Salt body density prediction method based on double-branch and multi-attention mechanism

Abstract

The application discloses a salt ore body density prediction method based on a double-branch and multi-attention mechanism, belongs to the technical field of machine learning and gravity inversion, and comprises the following steps: constructing a three-dimensional density model dataset based on gravity observation surface data and gravity field potential field migration theory; constructing a multi-attention mechanism fusion neural network with double-path feature fusion and training and optimizing the three-dimensional density model data; wherein the multi-attention mechanism fusion neural network with double-path feature fusion comprises two branches, one branch is a U-Net branch, and the other branch is a K-Net branch; the U-Net branch comprises a channel attention module, a self-attention mechanism module and a cross-resolution residual feature block; the gravity data of a salt ore body to be predicted is converted into corresponding three-dimensional body companion operators, and the deep learning network after training and optimization is processed to obtain a salt ore body density prediction result. The application has excellent effects in gravity field value recovery and deep structure boundary depiction.

Description

Technical Field

[0001] This invention belongs to the fields of machine learning and gravity inversion technology, and in particular relates to a method for predicting the density of salt ore bodies based on a bi-branch and multi-attention mechanism. Background Technology

[0002] In the field of geophysical exploration, gravity exploration is an important technical method. Based on Newton's law of universal gravitation, it utilizes the changes in surface gravitational acceleration caused by density differences between rock masses and ore bodies. When a density difference exists between the geological body being explored and the surrounding rock mass, gravity anomalies can be detected using sophisticated instruments such as gravimeters. These anomalies are then interpreted qualitatively and quantitatively in conjunction with geological and other geophysical data, allowing for the inference of the burial status of underground ore bodies and rock strata, and the determination of the location of concealed ore bodies and geological structures. Gravity inversion is a crucial step in using gravity exploration to study geological structures. Traditional gravity inversion methods often employ linear iterative approaches, heavily relying on prior information such as geological and drilling data to determine the initial model. Without accurate prior data, the inversion results are prone to multiple interpretations, making it difficult to accurately determine the geological structure.

[0003] In recent years, deep neural networks have been gradually introduced into inversion. Convolutional neural networks such as U-Net have advantages in extracting spatial local features and can reduce the strong dependencies of prior models compared to traditional inversion. However, they are limited by the local receptive field of the convolutional kernel, and their ability to capture long-range dependencies is limited. In addition, the fusion strategy between feature channels is relatively simple and prone to generating redundant information interference, affecting the final inversion accuracy. The multi-attention mechanism fusion network proposed in this paper is based on the architecture of U-Net and K-Net networks. By embedding a dual-branch structure and cross-resolution residual feature modules, the receptive field of the neural network is expanded, alleviating the problem of redundant information transmission caused by skip connections. However, when dealing with complex 3D geological structures, there are still problems of insufficient semantic integration and missing attention in geological information, resulting in poor performance in the identification of fuzzy boundaries or weakly reactive areas. The self-attention mechanism and the channel attention module can respectively achieve cross-regional long-range dependency modeling and weight labeling of channel features through the self-attention mechanism. Thus, the problems of weak key semantic recognition and insufficient integration are effectively solved. However, most current methods still use two-dimensional neural networks to process gravity data. Although efficient, they are difficult to characterize the depth structure, which limits the accuracy of three-dimensional anomaly inversion. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a salt ore body density prediction method based on a bi-branch and multi-attention mechanism, thereby resolving the issues present in the prior art.

[0005] To achieve the above objectives, this invention provides a method for predicting the density of salt ore bodies based on a bi-branch and multi-attention mechanism, comprising: A three-dimensional density model dataset was constructed based on gravity observation surface data and gravity field potential field migration theory. A multi-attention mechanism fusion neural network for dual-path feature fusion is constructed and trained and optimized using the aforementioned 3D density model dataset. The multi-attention mechanism fusion neural network adopts a dual-branch architecture, including a U-Net branch and a K-Net branch. The U-Net branch embeds a channel attention module, a self-attention mechanism module, and a cross-resolution residual feature block. The gravity data of the salt ore body to be predicted is converted into the corresponding three-dimensional volume adjoint operator, and then processed by a trained and optimized multi-attention mechanism fused neural network to obtain the salt ore body density prediction result.

