Gravity inversion method and system based on dual-network driving

Abstract

The invention discloses a gravity inversion method and system based on dual-network driving, and the method comprises the steps: obtaining a training data set which comprises an actual underground medium density model and actual gravity data; constructing a dual-network cascade architecture comprising a downlink density prediction network and an uplink physical property correction network; inputting the gravity data in the training set into a downlink density prediction network to obtain prediction model data; inputting the prediction model data into an uplink physical property correction network to obtain prediction gravity data; potential field loss constraints and model loss constraints are obtained through the prediction data and the real data; performing weighted optimization on the dual-network cascade architecture through potential field loss constraint, model loss constraint and physical loss constraint controlled by a gravity forward kernel matrix operator to obtain an inversion model; and performing inversion on the to-be-inverted gravity data through the inversion model to obtain underground medium density distribution. According to the invention, underground detail features can be reflected more accurately.

Description

Technical Field

[0001] The present invention belongs to the technical field of gravity inversion, and particularly relates to a gravity inversion method and system driven by a dual network. Background Art

[0002] Gravity field inversion is a key technology in the field of geophysical exploration, aiming to infer the density distribution of underground media by analyzing gravity anomalies on the earth's surface, and further reveal the distribution of underground structures and mineral resources. Traditional gravity inversion methods, such as iterative optimization methods based on forward models, although they can provide certain information about the underground density distribution, have some significant problems. These problems include the non-uniqueness of inversion results, low depth resolution, high computational cost when dealing with large-scale datasets, and the need for a large amount of prior information and parameter adjustment.

[0003] With the rapid development of deep learning technology, data-driven gravity inversion methods have begun to receive extensive attention. In particular, convolutional neural networks (CNNs) and Transformer models have shown significant advantages in dealing with non-linear problems and high-dimensional data. These deep learning methods are expected to significantly improve the accuracy and efficiency of inversion by directly learning the complex mapping relationship between gravity data and the density distribution of underground media.

[0004] However, the existing deep learning-based gravity inversion methods mainly have the following deficiencies: First, most methods adopt a single network architecture, such as U-Net. Although these models perform well in local feature extraction, they have limitations in capturing the complex characteristics and long-range dependencies of underground media. Second, existing methods often focus on data fitting while ignoring the physical rationality of geophysical processes, resulting in insufficient generalization ability of inversion results in complex geological backgrounds. Finally, in practical applications, gravity data is often affected by noise, and the robustness of existing methods in a noisy environment needs to be improved. Summary of the Invention

[0005] The present invention proposes a gravity inversion method and system driven by a dual network to solve the problems existing in the above-mentioned prior art.

[0006] To achieve the above object, the present invention provides a gravity inversion method driven by a dual network, including the following steps:

[0007] Obtain a training dataset, where the training dataset includes an actual underground media density model and actual gravity data;

[0008] Construct a dual network cascade architecture including a downward density prediction network and an upward physical property correction network;

[0009] Input the gravity data in the training set into the downward density prediction network to obtain prediction model data;

[0010] Input the prediction model data into the upward physical property correction network to obtain predicted gravity data;

[0011] Obtain the model loss constraint through the prediction model data and the actual underground medium density model, and obtain the potential field loss constraint through the predicted gravity data and the actual gravity data;

[0012] Perform weighted optimization on the dual-network cascade architecture through the potential field loss constraint, the model loss constraint, and the physical loss constraint controlled by the gravity forward kernel matrix operator to obtain an inversion model;

[0013] Invert the gravity data to be inverted through the inversion model to obtain the underground medium density distribution.

[0014] Preferably, the downward density prediction network includes:

[0015] A first encoder for extracting multi-scale features of gravity data;

[0016] A Transformer bottleneck layer for capturing long-range geological dependencies of gravity data;

[0017] A first decoder for fusing multi-scale features through skip connections and reconstructing the three-dimensional density distribution;

[0018] Preferably, the first encoder adopts a convolution operation based on the Kolmogorov-Arnold network and combines a radial basis function mapping to enhance the non-linear feature modeling ability.

