Method for improving water depth inversion accuracy based on neural network - wavelet decomposition of gravity information

Abstract

The present invention discloses a method for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information, including: eliminating outliers from shipborne sounding data to obtain the depth Z of shipborne sounding control points; meanwhile, using the Parker algorithm to forward model the gravity anomaly and vertical gravity gradient anomaly of the ETOPO1 water depth model respectively to obtain the gravity information forward modeled by the ETOPO1 water depth model; performing wavelet decomposition on the gravity anomaly and vertical gravity gradient anomaly obtained by satellite altimetry inversion to obtain the wavelet - decomposed gravity information; determining the optimal order of wavelet decomposition through correlation analysis and comparison; constructing and training a network model; constructing a water depth inversion model; inputting the gridded gravity information after wavelet decomposition and the corresponding coordinate information into the water depth inversion model, thereby inversely obtaining a 1′×1′ water depth model in the study area. The method of the present invention provides a useful reference for constructing water depth models in large - scale areas using multi - source gravity data.

Description

Technical Field

[0001] The present invention belongs to the cross - technical fields of underwater navigation, marine surveying and mapping, etc., and particularly relates to a method for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information. Background Art

[0002] High - precision water depth models provide guarantees for maritime navigation safety and marine resource development, and provide basic data for studying ocean circulation and constructing tsunami prediction models. Traditional depth measurement methods are classified into ship - borne, airborne, and space - borne sounding technologies according to the carrying platforms. Among them, ship - borne sounding technologies include single - beam sonar, multi - beam sonar, side - scan sonar, etc., which have high measurement accuracy but low efficiency. Airborne lidar sounding technology, although its sounding efficiency is improved compared with ship - borne sounding, is applicable to clear shallow water areas. Space - borne sounding technology uses optical remote sensing satellite images to invert water depth. Although this method can achieve large - scale depth measurement, it is only applicable to areas shallower than 30m and with good water quality. If traditional ship - borne sounding technology is used to complete global - scale measurement, it will take at least 200 years. In order to achieve large - scale and rapid water depth measurement globally, new sounding means are urgently needed. In 1983, Dixon proved that there is a certain correlation between seabed topography and gravity anomaly, providing a theoretical basis for using gravity information to invert water depth. Therefore, for water depth detection in large - scale deep - water areas, gravity information retrieved based on satellite altimetry is an effective technical means.

[0003] With the development of satellite altimetry technology, numerous scholars have proposed various methods for sea depth inversion using gravity information, including statistical methods (such as least squares collocation method), physical methods (such as GGM method and SAS method), intelligent algorithms (such as artificial neural network, simulated annealing method (SA)), etc. Among them, the least squares collocation method requires constructing a covariance matrix between depth and gravity anomaly, with a large amount of calculation and low efficiency. Hwang derived the least squares collocation method in the frequency domain through Fourier transform, improving the efficiency of water depth inversion, but did not consider the non-linear influence of gravity anomaly on water depth inversion. The GGM method decomposes the gravity anomaly into regional and residual gravity anomalies based on the Bouguer plate formula, and then establishes the relationship between depth and residual gravity anomaly. The method is simple and has high calculation efficiency. However, it is affected by the density difference parameter between seawater and the crust and the construction of regional gravity field interpolation. Kim et al. used the iterative method to determine the optimal density difference, reducing the influence of the density difference parameter on the inverted depth. However, the density difference parameter in the formula has lost its original physical meaning and has a large amount of computation. Sun Yongjin et al. aimed at the problem of low construction accuracy of the regional gravity field, introduced a topographic factor during the interpolation process, proposed a method for optimizing the weight of the topographic constraint factor and improved the water depth inversion accuracy. The SAS method needs to consider the influence of density parameters, inversion bands, and high-order terms in the Parker formula during the inversion process. Sandwell et al. inverted the bathymetry of the Southern Ocean through filtering and correlation analysis methods. Fan Diao et al. optimized the linear scale factor between topography and gravity anomaly using the robust estimation method and obtained a good inversion result. However, neither of the above two methods considered the influence of non-linear terms on the inversion result. With the continuous development of intelligent algorithms, in 2012, Jane et al. proposed a method for inverting water depth using a radial basis function neural network and successfully detected two unobserved seamounts in the Arabian Sea. However, only gravity anomaly data was used as input without considering vertical gravity gradient anomaly and coordinate information. Vertical gravity gradient anomaly data can better reflect the detailed changes in topography. Wang derived in detail the relationship between vertical gravity gradient anomaly and bathymetry in the spatial domain and used the least squares collocation method for water depth calculation. Hu Minzhang et al. derived the relationship between bathymetry and vertical gravity gradient anomaly based on the Parker theory and inverted the global bathymetry model through linear regression technology using a designed filter. Yang Junjun et al. proposed using the SA method to continuously adjust and improve function parameters to calculate the globally optimal water depth model based on airborne gravity gradient data. However, the above methods all use a single gravity information as the input source and do not consider the joint application of gravity anomaly and vertical gravity gradient anomaly. Subsequently, Fan Diao et al. used the multiple linear regression technique to jointly use gravity and gravity gradient data to improve the bathymetry accuracy in the Indian Ocean region, demonstrating the importance of applying multi-source gravity data in bathymetry inversion. The present invention attempts to propose a more comprehensive inversion method on the basis of considering the combined influence of multi-source gravity data and non-linear factors.

[0004] In recent years, artificial neural networks, as a highly nonlinear model, can fit the functional relationship between input and output by continuously adjusting the number of neurons and the number of neural network layers, and have been widely used in many fields such as hydrology and geophysics. Depending on whether the neuron feeds back its own output signal as an input signal to other neurons at the same time, it is divided into two types: feedback neural networks and feedforward neural networks. Among them, multi-layer feedforward neural networks are widely used in remote sensing water depth inversion and GNSS-R sea surface height prediction because they can better combine multi-source data and establish a multi-input single-output relationship model. In addition, due to the influence of the isostatic effect of the crust and the density difference parameter, there is a nonlinear relationship between gravity information and water depth. If the neural network is directly used to invert the water depth, it will inevitably lead to a decrease in the stability of the inversion model. Summary of the invention

[0005] The technology of the present invention solves the problem: overcomes the shortcomings of the prior art, provides a method for improving the accuracy of water depth inversion based on neural network-gravity information wavelet decomposition, and provides a useful reference for constructing water depth models in a large area using multi-source gravity data.

[0006] In order to solve the above technical problems, the present invention discloses a method for improving the water depth inversion accuracy based on neural network-gravity information wavelet decomposition, comprising:

[0007] The ETOPO1 water depth model, gravity anomaly, vertical gravity gradient anomaly, and shipborne bathymetric data of the study area were selected, and the outliers of the shipborne bathymetric data were removed to obtain the depth Z of the shipborne bathymetric control point; at the same time, the gravity anomaly Δg of the ETOPO1 water depth model was forward modeled using the Parker algorithm. f (x,y) and vertical gravity gradient anomaly Δg fv (x, y), and obtain the gravity information Δg of the ETOPO1 water depth model forward simulation f ;

[0008] Obtain the gravity anomaly Δg(x,y) and vertical gravity gradient anomaly Δg obtained by satellite altimetry inversion v (x,y), respectively for Δg(x,y) and Δg v (x, y) is decomposed by wavelet to obtain the gravity information Δg after wavelet decomposition; the gravity information Δg obtained after wavelet decomposition is compared with the gravity information Δg forward modeled by the ETOPO1 water depth model through correlation analysis. f and the depth Z of the shipborne sounding control point to obtain the correlation coefficient result; according to the correlation coefficient result, the optimal order i and j of wavelet decomposition are determined;

[0009] Constructing and training a network model: Bilinear interpolation is used to obtain the gravity information Δg and the corresponding coordinate information of the wavelet decomposition results at the positions of the shipborne sounding control points, and normalization processing is performed. The normalized result G is used as the input of the network model; the depth Z of the shipborne sounding control points is used as the output of the network model; the weights and bias parameters of the network model are adjusted through error backpropagation until the set value or the number of iteration steps is reached, and the training is completed.

