Methods, systems, equipment, media, and products for modeling sound velocity profiles in the air-sea interaction layer.

Abstract

This invention provides a method, system, device, medium, and product for modeling sound velocity profiles in the air-sea interaction layer, comprising the following steps: Step S1: Acquire temperature and salinity field data of the target sea area; Step S2: Based on the temperature and salinity field data, construct a covariance matrix and perform intrinsic mode decoupling, extracting the first few modes as the spatially dominant modes; Step S3: Perform cubic B-spline interpolation and fitting on the vertical weight coefficients of the spatially dominant modes, and use radial basis function interpolation to perform spatial mode continuity processing, obtaining a spatial distribution model of the temperature and salinity field data; Step S4: After applying constraints to the vertical distribution of the spatial distribution model at the air-sea boundary, substitute it into the empirical formula for sound velocity to complete the sound velocity profile modeling. This method overcomes the limitations of the traditional quasi-static one-dimensional sound field assumption, constructing a sound velocity profile model of the air-sea interaction layer that integrates horizontal distance and vertical depth.

Description

Technical Field

[0001] This invention relates to the field of marine acoustic engineering technology, specifically to a method, system, device, medium, and product for modeling sound velocity profiles of the air-sea interaction layer. Background Technology

[0002] In the field of marine acoustic engineering, such as underwater target detection and positioning, marine environmental monitoring, and underwater communication and navigation, sound waves are the primary carrier of information transmission. The propagation characteristics of sound waves in seawater, particularly their propagation path, energy attenuation, and signal distortion, are highly dependent on the spatial distribution of sound velocity in the marine medium. The sound velocity profile, i.e., the vertical distribution structure of sound velocity from the sea surface to the seabed, is the core parameter describing this sound velocity distribution and has a decisive influence on sound propagation behavior. The air-sea interaction layer, as the interface between the ocean surface and the atmosphere, exhibits significant spatial variability in its sound velocity distribution.

[0003] Traditional modeling methods for the horizontal spatial variability of sound velocity in the air-sea interaction layer generally employ a quasi-static one-dimensional sound field assumption, simplifying sound velocity into a function that varies only with depth, leading to the loss of horizontal gradient information. Studies have shown that such simplified models induce a cumulative shift in sound ray trajectories of 2-5 km in sound propagation simulations at a 100 km scale. This shift severely restricts the overall perception accuracy and environmental adaptability of underwater acoustic systems in target detection and localization, marine environmental monitoring, and communication and navigation tasks.

[0004] Current sound velocity profile construction techniques mainly rely on three types of methods: empirical formula methods generate idealized sound velocity distributions based on historical statistical patterns, which cannot reflect the dynamic changes in actual sea areas; vertical interpolation methods calculate sound velocity using measured temperature, salinity, and pressure data, but ignore horizontal spatial correlations, resulting in an error of over 40% in describing the gradient of the air-sea interaction layer; and data-driven models, while capable of fusing multi-source observation data, are difficult to embed into acoustic physics equations due to their "black box" nature, limiting their extrapolation capabilities. More seriously, existing methods are prone to gradient jumps at the junction of the air-sea interaction layer and deep sound velocity profiles, causing ray tracing algorithms to diverge, thus restricting the engineering practicality of underwater acoustic systems. Summary of the Invention

[0005] This invention proposes a method, system, equipment, medium, and product for modeling sound velocity profiles in the air-sea interaction layer, in order to solve the technical problem that existing technologies are unable to reflect the dynamic changes in actual sea areas and have large quantification errors for the spatial variability of sound velocity in the air-sea interaction layer.

