A gravity inversion method and system based on double network driving

Abstract

This invention discloses a gravity inversion method and system based on dual-network driving, comprising: acquiring a training dataset, wherein the training dataset includes an actual subsurface medium density model and actual gravity data; constructing a dual-network cascaded architecture including a downlink density prediction network and an uplink property correction network; inputting the gravity data in the training set into the downlink density prediction network to obtain prediction model data; inputting the prediction model data into the uplink property correction network to obtain predicted gravity data; obtaining potential field loss constraints and model loss constraints through the predicted data and the actual data; performing weighted optimization on the dual-network cascaded architecture through the potential field loss constraints, model loss constraints, and physical loss constraints controlled by the gravity forward modeling kernel matrix operator to obtain an inversion model; and inverting the gravity data to be inverted using the inversion model to obtain the subsurface medium density distribution. This invention can more accurately reflect the detailed features of the subsurface.

Description

Technical Field

[0001] This invention belongs to the field of gravity inversion technology, and particularly relates to a gravity inversion method and system based on dual-network driving. Background Technology

[0002] Gravity field inversion is a key technology in geophysical exploration, aiming to infer the density distribution of subsurface media by analyzing gravity anomalies at the Earth's surface, thereby revealing the distribution of subsurface structures and mineral resources. Traditional gravity inversion methods, such as iterative optimization methods based on forward models, while providing some information on subsurface density distribution, suffer from several significant problems. These problems include multiple solutions in the inversion results, low depth resolution, high computational cost when processing large-scale datasets, and the need for extensive prior information and parameter adjustments.

[0003] With the rapid development of deep learning technology, data-driven gravity inversion methods have begun to attract widespread attention. Convolutional Neural Networks (CNNs) and Transformer models, in particular, have demonstrated significant advantages in handling nonlinear problems and high-dimensional data. These deep learning methods, by directly learning the complex mapping relationship between gravity data and the density distribution of the subsurface medium, promise to significantly improve the accuracy and efficiency of inversion.

[0004] However, existing deep learning-based gravity inversion methods suffer from the following shortcomings: First, most methods employ a single network architecture, such as U-Net. While these models perform well in local feature extraction, they are limited in capturing the complex characteristics and long-range dependencies of the subsurface medium. Second, existing methods often focus on data fitting while neglecting the physical plausibility of geophysical processes, resulting in insufficient generalization ability of the inversion results in complex geological contexts. Finally, in practical applications, gravity data is often affected by noise, and the robustness of existing methods in noisy environments needs improvement. Summary of the Invention

[0005] This invention proposes a gravity inversion method and system based on dual network drive to solve the problems existing in the prior art.

[0006] To achieve the above objectives, this invention provides a gravity inversion method based on dual-network driving, comprising the following steps:

[0007] Obtain the training dataset, which includes a real subsurface density model and real gravity data;

[0008] Construct a dual-network cascaded architecture comprising a downlink density prediction network and an uplink property correction network;

[0009] The gravity data in the training set is input into the downlink density prediction network to obtain the prediction model data;

[0010] The predicted model data is input into the uplink property correction network to obtain the predicted gravity data;

[0011] Model loss constraints are obtained by combining predicted model data and actual underground medium density models, and potential field loss constraints are obtained by combining predicted gravity data and actual gravity data.

[0012] By using potential field loss constraints, model loss constraints, and physical loss constraints controlled by the gravity forward modeling kernel matrix operator, the dual-network cascaded architecture is weighted and optimized to obtain the inversion model.

[0013] The inversion model is used to invert the gravity data to be inverted, and the density distribution of the underground medium is obtained.

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

[0015] The first encoder is used to extract multi-scale features from gravity data;

[0016] Transformer bottleneck layer, used to capture long-range geological dependencies of gravity data;

[0017] The first decoder is used to fuse multi-scale features and reconstruct the 3D density distribution through skip connections;

[0018] Preferably, the first encoder employs convolutional operations based on the Kolmogorov-Arnold network and combines radial basis function mapping to enhance nonlinear feature modeling capabilities.

[0019] Preferably, the uplink property correction network includes:

[0020] The second encoder, employing a 3D Swin Transformer structure, is used to extract global contextual information about the three-dimensional density distribution.

