particular solution of expression (8) in the second layer of seawater where the sound source is located is then... Its first derivative is: (11) (12) in: (13) (14) (15) special solution Its first derivative is: (16) (17) If the first If the seawater layer does not contain a sound source, then the unconditionally stable depth Green's function and its first derivative can be expressed as: (18) If the first Seawater contains sound sources, such as Figure 2 The sound source shown is located in the second layer. Therefore, the unconditionally stable depth Green's function and its first derivative can be expressed as: (19) The Green's function for the depth of the seabed is: (20).

[0012] As another aspect of the above method, the water body is characterized by using... The linear sound velocity layer is approximated, and the layer where the sound source is located is denoted as the first. When layered, in Establish under the condition of boundary Several equations form a matrix equation. Its global coefficient matrix Represented as: (twenty four) column vector for: (25) T represents the matrix transpose. For the right-hand column vector: (26) in: , , , .

[0013] As another approach to the above method, the feature is that a sparse coefficient matrix linear equation solver is used for efficient solution to obtain the depth Green's function of each layer.

[0014] As a further embodiment of the above method, the characteristic is that, in step S4, the depth Green's function is substituted into equation (3) to obtain the acoustic field displacement potential, specifically by using the complex contour integral method and introducing the complex wave number: (27) in , , , , For the integration interval, Let be the number of discrete points of the horizontal wavenumber; the displacement potential of the sound field is expressed as: (28).

[0015] As a further embodiment of the above method, the calculation of the acoustic field displacement potential in step S4 is simplified to: (29).

[0016] As a further embodiment of the above method, the characteristic is that the propagation loss in the underwater sound field is calculated in step S5 as follows: (30) The reference sound pressure is taken in the formula. ,in denoted as the medium wavenumber at the sound source.

[0017] To achieve the above objectives, this application also provides an underwater acoustic field calculation system based on wavenumber integral theory, comprising: Memory, used to store data and computer programs; A processor is used to execute the computer program to implement the steps of the underwater acoustic field calculation method based on wavenumber integral theory described above.

[0018] Compared with the prior art, the present invention has significant technical effects, including the following: Traditional acoustic field calculation models, due to differences in their theoretical foundations and solution strategies, each have their own advantages in terms of applicable scenarios and computational performance, but also have corresponding limitations. Acoustic field calculation methods based on the wavenumber integral method, which solve the acoustic field through direct numerical integration, have advantages in near-field calculations and numerical stability; however, previously developed wavenumber integral methods are generally only applicable to acoustic field simulations in specific waveguide environments (such as Pekeris waveguides and negative gradient waveguides), and there is a risk of numerical overflow under positive gradient sound velocity profile conditions. This invention can handle and achieve efficient and stable solutions for the depth Green's function in waveguides with obvious linear characteristics of sound velocity profiles (such as waveguides containing positive gradient water layers, negative gradient water layers, homogeneous water layers, and homogeneous liquid half-space seabed waveguide environments), and simultaneously employs the FFP+ method strategy to calculate the acoustic field potential function, thereby achieving high-precision and high-efficiency computational simulation of underwater acoustic fields. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the underwater acoustic field calculation method based on the wavenumber integral method in a specific implementation. Figure 2 For specific implementation methods Schematic diagram of a linear water layer; Figure 3 This is a schematic diagram of the Munk sound velocity profile in a specific implementation method; Figure 4 A comparison of propagation loss as a function of distance and depth when the sound source frequency is 50Hz. Figure 5 A comparison of the propagation loss at the sound source depth as a function of distance for the four models at different frequencies; Figure 6A comparison of the calculation time versus frequency for four models in the Munk waveguide environment. Detailed Implementation

[0020] This invention relates to the field of underwater acoustic field calculation technology, and in particular to a method and system for calculating underwater acoustic fields based on wavenumber integral theory. This method achieves a unified solution for the acoustic field of a horizontally invariant waveguide by introducing a minimal sound velocity gradient in a homogeneous layer and analytically constructing an unconditionally stable active acoustic field depth Green's function based on the Airy function. The core steps of this invention include the following parts: First, the wave equation is solved using wavenumber integral theory, decomposing it to obtain the displacement potential function that needs to be solved. This is the foundation of this method, providing the solution approach and the target quantity for subsequent numerical solution steps.