[0010] Based on the finally obtained weights and bias parameters through training, a water depth inversion model is constructed; the gridded gravity information and the corresponding coordinate information after wavelet decomposition are input into the water depth inversion model, so as to inversely obtain a 1′×1′ water depth model in the study area.

[0011] In the above method for improving the accuracy of water depth inversion based on neural network-wavelet decomposition of gravity information, the Parker algorithm is used to forward model the gravity anomaly Δg f (x, y) and the vertical gravity gradient anomaly Δg fv (x, y) of the ETOPO1 water depth model, and the gravity information Δg f obtained by forward modeling of the ETOPO1 water depth model is obtained, including:

[0012] The gravity anomaly Δg f (x, y) and the vertical gravity gradient anomaly Δg fv (x, y) of the ETOPO1 water depth model are respectively forward modeled through the following formulas (1.4) and (1.5):

[0013]

[0014]

[0015] Among them, F represents the Fourier transform, γ represents the gravitational constant, ρ c and ρ w respectively represent the average densities of the oceanic crust and seawater, k represents the radial frequency, d represents the average water depth, h n (x, y) represents the topographic undulation relative to the average water depth, and n represents the order of summation;

[0016] The Δg f (x, y) and Δg fv (x, y) calculated respectively through formulas (1.4) and (1.5) are used as the gravity information Δg f obtained by forward modeling of the ETOPO1 water depth model.

[0017] In the above method for improving the accuracy of water depth inversion based on neural network-wavelet decomposition of gravity information, Δg(x, y) and Δg v(x, y) is subjected to wavelet decomposition to obtain the gravity information Δg after wavelet decomposition, including:

[0018] Δg(x, y) and Δg are respectively subjected to wavelet decomposition through the following formulas (1.2) and (1.3): v (x, y) for wavelet decomposition:

[0019]

[0020]

[0021] where A I G represents the approximation part of the I-th order wavelet decomposition, and D i G represents the gravity anomaly detail part after i times of wavelet decomposition, i = 1, 2,..., I; represents the approximation part of the J-th order wavelet decomposition, represents the detail part after j times of wavelet decomposition, j = 1, 2,..., J;

[0022] The obtained A I G, D i G, and are used as the gravity information Δg after wavelet decomposition.

[0023] In the above method for improving the water depth inversion accuracy based on neural network - wavelet decomposition of gravity information, the gravity information Δg obtained after wavelet decomposition is compared with the gravity information Δg f forward modeled by the ETOPO1 water depth model and the depth Z of the shipborne sounding control points through correlation analysis to obtain the correlation coefficient results, including:

[0024] Through the following formulas (1.7) and (1.8), the gravity information Δg obtained after wavelet decomposition is analyzed and compared with Δg f and Z to obtain the correlation coefficient ρ1 between the gravity after wavelet decomposition and the water depth and the correlation coefficient ρ2 between the gravity after wavelet decomposition and the forward modeled gravity:

[0025]

[0026]

[0027] where Z m represents the water depth value at the position of the corresponding point m, represents the forward modeled gravity information at the position of point m, and Δg m represents the gravity information retrieved by satellite altimetry at the position of point m, and respectively represent Δg, Z, and Δg fThe average value, M represents the total number of ship-measured control points, m = 1, 2,..., M;

[0028] Then, the correlation coefficient result ρ is:

[0029] ρ = (ρ1 + ρ2) / 2 (1.6).

[0030] In the above method for improving the water depth inversion accuracy based on neural network - gravity information wavelet decomposition, determining the optimal orders i and j of wavelet decomposition according to the correlation coefficient result includes: as the wavelet decomposition order is different, when ρ is the maximum, determining the optimal orders i and j of wavelet decomposition.

[0031] In the above method for improving the water depth inversion accuracy based on neural network - gravity information wavelet decomposition, adjusting the weight and bias parameters of the network model through error backpropagation until a set value or iteration step is met to complete the training, including:

[0032] Based on the following formula (1.9), adjusting the weight and bias parameters of the network model until a set value or iteration step is met to complete the training:

[0033]

[0034] Where, represents the transfer function between network layers; W (1) represents the weight matrix from the input layer to the hidden layer; W (2) represents the weight matrix between hidden layers; W (3) represents the hidden

[0035] layer to the output layer weight matrix; the above weight matrices are constructed by the weight values ω between neurons; b1 represents the bias parameter vector of 5 who, b2 represents the bias parameter vector of who, and b3 represents the bias parameter vector of who.

[0036] In the above method for improving the water depth inversion accuracy based on neural network - gravity information wavelet decomposition, G = [ga, vga, lon, lat] T , ga represents the gravity anomaly after wavelet decomposition and normalization processing, vga represents the vertical gravity gradient anomaly after wavelet decomposition and normalization processing, lon represents the longitude of the ship - measured control point, and lat represents the latitude of the ship - measured control point.

[0037] Correspondingly, the present invention also discloses a system for improving the water depth anti -

[0038] inversion accuracy based on neural network - gravity information wavelet decomposition, including:

[0039] The first data processing module is used to select the ETOPO1 water depth model, gravity anomaly and vertical gravity gradient anomaly, and shipborne bathymetric data in the study area, and remove outliers from the shipborne bathymetric data to obtain

[0040] The depth Z of the shipborne sounding control point; at the same time, the Parker algorithm is used to forward model the 5 gravity anomalies Δg of the ETOPO1 water depth model f (x,y) and vertical gravity gradient anomaly Δg fv (x, y), and obtain the gravity information Δg of the ETOPO1 water depth model forward simulation f ;

[0041] The second data processing module is used to obtain the gravity anomaly Δg(x,y) and vertical gravity gradient anomaly Δg obtained by satellite altimetry inversion. v (x,y), respectively for Δg(x,y) and Δg v (x, y) is decomposed by wavelet to obtain the gravity information Δg after wavelet decomposition; the gravity information Δg obtained after wavelet decomposition is compared with the gravity information Δg forward modeled by the ETOPO1 water depth model through correlation analysis. f and the depth Z of the shipborne sounding control point to obtain the correlation coefficient result; according to the correlation coefficient result, the optimal order i and j of wavelet decomposition are determined;

[0042] The model building and training module is used to build and train the network model: bilinear interpolation is used to obtain the gravity information Δg and the corresponding coordinate information of the wavelet decomposition result at the position of the ship-borne bathymetric control point, and normalization is performed, and the normalized result G is used as the input of the network model; the depth Z of the ship-borne bathymetric control point is used as the output of the network model; the weights and bias parameters of the network model are adjusted through error back propagation until the set value or iteration step is obtained to complete the training;

[0043] The inversion module is used to construct a water depth inversion model based on the final weights and bias parameters obtained through training; the gridded gravity information and the corresponding coordinate information after wavelet decomposition are input into the water depth inversion model, thereby inverting a 1′×1′ water depth model in the study area.