[0019] Preferably, the upward physical property correction network includes:

[0020] A second encoder adopting a 3D Swin Transformer structure for extracting global context information of the three-dimensional density distribution;

[0021] A second decoder adopting a U-Net structure for mapping the three-dimensional features extracted by the second encoder to two-dimensional gravity anomaly data.

[0022] Preferably, the potential field loss constraint is used to measure the deviation between the predicted gravity data and the actual gravity data in the training set; the model loss constraint is used to measure the deviation between the prediction model data and the actual underground medium density model in the training set; the physical loss constraint is used to measure the physical consistency controlled by the gravity forward kernel matrix operator between the output results of the two networks.

[0023] Preferably, the overall loss function of the dual-network framework is:

[0024] L = αU1 + βU2 + γδ;

[0025] Wherein, U1 is the model loss constraint, U2 is the potential field loss constraint, δ is the physical loss constraint, α is the weight coefficient of the model loss constraint, β is the weight coefficient of the potential field loss constraint, and γ is the weight coefficient of the physical loss constraint.

[0026] The present invention also provides a gravity inversion system based on dual-network drive, including:

[0027] A data acquisition unit for acquiring a training data set, where the training data set includes an actual underground medium density model and actual gravity data;

[0028] A network architecture construction unit for constructing a dual-network cascade architecture including a downward density prediction network and an upward physical property correction network;

[0029] A downward prediction processing unit for inputting the gravity data in the training set into the downward density prediction network to obtain predicted model data;

[0030] An upward correction processing unit for inputting the predicted model data into the upward physical property correction network to obtain predicted gravity data;

[0031] A loss constraint acquisition unit for obtaining a model loss constraint through the predicted model data and the actual underground medium density model, and obtaining a potential field loss constraint through the predicted gravity data and the actual gravity data;

[0032] An optimization and inversion model acquisition unit for performing weighted optimization on the dual-network cascade architecture through the potential field loss constraint, the model loss constraint, and the physical loss constraint controlled by the gravity forward kernel matrix operator to obtain an inversion model;

[0033] A gravity data inversion unit for inversing the gravity data to be inverted through the inversion model to obtain the underground medium density distribution.

[0034] The present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory, and the processor executes the computer program to implement the steps of the method.

[0035] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method are implemented.

[0036] The present invention also provides a computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the method are implemented.

[0037] Compared with the prior art, the present invention has the following advantages and technical effects:

[0038] By introducing geophysical consistency constraints and adopting a dual-network cascade architecture, including a downward density prediction network and an upward physical property correction network, the present invention improves the accuracy, generalization ability, and physical rationality of the inversion results. This method can not only fully utilize the multi-network architecture to perform multi-dimensional feature extraction on gravity data and its corresponding model density distribution, fully mining the potential information in the data, but also incorporate the geophysical consistency constraint conditions into the network training process, making the network learning process more in line with physical laws. In addition, this method can also dynamically adjust network parameters and constraint weights according to different geological scenarios to adapt to diverse inversion requirements. By adopting a multi-network architecture, incorporating geophysical constraints, and dynamically adjusting parameters, etc., the method of the present invention can more accurately reflect the underground detail features, thus providing a new and effective strategy for predicting and reconstructing underground geological information in gravity exploration. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0040] Figure 1 It is a technical solution diagram of the dual-network inversion framework according to an embodiment of the present invention;

[0041] Figure 2 It is a schematic structural diagram of the dual-network inversion framework according to an embodiment of the present invention;

[0042] Figure 3 It is an encoding-decoding schematic diagram of GravCTUNet according to an embodiment of the present invention;

[0043] Figure 4 It is a structural diagram of the DoubleConv module according to an embodiment of the present invention;

[0044] Figure 5 It is an encoding-decoding schematic diagram of GravSwinTransUNet according to an embodiment of the present invention;

[0045] Figure 6 It is a structural diagram of the Swin Transformer Block according to an embodiment of the present invention;

[0046] Figure 7 It is a 3D view and sectional view of the synthetic model according to an embodiment of the present invention; wherein, (a) is the three-dimensional view of the three-cube model; (b) is the cross-sectional view of the three-cube model at y = 1600m; (c) is the longitudinal sectional view of the three-cube model at x = 1000m;