[0021] Secondly, linear layered modeling of the sound velocity profile is performed. Under the condition of a uniform liquid half-space on the seabed, a minimal sound velocity gradient is introduced for the isovelocity layer, and a reasonable normalization strategy is adopted. This overcomes the limitations of existing algorithms for negative gradient waveguides and achieves unified modeling for general horizontally invariant waveguides. Based on the analytical construction of the Airy function, it exhibits unconditional stability in numerical calculations while maintaining the high accuracy of the wavenumber integral method for unconditionally stable solution of the depth Green's function. This step is the innovation of this invention. Through systematic expansion and improvement, it can uniformly handle waveguide acoustic propagation problems including positive gradient water layers, negative gradient water layers, and uniform water layers, obtaining an unconditionally stable depth Green's function in water.

[0022] Then, considering the contribution of the internal traveling wave term, the FFP+ method is adopted to calculate the acoustic field displacement potential, which balances both calculation speed and accuracy.

[0023] Finally, the obtained acoustic field displacement potential function is substituted into the calculation of underwater acoustic propagation loss to obtain the acoustic propagation loss distribution of the underwater acoustic field. This is the ultimate goal of this invention. Through this step, a unified and accurate acoustic field distribution for a general horizontal invariant waveguide can be obtained, effectively improving the efficiency and accuracy of acoustic field numerical calculations based on the wavenumber integration method.

[0024] In summary, this invention proposes and implements an unconditionally stable, accurate, and efficient underwater sound field calculation method based on the wavenumber integral method. This method uses several linearly varying layers to approximate the sound velocity profile that varies with depth, replacing the uniform layering approximation commonly used in traditional methods. This significantly improves computational efficiency while retaining the high accuracy characteristic unique to the wavenumber integral method. By introducing a reasonable normalization method to represent the ascending and descending waves in each layer, the numerical stability of the depth Green's function is ensured. The proposed wavenumber integral method based on the linear layering strategy has advantages such as good stability, high efficiency, and ease of programming implementation. It can not only provide a reference solution for single-frequency sound field calculations but also has important reference value for the rapid simulation of broadband deep-sea sound fields.

[0025] For the general problem of sound propagation in horizontally invariant waveguides, including positive gradient water layers, negative gradient water layers, uniform water layers, and seabeds that are uniform liquid half-spaces, this invention, within the framework of traditional wavenumber integral theory, further develops a more efficient linear layered wavenumber integral model WI2 based on the classic uniform layered wavenumber integral model WI1. The unconditionally stable depth Green's function under the condition of a positive gradient sound velocity profile is theoretically analyzed and derived, thus achieving efficient and stable solutions for the depth Green's function in waveguides with obvious linear characteristics of sound velocity profiles. This invention achieves a unified solution for the sound field of horizontally invariant waveguides by introducing a minimal sound velocity gradient in the uniform layer and analytically constructing an unconditionally stable active sound field depth Green's function based on the Airy function. However, underwater sound field calculation is a computationally intensive task, especially for high-precision solutions to wave equations, which places significant demands on computational resources. To address this problem, high-performance computing and optimization algorithms are typically used to improve computational speed. With the development of computer hardware, high-performance computers can now be used to handle large-scale computational tasks. When computational resources are limited, optimizing the sound field solution algorithm becomes the fundamental way to reduce the computational load required for numerical simulation of the sound field. In terms of sound field calculation, this invention adopts the FFP+ model method to calculate the sound field displacement potential, which further improves the overall computational efficiency while ensuring near-field accuracy.