[0044] The present invention has the following advantages:

[0045] The present invention discloses a method for improving the accuracy of water depth inversion based on neural network-gravity information wavelet decomposition. Ocean gravity information inverted based on satellite altimetry can quickly obtain a large-scale seabed terrain model. However, the use of ocean gravity information to invert water depth is affected by non-correlation factors such as crustal equilibrium. In addition, the problem of how to quickly and effectively combine gravity anomalies and vertical gravity gradient anomalies for water depth inversion is also urgently needed to be solved. Therefore, the present invention uses a multi-layer neural network method to achieve the purpose of improving the accuracy of water depth inversion by combining multi-source gravity information. First, based on the traditional multi-layer neural network algorithm, wavelet decomposition and correlation analysis are used to effectively apply multi-source gravity information to construct a new neural network-gravity information wavelet decomposition combined method (Combined Neural Network and Gravity Information Wavelet Decomposition Method, CNNGWD). Second, the CNNGWD method and the traditional neural network method are used to invert the water depth of the Manila Trench area in the sea, and the accuracy of the inversion results is evaluated using ship-borne bathymetric data and the internationally universal water depth model ETOPO1 and GEBCO_2021 model. The results show that the root mean square error of the BM1 (Bathymetric Model 1) water depth model inverted by the CNNGWD method and the difference between the shipborne bathymetric checkpoints is 59.90m, which is 12.45%, 64.70% and 28.68% higher than the BM2 (Bathymetric Model 2) model, ETOPO1 model and GEBCO_2021 model inverted by the traditional neural network. Third, the accuracy of the four water depth models was analyzed by using shipborne measured data. The results show that the accuracy of the four models is significantly better than that of the rugged seamount area in the gently changing deep-sea trough, but the BM1 model has a better advantage in the rugged sea area. In addition, the accuracy of the BM1 model is less affected by the change of water depth, and the overall stability of the model is better than that of the international model. Therefore, the CNNGWD method proposed in the present invention provides a useful reference for the construction of water depth models in a large area using multi-source gravity data. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of a method for improving water depth inversion accuracy based on neural network-gravity information wavelet decomposition in an embodiment of the present invention;

[0047] Figure 2 It is a structural schematic diagram of a neural network-gravity information wavelet decomposition joint method in an embodiment of the present invention;

[0048] Figure 3 is a schematic diagram of the location of a research area in an embodiment of the present invention;

[0049] Figure 4It is a schematic diagram of the gravity anomaly result in an embodiment of the present invention; among them, 4(a) is the result of satellite altimetry inversion; 4(b) is the forward modeling result of the water depth model;

[0050] Figure 5 It is a schematic diagram of the wavelet decomposition approximation result of the gravity anomaly in an embodiment of the present invention; among them, from left to right and from top to bottom are the results of the 1st to 8th order decompositions in sequence;

[0051] Figure 6 It is a schematic diagram of the wavelet decomposition detail result of the gravity anomaly in an embodiment of the present invention; among them, from left to right and from top to bottom is the accumulation of the 1st to 8th order decompositions in sequence;

[0052] Figure 7 It is a schematic diagram of the correlation curve of the gravity anomaly decomposition result in an embodiment of the present invention;

[0053] Figure 8 It is a schematic diagram of the vertical gravity gradient anomaly in an embodiment of the present invention; among them, 8(a) is the satellite altimetry result; 8(b) is the forward modeling result of the water depth model;

[0054] Figure 9 It is a schematic diagram of the wavelet decomposition approximation result of the gravity gradient in an embodiment of the present invention; among them, from left to right and from top to bottom are the results of the 1st to 8th order decompositions in sequence;

[0055] Figure 10 It is a schematic diagram of the wavelet decomposition detail result of the gravity gradient in an embodiment of the present invention; among them, from left to right and from top to bottom is the accumulation of the 1st to 8th order decompositions in sequence;

[0056] Figure 11 It is a correlation curve diagram of the vertical gravity gradient anomaly decomposition in an embodiment of the present invention;

[0057] Figure 12 It is a schematic diagram of the water depth model result in an embodiment of the present invention; among them, 12(a) is BM1; 12(b) is BM2; 12(c) is the ETOPO1 model; 12(d) is the GEBCO model;

[0058] Figure 13 It is a schematic diagram of the model difference result in an embodiment of the present invention; among them, 13(a) is the difference between BM1 and ETOPO1; 13(b) is the difference between BM1 and GEBCO; 13(c) is the difference between BM1 and BM2; 13(d) is the difference between BM2 and ETOPO1; 13(e) is the difference between BM2 and GEBCO; 13(f) is the difference between ETOPO1 and GEBCO;

[0059] Figure 1414(a) is a histogram of the difference values ​​of the ship measurement and verification points in an embodiment of the present invention; wherein 14(a) is BM1; 14(b) is BM2; 14(c) is ETOPO1; 14(d) is GEBCO;

[0060] Figure 15 15(a) is a relative error distribution diagram in an embodiment of the present invention; wherein 15(a) is BM1; 15(b) is BM2; 15(c) is ETOPO1; 15(d) is GEBCO;

[0061] Figure 16 16(a) is BM1; 16(b) is BM2; 16(c) is ETOPO1; and 16(d) is GEBCO. DETAILED DESCRIPTION

[0062] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments disclosed in the present invention will be further described in detail below with reference to the accompanying drawings.

[0063] Different from previous studies, in order to effectively combine multi-source gravity information and reduce the interference of noise in the information, the present invention decomposes the input gravity anomaly and vertical gravity gradient anomaly based on wavelet transform, constructs a new neural network-gravity information wavelet decomposition combined method (Combined Neural Network Gravity Information Wavelet Decomposition Method, CNNGWD) through correlation analysis, and applies it to the construction of 1′×1′ water depth model in the Manila Trench area. The CNNGWD method can be summarized into the following steps: First, preprocess the shipborne bathymetric data to remove the existing bathymetric outliers, and then use the Parker algorithm to forward model the gravity information of the ETOPO1 water depth model. Second, use wavelet decomposition to decompose the gravity anomaly and vertical gravity gradient anomaly inverted by satellite altimetry to obtain the approximate results and detailed results of gravity information of different orders. Third, analyze the correlation between the gravity information of different wavelet decomposition orders and the shipborne bathymetric data and the forward gravity information, and determine the optimal order of the above wavelet decomposition. Fourth, the gravity anomaly and vertical gravity gradient anomaly grid data after optimal wavelet decomposition and their corresponding longitude and latitude coordinates are used as the input of the neural network to invert the water depth in the study area. The accuracy of the inversion results is evaluated using shipborne measured data and the existing international models ETOPO1 and GEBCO_2021, thereby verifying the effectiveness and applicability of the CNNGWD method.

[0064] like Figure 1 In this embodiment, the method for improving water depth inversion accuracy based on neural network-gravity information wavelet decomposition includes:

[0065] Step 1: Select the ETOPO1 bathymetric model, gravity anomaly, and vertical gravity gradient anomaly of the study area, as well as the shipborne sounding data. Remove the outliers from the shipborne sounding data to obtain the depth Z of the shipborne sounding control points. At the same time, use the Parker algorithm to forward model the gravity anomaly Δg f (x,y) and the vertical gravity gradient anomaly Δg fv (x,y) of the ETOPO1 bathymetric model to obtain the gravity information Δg f .