[0021] The second decoder, employing a U-Net structure, is used to map the three-dimensional features extracted by the second encoder onto the 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 predicted model data and the actual underground medium density model in the training set; and the physical loss constraint is used to measure the physical consistency between the outputs of the two networks controlled by the gravity forward modeling kernel matrix operator.

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

[0024] L = αU1 + βU2 + γδ;

[0025] 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.

[0026] This invention also proposes a gravity inversion system based on dual-network drive, comprising:

[0027] The data acquisition unit is used to acquire the training dataset, which includes the actual underground medium density model and actual gravity data.

[0028] Network architecture building unit, used to build a dual-network cascaded architecture including a downlink density prediction network and an uplink property correction network;

[0029] The downlink prediction processing unit is used to input gravity data from the training set into the downlink density prediction network to obtain prediction model data.

[0030] An uplink correction processing unit is used to input the prediction model data into an uplink property correction network to obtain predicted gravity data;

[0031] The loss constraint acquisition unit is used to acquire model loss constraints through predicted model data and actual underground medium density model, and to acquire potential field loss constraints through predicted gravity data and actual gravity data.

[0032] The optimization and inversion model acquisition unit is used to perform weighted optimization on the dual-network cascaded architecture through potential field loss constraints, model loss constraints, and physical loss constraints controlled by the gravity forward modeling kernel matrix operator to obtain the inversion model;

[0033] The gravity data inversion unit is used to invert the gravity data to be inverted through the inversion model to obtain the density distribution of the underground medium.

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

[0035] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0036] The present invention also proposes a computer program product, including a computer program that, when executed by a processor, implements the steps of the method.

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

[0038] This invention improves the accuracy, generalization ability, and physical plausibility of inversion results by introducing geophysical consistency constraints and employing a dual-network cascaded architecture, including a downlink density prediction network and an uplink property correction network. This method not only fully utilizes the multi-network architecture to extract multi-dimensional features from gravity data and its corresponding model density distribution, thus fully mining the potential information within the data, but also integrates geophysical consistency constraints into the network training process, making the network learning process more consistent with physical laws. Furthermore, this method can dynamically adjust network parameters and constraint weights according to different geological scenarios to adapt to diverse inversion needs. By adopting a multi-network architecture, incorporating geophysical constraints, and dynamically adjusting parameters, the method of this invention can more accurately reflect subsurface detail features, thus providing a new and effective strategy for predicting and reconstructing subsurface geological information in gravity exploration. Attached Figure Description

[0039] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

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

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

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

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

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

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

[0046] Figure 7 The following are 3D views and slices of the synthetic model according to an embodiment of the present invention; wherein, (a) is a three-dimensional view of the three-cube model; (b) is a cross-sectional view of the three-cube model at y=1600m; (c) is a longitudinal section view of the three-cube model at x=1000m; and (d) is a density value color-coded image.

[0047] Figure 8The diagram shows a comparison of the prediction results of the dual-network inversion framework and the single U-Net network for the synthetic model in an embodiment of the present invention. (a) is the prediction result of the dual-network inversion framework for the AA' slice; (b) is the prediction result of the single U-Net network for the AA' slice; (c) is the difference between the prediction results of the dual-network inversion framework and the single U-Net network for the AA' slice; (d) is the error analysis diagram of the prediction result of the dual-network inversion framework for the AA' slice; and (e) is the density value color-coded diagram.

[0048] Figure 9 The diagram shows a comparison of the prediction results of the dual-network inversion framework and the single U-Net network for the synthetic model in this embodiment of the invention. (a) is the prediction result of the dual-network inversion framework for the BB' slice; (b) is the prediction result of the single U-Net network for the BB' slice; (c) is the difference between the prediction results of the dual-network inversion framework and the single U-Net network for the BB' slice; (d) is the error analysis diagram of the prediction result of the dual-network inversion framework for the BB' slice; and (e) is the density value color-coded diagram.

[0049] Figure 10 This is a graph showing the mean square error (MSE) loss curves of the training and validation sets during the training process of the dual-network framework in this embodiment of the invention.