[0026] The core component of this invention's system is an underwater acoustic field numerical simulation hardware platform. This platform includes a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit). The CPU, as the system's main computing core, handles most of the computational tasks, while the GPU is responsible for graphics processing and highly parallel computational tasks. The combination of these two components enables the system to process large amounts of data simultaneously, further improving the efficiency of numerical computation. The collaborative work of the CPU and GPU fully leverages their respective advantages, resulting in a significant improvement in processing speed while ensuring the accuracy of the numerical simulation.

[0027] The technical solutions provided in this application are further illustrated below with reference to the embodiments.

[0028] like Figure 1 As shown in the figure, a specific implementation method for calculating underwater acoustic fields based on wavenumber integral theory includes the following steps: Step S1: Solve the wave equation using wavenumber integral theory to obtain the displacement potential function to be solved; this displacement potential function includes the depth Green's function.

[0029] The depth of the point sound source in cylindrical coordinates is At that time, displacement potential The Helmholtz equation is: (1) in: For the intensity of the sound source, Let the wave number be denoted by . Using the Hankel transform: (2) (3) in For horizontal wavenumber, Given a zero-order Bessel function, the wave equation with distance and depth separation can be obtained: (4) in The depth Green's function is obtained by solving this equation. Then, by substituting into equation (3), the acoustic field displacement potential in the spatial domain can be obtained. Therefore, the key to the numerical solution of the acoustic field using wavenumber integrals lies in solving the depth Green's function.

[0030] This invention systematically extends and improves the wavenumber integral method for solving the acoustic field in linear marine waveguide environments with multiple sound velocity gradients, enabling it to uniformly handle waveguide acoustic propagation problems involving positive gradient water layers, negative gradient water layers, and homogeneous water layers. Next, a linear layered modeling method based on sound velocity profiles is first employed, followed by an unconditionally stable solution for the depth Green's function.

[0031] Step S2, linear layered modeling based on sound velocity profile; In practical applications, the waveguide structure will be layered according to the data acquisition conditions and the accuracy requirements of the acoustic field simulation. This layering includes a uniform layer, multiple negative gradient layers, multiple positive gradient layers, and a seabed layer, which will be detailed later. Considering... Figure 2 Under the point source conditions shown Linear waveguide problem. This waveguide structure comprises a uniform layer 1 (first layer), a negative gradient layer 2 (second layer), a positive gradient layer 3 (third layer), and a uniform liquid half-space seabed 4 (fourth layer). These four layers represent a typical layered structure. The sound source can be placed in any location; the example in the diagram places it within the second layer. Figure 2 The coordinate z in the second layer s To maintain consistency in the calculation of the depth Green's function, the sound velocity distribution of the uniform layer was appropriately processed to ensure that the sound velocities at the upper and lower interfaces maintained a set small difference, for example... Through this process, the homogeneous layer can be considered as a positive gradient layer with minimal gradient, and the sound velocity-depth relationship in each water layer can be uniformly expressed as: (5) Where c j (z) represents the speed of sound at depth z of the j-th layer, a j For the j-th layer Linear gradient in a linear layer, b j The constant for the j-th layer is calculated based on depth and sound speed. Step S3: Solve for the theoretical numerical value of the depth Green's function in a linear layered ocean waveguide environment; Then in equation (4) for: (6) By introducing variable substitution: (7) Will Substituting into equation (4) yields information about The equation: (8) Existing methods have derived the numerically stable depth Green's function homogeneous solution of equation (8) under negative gradient conditions as follows: (9) in , For the Airy function, For the normalized Airy function, , The subscripts u and d represent the values ​​of the variable at the upper and lower boundaries of the linear layer, respectively.

[0032] It exhibits unconditional stability under negative gradient water layer conditions; however, under positive gradient sound velocity profile conditions, due to the linear layer slope... As can be seen from equation (7), equation (9) contains an exponential term. The corresponding index factor and Under these conditions, all values ​​are positive. When the sound source frequency is high, the exponential term increases rapidly, leading to numerical overflow when used to calculate positive gradient problems. Therefore, this method expresses the homogeneous solution of the depth Green's function under positive gradient conditions as: (10) exist When, the exponential factor in equation (10) and All values ​​are negative, thus ensuring the numerical stability of the exponential function across the entire computational domain. Therefore, the deep Green's function in this form is numerically unconditionally stable.