[0066] In this embodiment, the gravity anomaly Δg f (x,y) and the vertical gravity gradient anomaly Δg fv (x,y) of the ETOPO1 bathymetric model can be forward modeled respectively through the following formulas (1.4) and (1.5):

[0067]

[0068]

[0069] where F represents the Fourier transform, γ represents the gravitational constant, ρ c and ρ w represent the average densities of the oceanic crust and seawater respectively, k represents the radial frequency, d represents the average water depth, h n (x,y) represents the topographic undulation relative to the average water depth, and n represents the order of summation. Preferably, considering the influence of the nonlinear terms in formulas (1.4) and (1.5) on the result of the forward modeled gravity information, n = 2 can be taken. If the gravity information generated by the ETOPO1 bathymetric model is to be solved, only the inverse Fourier transform needs to be performed on both sides of formulas (1.4) and (1.5).

[0070] Take the Δg f (x,y) and Δg fv (x,y) calculated through formulas (1.4) and (1.5) respectively as the gravity information Δg f of the forward modeling of the ETOPO1 bathymetric model.

[0071] Step 2: Obtain the gravity anomaly Δg(x,y) and the vertical gravity gradient anomaly Δg v (x,y) obtained by satellite altimetry inversion. Perform wavelet decomposition on Δg(x,y) and Δg v (x,y) respectively to obtain the gravity information Δg after wavelet decomposition. Compare the gravity information Δg obtained after wavelet decomposition with the gravity information Δg fObtain the correlation coefficient result with the depth Z of the shipborne sounding control point; determine the optimal orders i and j of wavelet decomposition according to the correlation coefficient result.

[0072] In this embodiment, the essence of retrieving water depth using multi-source gravity information obtained by satellite altimetry is to analyze the correlation between gravity information and water depth based on the constraint of shipborne sounding data, and then establish a corresponding inversion model, that is, a problem of multiple inputs and single output. And artificial neural network is an information processing technology that uses known constraint points for training and thereby establishes a relationship model between input and output. Therefore, water depth inversion based on neural network is a fast and relatively effective method. However, the gravity anomaly (GA) and vertical gravity gradient anomaly (VGG) retrieved by satellite altimetry are the comprehensive reflections of the undulations of different material density interfaces from the sea surface to the deep mantle, while the water depth is the undulation depth of the density interface between the seawater layer and the sediment layer (or basement). Therefore, the superposition of anomaly information generated by different interfaces interferes with the extraction of gravity information caused by changes in seawater depth. So, it is necessary to adopt a certain method to appropriately separate the gravity information and extract the gravity information generated by changes in seawater depth.

[0073] Wavelet transform has been widely used in the multi-scale decomposition process of signals. It decomposes a signal into an approximation component and a detail component through continuous low-pass and high-pass iterative filtering. The results of multi-scale wavelet decomposition of gravity information can effectively reflect the signals of different geological body burial depths, thus providing a new idea for extracting gravity information caused by water depth. Therefore, based on the basic theory of wavelet transform, the wavelet decomposition expression of two-dimensional gravity information (GA or VGG) f(x, y) ∈ L 2 (R 2 ) is defined as:

[0074]

[0075] Among them, ψ*(x, y) represents the complex conjugate of the wavelet function; a represents the dilation coefficient, which is used to control the size of the wavelet function; b, c represent the translation coefficients, which are used to control the position of the wavelet function. For the convenience of quickly implementing the continuous wavelet decomposition of the above formula (1.1),

[0076] Preferably, the wavelet two-dimensional decomposition of gravity anomaly and vertical gravity gradient anomaly can be based on the Mallat algorithm. Specifically for the wavelet decomposition of Δg(x, y) and Δg v (x, y), there are:

[0077] Perform wavelet decomposition on Δg(x, y) and Δg v (x, y) respectively through the following formula (1.2) and formula (1.3):

[0078]

[0079]

[0080] Among them, A I G represents the approximation part of the i-th order wavelet decomposition, and D i G represents the gravity anomaly detail part after i times of wavelet decomposition, where i = 1, 2,..., I; represents the approximation part of the J-th order wavelet decomposition, represents the detail part after j times of wavelet decomposition, where j = 1, 2,..., J.

[0081] The obtained A I G, D i G, and are used as the gravity information Δg after wavelet decomposition.

[0082] Preferably, the optimal orders i and j of wavelet decomposition are determined as follows:

[0083] By using the following formulas (1.7) and (1.8), analyze and compare the gravity information Δg obtained after wavelet decomposition with Δg f and Z, and obtain the correlation coefficient ρ1 between the gravity after wavelet decomposition and water depth and the correlation coefficient ρ2 between the gravity after wavelet decomposition and the forward gravity:

[0084]

[0085]

[0086] Among them, Z m represents the water depth value at the position of the corresponding point m, represents the forward gravity information at the position of point m, and Δg m represents the gravity information inverted by satellite altimetry at the position of point m, and respectively represent the average values of Δg, Z, and Δg f , and M represents the total number of ship-measured control points, where m = 1, 2,..., M.

[0087] Then, the correlation coefficient result ρ is:

[0088] ρ = (ρ1 + ρ2) / 2 (1.6)

[0089] As the wavelet decomposition order varies, when ρ is the maximum, determine the optimal orders i and j of wavelet decomposition.

[0090] Step 3, construct and train the network model: Use bilinear interpolation to obtain the gravity information Δg and the corresponding coordinate information of the wavelet decomposition result at the positions of the shipborne sounding control points, and perform normalization processing. Take the normalized result G as the input of the network model; take the depth Z of the shipborne sounding control points as the output of the network model; adjust the weight and bias parameters of the network model through error backpropagation until the set value or the iteration step is met, and complete the training.

[0091] In this embodiment, in order to improve the accuracy of the model during the training of the multi-layer neural network, error backpropagation is usually used to each network layer, and the Levenberg-Marquardt training algorithm is used to continuously adjust the weights and bias parameters of the network to minimize the error of the trained network model. In addition, in order to balance the dimensional differences between the input data and the output data and improve the convergence speed of the neural network training, linear normalization processing is performed on the input data.

[0092] Preferably, based on the following formula (1.9), adjust the weight and bias parameters of the network model until the set value or the iteration step is met, and complete the training:

[0093]

[0094] where represents the transfer function between each network layer; W (1) represents the weight matrix from the input layer to the hidden layer; W (2) represents the weight matrix between the hidden layers; W (3) represents the weight matrix from the hidden layer to the output layer; the above weight matrices are constructed by the weight values ω between neurons; b1 represents the bias parameter vector of whom, b2 represents the bias parameter vector of whom, and b3 represents the bias parameter vector of whom.

[0095] Preferably, G = [ga, vga, lon, lat] T ; where ga represents the gravity anomaly after wavelet decomposition and normalization processing, vga represents the vertical gravity gradient anomaly after wavelet decomposition and normalization processing, lon represents the longitude of the ship measurement control point, and lat represents the latitude of the ship measurement control point.

[0096] Step 4, construct a water depth inversion model based on the finally obtained weight and bias parameters after training; input the gridded gravity information and the corresponding coordinate information after wavelet decomposition into the water depth inversion model, so as to inversely obtain a 1′×1′ water depth model in the study area.

[0097] On the basis of the above embodiments, the verification and application of the method for improving the water depth inversion accuracy based on neural network - wavelet decomposition of gravity information will be described below.