[0047] Figure 8Comparison chart of the prediction effects of the dual-network inversion framework and the single U-Net network of the embodiments of the present invention on the AA' slice of the synthetic model; where (a) is the prediction result chart of the dual-network inversion framework on the AA' slice; (b) is the prediction result chart of the single U-Net network on the AA' slice; (c) is the difference chart of the prediction results of the dual-network inversion framework and the single U-Net network on the AA' slice; (d) is the error analysis chart of the prediction result of the dual-network inversion framework on the AA' slice;

[0048] Figure 9 Comparison chart of the prediction effects of the dual-network inversion framework and the single U-Net network of the embodiments of the present invention on the BB' slice of the synthetic model; where (a) is the prediction result chart of the dual-network inversion framework on the BB' slice; (b) is the prediction result chart of the single U-Net network on the BB' slice; (c) is the difference chart of the prediction results of the dual-network inversion framework and the single U-Net network on the BB' slice; (d) is the error analysis chart of the prediction result of the dual-network inversion framework on the BB' slice;

[0049] Figure 10 Mean squared error (MSE) loss curve chart of the training set and the validation set during the training process of the dual-network framework of the embodiments of the present invention;

[0050] Figure 11 Gravity anomaly component g z and g zz fitting error chart output by the upward PCN network of the embodiments of the present invention; where (a) is the fitting error chart of the gravity anomaly component g z output by the upward PCN network; (b) is the fitting error chart of the gravity anomaly component g zz output by the upward PCN network; (c) is the comparison chart of the fitting errors of the dual-network inversion framework and the single U-Net network for the gravity anomaly component g z ; (d) is the comparison chart of the fitting errors of the dual-network inversion framework and the single U-Net network for the gravity anomaly component g zz ; (e) is the detailed analysis chart of the fitting error of the dual-network inversion framework for the gravity anomaly component g z ; (f) is the detailed analysis chart of the fitting error of the dual-network inversion framework for the gravity anomaly component g zz ; Specific implementation manners

[0051] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the drawings and in conjunction with the embodiments.

[0052] Note that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. And although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0053] Embodiment 1

[0054] As Figures 1-6 shown, in this embodiment, a gravity inversion method based on dual-network drive is provided, including the following steps:

[0055] Obtain a training data set, where the training data set includes an actual underground medium density model and actual gravity data;

[0056] Construct a dual-network cascade architecture including a downward density prediction network and an upward physical property correction network;

[0057] Input the gravity data in the training set into the downward density prediction network to obtain predicted model data;

[0058] Input the predicted model data into the upward physical property correction network to obtain predicted gravity data;

[0059] Obtain a model loss constraint through the predicted model data and the actual underground medium density model, and obtain a potential field loss constraint through the predicted gravity data and the actual gravity data;

[0060] Perform weighted optimization on the dual-network cascade architecture through the potential field loss constraint, the model loss constraint, and the physical loss constraint controlled by the gravity forward kernel matrix operator to obtain an inversion model;

[0061] Invert the gravity data to be inverted through the inversion model to obtain the underground medium density distribution.

[0062] Furthermore, the downward density prediction network is named GravCTUNet, which aims to fuse the local feature extraction ability of CNN and the global modeling ability of Transformer, and is applicable to the density distribution prediction of single-component and multi-component gravity data. GravCTUNet adopts a convolution operation based on the Kolmogorov-Arnold network (KAN) (FastKANConvLayer) to enhance its modeling ability for non-linear features, and combines the Transformer bottleneck layer to capture long-range geological dependencies. This network supports flexible input configurations: single-component input (such as g zFor single-component input (with a dimension of (B, 1, H, W)) or multi-component input (such as 7-component with a dimension of (B, 7, H, W)), the output is a three-dimensional density distribution (with a dimension of (B, D×H×W)). By comparing the performance of single-component and multi-component inputs, GravCTUNet provides a systematic analysis of the influence on the information content of gravity data.