[0050] Figure 11 The gravity anomaly component g output by the uplink PCN network in this embodiment of the invention. z and g zz The fitting error plot; where (a) is the gravity anomaly component g output by the uplink PCN network. z (a) shows the fitting error plot; (b) shows the gravity anomaly component g output by the uplink PCN network. zz (c) shows the fitting error plots of the dual-network inversion framework and the single U-Net network for the gravity anomaly component g. z A comparison of fitting errors; (d) shows the results of the dual-network inversion framework and the single U-Net network for the gravity anomaly component g. zz A comparison of fitting errors; (e) shows the fitting error of the dual-network inversion framework for the gravity anomaly component g. z Detailed analysis of fitting error; (f) shows the effect of the dual-network inversion framework on the gravity anomaly component g. zz Detailed analysis of fitting error: (g) is a color-coded map of gravity anomalies, (h) is a color-coded map of relative error, (i) is a color-coded map of gravity gradient values, and (j) is a color-coded map of relative error. Detailed Implementation

[0051] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

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

[0053] Example 1

[0054] like Figure 1-6 As shown, this embodiment provides a gravity inversion method based on dual-network driving, including the following steps:

[0055] Obtain the training dataset, which includes a real subsurface density model and real gravity data;

[0056] Construct a dual-network cascaded architecture comprising a downlink density prediction network and an uplink property correction network;

[0057] The gravity data in the training set is input into the downlink density prediction network to obtain the prediction model data;

[0058] The predicted model data is input into the uplink property correction network to obtain the predicted gravity data;

[0059] Model loss constraints are obtained by combining predicted model data and actual underground medium density models, and potential field loss constraints are obtained by combining predicted gravity data and actual gravity data.

[0060] By using potential field loss constraints, model loss constraints, and physical loss constraints controlled by the gravity forward modeling kernel matrix operator, the dual-network cascaded architecture is weighted and optimized to obtain the inversion model.

[0061] The density distribution of the underground medium is obtained by inverting the gravity data to be inverted using an inversion model.

[0062] Furthermore, the downlink density prediction network, named GravCTUNet, aims to integrate the local feature extraction capabilities of CNNs with the global modeling capabilities of Transformers, making it suitable for density distribution prediction of single-component and multi-component gravity data. GravCTUNet employs a convolutional operation based on the Kolmogorov-Arnold network (KAN) (FastKANConvLayer) to enhance its ability to model nonlinear features, and combines a Transformer bottleneck layer to capture long-range geological dependencies. This network supports flexible input configurations: single-component inputs (such as g...) zGravCTUNet takes single-component (B,1,H,W) or multi-component inputs (e.g., 7-component dimension (B,7,H,W)) as inputs and outputs a three-dimensional density distribution (B,D×H×W). By comparing the performance of single-component and multi-component inputs, GravCTUNet provides a systematic analysis of the impact on the information content of gravity data.

[0063] GravCTUNet's design takes into account the diversity of gravity data: gravity anomalies, due to their integral properties, are better suited to reflecting deep density structures, while gravity gradient data, by highlighting local variations, is more beneficial for parsing shallow features. 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 uplink PCN network.

[0064] Figure 3 The encoding-decoding diagram of GravCTUNet is shown. The following describes each module and its relationship with gravity data in detail.

[0065] 1. GravCTUNet's encoder (first encoder): adapts to multi-scale feature extraction of single and multi-component components;

[0066] Local features of gravity data (such as g) z Shallow density anomalies or g xx Horizontal gradient changes in deep features require high-resolution extraction, while deep features (such as basins or faults) require downsampling to capture low-frequency information. GravCTUNet's encoder employs FastKANConvLayer, which enhances its ability to model single-component and multi-component nonlinear features through radial basis functions (RBF). For input x∈RB×Cin×H×W (where Cin=1 represents a single component g...), ... z (Cin=7 indicates multiple components), the RBF mapping is defined as:

[0067] (1)

[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. RBF mapping maps the input to a high-dimensional feature space, and the output ϕ(x)∈RB×Cin×H×W×Ngrids is reshaped into (B,Cin×Ngrids,H,W), subsequently extracting local features through convolution operations:

[0069] (2)

[0070] Where W∈RCout×(Cin×Ngrids)×3×3 are the convolution kernel weights, and b∈RCout is the bias. RBF is a nonlinear mapping, particularly suitable for processing g. z A unimodal distribution or abrupt gradient changes in multiple components (e.g., gxz at faults).