[0098] 2.1 Data description and preprocessing

[0099] This invention selects the sea area near the eastern part of the Manila Trench and the Luzon Strait in the South China Sea (119° - 121°E, 19° - 21°N) to conduct research (such as Figure 3 ). The water depth varies from -700 to -4300 m. This area is formed by the subduction of the Sunda Plate in the Eurasian continent into the Philippine Plate, with complex topographic features such as seamounts and deep-sea troughs near the eastern Luzon Island Arc. As an important international navigation area connecting the South China Sea and the Philippine Sea, obtaining accurate water depth information is of great significance for studying the physical oceanographic processes in this area. In the research, 105,396 shipborne bathymetric data points and the ETOPO1 water depth model in the area are obtained from NGDC (such as Figure 3 ). The gravity anomaly data ( Figure 4 (a)) and the vertical gravity gradient anomaly data ( Figure 8 (a)) are obtained through the Scripps Institution of Oceanography, USA. The GEBCO_2021 version (15″×15″) water depth model ( Figure 12 (d)) for comparative analysis is obtained from the British Oceanographic Data Centre and the International Hydrographic Organization, and is downsampled for convenient analysis in the experiment.

[0100] Since the shipborne bathymetric data collected by NGDC has a wide range of sources and certain time intervals, and there are differences between experimental instruments, there are inevitably certain errors. Therefore, it is necessary to preprocess it to ensure the quality of the shipborne bathymetric data. This invention uses the existing ETOPO1 model to determine outliers in the shipborne bathymetric data. First, bilinear interpolation is used to obtain the model value at the position of the shipborne bathymetric point, and the difference between the model value and the measured value is determined. Then, three times the standard deviation of the difference value is used as the standard for evaluating outliers. If the difference value at a point is greater than this standard, it is considered a bathymetric anomaly. Finally, the preliminarily identified outliers are deleted.

[0101] The standard deviation of the difference between the shipborne bathymetric data and the ETOPO1 model is 253.48 m, and three times of it (760.44 m) is used to preprocess the shipborne bathymetric data. The standard deviation after processing is reduced from 881.10 m to 860.18 m, and the stability of the data is significantly improved. In addition, it is found from the statistics of the original dataset that its maximum depth value is 11,966.29 m, which is extremely inconsistent with the actual situation according to the research location. After preprocessing, the maximum depth value is reduced to 4,492.90 m. Finally, 279 measurement points are determined as abnormal values, and 105,117 data points remain. Among them, 2 / 3 are selected as control points for water depth model inversion, and the remaining 1 / 3 are check points for evaluating the accuracy of the inverted water depth model. Their distribution is shown in Figure 3Midpoint distribution. Subsequently, wavelet decomposition is performed on the gravity anomaly and vertical gravity gradient anomaly.

[0102] 2.2 Determination of the optimal decomposition result of gravity information

[0103] There is a certain correlation between water depth and gravity information. However, this relationship is affected by the deep crustal materials. If the gravity information retrieved by satellite altimetry is directly used to retrieve water depth, it will inevitably cause large errors. Therefore, in the present invention, based on the Daubechies5 wavelet basis function, wavelet decomposition of the gravity anomaly and vertical gravity gradient anomaly is respectively performed at the 8th order using formulas (1.2) and (1.3).

[0104] 2.2.1 Optimal decomposition result of gravity anomaly

[0105] Select the SIO V29.1 gravity anomaly data as Figure 4 (a) shown. To determine the optimal wavelet decomposition order, the shipborne water depth data and the forward gravity and wavelet decomposition results of the water depth model are respectively analyzed. Among them, the gravity anomaly obtained by forward modeling the ETOPO1 water depth model using the Parker formula (1.4) is as Figure 4 (b) shown.

[0106] The gravity anomaly result based on wavelet decomposition can be divided into two parts: the approximation anomaly and the detail anomaly, as Figure 5 and Figure 6 shown. The approximation result of wavelet decomposition is the low-pass filtering process of the gravity anomaly, while the detail result is the high-pass filtering of the gravity anomaly. As the decomposition order increases, the low-pass and high-pass filtering of the previous approximation result are iterated until the set decomposition order is satisfied. As can be seen from Figure 5 it, as the decomposition order increases, the gravity anomaly gradually becomes smoother, and when decomposed to the 4th order, a relatively obvious smoothing result appears. It can be considered that the approximation result of the gravity anomaly is the gravity anomaly generated by the deep earth structure, and as the decomposition order increases, it reflects the gravity anomaly generated by materials buried deeper.

[0107] According to formulas (1.7) and (1.8), the correlations between the shipborne measurement depth, the terrain forward gravity anomaly, and the gravity anomalies of different orders of wavelet decomposition are calculated, and the curve of the correlation coefficient changing with the wavelet decomposition order is plotted as Figure 7 shown. As can be seen from Figure 7It can be seen that as the wavelet decomposition order increases, the correlation between the depth, forward gravity anomaly and the detailed results of wavelet decomposition shows a positive correlation trend of increasing first and then decreasing. It can be calculated from formula (1.6) that when the order is 6, the correlation coefficient reaches the maximum value of about 0.41, which is about 97.56% higher than the gravity result without decomposition. This correlation result reflects from the side that there may be many complex geological bodies in the area, and it is difficult to separate the gravity anomalies generated by them in detail using the wavelet decomposition method. However, the overall correlation of the gravity anomaly after wavelet decomposition is significantly improved compared with that before decomposition, which is of great significance for the construction of the CNNGWD method model.

[0108] In contrast, both the water depth and the forward gravity anomaly show a negative correlation with the approximation results of wavelet decomposition. And as the decomposition order increases, the correlation first increases and then decreases, and the highest correlation is about -0.49 at the 7th order. When studying the Earth's gravity field and its deep tectonic structure, two density interfaces that generate gravity anomalies are mainly concerned, one is the contact surface between the seabed bedrock and seawater, and the other is the Moho undulation interface. According to the isostatic hypothesis of the crust, the undulation of the seabed topography and the Moho interface undulation show an approximate mirror image relationship. It can be seen from the wavelet decomposition results that the approximation model of the gravity anomaly decomposed at the 7th order may be caused by the undulation of the Moho interface. Based on the above correlation analysis of the gravity anomaly after wavelet decomposition, the forward gravity anomaly and the shipborne measured data, the sum of the detailed results of the gravity anomaly decomposed from the 1st to the 6th order is used as the input for the training of the CNNGWD model in the present invention.

[0109] 2.2.2 Optimal decomposition result of vertical gravity gradient anomaly

[0110] Select the SIO V29.1 vertical gravity gradient anomaly data as Figure 8 (a) shows. Consistent with the above analysis, in order to determine the optimal wavelet decomposition order, the vertical gravity gradient anomaly of the ETOPO1 water depth model is forward calculated using formula (1.5) as Figure 8 (b) shows. Compared with the gravity anomaly, the vertical gravity gradient anomaly reflects more detailed information.

[0111] Same as the wavelet decomposition result of the gravity anomaly, the approximation and detailed parts of the vertical gravity gradient anomaly are respectively calculated through iterative low-pass and high-pass filtering processes, and the results are respectively as Figure 9 and Figure 10 shown. It can be seen from Figure 9 that as the decomposition order increases, the vertical gravity gradient anomaly gradually becomes smoother, and theoretically it reflects more anomaly information caused by deep substances. And the corresponding detailed results of wavelet decomposition are as Figure 10As shown, it reflects the vertical gravity gradient anomaly caused by shallow substances, embodying more topographic detail information. However, in the present invention, the correlations between the shipborne measurement depth, the vertical gravity gradient anomaly forward modeled by the water depth model, and the vertical gravity gradient anomalies of different orders obtained by wavelet decomposition are calculated according to Formulas (1.7) and (1.8) respectively, and the curve of the correlation coefficient varying with the wavelet decomposition order is plotted, obtaining different conclusions.