[0006] To address the aforementioned technical problems, this invention provides a method for modeling the sound velocity profile of the air-sea interaction layer, comprising the following steps:

[0007] Step S1: Obtain temperature and salinity field data for the target sea area;

[0008] Step S2: Based on the temperature field and salinity field data, construct the covariance matrix and perform intrinsic mode decoupling, extracting the first few modes as the dominant spatial modes;

[0009] Step S3: Perform cubic B-spline interpolation and fitting on the vertical weight coefficients of the dominant spatial mode, and use radial basis function interpolation to perform spatial mode continuity processing to obtain the spatial distribution model of the temperature field data and salinity field data;

[0010] Step S4: After applying constraints to the vertical distribution of the spatial distribution model at the air-sea boundary, substitute the empirical formula for sound speed to complete the sound speed profile modeling.

[0011] Preferably, the expression for B-spline interpolation of the vertical weighting coefficient in step S3 is as follows:

[0012] ;

[0013] In the formula, Indicates the first The first mode is in the depth layer Vertical weighting coefficient at that time; The number of control points for the B-spline interpolation; Represents the coefficients of B-spline interpolation; For the definition in the node vector The cubic B-spline basis functions on the surface.

[0014] Preferably, the expression for spatial modal continuity processing using radial basis function interpolation in step S3 is as follows:

[0015] ;

[0016] In the formula, Indicates the weighting coefficient; Indicates bandwidth parameter; Indicates the coordinates of the target point; For the first The planar coordinates of each grid point; This indicates the number of horizontal grid points.

[0017] Preferably, the expression for applying constraints to the vertical distribution of the spatial distribution model in step S4 is:

[0018] ;

[0019] ;

[0020] In the formula, and A spatial distribution model representing temperature field data and salinity field data; and This represents a spatial distribution model of temperature and salinity field data after constraints have been applied. The weighting function is a cubic polynomial. Horizontal distance; Vertical depth This refers to the depth of the air-sea interaction layer. Indicates the thickness of the transition layer; It represents the constant temperature value of deep seawater below the bottom of the air-sea interaction layer; The constant salinity value of deep seawater below the bottom of the air-sea interaction layer.

[0021] Preferably, the cubic polynomial weighting function The expression is:

[0022] .

[0023] The present invention also provides a sound velocity profile modeling system for the air-sea interaction layer, which includes an observation module for acquiring temperature, salinity, and pressure data, a modeling module for performing sound velocity profile modeling, and a display module for outputting the sound velocity profile. The modeling module is used to implement the above-described method.

[0024] The present invention also provides an electronic computer device, which includes a processor and a memory, wherein the memory stores a program that, when executed by the processor, is used to implement the above-described method.

[0025] The present invention also provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the above-described method.

[0026] The present invention also provides a computer program product, including instruction code for implementing the above method, the instruction code being stored in a non-transient computer-readable medium.

[0027] The beneficial effects of this invention include at least the following: This invention extracts the spatial dominant modes of gridded temperature, salinity, and pressure data through intrinsic mode decoupling of the sound velocity field, establishes a three-dimensional continuous sound velocity field by combining it with the sound velocity equation, and eliminates the discontinuity of sound velocity at the layered interface by employing cubic B-spline interpolation and transition function constraints, ensuring the smoothness of the profile. It overcomes the vertical layering limitations of traditional models, suppresses sound propagation trajectory deviation, and significantly improves the overall perception accuracy and environmental adaptability of underwater acoustic systems in target detection and positioning, marine environmental monitoring, and communication and navigation tasks, bringing a comprehensive improvement to underwater acoustic systems. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the method flow of an embodiment of the present invention;

[0029] Figure 2This is the original temperature field dataset for an embodiment of the present invention;

[0030] Figure 3 This is the original salinity field dataset for an embodiment of the present invention;

[0031] Figure 4 This is a continuous temperature distribution model after decoupling the intrinsic modes of the sound velocity field according to an embodiment of the present invention.

[0032] Figure 5 This is a continuous salinity distribution model after decoupling the intrinsic modes of the sound velocity field according to an embodiment of the present invention.

[0033] Figure 6 This is a schematic diagram of the horizontal spatial variability distribution of sound velocity in the air-sea interaction layer according to an embodiment of the present invention.

