Physical information constrained three-dimensional gravity gradient tensor inversion method

Abstract

The invention provides a physical information constrained three-dimensional gravity gradient tensor inversion method, which belongs to the field of geophysics, and comprises the following steps of: firstly, establishing a coordinate system according to gravity gradient tensor data, subdividing an underground space, and extracting and standardly normalizing coordinates of a center point of a cube; then, constructing a seven-layer full-connection neural network to output network output parameters; then, calculating gravity gradient tensor data on an observation surface; constructing an objective function through observation data and calculation data, wherein the objective function comprises a data item and a regularization item; and finally, automatically differentiating the objective function to update network parameters and optimize network output parameters until the maximum number of training times is reached, and outputting a result. By adopting the three-dimensional gravity gradient tensor inversion method constrained by the physical information, multiple challenges in the prior art are overcome, including the problems of excessive dependence on initial parameters, excessive simplification and hypothesis limitation of a model, insufficient capability of processing a non-linear relationship, poor generalization performance and the like.

Description

Technical Field

[0001] The invention relates to the field of geophysics, and in particular to a three-dimensional gravity gradient tensor inversion method constrained by physical information. Background Art

[0002] The gravity field is one of the basic physical fields of the earth, which reflects the distribution of earth's matter and its changes in space and time. The gravity gradient field, as the rate of change of the gravity field in space, has a higher resolution than the gravity field. Therefore, it is widely used in many important fields such as natural resource exploration, topographic mapping, hydrocarbon exploration, microgravity research, and underground military target detection. In recent years, airborne gravity gradient measurement technology has made significant progress, especially in the measurement of complex terrain areas such as mountainous areas, offshore waters, lakes, swamps, etc. It has shown high efficiency. The full tensor gravity gradient data consists of five independent components, has a higher sensitivity to spatial anomalies, and can finely characterize the structural characteristics and location of underground anomalies.

[0003] The inversion of airborne gravity gradient tensor data mainly includes physical property inversion and geometric parameter inversion. Geometric parameter inversion can quickly locate the spatial distribution characteristics and position of the anomaly through imaging methods, while physical property inversion can provide more detailed information about the anomaly, such as shape, volume and physical property parameters. However, traditional inversion methods have limitations such as easy to fall into local minimum values, excessive dependence on initial parameters, model simplification and assumption restrictions, and limited ability to handle nonlinear relationships.

[0004] With the rapid development of artificial intelligence technology, deep learning has provided new ideas and methods for the field of geophysics. Geophysicists apply deep learning technology to the joint inversion of gravity gradient tensor data, and use data-driven convolutional neural networks (CNNs) to establish a mapping relationship between input and output, effectively improving the inversion accuracy and reducing the reliance on prior knowledge and model settings in traditional inversion methods.

[0005] However, data-driven deep learning methods also have shortcomings, such as the need for a large amount of training data, reduced generalization, and poor interpretability. To address these issues, researchers have proposed a strategy to embed physical information constraints in deep learning networks. By incorporating the forward process based on physical laws into the training process of the neural network, the network can not only learn the features in the data, but also ensure that the inversion results conform to the laws of physics, thereby enhancing the interpretability and generalization ability of the model. This strategy provides a solution to the key challenges of solving the generalization and data dependency problems of the inversion problem. Summary of the invention

[0006] The purpose of the present invention is to provide a three-dimensional gravity gradient tensor inversion method constrained by physical information, which can significantly overcome multiple challenges in the prior art, including over-reliance on initial parameters, over-simplification of models and assumption limitations, insufficient ability to handle nonlinear relationships, and poor generalization performance. By integrating physical information constraints into a deep learning network, this method realizes three-dimensional gravity gradient tensor inversion under the dual guidance of data-driven and physical laws, providing an innovative intelligent solution for three-dimensional inversion tasks in the field of gravity gradient exploration.

[0007] To achieve the above object, the present invention provides a physical information constrained three-dimensional gravity gradient tensor inversion method, comprising the following steps:

[0008] S1. According to the measured data of gravity gradient tensor, a ground rectangular coordinate system is established. The underground space is divided into small cubes with constant intervals along the x, y, and z directions. The interval sizes of the underground space are Δx, Δy, and Δz respectively. The number of grids divided in the x, y, and z directions is M, N, and L respectively. The total number of cubes is N. s =M×N×L, extract N s The coordinates of the center points of the cubes are normalized to form the normalized coordinates d input ;

[0009] S2. Construct a seven-layer fully connected neural network framework, with ReLU as the activation function, Adam optimizer as the optimizer, and the input as the standard normalized coordinate d input , get the network output parameter ρ;