[0112] As Figure 11 shown, the vertical gravity gradient anomaly forward modeled by the water depth model is closer to the approximation result of the first-order wavelet decomposition. Compared with Figure 7 the gravity anomaly variation curve, it shows that the vertical gravity gradient anomaly has a better correlation with the seabed topography and can better reflect the characteristics of the seabed topography. Therefore, applying the vertical gravity gradient anomaly to invert the seabed topography can effectively improve the inversion accuracy, and relevant research has also verified this conclusion. From the variation curve graph ( Figure 11 ) it can be seen that as the wavelet decomposition order increases, the correlation between the shipborne measurement depth, the gravity forward modeled by the model, and the detail results of wavelet decomposition shows a positive correlation trend of first increasing and then decreasing. The correlation coefficient between the water depth and the detail model is below 0.25, probably due to the influence of noise in the vertical gravity gradient anomaly. In addition, from the result of Formula (1.6), it can be seen that at the 5th order, the correlation coefficient of the wavelet detail result reaches the highest, about 0.30. In comparison, when the wavelet decomposition approximation result is at the 5th decomposition, the correlation coefficient of both the water depth and the decomposition result and the forward modeled gravity and the decomposition result reaches the highest, about 0.49. Therefore, the present invention adopts the approximation result of the 5th-order wavelet decomposition to carry out water depth inversion.

[0113] 2.3 Results and Analysis of Water Depth Inversion by the CNNGWD Method

[0114] The present invention analyzes the water depth results inverted by the CNNGWD method and compares them with the inversion results of the traditional multi-layer neural network method and the internationally common water depth models ETOPO1 and GEBCO model. According to the distribution of the shipborne sounding data, the data set is divided into two parts as Figure 3 shown, with a total of 70078 points as control point data for accuracy evaluation of the water depth model. First, the gravity anomaly and the vertical gravity gradient anomaly at the control point positions are obtained through the bilinear interpolation algorithm. Then, based on the CNNGWD method, by continuously adjusting the network structure parameters, a network model structure as Figure 2 shown is constructed. Finally, the gridded gravity anomaly and vertical gravity gradient anomaly obtained by wavelet decomposition and their corresponding longitude and latitude coordinates are input into the trained model for water depth inversion, and the result of the water depth model BM1 is obtained as Figure 12 (a) shown. And the result of the water depth model BM2 inverted by the traditional multi-layer neural network method is as Figure 12 (b) shown.

[0115] From Figure 12 It can be seen from the bathymetry model results that the bathymetry model inverted by the CNNGWD method proposed in the present invention is basically consistent with the existing model in terms of the change trend, and there are only some differences in certain detailed areas. To further analyze the similarities and differences between different models, the model information and the correlation coefficients between the models are respectively counted. The average value and standard deviation of the BM1 model are -3179.75 m and 686.56 m respectively; while the average value and standard deviation of the BM2 model are -3182.31 m and 682.34 m respectively. Comparing the correlation coefficients of the inversion model with the international bathymetry models, the correlation coefficients of the BM1 model with the ETOPO1 model and the GEBCO model are 0.973 and 0.978 respectively; while the correlation coefficients of the BM2 model with the ETOPO1 and GEBCO models are 0.968 and 0.973 respectively. Therefore, compared with the BM2 model, the BM1 model is closer to the international general models.

[0116] To further compare the differences of the bathymetry models in different regions, the differences between the models are calculated respectively, and the results are as Figure 13 shown. By comparing Figure 13 (a), 13(d) and Figure 13 (b), 13(e) respectively, it can be seen that the difference patterns of the BM1 model and the BM2 model with the international general models are basically the same as a whole, and the differences are more reflected in the local details. And the BM1 model is closer to the two international general models. The standard deviations of the differences between the BM1 and the ETOPO1 and GEBCO are 159.76 m and 145.17 m respectively, while the standard deviations of the differences between the BM2 and the ETOPO1 and GEBCO are 171.83 m and 159.21 m respectively. It can be seen from Figure 13 (c) that the BM1 and the BM2 are basically the same in the entire study area, but the differences are relatively large in the areas with drastic bathymetry changes. Especially, the difference reaches more than 2000 m at the edge in the southeast direction of the study area, which is considered to be caused by the reduction of the gravity anomaly recovered by satellite altimetry and the accuracy of shipborne bathymetry due to the proximity of this area to the island reefs. Similarly, this difference also exists between the ETOPO1 and GEBCO models, which is caused by the different gravity anomaly models and modeling methods used in the construction of the two models. However, the comparison between the models can only indirectly show that the BM1 model is closer to the international models than the BM2 model. Therefore, the present invention uses the measured shipborne bathymetry data to further evaluate the accuracy of the model.

[0117] To further illustrate the effectiveness of the CNNGWD method of the present invention, Figure 3A total of 35,039 shipborne survey data (SSD) were used to evaluate the accuracy of the bathymetric models. Bilinear interpolation was adopted to determine the model values of the four bathymetric models at the positions of the verification points. Using the shipborne survey data as the true values, the differences between the model values and the measured values were compared by taking the differences. A statistical histogram of the number of verification points changing with the difference was plotted ( Figure 14 ). In addition, the present invention defines the relative error, that is, the percentage of the absolute value of the ratio of the difference between the model value and the true value to the true value, which can indirectly reflect the variation of the difference value at different depths. RESTD represents the standard deviation of the relative error and is used as the criterion for judging large differences.

[0118] It can be seen from Figure 14 that the peak value of BM1 is significantly higher than the other three models. There are 32,198 verification points with the absolute value of the difference less than 100 m, accounting for about 91.89%; the number of verification points within 250 m accounts for about 99.43%. For the BM2 model, the proportion of verification points with the absolute value of the difference within 100 m is about 89.39%, and within 250 m is about 99.25%. The distribution of the differences of the verification points of the ETOPO1 model is relatively discrete, and its peak value is significantly smaller than the other three models. The data with the difference less than 100 m accounts for about 57.43%, and within 250 m accounts for about 85.25%, indicating that the accuracy of the ETOPO1 model is relatively poor. The number of verification points of the GEBCO model with the difference less than 100 m is 28,060, accounting for about 80.08%, and within 250 m accounts for about 98.22%. From the proportion of the differences of the verification points in different depth ranges, it can be seen that the BM1 model has the best accuracy, followed by the BM2 model, the GEBCO model and the ETOPO1 model in turn.

[0119] The maximum difference between the BM1 model and the measured data is approximately 800 m, while that between the BM2 model and the GEBCO model exceeds 1000 m. In addition, the root mean square error of BM1 is approximately 59.90 m, while those of the BM2, ETOPO1, and GEBCO models are 68.41 m, 169.71 m, and 87.40 m, respectively. The accuracy of the BM1 model inverted based on the CNNGWD method is improved by 12.45%, 64.70%, and 28.68% compared with the BM2, ETOPO1, and GEBCO models, respectively. Among the four models, the ETOPO1 model has the lowest accuracy, mainly because it uses a gravity anomaly model with relatively low accuracy and is constructed by fusing ship-measured water depths. The GEBCO model is mainly based on the fusion of multi-beam ship-measured data, single-beam ship-measured data, and water depth data inverted from gravity anomalies, without considering the water depth inverted from vertical gravity gradient anomalies, so its accuracy is not very satisfactory among the four models. In contrast, both the BM1 model and the BM2 model are obtained by inverting gravity anomalies and vertical gravity gradient anomalies, and the model accuracy has been significantly improved. However, the BM1 inverted by the CNNGWD method of the present invention has the best accuracy. Therefore, the CNNGWD method effectively fuses multi-source gravity data, weakens the influence of noise in gravity information, and is of great significance for improving the accuracy of water depth inversion.