[0063] The design of GravCTUNet takes into account the diversity of gravity data: due to its integral property, gravity anomaly is more suitable for reflecting the deep density structure, while gravity gradient data is more conducive to the analysis of shallow features by highlighting local changes. Therefore, GravCTUNet adopts a modular architecture that supports dynamic adjustment of the number of input channels. Its core consists of an encoder, a Transformer bottleneck layer, and a decoder, supplemented by skip connections to fuse multi-scale features, providing input for the subsequent upsampling PCN network.

[0064] Figure 3 Figure 1 shows the encoding-decoding schematic diagram of GravCTUNet, and each module and its association with gravity data are described in detail below.

[0065] 1. The encoder of GravCTUNet (the first encoder): Adapt to multi-scale feature extraction for single-component and multi-component;

[0066] Local features of gravity data (such as shallow density anomalies in g z or horizontal gradient changes in g xx ) require high-resolution extraction, while deep features (such as basins or faults) need to capture low-frequency information through downsampling. The encoder of GravCTUNet adopts FastKANConvLayer to enhance the modeling ability of single-component and multi-component non-linear features through the Radial Basis Function (RBF). For the input x ∈ RB×Cin×H×W (where Cin = 1 represents single-component g z , and Cin = 7 represents multi-component), the RBF mapping is defined as:

[0067]

[0068] where c is the center of the basis function and σ is the width parameter. Here, ci is the center of the i-th basis function, σ is the width parameter (determined by the grid range [-2, 2]), and Ngrids = 4. The RBF mapping can map the input to a high-dimensional feature space, and the output φ(x) ∈ RB×Cin×H×W×Ngrids is reshaped to (B, Cin×Ngrids, H, W), and then local features are extracted through convolution operations:

[0069] y = W*φ(x) + b, (2)

[0070] where \(W\in\mathbb{R}^{C_{out}\times(C_{in}\times N_{grids})\times3\times3}\) is the convolutional kernel weight and \(b\in\mathbb{R}^{C_{out}}\) is the bias. The non - linear mapping of RBF is especially suitable for processing the unimodal distribution of \(g\) z or the gradient mutation in multi - components (such as \(g_{xz}\) at the fault).

[0071] The encoder consists of 5 layers, and each layer is composed of a double - convolution module (DoubleConv) and a max - pooling operation (MaxPool2d), gradually extracting multi - scale features to adapt to the spatial variations of single - component and multi - component.

[0072] The DoubleConv module of each layer is defined as:

[0073] DoubleConv(x)=\(\text{ReLU}(\text{BN}(\text{FastKANConv}(\text{ReLU}(\text{BN}(\text{FastKANConv}(x))))))\) (3)

[0074] where BN represents batch normalization and ReLU is the activation function. For the single - component \(g\) z , the encoder mainly extracts the density change in the vertical direction; for multi - components, the network uses gravity gradient information (such as \(g_{xy}\) and \(g\) zz ) to enhance the multi - directional feature representation.

[0075] Figure 4 Shows the structural diagram of the DoubleConv module of each layer.

[0076] For the single - component \(g\) z , the encoder mainly extracts the density change in the vertical direction; for multi - components, the network uses gravity gradient information (such as \(g_{xy}\) and \(g\) zz ) to enhance the multi - directional feature representation.

[0077] 2. The Transformer bottleneck layer of GravCTUNet: Global dependency modeling;

[0078] The deep geological structure of gravity data (such as underground basins or tectonic belts) shows long - range spatial dependency relationships, which are difficult to be fully reflected by the single - component \(g\) z . And the low - frequency components such as \(g\) in multi - component data zz provide global information. To capture these dependencies, GravCTUNet introduces a Transformer module at the bottom layer of the encoder. The input is \(x_5\in\mathbb{R}^{B\times(1024 / f)\times2\times2}\), which is reshaped into a sequence \(X'\in\mathbb{R}^{(H\cdot W)\times B\times C}\) (\(H\cdot W = 4\), \(C = 1024 / f\)). \(X'\) represents the flattened spatial sequence for subsequent multi - head self - attention calculation.

[0079] The Transformer module contains the Multi-Head Self-Attention (MHSA) and the Feed-Forward Network (FFN). The attention mechanism is defined as:

[0080]

[0081] where Q = X'WQ, K = X'WK, V = X'WV are the query, key, and value matrices, dk = C / num_heads is the dimension of the key, and in this paper, num_heads = 8 is set.