[0034] Figure 7 This is a spatially variable sound velocity profile curve related to horizontal distance and vertical depth in an embodiment of the present invention;

[0035] Figure 8 This is a color mapping diagram of the spatial variability of sound velocity profiles related to horizontal distance and vertical depth in an embodiment of the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0037] like Figure 1 As shown, this embodiment of the invention provides a method for modeling the sound velocity profile of the air-sea interaction layer, including the following steps:

[0038] Step S1: Obtain temperature and salinity field data for the target sea area.

[0039] Specifically, in this embodiment of the invention, to construct a nonlocal sound velocity profile of the air-sea interaction layer, the data source used is ocean spatial temperature, salinity, and pressure data. The applied data includes longitude, latitude, pressure, salinity, temperature, and air-sea interaction layer depth. The data source is the global ocean Argo grid dataset (BOA_Argo). This dataset has a horizontal spatial range of 180°W-180°E and 79.5°S-79.5°N, a spatial resolution of 1°×1°, and 58 vertical standard layers ranging from 0 to 1975 dbar. After acquiring the measured data, the data is preprocessed by regional cropping according to the sea area under study. First, the geographical boundaries of the target sea area need to be defined, including the longitude and latitude ranges. Since the original data uses a regular latitude and longitude grid with a step size of 1°, the target latitude and longitude values ​​need to be mapped to the grid index.

[0040] Step S2: Based on temperature and salinity field data, construct the covariance matrix and perform intrinsic mode decoupling, extracting the first few modes as the dominant spatial modes.

[0041] Specifically, based on BOA_Argo global gridded temperature, salinity, and pressure data, a data-driven hierarchical interpolation technique is used to establish a coupling function relationship between the temperature field, salinity field, horizontal distance, and vertical depth. The core of this invention lies in converting discrete gridded measured data into continuously distributed analytical functions and ultimately embedding an empirical formula for sound velocity, thereby achieving a high-precision characterization of the horizontal spatial variability of sound velocity in the air-sea interaction layer.

[0042] To accurately characterize the continuous spatial distribution of temperature, salinity, and pressure, this invention employs a sound velocity field eigenmode decoupling method, combined with measured data and function interpolation techniques, to construct a parameterized model of the temperature field. This model transforms discrete, gridded observation data into a parameterized model of the temperature field with horizontal distances. and vertical depth The core idea of ​​this method is to extract the spatial dominant modes of the temperature field through classical orthogonal function decomposition and to achieve the joint expression of the modes through vertical interpolation and spatial continuity techniques.

[0043] The original temperature and salinity data had a horizontal resolution of 1°×1° and was vertically divided into 10m intervals within the air-sea interaction layer. This data underwent preprocessing to eliminate dimensional differences in the vertical layers and highlight the spatial characteristics of the temperature and salinity field, for each depth layer. The temperature and salinity field is standardized, and the calculation formula is as follows:

[0044] ;

[0045] in, It is a temperature field function; This is the salinity field function; To create an east-west stratified area based on the latitude and longitude of the target sea area, Stratify the area along the north-south direction, for example, when the target sea area is 113°E-120°E and 15°N-20°N. , ; This represents the layer boundary depth corresponding to the depth of the air-sea interaction layer when the layers are layered at 10m intervals. Representing depth layer Average temperature and salinity at that location; Let be the standard deviation of temperature and salinity; this is illustrated using the temperature mean and temperature standard deviation of the temperature field function, expressed as follows:

[0046] ;

[0047] ;

[0048] The salinity mean and salinity standard deviation of the salinity field function are calculated using the same method as the temperature field, and will not be elaborated further here.