[0010] S3. Set observation surface N0 at z=z0 and divide the observation surface into N O =M×N, get the observation point coordinates (x m ,y n ,z0), calculate the kernel matrix according to the spatial position of each cube and observation point, bring the network output parameter ρ and the kernel matrix into the gravity gradient tensor calculation formula to obtain the gravity gradient tensor data;

[0011] S4, constructing a data item in the objective function through the gravity gradient tensor observation data and the gravity gradient tensor data obtained in S3, constructing a regularization item in the objective function using the kernel matrix and the network output parameter ρ, and combining the data item and the regularization item to obtain the objective function;

[0012] S5. Automatic differentiation is performed according to the objective function constructed in S4 to update the network parameters, thereby optimizing the network output parameter ρ and fitting the measured data. When the number of training times reaches the maximum number, the result is output.

[0013] Preferably, the standard normalization formula in S1 is:

[0014]

[0015] Among them, ξ, η, ζ are the coordinate values ​​of the three directions of the center point of the cube, μ is the average value of all coordinates, and δ is the standard deviation of all coordinates;

[0016] The calculation formulas for μ and δ are:

[0017]

[0018] Among them, ξ p , η p , p They are the coordinates of the three directions of the center point of the p-th cube;

[0019] Standard normalized coordinates d input for:

[0020] d input =[ξ * ,η * ,ζ * ];

[0021] Among them, ξ * , η * , * They are the coordinate values ​​of the cube center point in three directions after standard normalization.

[0022] Preferably, the kernel matrix formula in S3 is:

[0023]

[0024] Among them, k xx , k yy , k zz , k xy , k xz , k yz They are the kernel matrices in six different directions; x i ,y j 、z k They are the distances between the two corner points of the cube and the observation point in three directions;

[0025] x i ,y j 、z k The calculation formula is:

[0026]

[0027] u ijk , R ijk The calculation formula is:

[0028]

[0029] Preferably, the gravity gradient tensor calculation formula in S3 is:

[0030]

[0031] in, They are the gravity gradient tensor data in six different directions, and ρ is the network output parameter.

[0032] Preferably, the formula for constructing the data item in S4 is:

[0033]

[0034] Among them, g xx , g yy , g zz , g xy , g xz , g yz These are the measured data of gravity gradient tensor in six different directions.

[0035] Preferably, the regularization term formula constructed in S4 is:

[0036] Loss m (ρ)=χ|Wρ|+(1-χ)||Wρ|| 2 ;

[0037] Where W is the depth weighting function based on the kernel matrix, and χ is the balance parameter that balances the two regularization terms;

[0038] The depth weighted function formula is:

[0039]

[0040] Preferably, the objective function formula in S4 is:

[0041] Loss(ρ)=Loss d (ρ)+λLoss m (ρ);

[0042] Among them, λ is the regularization coefficient that balances the data term and the regularization term.

[0043] Therefore, the present invention adopts the above-mentioned three-dimensional gravity gradient tensor inversion method constrained by physical information, and the technical effects are as follows: the method proposed in the present invention utilizes physical information constrained neural network to perform three-dimensional gravity gradient tensor inversion, effectively avoiding the shortcomings of existing methods such as excessive dependence on initial parameters, model simplification and assumption restrictions, limited ability to handle nonlinear relationships, and poor generalization, and combines the traditional forward modeling of three-dimensional gravity gradient tensor with neural network technology to achieve efficient and high-precision three-dimensional gravity gradient tensor inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A three-dimensional synthetic model of a three-dimensional gravity gradient tensor inversion method constrained by physical information according to the present invention;

[0045] Figure 2 A schematic diagram of the structure of the subdivided underground space of a three-dimensional gravity gradient tensor inversion method constrained by physical information of the present invention;

[0046] Figure 3 A seven-layer fully connected neural network framework flow chart of a physical information constrained three-dimensional gravity gradient tensor inversion method of the present invention;

[0047] Figure 4 A three-dimensional inversion result of a three-dimensional gravity gradient tensor inversion method constrained by physical information according to the present invention;

[0048] Figure 5 The invention discloses synthetic data of a three-dimensional gravity gradient tensor inversion method constrained by physical information, a forward response of an inversion model and the absolute error between the two. DETAILED DESCRIPTION

[0049] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0050] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0051] Embodiment 1

[0052] The present invention provides a three-dimensional gravity gradient tensor inversion method constrained by physical information, and the specific steps are as follows:

[0053] S1. Establish a ground rectangular coordinate system based on the measured data of the gravity gradient tensor, such as Figure 1-Figure 2 As shown, in Figure 1 In the figure, (a) is the three-dimensional synthetic real model of the present invention, (b) is the slice diagram when y=0, (c) is the slice diagram when z=1.25, and (d) is the slice diagram when x=2. The underground space is divided into small cubes with constant intervals along the x, y, and z directions. The interval sizes of the underground space are 0.25km, 0.25km, and 0.25km respectively. The number of grids divided in the x, y, and z directions are 40, 40, and 20 respectively. The total number of cubes is N. s =40×40×20, extract the coordinates of 32,000 cube center points for standard normalization, and form the normalized coordinate d input .