[0082] The multi-head mechanism calculates multiple attention heads in parallel and concatenates them:

[0083] MHSA(X') = Concat(head1, head2,..., head h )W O (5)

[0084] where h = num_heads, WO ∈ RC×C. The output of MHSA passes through residual connection and layer normalization:

[0085] X″ = LayerNorm(X' + MHSA(X')).(6)

[0086] where X″ represents the features after MHSA, the first residual connection, and layer normalization, and is used for subsequent FFN processing. The feature X″ enters the FFN module, and the FFN consists of two linear transformations, with a GELU activation function in between:

[0087] FFN(X″) = W2·ReLU(W1X″ + b1) + b2,(7)

[0088] where W1 ∈ RC×dff, W2 ∈ Rdff×C, and dff = 2048. The output of FFN passes through residual connection and layer normalization:

[0089] Xout = LayerNorm(X″ + Dropout(FFN(X″))),(8)

[0090] After reshaping, it is (B, 1024 / f, 2, 2). For a single component g z , the Transformer enhances the modeling of deep vertical dependencies; for multiple components, the network uses gravity gradient information to associate deep features in different directions.

[0091] 3. The decoder of GravCTUNet (the first decoder): density distribution reconstruction and multi-scale fusion;

[0092] The decoder is responsible for reconstructing the density distribution from the bottleneck layer features, fusing the multi-scale features of the encoder to retain the detailed information of the gravity data. The single-component g z provides shallow information, and the multi-component data enhances the deep information through the gradient components. The decoder consists of 5 layers, and each layer is composed of an upsampling, feature concatenation, and DoubleConv module. The upsampling uses the following bilinear interpolation:

[0093] Upsample(x,scale_factor)=Bilinear(x,scale_factor),(9)

[0094] where scale_factor = 2. The skip connection concatenates the encoder feature xskip and the upsampled feature xup:

[0095] x concat =Concat(x skip ,x up ,dim=1).(10)

[0096] The features are flattened to (B, C′×H×W), and the downsampled output is generated through a linear layer:

[0097] y=W·x flat +b,(11)

[0098] where W∈R(D*H*W)×(C′*H*W), b∈RD*H*W, and the output y∈RB×(D*H*W). The skip connection ensures that both the shallow and deep information in the single-component and multi-component data is retained. The downsampled output is then waiting to be input into the subsequent upsampling PCN network.

[0099] 4. Loss function and training of the downsampling DPN network;

[0100] The GravCTUNet model is optimized using the mean squared error (MSE) loss function:

[0101]

[0102] where y i is the true density, is the predicted value, and N = B×(D*H*W). MSE is suitable for density regression tasks and applicable to both single-component and multi-component experiments. The network uses the Adam optimizer (learning rate 0.0001) and adopts a custom StepLR decay strategy:

[0103] StepLR=(Epoch·α+1)×(Train_num / / Batch_size+1)(13)

[0104] Among them, the value range of the attenuation interval period coefficient α is from 0 to 1. The StepLR attenuation strategy means that the first learning rate adjustment occurs at the α percentage of the total number of iterations, and subsequent adjustments are performed at the same interval period.

[0105] The GravCTUNet network realizes the inversion mapping from two-dimensional gravity data to three-dimensional density distribution, but the effectiveness of its inversion results still needs to be verified: that is, generating predicted gravity data from the predicted density distribution and comparing it with the true gravity observation data in the training set. Therefore, this embodiment proposes an uplink network based on SwinTransformer - GravSwinTransUNet. This model combines the global modeling ability of SwinTransformer and the pixel-level prediction ability of U-Net, and extends 2D SwinTransformer to 3D form to achieve an efficient mapping from three-dimensional density distribution to two-dimensional gravity anomaly. GravSwinTransUNet takes the three-dimensional density predicted by GravCTUNet as input, simulates the physical mechanism of gravity forward modeling, and forms a complementary relationship with GravCTUNet: the former is used for the forward modeling from density to gravity anomaly, and the latter is used for the inversion from gravity anomaly to density. The two constitute an end-to-end dual-network-driven inversion framework to improve the physical consistency and accuracy of gravity inversion. Figure 5 The encoding-decoding schematic diagram of GravSwinTransUNet is shown, and each module is described in detail below.