[0006] Optionally, the process of constructing a 3D density model dataset includes: Based on the gravity field potential field migration theory, the adjoint operator based on the stable transformation of gravity observation surface data is calculated. Combined with the edge data difference recovery technology, the gravity observation surface data is converted into a three-dimensional volume adjoint operator with the same dimension as the underground density as the input data, and the corresponding three-dimensional density model is constructed as the label to obtain the three-dimensional density model dataset.

[0007] Optionally, the adjoint operator formula obtained based on the theory of gravitational potential field migration is as follows: ; in, It is gravity observation data. The spatial distance between the observation point and the underground grid. For kernel function, x, y, and z represent the horizontal, vertical, and longitudinal coordinates of the underground space, respectively. It is gravity observation data. The spatial distance between the observation point and the underground grid. This indicates that the horizontal, vertical, and longitudinal coordinates of the observation point and the underground grid are taken separately and the difference is calculated. S is the area integral operator.

[0008] Optionally, after the three-dimensional volume adjoint operator is input into the U-Net branch, the input three-dimensional volume adjoint operator is subjected to feature extraction through continuous three-dimensional convolution operations. Each convolution is followed by a max pooling operation to extract multi-scale feature information and reduce the feature map size to obtain a multi-scale feature map.

[0009] Optionally, the multi-scale feature map is input into the channel attention module, which performs global average pooling on the multi-scale feature map to obtain a global feature representation for each channel; the global feature representation is learned through two fully connected layers to obtain the weight coefficients for each channel; the obtained weight coefficients are multiplied by the corresponding channels of the original feature map to complete the channel recalibration of the feature map.

[0010] Optionally, the U-Net branch introduces a self-attention mechanism module, which dynamically models the global dependencies between different scales and semantic levels through a multi-head self-attention mechanism. The self-attention mechanism module normalizes the input feature map; divides the normalized feature map into multiple heads, and calculates the query vector, key vector, and value vector for each head. The weight relationship between features is calculated through the self-attention mechanism; and a nonlinear transformation is performed on the feature map after the self-attention operation to obtain a global dependency enhancement feature map.

[0011] Optionally, the K-Net branch performs three convolutions and two pooling operations on the input 3D volume adjoint operator to obtain lightweight local features.

[0012] Optionally, cross-resolution residual feature blocks are embedded in each stage of the encoder and decoder of the U-Net and K-Net branches. During the encoding stage, the cross-resolution residual feature blocks are used to extract cross-residual features from the feature maps of the two branches through three-dimensional convolution operations and then fused back to their respective branches. During the decoding stage, the feature maps of the two branches are fused through residual connections. The output feature maps of the U-Net and K-Net branches are fused by addition and the salt body density prediction result is generated by convolution.

[0013] Optionally, the training optimization employs the SmoothL1Loss loss function, which is obtained by combining absolute error and relative error.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: The neural network proposed in this invention, based on the fusion of dual-branch and multi-attention mechanisms, exhibits significant advantages in the three-dimensional inversion of gravity anomaly data. Its network structure achieves high-precision gravity field value recovery and clear characterization of deep structure boundaries through the collaborative modeling of integrated channel, spatial and global dependencies, effectively overcoming the inherent defects of low resolution and blurred boundaries in traditional linear inversion methods. Attached Figure Description