[0033] use Expression (8) in the first Numerically stable homogeneous solutions in layered seawater, using The particular solution of expression (8) in the second layer of seawater where the sound source is located is then... Its first derivative is: (11) (12) in: (13) (14) (15) special solution Its first derivative is: (16) (17) If the first If the seawater layer does not contain a sound source, then the unconditionally stable depth Green's function and its first derivative can be expressed as: (18) If the first Seawater contains sound sources, such as Figure 2 The sound source shown is located in the second layer. Therefore, the unconditionally stable depth Green's function and its first derivative can be expressed as: (19) The Green's function for the depth of the seabed is: (20) for Figure 2 The sound field calculation problem shown differs from the uniform stratification method. Using a linear approximation, the seawater only needs to be divided into three layers, and the matrix equation can be obtained using seven boundary conditions. Global coefficient matrix for: (twenty one) in: , , , , , , For the current example . For unknown column vectors: (twenty two) For column vectors: (twenty three) in: , , , . For any horizontally invariant waveguide under liquid half-space seabed conditions, the water body can be used The linear sound velocity layer is approximated, and the layer where the sound source is located is denoted as the first. Layers, similar to a uniform layering method, can be used Establish under the condition of boundary Several equations form a matrix equation. Its global coefficient matrix It can be represented as: (twenty four) column vector for: (25) T represents the matrix transpose. For the right-hand column vector: (26) in: , , , .

[0034] Due to the matrix For a highly sparse banded array, this method uses a sparse coefficient matrix linear equation solver for efficient solution, which can quickly obtain the wavenumber domain displacement potential, i.e., the deep Green's function.

[0035] Step S4: Calculate the acoustic field displacement potential based on the depth Green's function; The above steps yield the unconditionally stable depth Green's function in water, which, when substituted into equation (3), provides the acoustic field displacement potential. In actual numerical calculations, to avoid the influence of singularities on the real axis on the integration path, the complex contour integration method is adopted, introducing the complex wave number: (27) in , , , , For the integration interval, Let be the number of discrete points of the horizontal wavenumber. Therefore, the displacement potential of the sound field can be expressed as: (28) In practical numerical calculations, directly integrating the wavenumber is extremely computationally intensive, resulting in low efficiency. To balance computational speed and accuracy, and considering the contribution of the inner traveling wave term, this method adopts the FFP+ approach to calculate the acoustic field displacement potential: (29) Step S5: Calculate the propagation loss of the underwater sound field based on the sound field displacement potential; According to the definition of propagation loss in an underwater sound field: (30) The reference sound pressure is taken in the formula. ,in Let be the wavenumber of the medium at the sound source. The displacement potential of the sound field can be obtained by solving the above steps. Solve for the underwater sound field, i.e., the propagation loss. .

[0036] Calculation example: Consider as Figure 3 The Munk waveguide shown is composed of A case study of the Munk sound velocity profile approximated by piecewise linear elements, with water depth... The density of the water is The sound source is placed in water depth The seabed is designed as a liquid half-space, with a sound speed of... The density is The absorption coefficient is .

[0037] This example demonstrates precise statistical calculations. The time required for internal propagation loss for each model. The lower limit of phase velocity integration for all wavenumber integral models is set to... The upper limit is The lower limit of phase velocity in the KRAKENC model is... The upper limit is also set to Sound source frequency At that time, the number of layers involved in the SCOOTER model was The uniformly layered wavenumber integral WI1 model involves the following number of layers: The number of layers increases exponentially with the source frequency. In contrast, the linear layered wavenumber integral WI2 model of this invention requires only the number of layers determined by the input sound velocity profile and does not change with the source frequency. At the source frequency... At that time, calculate The propagation loss within the range, the number of wavenumber sampling points involved in the SCOOTER model is Furthermore, the number of wavenumber sampling points doubles with increasing frequency. When the sound source frequency is the same and the number of wavenumber sampling points is consistent, the computable farthest propagation distance of each wavenumber integral model is consistent. Specifically, the SCOOTER model is accurate within one-quarter of the farthest distance, while the WI1 and WI2 models are accurate within half of the farthest distance. Therefore, the number of wavenumber discrete points for the WI1 and WI2 models of this method is set to half that of the SCOOTER model at the same frequency. Figure 4 Four models were demonstrated at the sound source frequency of The result of how propagation loss varies with distance and depth. Figure 5 The comparison was then made at sound source frequencies of... , , The propagation loss curves obtained by each model at the sound source depth are shown. The results show that the calculation results of each model are highly consistent.