[0106] 1. Encoder (the second encoder) of GravSwinTransUNet: Feature extraction based on 3D SwinTransformer;

[0107] The encoder of GravSwinTransUNet adopts a 3D Swin Transformer structure to process the three-dimensional density distribution x ∈ RB×1×D×H×W output by GravCTUNet. The encoder extracts multi-scale features through multi-stage downsampling to capture the global context information of the three-dimensional density distribution, such as the long-distance influence of deep density bodies on surface gravity.

[0108] First, the input is divided into non-overlapping three-dimensional patches. Each patch is flattened into a C″-dimensional vector and mapped to the embedding dimension C′ through a linear layer to generate the initial feature X0 ∈ RB×512×96. This step decomposes the density distribution into a sequence of patches, providing input for subsequent Swin Transformer processing.

[0109] The Swin Transformer Block consists of window-based self-attention (W-MSA), shifted window-based self-attention (SW-MSA), layer normalization (LayerNorm), and a feed-forward network (FFN). Its core attention mechanism is the same as that of the Transformer module in GravCTUNet (see the previous section for details). Swin Transformer reduces the computational complexity through windowing design. The feature X ∈ R B×N×C is reshaped into a three-dimensional grid (B, C, 8, 8, 8) and divided into windows of size 2×2×2 (a total of 64 windows). W-MSA calculates self-attention within the window, and SW-MSA enhances cross-window connections through shifted windows to capture dependencies in different depths and regions of the density distribution.

[0110] The encoder consists of 4 stages, each stage composed of several Swin Transformer blocks and Patch Merging. The Patch Merging operation reduces the dimension through a linear layer and concatenates patch features, gradually compressing the spatial resolution. Compared with the encoder of GravCTUNet, the encoder of GravSwinTransUNet focuses more on the global feature extraction of three-dimensional data, providing deep information for the forward modeling task. Figure 6 Shows the structural diagram of the Swin Transformer Block.

[0111] 2. The decoder of GravSwinTransUNet (the second decoder): gravity anomaly reconstruction;

[0112] The decoder of GravSwinTransUNet adopts a U-Net structure. Through multi-stage upsampling and skip connections, it maps the three-dimensional features of the encoder to two-dimensional gravity anomaly data. The decoder is similar in structure to the decoder of GravCTUNet, but its goal is to generate two-dimensional gravity anomalies from the three-dimensional density distribution, simulating the projection mechanism of gravity forward modeling.

[0113] The decoder consists of 4 stages, and each stage upsamples through Patch Expanding and fuses the features of the corresponding stage of the encoder. Patch Expanding is the inverse operation of Patch Merging, doubling the feature resolution by 2×2×2 and halving the number of channels. For example, the input (B, 768, 1, 1, 1) is expanded to (B, 384, 2, 2, 2) through a linear layer.

[0114] Finally, the decoder maps the three-dimensional features to two-dimensional gravity anomaly data through the projection layer. The features (B, Cout, D / 2, H / 2, W / 2) are averaged along the depth dimension to generate (B, Cout, H / 2, W / 2), which are then upsampled to (B, Cout, H, W) through bilinear interpolation. This process simulates the gravity response of the three-dimensional density body to the surface in the forward gravity modeling, forming a closed loop with the input of GravCTUNet.

[0115] 3. Loss function and training of the upward PCN network;

[0116] GravSwinTransUNet is also optimized using the mean squared error (MSE) loss, which is consistent with GravCTUNet. The MSE loss directly measures the deviation between the predicted gravity anomaly and the true data in the training set and is suitable for the regression task of forward gravity modeling. This consistency ensures the coordination of the dual networks in the inversion-forward closed-loop framework.

[0117] Loss constraint

[0118] This dual-network framework includes two types of loss functions: task loss and physical loss. The overall loss function is as follows:

[0119]

[0120] where m and g represent the true density model and its corresponding gravity data in the training set, respectively; α, β, and γ represent the loss weight values. After optimal verification, α = 0.5, β = 0.3, and γ = 0.2 are taken in this paper; represents the predicted density model obtained by the downward DPN network, is the predicted gravity data obtained by the upward PCN network based on the output of the downward DPN network ; represents the model loss constraint of the downward DPN network; represents the potential field loss constraint of the upward PCN network; represents the physical loss constraint controlled by the forward kernel matrix operator K between the output results of the two networks.