[0071] The encoder consists of 5 layers, each composed of a double convolutional module (DoubleConv) and a max pooling operation (MaxPool2d), progressively extracting multi-scale features to adapt to spatial variations of single and multi-component components. The DoubleConv module of each layer is defined as follows:

[0072] (3)

[0073] Where BN represents batch normalization, and ReLU is the activation function. For a single component g z The encoder primarily extracts density changes in the vertical direction; for multi-component networks, the network utilizes gravity gradient information (such as gxy and g...). zz Enhance multi-directional feature representation.

[0074] Figure 4 The structure diagram of the DoubleConv module at each level is shown.

[0075] For a single component g z The encoder primarily extracts density changes in the vertical direction; for multi-component networks, the network utilizes gravity gradient information (such as gxy and g...). zz Enhance multi-directional feature representation.

[0076] 2. GravCTUNet's Transformer bottleneck layer: global dependency modeling;

[0077] Gravity data for deep geological structures (such as subsurface basins or tectonic zones) exhibits long-range spatial dependence, with single-component g... z It is difficult to fully reflect the situation, and g in multi-component data zz Low-frequency components provide global information. To capture these dependencies, GravCTUNet introduces a Transformer module at the lowest level of the encoder. The input x5∈RB×(1024 / f)×2×2 is reshaped into a sequence X′∈R(H⋅W)×B×CX' (H⋅W=4, C=1024 / f). X′ represents the flattened spatial sequence, which is used for subsequent multi-head self-attention calculations.

[0078] The Transformer module includes Multi-Head Self-Attention (MHSA) and a Feed-Forward Network (FFN). The attention mechanism is defined as follows:

[0079] (4)

[0080] Where Q=X′WQ, K=X′WK, and V=X′WV are the query, key, and value matrices, and dk=C / num_heads is the dimension of the key. In this paper, num_heads is set to 8.

[0081] The multi-head mechanism computes multiple attention heads in parallel and then concatenates them:

[0082] (5)

[0083] Where h = num_heads, WO ∈ RC × C. MHSA output is processed through residual connections and layer normalization:

[0084] (6)

[0085] Here, X′′ represents the feature after MHSA, the first residual connection, and layer normalization, used for subsequent FFN processing. Feature X′′ enters the FFN module, which consists of two linear transformations with a GELU activation function in between.

[0086] (7)

[0087] Where W1∈RC×dff, W2∈Rdff×C, dff=2048. The FFN output is processed through residual connections and layer normalization:

[0088] (8)

[0089] After reshaping, it becomes (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.

[0090] 3. GravCTUNet's decoder (first decoder): density distribution reconstruction and multi-scale fusion;

[0091] The decoder is responsible for reconstructing the density distribution from the bottleneck layer features and fusing the multi-scale features from the encoder to preserve the detailed information of the gravity data. (Single component g) zIt provides shallow information, and multi-component data enhances deeper information through gradient components. The decoder consists of 5 layers, each composed of upsampling, feature concatenation, and a DoubleConv module. Its upsampling uses the following bilinear interpolation:

[0092] (9)

[0093] Where scale_factor=2. Skip connections concatenate encoder features xskip with upsampled features xup:

[0094] (10)

[0095] The feature is flattened to (B, Cʹ×H×W), and a downlink output is generated through a linear layer:

[0096] (11)

[0097] Where W∈R(D) H W)×(Cʹ H W), b∈RD H W, output y∈RB×(D) H (W). Skip connections ensure that both shallow and deep information in single-component and multi-component data is preserved. Downlink outputs are then awaited input into subsequent uplink PCN networks.

[0098] 4. Loss function and training of downlink DPN networks;

[0099] The GravCTUNet model is optimized using the mean squared error (MSE) loss function:

[0100] (12)

[0101] Where y i For true density, For the predicted value, N = B × (D) H W). MSE is suitable for density regression tasks and is applicable to both single-component and multi-component experiments. The network uses the Adam optimizer (learning rate 0.0001) and employs a custom StepLR decay strategy:

[0102] (13)

[0103] The decay interval coefficient α ranges from 0 to 1. The StepLR decay strategy means that the first learning rate adjustment occurs at α percent of the total number of iterations, and subsequent adjustments are performed at the same interval.