[0015] 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: Figure 1 The six models randomly selected from the dataset constructed in the embodiments of the present invention are: (a) a multi-body positive density cubic model; (b) a single-body positive density cubic model; (c) a two-body positive density cubic model; (d) a single-body negative density positive droplet model; (e) a single-body negative density reverse droplet model; and (f) a multi-body negative density positive droplet model. Figure 2 This is a schematic diagram of a neural network architecture based on the fusion of dual-branch and multi-attention mechanisms according to an embodiment of the present invention; Figure 3 This is a network architecture diagram of the channel attention module according to an embodiment of the present invention; Figure 4 This is a diagram illustrating the self-attention mechanism architecture of an embodiment of the present invention. Figure 5 The following are schematic diagrams of the three-dimensional view and three-dimensional slice positions of the discrete model in an embodiment of the present invention; (a) is a schematic diagram of the three-dimensional space of the discrete model; (b), (c), and (d) are schematic diagrams of the cross-sectional positions of the discrete model in three-dimensional space when the cut surfaces are made along the directions x=1000, y=1800, and z=1600, respectively. Figure 6 The above are the gravity field prediction results and density prediction slices of the dispersion model in this embodiment of the invention. Figure 7 The figures show a comparison of the absolute and relative errors of the field map prediction results of the discrete model and the original field map in an embodiment of the present invention. (a)-(c) are the absolute errors of the field map predicted by the discrete model after the multi-attention mechanism fusion neural network, U-Net and Segvol network and the original field map, respectively; (d)-(f) are the relative errors of the field map predicted by the discrete model after the multi-attention mechanism fusion neural network, U-Net and Segvol network and the original field map, respectively. Figure 8 The following are schematic diagrams of the three-dimensional view and three-dimensional slice positions of the water droplet model according to an embodiment of the present invention: (a) is a schematic diagram of the three-dimensional space of the water droplet model. The filling density is -0.3 g / cm³; (b)-(d) are schematic diagrams of the cross-sectional positions of the discrete model in three-dimensional space, respectively, when the cut surfaces are made along x=1200, y=1800, and z=1600. Figure 9 These are the field prediction results and density prediction slices of the water droplet model according to an embodiment of the present invention. Figure 10 The absolute and relative errors of the field map prediction results of the water droplet model in this embodiment of the invention are compared with those of the original field map; (a)-(c) are the absolute errors of the field map predicted by the water droplet model after the fusion of the multi-attention mechanism neural network, U-Net and Segvol network and the original field map, respectively; (d)-(f) are the relative errors of the field map predicted by the water droplet model after the fusion of the multi-attention mechanism neural network, U-Net and Segvol network and the original field map, respectively. Detailed Implementation

[0016] 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.

[0017] 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.

[0018] Example 1.

[0019] This embodiment provides a method for predicting the density of salt deposits based on a deep learning network with a dual-branch and multi-attention mechanism (hereinafter referred to as a multi-attention mechanism fusion neural network), including: (I) Gravitational field potential field shift theory.

[0020] Zhdanov's three-dimensional potential field migration theory, based on a stable integral transformation mechanism, achieves the conversion from observed gravity data to subsurface density distribution. This theory constructs a migration field by spatially migrating the observed gravity field source, completely preserving the true source information during the transformation process, thus overcoming the limitation of traditional potential field extensions that rely on specific extension surfaces. The three-dimensional migration operator constructed based on this theory in this embodiment is the adjoint operator obtained from the stable change of the source information during the variable migration process.

[0021] Gravity anomalies can reveal information about underground mineral deposits, geological structures, and other geological features. Gravity field. Satisfying equations (1) and (2): (1) (2) Where ∇ is the Nable operator, ∇⋅ calculates the divergence of vector g, and ∇× calculates the curl of vector g. It is the gravitational constant. , The abnormal density distribution within the defined domain, the solution to these two equations, i.e. the expression for the gravitational field, can be represented by equation (3): (3) Among them, in formula (3) To obtain the full three-dimensional spatial extent of the integral, In Indicates along The gravitational response is calculated from the gravitational field components in three directions. For the density of the underground grid, kernel function according to The definition is as shown in equation (4), where represents the vertical distance in the x, y, and z directions: (4) Introducing a deflected gravitational field As a gravitational adjoint operator, it was applied to the observation of gravitational field components to obtain the results (5): (5) In summary, regarding the gravitational migration field adjoint operator for gravity problems It can be expressed by equation (6): (6) In the above formula, It is gravity observation data. The spatial distance between the observation point and the underground grid. The kernel function mentioned above, x, y and z These represent the horizontal, vertical, and lateral coordinates of the underground space. This indicates that the horizontal, vertical, and longitudinal coordinates of the observation point and the underground grid are taken separately and the difference is calculated. S is the area integral operator.