[0120] To further analyze the stability of the water depth model at different water depths, Figure 15 show the spatial distribution of the relative error. From Figure 15 it can be seen that the relative error of BM1 is significantly lower than those of the BM2 model, ETOPO1 model, and GEBCO model. The distributions of the BM1 and GEBCO models in the study area are similar, with only certain differences in the seamount areas in the northeast and southwest directions. The reason may be that the GEBCO model fuses the shipborne measured depth data and the water depth data inverted from gravity during the construction process, which improves the accuracy of the model at the verification point location. From the overall distribution of the relative error, it can be seen that the relative errors of the four models are relatively small in the area where the water depth changes relatively gently (the central and western parts of the study area), while the relative errors are relatively large in the area with large water depth fluctuations in the northeast. One reason for this phenomenon may be that the large deposition of sediments in the orogenic belt in Taiwan, China, leads to a decrease in the correlation between water depth and gravity information; on the other hand, due to large water depth fluctuations, the abnormal data determination during the preprocessing of shipborne bathymetric data is insufficient, which affects the accuracy of water depth inversion.

[0121] The present invention selects the standard deviation of the relative error as the criterion for determining whether it is a large difference value. The average value (3.48%) of the RESTD of the four models is selected to determine a large difference. If the relative error is greater than 3.48%, it is considered a large difference. The distribution of the large difference points among the four models is as Figure 16Midpoint distribution. The minimum number of midpoint distributions in the BM1 model inverted by the CNNGWD method is 5,411, followed by the BM2 model (6,731), 9,509 in the GEBCO model, and the largest number (18,121) in the ETOPO1 model. It can be seen from the midpoint distribution in the figure that the midpoints are concentrated in the eastern part of the study area, which is mostly seamount landforms with drastic water depth changes. In the area with relatively gentle water depth, the midpoint distribution is relatively less. This is basically consistent with the above relative error distribution map ( Figure 15 ). Therefore, whether it is an internationally common model or the inversion model of the present invention, its accuracy is greatly affected by water depth changes. However, the BM1 model has better stability in the area with drastic water depth changes.

[0122] To further analyze the accuracy of the four models under different geomorphic types, two regions, A and B, were selected from Figure 16 for analysis. Among them, Region A (120.6° - 121°E, 19.8° - 20.2°N) is located on the eastern ridge of the Manila Trench with rugged terrain. There are 7,062 shipborne bathymetric verification points, the maximum water depth is -3,476.70 m, the minimum water depth is -1,479.00 m, and the average water depth is -2,190.30 m; Region B (119.6° - 120°E, 19.2° - 19.4°N) is located within the Manila Trough with gentle terrain undulation. There are 116 shipborne bathymetric verification data points, the maximum water depth is -3,476.70 m, the minimum water depth is -1,479.00 m, and the average water depth is -4,160.73 m.

[0123] There are significant differences in the accuracies of the four models under different geomorphic types. In area A, where the terrain has large undulations, the maximum value of the BM1 model is 731.89 m, the minimum value is -784.32 m, the mean value is 3.72 m, and the root mean square error is 52.74 m. The accuracy of the BM2 model is second, at 58.95 m. However, the accuracies of the internationally common ETOPO1 model and the GEBCO model are 119.99 m and 139.87 m respectively. In comparison, in the relatively rugged ridge and seamount geomorphic types, relatively ideal results can be obtained using the CNNGWD method. In addition, for the relatively flat trough area B, the accuracies of the four models have a relatively obvious improvement compared to area A. It is worth noting that in this area, the GEBCO model has the best accuracy, followed by the ETOPO1 model, the BM1 model, and the BM2 model in sequence. Analyzing the reasons, on the one hand, the thick sediment cover in the trough area reduces the correlation between water depth and gravity information; on the other hand, the ETOPO1 model and the GEBCO model incorporate existing shipborne measured data during the construction process, which helps to improve the accuracy of the models. Therefore, when inverting the water depth model over a large area, it is necessary to focus on considering the water depth model construction method under different geomorphic types or perform weighted fusion of different depth models. In addition, by comparing the root mean square changes of the same models in areas A and B, it can be seen that the accuracy of the BM1 model has increased from 52.74 m to 27.13 m, with a change rate of approximately 48.56%. The change rates of the BM2 model, the ETOPO1 model, and the GEBCO model are approximately 24.31%, 84.26%, and 95.55% respectively. Among the four models, the overall accuracy change rate of the BM2 model is the smallest, followed by the BM1 model, which reflects its good model stability. Although the GEBCO model has better accuracy in local areas, the overall stability of the model is poor. Based on the above analysis, the accuracy of the BM1 model inverted based on the CNNGWD method is better than the other four models, with obvious advantages in rugged terrain areas and relatively good model stability, thus demonstrating the effectiveness and practicality of the CNNGWD method proposed by the present invention.

[0124] Based on the above embodiments, the present invention also discloses a system for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information, including: a first data processing module, configured to select the ETOPO1 water depth model, gravity anomaly, and vertical gravity gradient anomaly of the research area, as well as shipborne sounding data, and eliminate outliers from the shipborne sounding data to obtain the depth Z of the shipborne sounding control points; at the same time, use the Parker algorithm to forward model the gravity anomaly Δg f (x,y) and the vertical gravity gradient anomaly Δg fv (x,y) of the ETOPO1 water depth model to obtain the gravity information Δg f. A second data processing module, configured to obtain the gravity anomaly Δg(x,y) and the vertical gravity gradient anomaly Δg v (x,y) obtained by satellite altimetry inversion, and perform wavelet decomposition on Δg(x,y) and Δg v (x,y) respectively to obtain the gravity information Δg after wavelet decomposition; compare the gravity information Δg obtained after wavelet decomposition with the gravity information Δg f forward modeled from the ETOPO1 bathymetry model and the depth Z of the shipborne sounding control points through correlation analysis to obtain the correlation coefficient result; determine the optimal orders i and j of wavelet decomposition according to the correlation coefficient result. A model construction and training module, configured to construct and train a network model: use bilinear interpolation to obtain the gravity information Δg and the corresponding coordinate information of the wavelet decomposition result at the positions of the shipborne sounding control points, and perform normalization processing, and use the normalized result G as the input of the network model; use the depth Z of the shipborne sounding control points as the output of the network model; adjust the weight and bias parameters of the network model through error backpropagation until the set value or the iteration step is satisfied, and complete the training. An inversion module, configured to construct a bathymetry inversion model based on the finally obtained weight and bias parameters after training; input the gridded gravity information after wavelet decomposition and the corresponding coordinate information into the bathymetry inversion model, so as to inversely obtain a 1′×1′ bathymetry model in the research area.

[0125] For the system embodiment, since it corresponds to the method embodiment, the description is relatively simple. For the relevant parts, please refer to the description in the method embodiment section.