[0121] To test the generalization of the network, a three-cube model that does not appear in the training set is extracted to test its learning ability. At the same time, uncorrelated Gaussian noise with a mean of zero and a standard deviation of 1% of the maximum amplitude of the forward simulation is added to the model samples to simulate real observational data and verify the anti-interference ability of the network. Its 3D view is as Figure 7 (a) shown. (a) Figure 7(b)-(c) represent the sliced diagrams of the model at y = 1600m and x = 1000m respectively. To detect the generalization ability of the newly proposed dual-network-driven inversion framework, in this embodiment, a common single U-Net network is used for comparison, and the model recovery capabilities of the single gravity anomaly data and the gravity anomaly + full tensor joint inversion are tested respectively.

[0122] Figure 8 、 Figure 9 show the prediction effects of the two network models on the AA′ and BB′ slices of the synthetic model using two types of data sources. Each row of the figure represents the prediction results of the g z data and the g z + 6 full gravity gradient tensor data under the same network, and each column represents the prediction results of different networks for the input of the same data source channel.

[0123] Figure 8 、 Figure 9 As shown, significant differences in effects can be observed: when the two networks use the input fused with 7 types of data sources, in terms of both model boundary recognition and density amplitude recovery, the dual-network inversion framework shows better prediction accuracy and generalization ability than the traditional single U-Net network, and both exceed their respective prediction performances when only using the single data source g z . This indicates that the multi-source data system can significantly improve the performance of the model in geological body boundary recognition and density distribution reconstruction, thereby further enhancing the prediction ability and accuracy of the model. At the same time, overall, for the dual-network inversion framework proposed in this paper, whether it is the input of a single data source channel or the input of the fused 7 types of data source channels, its prediction results are better than those of the U-net network in terms of overall effect, showing stronger noise robustness. This indicates that the dual-network inversion framework has stronger capabilities in feature extraction and information fusion, can more effectively suppress the influence of noise, and thus improve the overall prediction accuracy and robustness of the model.

[0124] Table 1 details the parameter settings of the dual-network inversion framework, including the training hyperparameters and the optimal weights of the three parts of the loss function (based on the best validation results).

[0125] Table 1

[0126]

[0127]

[0128] Figure 10The mean squared error (MSE) loss curves of the training set and the validation set during the entire training process of the dual-network framework are shown. The horizontal axis represents the number of iterations during the training process, and the vertical axis represents the corresponding mean squared error value. During the entire training, the StepLR decay strategy operation and the early stopping mechanism are adopted to prevent the network from overfitting. It can be seen that as the training continues, the loss values of both the training set and the validation set show a gradually convergent trend, indicating that the fitting performance of the model on the training data and the validation data is continuously improving, and at the same time reflecting the effectiveness of this network during the optimization process.

[0129] To test the data fitting ability of the dual-network framework for the joint inversion of gravity and gradient tensors, this paper selects the output results of the upward PCN network GravSwinTransUNet for inspection. Here, the g z and g zz components are taken as examples. Figure 11 It can be seen that the fitting relative error values of g z and g zz are both less than 5%, meeting the reasonable error range.

[0130] This embodiment also proposes a gravity inversion system based on dual-network drive, including:

[0131] A data acquisition unit for acquiring a training data set, where the training data set includes an actual underground medium density model and actual gravity data;

[0132] A network architecture construction unit for constructing a dual-network cascade architecture including a downward density prediction network and an upward physical property correction network;

[0133] A downward prediction processing unit for inputting the gravity data in the training set into the downward density prediction network to obtain predicted model data;

[0134] An upward correction processing unit for inputting the predicted model data into the upward physical property correction network to obtain predicted gravity data;

[0135] A loss constraint acquisition unit for obtaining a model loss constraint through the predicted model data and the actual underground medium density model, and obtaining a potential field loss constraint through the predicted gravity data and the actual gravity data;

[0136] An optimization and inversion model acquisition unit for performing weighted optimization on the dual-network cascade architecture through the potential field loss constraint, the model loss constraint, and the physical loss constraint controlled by the gravity forward kernel matrix operator to obtain an inversion model;

[0137] A gravity data inversion unit for inversing the gravity data to be inverted through the inversion model to obtain the underground medium density distribution.