[0038] Table 1 shows the computation time of each model at different frequencies. Figure 6 The corresponding comparison curves are shown. In deep-sea environments, due to the greater depth, the number of grids required in the vertical direction for WI1 and SCOOTER increases significantly, and the number of normal modes required by KRAKENC also increases substantially, causing the computational efficiency of all three to decrease sharply with increasing frequency. In contrast, the computational efficiency of the WI2 model is basically unaffected by water depth. Under high-frequency conditions, it only takes about 30 seconds to calculate the entire sound field, which is about 2 orders of magnitude faster than WI1 and about 1–2 orders of magnitude faster than SCOOTER and KRAKENC.

[0039] Table 1 Comparison of computation times for four Munk waveguide models

[0040] This invention also provides an underwater acoustic field calculation system based on wavenumber integral theory, comprising: Memory, used to store data and computer programs; A processor is used to execute the computer program to implement the steps of the underwater acoustic field calculation method based on wavenumber integral theory described above.

[0041] Preferably, the processor includes a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit); the CPU is used for the main operations of the system and handles most of the computational tasks; the GPU is used for graphics and highly parallel computing tasks.

[0042] As can be seen from the above detailed description of this application, the present invention has the following significant technical effects: Traditional acoustic field calculation models, due to differences in their theoretical foundations and solution strategies, each have their own advantages in terms of applicable scenarios and computational performance, but also have corresponding limitations. Acoustic field calculation methods based on the wavenumber integral method, which solve the acoustic field through direct numerical integration, have advantages in near-field calculations and numerical stability; however, previously developed wavenumber integral methods are generally only applicable to acoustic field simulations in specific waveguide environments (such as Pekeris waveguides and negative gradient waveguides), and there is a risk of numerical overflow under positive gradient sound velocity profile conditions. This invention can handle and achieve efficient and stable solutions for the depth Green's function in waveguides with obvious linear characteristics of sound velocity profiles (such as waveguides containing positive gradient water layers, negative gradient water layers, homogeneous water layers, and homogeneous liquid half-space seabed waveguide environments), and simultaneously employs the FFP+ method strategy to calculate the acoustic field potential function, thereby achieving high-precision and high-efficiency computational simulation of underwater acoustic fields.

[0043] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating underwater acoustic fields based on wavenumber integral theory, characterized in that, Includes the following steps: Step S1: Solve the wave equation using wavenumber integral theory to obtain the displacement potential function to be solved; the displacement potential function includes the depth Green's function. Step S2: Based on linear layered modeling of the sound velocity profile, the underwater waveguide structure is divided from top to bottom into a uniform layer, multiple negative gradient layers, multiple positive gradient layers, and a uniform liquid half-space seabed. Step S3: Solve for the numerical value of the depth Green's function in a linear layered waveguide environment; Step S4: Calculate the acoustic field displacement potential based on the depth Green's function; Step S5: Calculate the propagation loss of the underwater sound field based on the sound field displacement potential.

2. The underwater acoustic field calculation method based on wavenumber integral theory according to claim 1, characterized in that, In step S1, the point sound source has a depth of [missing information] in cylindrical coordinates. At that time, displacement potential The Helmholtz equation is: (1) in: For the intensity of the sound source, Wavenumber; using Hankel transform: (2) (3) in For horizontal wavenumber, Given a zero-order Bessel function, we obtain the wave equation with distance and depth separation: (4) in ; The depth Green's function is obtained by solving the wave equation based on the separation of distance and depth. Then, substitute it into equation (3) to obtain the acoustic field displacement potential in the spatial domain.