[0126] Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0127] The content not detailedly described in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. A method for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information, characterized in that, Including: Select the ETOPO1 bathymetry model, gravity anomaly, and vertical gravity gradient anomaly in the study area, as well as the shipborne sounding data. Remove the outliers from the shipborne sounding data to obtain the depth Z of the shipborne sounding control points. At the same time, use the Parker algorithm to forward model the gravity anomaly Δg f (x,y) and the vertical gravity gradient anomaly Δg fv (x,y) of the ETOPO1 bathymetry model to obtain the gravity information Δg f ; Obtain the gravity anomaly Δg(x,y) and vertical gravity gradient anomaly Δg v (x,y) obtained by satellite altimetry inversion. Perform wavelet decomposition on Δg(x,y) and Δg v (x,y) respectively to obtain the gravity information Δg after wavelet decomposition. Compare the gravity information Δg obtained after wavelet decomposition with the gravity information Δg f forward modeled from the ETOPO1 bathymetry model and the depth Z of the shipborne sounding control points to obtain the correlation coefficient results. Determine the optimal orders i and j of wavelet decomposition according to the correlation coefficient results; Constructing and training a network model: Bilinear interpolation is used to obtain the gravity information Δg and the corresponding coordinate information of the wavelet decomposition results at the positions of the shipborne sounding control points, and normalization processing is performed. The normalized result G is used as the input of the network model; the depth Z of the shipborne sounding control points is used as the output of the network model. Adjust the weight and bias parameters of the network model through error backpropagation until the set value or the number of iteration steps is reached, and the training is completed. Based on the final weight and bias parameters obtained from training, construct a water depth inversion model; input the gridded gravity information and the corresponding coordinate information after wavelet decomposition into the water depth inversion model, so as to inversely obtain a 1′×1′ water depth model in the study area.

2. The method for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information according to claim 1, characterized in that, Forward model the gravity anomaly Δg of the ETOPO1 bathymetric model using the Parker algorithm f (x,y) and the vertical gravity gradient anomaly Δg fv (x,y), and obtain the gravity information Δg forward modeled from the ETOPO1 bathymetric model f , including: Forward model the gravity anomaly Δg of the ETOPO1 bathymetry model and the vertical gravity gradient anomaly Δg fv (x,y) respectively through the following formulas (1.4) and (1.5): f (x,y) and the vertical gravity gradient anomaly Δg fv fv (x,y): where F represents the Fourier transform, γ represents the gravitational constant, and ρ c and ρ w represent the average densities of the oceanic crust and seawater, respectively, k represents the radial frequency, d represents the average water depth, and h n (x, y) represents the topographic undulation relative to the average water depth, and n represents the order of summation; Δg will be calculated separately through formulas (1.4) and (1.5). f Δg(x,y) and fv Δg(x,y) are used as the gravity information Δg for the forward modeling of the ETOPO1 bathymetry model f .

3. The method for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information according to claim 1, characterized in that, Perform wavelet decomposition on Δg(x,y) and Δg v (x,y) respectively to obtain the gravity information Δg after wavelet decomposition, including: Perform wavelet decomposition on Δg(x,y) and Δg respectively through the following formulas (1.2) and (1.3): v (x,y): Among them, A I G represents the approximation part of the i-th order wavelet decomposition, D i G represents the gravity anomaly detail part after i times of wavelet decomposition, i = 1, 2,..., I; represents the approximation part of the j-th order wavelet decomposition, D j v G v represents the detail part after j times of wavelet decomposition, j = 1, 2,..., J; The obtained A I G, D i G, and are used as the gravity information Δg after wavelet decomposition.

4. The method for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information according to claim 3, characterized in that, Compare the gravity information Δg obtained after wavelet decomposition with the gravity information Δg forward modeled by the ETOPO1 bathymetry model through correlation analysis f and the depth Z of the shipborne sounding control points to obtain the correlation coefficient results, including: Analyze and compare the gravity information Δg and Δg obtained after wavelet decomposition through the following formulas (1.7) and (1.8). f And Z to obtain the correlation coefficient ρ1 between the gravity after wavelet decomposition and the water depth and the correlation coefficient ρ2 between the gravity after wavelet decomposition and the forward gravity: Among them, Z m represents the water depth value at the position of the corresponding point m, represents the forward gravity information at the position of point m, Δg m represents the gravity information retrieved from satellite altimetry at the position of point m, and respectively represent the average values of Δg, Z, and Δg f and M represents the total number of ship - measured control points, where m = 1, 2,..., M; Then, the correlation coefficient result ρ is: ρ = (ρ1 + ρ2) / 2 (1.6).

5. The method for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information according to claim 4, characterized in that, Determine the optimal orders i and j of wavelet decomposition according to the correlation coefficient result, including: As the order of wavelet decomposition varies, when ρ is the maximum, determine the optimal orders i and j of wavelet decomposition.

6. The method for improving the accuracy of water depth inversion based on neural network - wavelet decomposition of gravity information according to claim 5, characterized in that, Adjust the weight and bias parameters of the network model through error backpropagation until the set value or the number of iteration steps is reached, and the training is completed, including: Based on the following formula (1.9), adjust the weight and bias parameters of the network model until the set value or the number of iteration steps is reached, and the training is completed: Among them, represents the transfer function between each network layer; W (1) represents the weight matrix from the input layer to the hidden layer; W (2) represents the weight matrix between the hidden layers; W (3) represents the weight matrix from the hidden layer to the output layer; the above weight matrices are constructed by the weight values ω between neurons; b1 represents the bias parameter vector of whom, b2 represents the bias parameter vector of whom, and b3 represents the bias parameter vector of whom.

7. The method for improving the accuracy of water depth inversion based on neural network-gravity information wavelet decomposition according to claim 6, wherein, G = [ga, vga, lon, lat] T , where ga represents the gravity anomaly after wavelet decomposition and normalization, vga represents the vertical gravity gradient anomaly after wavelet decomposition and normalization, lon represents the longitude of the shipboard measurement control point, and lat represents the latitude of the shipboard measurement control point.

8. A system for improving the accuracy of water depth inversion based on neural network-gravity information wavelet decomposition, wherein, Including: The first data processing module is used to select the ETOPO1 bathymetric model, gravity anomaly, vertical gravity gradient anomaly of the study area, and shipborne sounding data, and eliminate outliers from the shipborne sounding data to obtain the depth Z of the shipborne sounding control points; at the same time, use the Parker algorithm to forward model the gravity anomaly Δg f (x, y) and the vertical gravity gradient anomaly Δg fv (x, y) of the ETOPO1 bathymetric model to obtain the gravity information Δg f ; The second data processing module is used to obtain the gravity anomaly Δg(x,y) and the vertical gravity gradient anomaly Δg v (x,y) obtained by satellite altimetry inversion, and perform wavelet decomposition on Δg(x,y) and Δg v (x,y) respectively to obtain the wavelet-decomposed gravity information Δg; through correlation analysis, compare the wavelet-decomposed gravity information Δg with the gravity information Δg f forward modeled from the ETOPO1 bathymetry model and the depth Z of the shipborne sounding control points to obtain the correlation coefficient result; determine the optimal orders i and j of wavelet decomposition according to the correlation coefficient result; A model construction and training module, which is used to construct and train a network model: Bilinear interpolation is used to obtain the gravity information Δg and the corresponding coordinate information of the wavelet decomposition results at the positions of the shipborne sounding control points, and normalization processing is performed. The normalized result G is used as the input of the network model; the depth Z of the shipborne sounding control points is used as the output of the network model. Adjust the weight and bias parameters of the network model through error backpropagation until the set value or the number of iteration steps is reached, and the training is completed. An inversion module, which is used to construct a water depth inversion model based on the final weight and bias parameters obtained from training; input the gridded gravity information and the corresponding coordinate information after wavelet decomposition into the water depth inversion model, so as to inversely obtain a 1′×1′ water depth model in the study area.

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