[0104] The GravCTUNet network achieves the inversion mapping from 2D gravity data to 3D 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 real gravity observation data in the training set. Therefore, this embodiment proposes an uplink network based on the Swing Transformer—GravSwinTransUNet. This model combines the global modeling capability of the Swing Transformer with the pixel-level prediction capability of U-Net, extending the 2D Swing Transformer to a 3D form to achieve efficient mapping from 3D density distribution to 2D gravity anomalies. GravSwinTransUNet uses the 3D density predicted by GravCTUNet as input to simulate the physical mechanism of gravity forward modeling, forming a complementary relationship with GravCTUNet: the former is used for forward modeling from density to gravity anomalies, and the latter is used for inversion from gravity anomalies 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 diagram of GravSwinTransUNet is shown below, and each module is described in detail below.

[0105] 1. GravSwinTransUNet encoder (second encoder): feature extraction based on 3D Swin Transformer;

[0106] The encoder of GravSwinTransUNet employs a 3D Swin Transformer architecture to process the 3D density distribution x∈RB×1×D×H×W output by GravCTUNet. The encoder extracts multi-scale features through multi-stage downsampling, capturing global contextual information of the 3D density distribution, such as the long-distance influence of deep density volumes on surface gravity.

[0107] First, the input is divided into non-overlapping 3D patches. Each patch is flattened into a Cʹʹ-dimensional vector and mapped to the embedding dimension Cʹ through a linear layer, generating initial features X0∈RB×512×96. This step decomposes the density distribution into a sequence of patches, providing input for subsequent Swin Transformer processing.

[0108] The Swin Transformer Block consists of Window-based Self-Attention (W-MSA), Shifted Window-based Self-Attention (SW-MSA), LayerNorm, and a Feedforward Network (FFN). Its core attention mechanism is consistent with the Transformer module of GravCTUNet (see the previous section for details). The Swin Transformer reduces computational complexity through a windowed design. Features X∈RB×N×C are reshaped into a three-dimensional grid (B,C,8,8,8), divided into 2×2×2 windows (64 windows in total). W-MSA computes self-attention within each window, while SW-MSA enhances cross-window connections through shifted windows, capturing dependencies between different depths and regions in the density distribution.

[0109] The encoder consists of four stages, each composed of several Swing Transformer blocks and Patch Merging. The Patch Merging operation reduces the spatial resolution progressively by using linear layers to reduce dimensionality and concatenate patch features. Compared to the GravCTUNet encoder, the GravSwinTransUNet encoder focuses more on global feature extraction from 3D data, providing deeper information for forward modeling tasks. Figure 6 The structure diagram of the Swing Transformer Block is shown.

[0110] 2. GravSwinTransUNet's decoder (second decoder): gravity anomaly reconstruction;

[0111] The GravSwinTransUNet decoder employs a U-Net architecture, mapping the encoder's 3D features to 2D gravity anomaly data through multi-stage upsampling and skip connections. While structurally similar to the GravCTUNet decoder, its goal is to generate 2D gravity anomalies from a 3D density distribution, simulating the projection mechanism of gravity forward modeling.

[0112] The decoder consists of four stages. Each stage upsamples and fuses the features from the corresponding stage of the encoder through Patch Expanding. Patch Expanding is the inverse operation of Patch Merging, which increases the feature resolution by a factor of 2×2×2 and halves 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.

[0113] Finally, the decoder maps the 3D features to 2D gravity anomaly data through a projection layer. The features (B,Cout,D / 2,H / 2,W / 2) are average-pooled along the depth dimension to generate (B,Cout,H / 2,W / 2), and then upsampled to (B,Cout,H,W) through bilinear interpolation. This process simulates the gravity response of the 3D density volume to the Earth's surface in gravity forward modeling, forming a closed loop with the input of GravCTUNet.

[0114] 3. Loss function and training of uplink PCN network;

[0115] GravSwinTransUNet also uses mean squared error (MSE) loss for optimization, consistent with GravCTUNet. MSE loss directly measures the deviation between the predicted gravity anomaly and the real data in the training set, making it suitable for gravity forward regression tasks. This consistency ensures the coordination of the two networks within the inversion-forward closed-loop framework.