[0054] The standard normalization formula is:

[0055]

[0056] Among them, ξ, η, ζ are the coordinate values ​​of the three directions of the center point of the cube, μ is the average value of all coordinates, and δ is the standard deviation of all coordinates;

[0057] The calculation formulas for μ and δ are:

[0058]

[0059] Among them, ξ p , η p , p They are the coordinates of the three directions of the center point of the p-th cube;

[0060] Standard normalized coordinates d input for:

[0061] d input =[ξ * ,η * ,ζ * ];

[0062] Among them, ξ * , η * , * They are the coordinate values ​​of the cube center point in three directions after standard normalization.

[0063] S2, such as Figure 3 As shown in the figure, a seven-layer fully connected neural network framework is constructed, the activation function is ReLU, the optimizer is Adam optimizer, and the input is the standard normalized coordinate d input , and obtain the network output parameter ρ.

[0064] S3, set the observation surface N0 at z = z0, divide the grids in the x and y directions into 40 and 40 respectively, divide the observation surface into N0 = 40 × 40, and obtain the observation point coordinates (x m ,y n ,z0), calculate the kernel matrix according to the spatial position of each cube and observation point, bring the network output parameter ρ and the kernel matrix into the gravity gradient tensor calculation formula to obtain the gravity gradient tensor data.

[0065] The kernel matrix formula is:

[0066]

[0067]

[0068] Among them, k xx , k yy , k zz , k xy, k xz , k yz They are the kernel matrices in six different directions; x i ,y j 、z k They are the distances between the two corner points of the cube and the observation point in three directions;

[0069] x i ,y j 、z k The calculation formula is:

[0070] x1=ξ p -0.5Δx-x m , x2=ξ p +0.5Δx-x m

[0071] y1=η p -0.5Δy-y n , y2=η p +0.5Δy-y n ;

[0072] z1=ζ p -0.5Δz-z0,z2=ζ p +0.5Δz-z0

[0073] u ijk , R ijk The calculation formula is:

[0074]

[0075] The gravity gradient tensor calculation formula is:

[0076]

[0077] in, They are the gravity gradient tensor data in six different directions, and ρ is the network output parameter.

[0078] S4. Construct the data item in the objective function through the gravity gradient tensor observation data and the gravity gradient tensor data obtained in S3, construct the regularization item in the objective function using the kernel matrix and the network output parameter ρ, and combine the data item and the regularization item to obtain the objective function.

[0079] The formula for constructing the data item is:

[0080]

[0081] Among them, g xx , g yy , g zz , g xy , gxz , g yz These are the measured data of gravity gradient tensor in six different directions.

[0082] The formula for constructing the regularization term is:

[0083] Loss m (ρ)=χ|Wρ|+(1-χ)||Wρ|| 2 ;

[0084] Where W is the depth weighting function based on the kernel matrix, χ is the balance parameter for balancing the two regularization terms, and the value of χ is 0.9;

[0085] The depth weighted function formula is:

[0086]

[0087] The objective function formula is:

[0088] Loss(ρ)=Loss d (ρ)+λLoss m (ρ);

[0089] Among them, λ is the regularization coefficient that balances the data term and the regularization term, and the value of λ is 0.25.

[0090] S5. Automatic differentiation is performed according to the objective function constructed in S4 to update the network parameters, thereby optimizing the network output parameter ρ and fitting the measured data. When the number of training times reaches the maximum number, the result is output.

[0091] like Figure 4-Figure 5 As shown, Figure 4 The three-dimensional inversion result of the embodiment is shown in FIG. Figure 4 (a) is a 3D visualization inversion model; (b) is a slice diagram at y = 0; (c) is a slice diagram at z = 1.25; (d) is a slice diagram at x = 2. The black frame line is the boundary of the real model. Figure 5 The synthetic data of the embodiment, the forward response of the inversion model and the absolute error between the two, Figure 5 (a)-(f) are synthetic data; (g)-(l) are Figure 4 Forward response of the inversion model; (m)-(r) is the absolute error between the two.