3. The underwater acoustic field calculation method based on wavenumber integral theory according to claim 2, characterized in that, In step S2, the sound velocity-depth relationship in each water layer can be uniformly expressed as: (5) Where c j (z) represents the speed of sound at depth z of the j-th layer, a j For the j-th layer Linear gradient in a linear layer, b j The constant for the j-th layer is calculated based on the depth and sound speed.

4. The underwater acoustic field calculation method based on wavenumber integral theory according to claim 3, characterized in that, Step S3 specifically includes the following steps: Step S3-1, the steps for solving the numerically stable depth Green's function under the negative gradient condition are as follows: In equation (4) for: (6) By introducing variable substitution: (7) Will Substituting into equation (4) yields information about The equation: (8) From equation (8), the homogeneous solution of the depth Green's function that is numerically stable under the negative gradient condition is: (9) in , For the Airy function, For the normalized Airy function, , The subscripts u and d represent the values ​​of the variable at the upper and lower boundaries of the linear layer, respectively; Step S3-2, the homogeneous solution of the depth Green's function under the positive gradient condition is expressed as: (10) Among them, When, the exponential factor in equation (10) and All are negative values; Step S3-3: Process the sound velocity distribution of the uniform layer to maintain a set difference in sound velocity between the upper and lower interfaces, so that the uniform layer is regarded as a positive gradient layer with minimal gradient. Step S3-4, calculate the depth Green's function for the uniform liquid half-space seabed as follows: use Expression (8) in the first Numerically stable homogeneous solutions in layered seawater, using The particular solution of expression (8) in the second layer of seawater where the sound source is located is then... Its first derivative is: (11) (12) in: (13) (14) (15) special solution Its first derivative is: (16) (17) If the first If the seawater layer does not contain a sound source, then the unconditionally stable depth Green's function and its first derivative can be expressed as: (18) If the first If a sound source is present in the second layer of seawater, for example, as shown in Figure 2, the sound source is located in the second layer, then the unconditionally stable depth Green's function and its first derivative can be expressed as: (19) The Green's function for the depth of the seabed is: (20)。 5. The underwater acoustic field calculation method based on wavenumber integral theory according to claim 4, characterized in that, water bodies The linear sound velocity layer is approximated, and the layer where the sound source is located is denoted as the first. When layered, in Establish under the condition of boundary Several equations form a matrix equation. Its global coefficient matrix Represented as: (24) column vector for: (25) T represents the matrix transpose. For the right-hand column vector: (26) in: , , , .

6. The underwater acoustic field calculation method based on wavenumber integral theory according to claim 5, characterized in that, A sparse coefficient matrix linear equation solver is used for efficient solving to obtain the depth Green's function for each layer.

7. The underwater acoustic field calculation method based on wavenumber integral theory according to claim 5, characterized in that, In step S4, the depth Green's function is substituted into equation (3) to obtain the acoustic field displacement potential. Specifically, the complex encirclement integral method is used, and the complex wave number is introduced: (27) in , , , , For the integration interval, Let be the number of discrete points of the horizontal wavenumber; the displacement potential of the sound field is expressed as: (28)。 8. The underwater acoustic field calculation method based on wavenumber integral theory according to claim 7, characterized in that, The calculation of the acoustic field displacement potential in step S4 is simplified as follows: (29)。 9. The underwater acoustic field calculation method based on wavenumber integral theory according to claim 7 or 8, characterized in that, In step S5, the propagation loss in the underwater sound field is calculated as follows: (30) The reference sound pressure is taken ,in denoted as the medium wavenumber at the sound source.

10. An underwater acoustic field calculation system based on wavenumber integral theory, comprising: Memory, used to store data and computer programs; A processor for executing the computer program to implement the steps of the underwater acoustic field calculation method based on wavenumber integral theory as described in any one of claims 1-9.

Images