[0116] Loss constraints

[0117] This dual-network framework includes two types of loss functions: task loss and physical loss. The overall loss function is as follows:

[0118] (14)

[0119] Where m and g represent the true density model in the training set and its corresponding gravity data, respectively; α, β, and γ represent the loss weights, which are set to α=0.5, β=0.3, and γ=0.2 after optimal validation; and represents the predicted density model obtained from the downlink DPN network. It is output from the uplink PCN network based on the downlink DPN network. The obtained predicted gravity data; This represents the model loss constraint for the downlink DPN network; This represents the bit field loss constraint of the uplink PCN network; This represents the physical loss constraint between the outputs of the two networks, controlled by the forward kernel matrix operator K.

[0120] To test the network's generalization ability, three-cube models not present in the training set were extracted to examine their learning capacity. Simultaneously, uncorrelated Gaussian noise with a mean of zero and a standard deviation equal to 1% of the maximum amplitude in the forward simulation was added to the model samples to simulate real-world observation data and verify the network's robustness to interference. Its 3D view is shown below. Figure 7 As shown in (a). Figure 7(b)-(c) represent the model slices at y=1600 m and x=1000 m, respectively. To test the generalization ability of the proposed dual-network driven inversion framework, this embodiment uses a commonly used single U-Net network for comparison, and tests the model recovery ability of single gravity anomaly data and gravity anomaly + full tensor joint inversion.

[0121] Figure 8 , Figure 9 This demonstrates the prediction performance of two network models using two types of data sources on two slices (AAʹ and BBʹ) of a synthetic model. Each row in the figure represents the prediction performance of the same network on slice g. z Data and g z The prediction results are from 6 full gravity gradient tensor datasets. Each column represents the prediction results of different networks for the same data source channel input.

[0122] Figure 8 , Figure 9 As shown, significant performance differences can be observed: when both networks use inputs from seven different data sources, the dual-network inversion framework demonstrates superior prediction accuracy and generalization ability compared to the traditional single U-Net network in both model boundary identification and density magnitude recovery, and surpasses its counterpart using only a single data source g. z The predictive performance of the model is shown in the results. This indicates that the multi-source data system can significantly improve the model's performance in geological body boundary identification and density distribution reconstruction, thereby further enhancing the model's predictive ability and accuracy. Furthermore, overall, the proposed dual-network inversion framework outperforms the U-net network in overall prediction results, whether using a single data source channel or fusion of seven data source channels, demonstrating stronger noise robustness. This indicates that the dual-network inversion framework has stronger capabilities in feature extraction and information fusion, and can more effectively suppress the influence of noise, thereby improving the model's overall prediction accuracy and robustness.

[0123] Table 1 details the parameter settings of the dual-network inversion framework, including the optimal weights of the training hyperparameters and the loss function (based on the best validation results).

[0124] Table 1

[0125]

[0126] Figure 10The diagram illustrates the mean squared error (MSE) loss curves of the dual-network framework on both the training and validation sets throughout the training process. The horizontal axis represents the number of iterations during training, and the vertical axis represents the corresponding MSE value. A StepLR decay strategy and an early stopping mechanism are employed throughout training to prevent overfitting. It can be seen that as training continues, the loss values ​​on both the training and validation sets gradually converge, indicating that the model's fitting performance on both training and validation data continuously improves, demonstrating the effectiveness of the network in the optimization process.

[0127] To test the data fitting capability of the dual-network framework for the joint inversion of gravity and gradient tensors, this paper selects the output results of the uplink PCN network GravSwinTransUNet for verification. Here, g... z and g zz Take the portion size as an example. Figure 11 It can be seen that g z and g zz The relative fitting errors are all less than 5%, which meets the reasonable error range.

[0128] This embodiment also proposes a gravity inversion system based on dual-network drive, including:

[0129] The data acquisition unit is used to acquire the training dataset, which includes the actual underground medium density model and actual gravity data.

[0130] Network architecture building unit, used to build a dual-network cascaded architecture including a downlink density prediction network and an uplink property correction network;

[0131] The downlink prediction processing unit is used to input gravity data from the training set into the downlink density prediction network to obtain prediction model data.