[0049] The core objective of sound velocity field eigenmode decoupling is to extract the main spatial variation modes of the temperature and salinity field through eigenvalue analysis of the covariance matrix. This applies to each depth layer within the air-sea interaction layer. To extract variation patterns from the data, the average value of the data is first calculated, and then the average value is subtracted to obtain the anomaly field. This allows the anomaly field to focus on variation patterns. The standardized temperature and salinity anomalies are then arranged as follows: matrix , ,in The number of horizontal grid points. The time evolution is expressed in months, and the covariance matrices of the sequence length, temperature, and salinity are given. The calculation formula is:

[0050] temperature: ;

[0051] salinity: ;

[0052] Each element of the matrix Indicates the first and The temperature-salinity covariance at each grid point reflects the coordinated spatial variation of these two parameters. This is achieved through eigenvalue decomposition. The eigenvalues ​​can be obtained by sorting them in descending order of variance contribution rate. and its corresponding eigenvectors The first three modes typically explain over 90% of temperature and salinity variations, and their spatial distribution patterns have clear physical meanings: the first mode characterizes large-scale temperature and salinity gradients, the second mode corresponds to mesoscale vortex structures, and the third mode describes local disturbances caused by fronts or freshwater inputs. Therefore, this embodiment selects the first three modes as the dominant modes, but the number of dominant modes is not a limitation of this invention.

[0053] Step S3: Perform cubic B-spline interpolation and fitting on the vertical weight coefficients of the dominant spatial modes, and use radial basis function interpolation to perform spatial mode continuity processing to obtain the spatial distribution models of temperature field data and salinity field data.

[0054] To establish a continuous function of the temperature-salinity field in the vertical direction, it is necessary to vertically align and interpolate the eigenmodes of the sound velocity field at different depths. First, mode alignment is achieved using the maximum correlation coefficient: taking the 0m depth layer (sea level) as the reference, the spatial correlation coefficients between the modes at other depths and the reference mode are calculated. :

[0055] ;

[0056] In the formula, The first layer represents the reference layer. The eigenvectors of the feature vectors correspond to modes. For the baseline layer, the eigenvectors of the feature vectors correspond to modes. For the feature vector of the th eigenvector First mode; Indicates the first The first layer Feature vector Indicates the first The first layer Eigenvectors and the first eigenvalue of the baseline layer Spatial correlation coefficients of eigenvectors. Using sea level as the reference layer, calculate the spatial correlation coefficients of eigenvectors at each depth level (e.g., 10m, 20m, and 30m) with the eigenvectors of the reference layer. Find the eigenvector with the highest similarity, considering it an extension of that mode. In this embodiment, the reference layer is sea level (z=0, k=1, 2, 3). The first floor is 10m, the second floor is 20m, and so on. The numbers are 1, 2, and 3.

[0057] The mode with the highest correlation coefficient is selected as the vertical extension for the corresponding order. Subsequently, the vertical weighting coefficients for each order mode, i.e., the first three orders mentioned above, are... Perform cubic B-spline interpolation:

[0058] ;

[0059] In the formula, The number of control points in the B-spline interpolation is represented by the number of nodes in the node vector in cubic B-spline interpolation, which is equal to the number of control points plus 3 plus 1. For the definition in the node vector The coefficients of the cubic B-spline basis function on m The measured vertical weight sequence was fitted using the least squares method.

[0060] Specifically, vertical weighting coefficients for depths of 10m, 20m, and 30m were obtained from gridded temperature, salinity, and pressure data. Cubic B-spline interpolation was then performed to construct a continuous, smooth function from the known discrete vertical weighting coefficients, allowing it to represent the variation of the vertical weighting coefficients with depth z. Therefore... It is both an input and an output, and at the same time, the coefficients The least squares method is used to make the theoretically calculated value and measured values This is obtained by minimizing the overall error (minimum sum of squared residuals) of the known vertical weighting coefficients for depth layers of 10m, 20m, and 30m.