[0022] For ease of reading, A will be used to represent the gravitational migration field adjoint operator throughout the text. .

[0023] (2) Construct the dataset.

[0024] To accurately represent the occurrence states of different underground geological targets, this embodiment constructs a three-dimensional density model sample containing various geological body morphologies. The spatial boundary range of the density model sample set is set as follows: Meters, divided into grids of 200 meters each, forming... Each density model consists of three-dimensional volumetric density units. During label generation, to mitigate boundary effects and errors caused by missing information in edge regions associated with operator A, a region with a width of three units (600 meters) was excluded around all density models. For density filling, a "discrete model" with multiple cubes irregularly distributed in space and a "droplet model" with irregular and directional anomalies were employed. Anomaly filling for the discrete model... The density, for the anomaly filling of the droplet model The density, other areas filled The density.

[0025] Figure 1 The image shows a randomly selected model. The dataset contains approximately 20,000 sets, and six sets were randomly selected from them. Figure 1 As shown in (a), (b), and (c), the geological anomalies in each density model dataset of the discrete model have different sizes and shapes, and there are three occurrence states: single anomaly, multiple separated anomalies, and multiple merged anomalies. The surrounding rock density of all geological anomalies is set to 0. Figure 1(d), (e), and (f) in the dataset are directional water droplet models inspired by the irregular underground occurrence of salt domes. These models resemble water droplets in shape, exhibiting directionality and significant non-smoothness at their edges, accompanied by numerous sharp, angular structures. This unique geometry increases the model's complexity. Throughout the density model dataset, considering various more complex scenarios, random seeds were used to generate models with different water droplet radii, orientations, and numbers during dataset creation, ensuring a sufficiently rich and diverse final dataset.

[0026] In the field of deep learning research on predicting subsurface density based on gravity anomaly data, many scholars have conducted related studies. Most of these scholars use three-dimensional density data to calibrate the modeling methods of two-dimensional gravity observation surfaces. This modeling strategy simplifies the training process to some extent, but it ignores the three-dimensional structural characteristics of subsurface density volumes, leading to significant deviations in spatial consistency and depth resolution. In recent years, three-dimensional convolutional neural networks have demonstrated unique advantages in volumetric data learning tasks due to their superior spatial structure perception capabilities. Compared to two-dimensional methods, three-dimensional models can effectively capture the interrelationship information within and between slices when processing three-dimensional volumetric data, thereby significantly improving segmentation performance and accuracy. For non-homogeneous media and nonlinear subsurface anomalies in geophysics, three-dimensional convolutional neural networks can simultaneously extract deep density spatial features along the x, y, and z directions, greatly enhancing the model's resolution. Traditional gravity inversion observation data is mostly presented in two-dimensional form, lacking isodimensional three-dimensional volumetric data that can be directly used to train three-dimensional neural networks. To address this issue, this embodiment calculates the three-dimensional volumetric adjoint operator (hereinafter uniformly labeled A) of the gravity migration field based on the stable transformation of gravity observation surface data according to equation (6) in the gravity field potential field migration theory. Combined with edge data difference recovery technology, the two-dimensional observation data is converted into a three-dimensional volumetric adjoint operator A with the same dimension as the subsurface density as the input data, and the label is the corresponding three-dimensional density model. A total of 10,000 sets of discrete models are randomly generated to fully simulate the complex geological occurrence of the model. A total of 10,000 sets of water droplet model training sets are generated. The two density model datasets contain a total of 20,000 sets of models, of which 18,000 sets are allocated for neural network training and 2,000 sets are allocated for validation.

[0027] (III) Network structure.