[0132] An uplink correction processing unit is used to input the prediction model data into an uplink property correction network to obtain predicted gravity data;

[0133] The loss constraint acquisition unit is used to acquire model loss constraints through predicted model data and actual underground medium density model, and to acquire potential field loss constraints through predicted gravity data and actual gravity data.

[0134] The optimization and inversion model acquisition unit is used to perform weighted optimization on the dual-network cascaded architecture through potential field loss constraints, model loss constraints, and physical loss constraints controlled by the gravity forward modeling kernel matrix operator to obtain the inversion model;

[0135] The gravity data inversion unit is used to invert the gravity data to be inverted through the inversion model to obtain the density distribution of the underground medium.

[0136] This embodiment also proposes a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0137] This embodiment also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method.

[0138] This embodiment also proposes a computer program product, including a computer program that, when executed by a processor, implements the steps of the method.

[0139] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A gravity inversion method based on dual-network driving, characterized in that, Includes the following steps: Obtain the training dataset, which includes a real subsurface density model and real gravity data; Construct a dual-network cascaded architecture comprising a downlink density prediction network and an uplink property correction network; The downlink density prediction network includes: The first encoder is used to extract multi-scale features from gravity data; Transformer bottleneck layer, used to capture long-range geological dependencies of gravity data; The first decoder is used to fuse multi-scale features and reconstruct the 3D density distribution through skip connections; The uplink property correction network includes: The second encoder, employing a 3D Swin Transformer structure, is used to extract global contextual information about the three-dimensional density distribution. The second decoder, using a U-Net structure, is used to map the three-dimensional features extracted by the second encoder to the two-dimensional gravity anomaly data. The gravity data in the training set is input into the downlink density prediction network to obtain the prediction model data; The predicted model data is input into the uplink property correction network to obtain the predicted gravity data; Model loss constraints are obtained by combining predicted model data and actual underground medium density models, and potential field loss constraints are obtained by combining predicted gravity data and actual gravity data. By using potential field loss constraints, model loss constraints, and physical loss constraints controlled by the gravity forward modeling kernel matrix operator, the dual-network cascaded architecture is weighted and optimized to obtain the inversion model. The inversion model is used to invert the gravity data to be inverted, and the density distribution of the underground medium is obtained.

2. The method according to claim 1, characterized in that, The first encoder employs convolutional operations based on the Kolmogorov-Arnold network and combines radial basis function mapping to enhance nonlinear feature modeling capabilities.

3. 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 outputs of the two networks, controlled by the gravity forward modeling kernel matrix operator.

4. The method according to claim 1, characterized in that, The overall loss function of the dual-network cascaded architecture 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.

5. A gravity inversion system based on dual-network drive, characterized in that, include: The data acquisition unit is used to acquire the training dataset, which includes the actual underground medium density model and actual gravity data. Network architecture building unit, used to build a dual-network cascaded architecture including a downlink density prediction network and an uplink property correction network; The downlink density prediction network includes: The first encoder is used to extract multi-scale features from gravity data; Transformer bottleneck layer, used to capture long-range geological dependencies of gravity data; The first decoder is used to fuse multi-scale features and reconstruct the 3D density distribution through skip connections; The uplink property correction network includes: The second encoder, employing a 3D Swin Transformer structure, is used to extract global contextual information about the three-dimensional density distribution. The second decoder, using a U-Net structure, is used to map the three-dimensional features extracted by the second encoder to the two-dimensional gravity anomaly data. The downlink prediction processing unit is used to input gravity data from the training set into the downlink density prediction network to obtain prediction model data. An uplink correction processing unit is used to input the prediction model data into an uplink property correction network to obtain predicted gravity data; The loss constraint acquisition unit is used to acquire model loss constraints through predicted model data and actual underground medium density model, and to acquire potential field loss constraints through predicted gravity data and actual gravity data. The optimization and inversion model acquisition unit is used to perform weighted optimization on the dual-network cascaded architecture through potential field loss constraints, model loss constraints, and physical loss constraints controlled by the gravity forward modeling kernel matrix operator to obtain the inversion model; The gravity data inversion unit is used to invert the gravity data to be inverted through the inversion model to obtain the density distribution of the underground medium.

6. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-4.

8. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-4.

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