[0061] Discrete sound velocity field eigenmodes need to be converted into continuous spatial functions to support temperature and salinity calculations at arbitrary locations. Radial basis function interpolation is used to transform the eigenvectors... Mapped to spatial modal continuous functions :

[0062] ;

[0063] Radial basis functions are used to construct a function defined at any location in the entire continuous space, based on known values ​​at grid points. Indicates the coordinates of the target point. Represents the known coordinates of the center point, i.e., the... If the planar coordinates of each grid point are given, the value of the radial function depends only on the Euclidean distance. , The bandwidth parameter is used to control the decay rate of the function, and the weighting coefficient is used for this purpose. This determines the contribution of the radial basis function at each center point to the final interpolation function. Kernel function bandwidth. In this embodiment, the interpolation smoothness is controlled at 50km, with weighting coefficients... By solving the system of linear equations Confirmed. Ultimately, the parameterized model of the air-sea interaction layer's temperature and salinity field can be comprehensively expressed as:

[0064] ;

[0065] ;

[0066] Through vertical weighting coefficients With spatial modal continuity function The coupling of temperature and salinity fields enables a continuous expression of their correlation with horizontal distance and vertical depth.

[0067] Based on BOA_Argo data, a horizontal-vertical distribution model of temperature and salinity was established using sound velocity field eigenmode decoupling, and its comparison with the original data is shown below. Figures 2 to 5 As shown.

[0068] Step S4: After applying constraints to the vertical distribution of the spatial distribution model at the air-sea boundary, substitute the empirical formula for sound speed to complete the sound speed profile modeling.

[0069] A spatial distribution model of the temperature field in the air-sea interaction layer was established. Spatial distribution model of salinity field Then, it was coupled with the empirical formula for sound speed to construct a piecewise continuous sound speed profile of the air-sea interaction layer. .

[0070] The empirical formula algorithms for seawater sound velocity used in this embodiment include, but are not limited to, the Del Grosso algorithm, the Wilson algorithm, and the Chen-Millero-Li algorithm, with standard errors of 0.05 m / s, 0.30 m / s, and 0.19 m / s, respectively. Therefore, the Del Grosso algorithm is used for sound velocity profile coupling in this embodiment of the invention.

[0071] Considering the horizontal spatial variability of sound speed in the air-sea interaction layer, the sound speed profile is segmented and described. The entire sound speed profile can be expressed by the following formula.

[0072] ;

[0073] sound speed profile The sound speed profile considers the variations in sound speed in the horizontal and vertical directions within the air-sea interaction layer. Only with depth does it change, among which Horizontal distance Vertical depth The depth of the air-sea interaction layer. The sea is deep. When At that time, the sound speed profile will fluctuate with changes in horizontal distance and vertical depth, exhibiting spatial variation distribution characteristics; when The speed of sound lies below the air-sea interaction layer and varies only with depth. A schematic diagram of this sound speed profile is shown below. Figure 6 As shown, the layer above the layer line is the air-sea interaction layer. The solid line represents a simple equivalent sound speed profile that ignores the uneven changes in the ocean environment, and the shaded area represents the range of fluctuations caused by the spatial variability of the sound speed distribution.

[0074] The mathematical expression of the Del Grosso algorithm is a function of temperature, salinity, and depth. By substituting the parameterized model of the salinity field in the air-sea interaction layer, the functional relationship between sound speed and horizontal distance and vertical depth can be obtained:

[0075] ;

[0076] To ensure the sound velocity profile is in For continuity at a given point to be possible, the following conditions must be met:

[0077] Function values ​​are continuous: ;

[0078] First derivative continuity: ;

[0079] To achieve this goal, constraints need to be imposed on the vertical distribution of the temperature-salinity field at the boundary point. The temperature and salinity at the bottom of the air-sea interaction layer need to smoothly transition to constant values ​​in the deeper layers. In this embodiment, the following transition function is introduced. accomplish:

[0080] ;

[0081] ;

[0082] It represents the constant temperature value of deep seawater below the bottom of the air-sea interaction layer; The constant salinity value of deep seawater below the bottom of the air-sea interaction layer.