[0092] Horizontal comparison Figure 5The six sets of data in the figure include the synthetic data, the forward response of the inversion model and the absolute error between the two. (a)-(f) represent the theoretical gravity gradient tensor data, which is the goal of the inversion. (g)-(l) are the gravity gradient tensor data obtained by forward calculation after the inversion results obtained by the method of the present invention. By comparing these two sets of data, it can be seen that the inversion results are very close to the synthetic data, indicating that the method of the present invention can accurately restore the density distribution of underground physical parameters. (m)-(r) represent the difference between the synthetic data and the forward response of the inversion model. It can be seen from the absolute error diagram that the error value is relatively small and evenly distributed, which further proves the high precision and stability of the method of the present invention. It can be obtained that the three-dimensional gravity gradient tensor inversion method constrained by physical information proposed by the present invention can achieve high-precision inversion of physical parameter density, and has significant technical advantages and practical effects.

[0093] Therefore, the present invention adopts the above-mentioned three-dimensional gravity gradient tensor inversion method constrained by physical information, and integrates the gravity gradient tensor forward operator to combine the traditional forward modeling of the three-dimensional gravity gradient tensor with the neural network technology, which significantly reduces the multi-solution of the inversion. Compared with the existing deep learning technology, this method effectively enhances the generalization of the inversion and reduces the dependence on data.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A three-dimensional gravity gradient tensor inversion method constrained by physical information, characterized in that: The following steps are involved: S1. According to the measured data of gravity gradient tensor, a ground rectangular coordinate system is established. The underground space is divided into small cubes with constant intervals along the x, y, and z directions. The interval sizes of the underground space are Δx, Δy, and Δz respectively. The number of grids divided in the x, y, and z directions is M, N, and L respectively. The total number of cubes is N. s =M×N×L, extract N s The coordinates of the center points of the cubes are normalized to form the normalized coordinates d input ; S2. Construct a seven-layer fully connected neural network framework, with ReLU as the activation function, Adam optimizer as the optimizer, and the input as the standard normalized coordinate d input , get the network output parameter ρ; S3. Set observation surface N0 at z=z0 and divide the observation surface into N O =M×N, get the observation point coordinates (x m ,y n ,z0), calculate the kernel matrix according to the spatial position of each cube and observation point, bring the network output parameter ρ and the kernel matrix into the gravity gradient tensor calculation formula to obtain the gravity gradient tensor data; S4, constructing a data item in the objective function through the gravity gradient tensor observation data and the gravity gradient tensor data obtained in S3, constructing a regularization item in the objective function using the kernel matrix and the network output parameter ρ, and combining the data item and the regularization item to obtain the objective function; S5. Automatic differentiation is performed according to the objective function constructed in S4 to update the network parameters, thereby optimizing the network output parameter ρ and fitting the measured data. When the number of training times reaches the maximum number, the result is output.

2. A three-dimensional gravity gradient tensor inversion method constrained by physical information according to claim 1, characterized in that: The standard normalization formula in S1 is: Among them, ξ, η, ζ are the coordinate values ​​of the three directions of the center point of the cube, μ is the average value of all coordinates, and δ is the standard deviation of all coordinates; The calculation formulas for μ and δ are: Among them, ξ p , η p , p They are the coordinates of the three directions of the center point of the p-th cube; Standard normalized coordinates d input for: d input =[ξ * ,or * ,g * ]; Among them, ξ * , η * , * They are the coordinate values ​​of the three directions of the center point of the cube after standard normalization.

3. The method for three-dimensional gravity gradient tensor inversion constrained by physical information according to claim 1, characterized in that: The kernel matrix formula in S3 is: Among them, k xx , k yy , k zz , k xy , k xz , k yz They are the kernel matrices in six different directions; x i ,y j 、z k They are the distances between the two corner points of the cube and the observation point in three directions; x i ,y j 、z k The calculation formula is: u ijk , R ijk The calculation formula is: u ijk ＝(-1) i+j+k 。 4. The method for three-dimensional gravity gradient tensor inversion constrained by physical information according to claim 1, characterized in that: The calculation formula of the gravity gradient tensor in S3 is: in, They are the gravity gradient tensor data in six different directions, and ρ is the network output parameter.

5. The method for three-dimensional gravity gradient tensor inversion constrained by physical information according to claim 1, characterized in that: The formula for constructing data items in S4 is: Among them, g xx , g yy , g zz , g xy , g xz , g yz These are the measured data of gravity gradient tensor in six different directions.

6. The method for three-dimensional gravity gradient tensor inversion constrained by physical information according to claim 1, characterized in that: The regularization term formula constructed in S4 is: Loss m (ρ)=χ|Wρ|+(1-χ)||Wρ|| 2 ; Where W is the depth weighting function based on the kernel matrix, and χ is the balance parameter that balances the two regularization terms; The depth weighted function formula is:

7. The method for three-dimensional gravity gradient tensor inversion constrained by physical information according to claim 1, characterized in that: The objective function formula in S4 is: Loss(ρ)=Loss d (ρ)+λLoss m (p); Among them, λ is the regularization coefficient that balances the data term and the regularization term.

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