[0138] This embodiment also provides a computer device, including a memory, a processor, and a computer program stored on the memory, where the processor executes the computer program to implement the steps of the method.

[0139] This embodiment also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method are implemented.

[0140] This embodiment also provides a computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the method are implemented.

[0141] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A gravity inversion method based on dual-network drive, characterized in that, It includes the following steps: Obtain a training data set, where the training data set includes an actual underground medium density model and actual gravity data; Construct a dual-network cascade architecture including a downward density prediction network and an upward physical property correction network; Input the gravity data in the training set into the downward density prediction network to obtain predicted model data; Input the predicted model data into the upward physical property correction network to obtain predicted gravity data; Obtain a model loss constraint through the predicted model data and the actual underground medium density model, and obtain a potential field loss constraint through the predicted gravity data and the actual gravity data; Perform weighted optimization on the dual-network cascade architecture through the potential field loss constraint, the model loss constraint, and a physical loss constraint controlled by a gravity forward kernel matrix operator to obtain an inversion model; Invert the gravity data to be inverted through the inversion model to obtain the underground medium density distribution.

2. The method according to claim 1, characterized in that The downward density prediction network includes: A first encoder for extracting multi-scale features of gravity data; A Transformer bottleneck layer for capturing long-range geological dependencies of gravity data; A first decoder for fusing multi-scale features through skip connections and reconstructing a three-dimensional density distribution.

3. The method according to claim 2, wherein The first encoder adopts a convolution operation based on a Kolmogorov-Arnold network and combines a radial basis function mapping to enhance the non-linear feature modeling ability.

4. The method according to claim 1, characterized in that The upward physical property correction network includes: A second encoder adopting a 3D Swin Transformer structure for extracting global context information of the three-dimensional density distribution; A second decoder adopting a U-Net structure for mapping the three-dimensional features extracted by the second encoder to two-dimensional gravity anomaly data.

5. The method according to claim 1, characterized in that, The potential field loss constraint is used to measure the deviation between the predicted gravity data and the actual gravity data in the training set; the model loss constraint is used to measure the deviation between the predicted model data and the actual underground medium density model in the training set; the physical loss constraint is used to measure the physical consistency between the output results of the two networks controlled by a gravity forward kernel matrix operator.

6. The method according to claim 1, characterized in that The overall loss function of the dual-network framework is: L = αU1 + βU2 + γδ; where U1 is the model loss constraint, U2 is the potential field loss constraint, δ is the physical loss constraint, α is the weight coefficient of the model loss constraint, β is the weight coefficient of the potential field loss constraint, and γ is the weight coefficient of the physical loss constraint.

7. A gravity inversion system based on dual-network drive, characterized in that, It includes: A data acquisition unit for obtaining a training data set, where the training data set includes an actual underground medium density model and actual gravity data; A network architecture construction unit for constructing a dual-network cascade architecture including a downward density prediction network and an upward physical property correction network; A downward prediction processing unit for inputting the gravity data in the training set into the downward density prediction network to obtain predicted model data; An upward correction processing unit for inputting the predicted model data into the upward physical property correction network to obtain predicted gravity data; A loss constraint acquisition unit for obtaining a model loss constraint through the predicted model data and the actual underground medium density model, and obtaining a potential field loss constraint through the predicted gravity data and the actual gravity data; An optimization and inversion model acquisition unit, which is used to perform weighted optimization on a dual-network cascade architecture through a potential field loss constraint, a model loss constraint, and a physical loss constraint controlled by a gravity forward kernel matrix operator, so as to obtain an inversion model; A gravity data inversion unit, which is used to invert the gravity data to be inverted through the inversion model to obtain the underground medium density distribution.

8. A computer device, comprising a memory, a processor, and a computer program stored on the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1-6.

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