[0083] in The weighting function is a cubic polynomial:

[0084] ;

[0085] To avoid excessively affecting the speed of sound, the thickness of the transition layer in this embodiment is... Only 2-5m is considered to ensure the continuity of the first derivative of the speed of sound. At this point, the temperature gradient at the bottom of the air-sea interaction layer... With salinity gradient The sound velocity will be smoothly attenuated to zero to avoid a broken line-shaped discontinuity at the boundary point.

[0086] Finally, the Bellhop underwater acoustic toolbox in Matlab can be used to plot the sound velocity profile of the air-sea interaction layer, generating sound velocity profile curves associated with horizontal distance and vertical depth, and color-mapped sound velocity profile images, as shown below. Figure 7 and Figure 8 As shown.

[0087] The present invention also provides a sound velocity profile modeling system for the air-sea interaction layer, which includes an observation module for acquiring temperature, salinity, and pressure data, a modeling module for performing sound velocity profile modeling, and a display module for outputting the sound velocity profile. The modeling module is used to implement the above-described method.

[0088] The present invention also provides an electronic computer device, which includes a processor and a memory, wherein the memory stores a program, which, when executed by the processor, is used to implement the above-described method.

[0089] The present invention also provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the above-described method.

[0090] The present invention also provides a computer program product, including instruction code for implementing the above method, the instruction code being stored in a non-transient computer-readable medium.

[0091] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0092] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for modeling a sea-air interface layer sound speed profile, the method comprising: The method comprises the following steps: ​ Step S1: obtaining temperature field and salinity field data of a target sea area; Step S2: based on the temperature field and salinity field data, constructing a covariance matrix and performing eigenmode decoupling, and extracting the first several orders of modes as spatial dominant modes; Step S3: performing cubic B-spline interpolation and fitting on the vertical weight coefficients of the spatial dominant modes, and performing spatial mode continuous processing by using radial basis function interpolation to obtain a spatial distribution model of the temperature field data and the salinity field data; Step S4: after applying a constraint to the vertical distribution of the spatial distribution model at the sea-air interface point, substituting it into an empirical formula of sound speed to complete the modeling of the sound speed profile; The expression of the spatial mode continuous processing by using radial basis function interpolation in step S3 is: ； In the formula, represents a weight coefficient; represents a bandwidth parameter; represents a target point coordinate; is the plane coordinate of the th grid point; represents the number of horizontal grid points; The expression of the constraint to the vertical distribution of the spatial distribution model in step S4 is: ； ； wherein and denote the spatial distribution model of the temperature field data and the salinity field data; and denote the spatial distribution model of the temperature field data and the salinity field data after applying the constraints; is a cubic polynomial weighting function; is the horizontal distance; is the vertical depth, is the air-sea interaction layer depth; denotes the transition layer thickness; denotes the constant temperature value of the deep ocean water below the bottom of the air-sea interaction layer; denotes the constant salinity value of the deep ocean water below the bottom of the air-sea interaction layer.

2. The method according to claim 1, wherein: The expression of the B-spline interpolation of the vertical weight coefficients in step S3 is: ； wherein denotes the vertical weight coefficient of the mode at the depth level ; denotes the number of control points of the B-spline interpolation; denotes the coefficients of the B-spline interpolation; are cubic B-spline basis functions defined on the node vector .

3. The method according to claim 1, wherein: The cubic polynomial weight function The expression is: 。 4. A sea-air interface layer sound speed profile modeling system comprising an observation module for obtaining temperature-salinity-pressure data, a modeling module for performing sound speed profile modeling, and a display module for outputting the sound speed profile, wherein the modeling module is configured to implement the method of any one of claims 1 to 3.

5. An electronic computer device comprising a processor and a memory, wherein the memory stores a program which, when executed by the processor, is configured to implement the method of any one of claims 1 to 3.

6. A computer-readable storage medium having a program stored thereon, wherein the program, when executed by a processor, implements the method of any one of claims 1 to 3.

7. A computer program product comprising instruction codes for implementing the method of any one of claims 1 to 3, wherein the instruction codes are stored in a non-transitory computer-readable medium.

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