[0028] Multi-attention mechanism fusion neural networks are a type of deep learning network specifically designed for three-dimensional volumetric geophysical gravity data, such as... Figure 2As shown, the proposed technique combines the dual-branch structure of U-Net 3D and K-Net 3D. There are four data flow paths, from left to right: U-Net branch downsampling, K-Net branch downsampling, U-Net branch upsampling, and K-Net branch upsampling. Data information interacts through cross-resolution residual feature blocks. The U-Net branch integrates a channel attention module, a self-attention mechanism, and cross-resolution residual feature blocks (CRFB) to achieve efficient feature extraction, global modeling, and feature fusion.

[0029] The network's input data is the gravity migration field adjoint operator from gravity exploration. Its value is derived from equation (6), and it is a three-dimensional tensor. In this embodiment, the training set is divided into... The network consists of three-dimensional volume elements, therefore the input tensor size is... Where B represents the batch size of the input offset field data, C represents the number of channels (here it is 1, i.e., single-channel gravity adjoint operator data), and D, H, and W correspond to the depth, height, and width in three-dimensional space, respectively. After entering the network, the adjoint operator data... Divided into exactly the same parts here and Enter the U-Net 3D branch and K-Net 3D branch respectively for encoding and decoding.

[0030] (1) U-Net branch.

[0031] The U-Net branch extracts the gravity adjoint operator through continuous 3D convolutions, channel attention modules, and downsampling. The spatial multi-scale features. The formula for the convolution part can be expressed by equation (7): in, and Representing the gravitational adjoint operator respectively Input and output feature maps and These are the adjoint operators Number of input and output channels It is half the size of the convolution kernel, and W is the weight parameter. i , j , k Representing the offset of the convolution kernel in the three spatial dimensions of depth, height, and width, d, h, and w correspond to the gravity adjoint operator at this point. The spatial depth, height, and width.

[0032] The accompanying operator feature map extracted by convolution is further input into the 3D Squeeze-and-Excitation module (channel attention module) for attention weighting in the channel dimension.

[0033] 1) Channel attention module.

[0034] To enhance the network's ability to model important feature channels and alleviate the problem of insufficient attention to deep semantics, a channel attention module is proposed. This module uses an explicit attention mechanism in the channel dimension to weight and label the importance of feature channels, thereby strengthening the expression of physically meaningful response regions, suppressing redundant information interference, and significantly improving spatial resolution accuracy and geological boundary characterization capabilities.

[0035] The channel attention module structure is as follows Figure 3 As shown, the encoder part, which mainly operates on the U-Net branch, optimizes the feature extraction process, making the network focus more on channel features crucial for the segmentation task. This module not only improves the feature quality of the U-Net branch but also indirectly enhances the feature representation capability of the K-Net branch through interaction layers, providing more discriminative input for the subsequent feature fusion stage. Its specific calculation process is shown below: ① F-Squeeze: ② F-Excitation: (9) ③ F-Scale, Feature Recalibration: (10) Where D, H, and W correspond to the depth, height, and width of the gravity adjoint operator space and the gravity model density space, respectively. It is the Sigmoid function. and It is a weighting factor. The weights are calculated using fully connected layers and activation functions, and their indices are... c This indicates that this corresponds to the first c The values ​​for each channel are generally between 0 and 1. It uses the ReLU activation function to help the network focus on positive features. Each convolution is followed by a max-pooling operation to extract the gravity adjoint operator. Multi-scale information enables the gravity adjoint operator The feature map size is gradually halved. For example, after the first convolution, the input size changes from [2,1,20,20,20] to [2,16,20,20,20], and after pooling it becomes [2,16,10,10,10].

[0036] 2) Self-attention mechanism.

[0037] To alleviate the problem of insufficient semantic integration, the self-attention mechanism module structure, through its multi-head self-attention mechanism, can dynamically model global dependencies between different scales and semantic levels, significantly enhancing long-range connections between deep features, mitigating the feature information silo effect, and thus improving the consistency of deep semantic integration and feature representation capabilities. Simultaneously, the positional encoding mechanism of the self-attention mechanism further strengthens the model's perception of 3D spatial structures, helping to capture fuzzy boundaries and weak geological signals, and improving the accuracy of complex geological body identification. Based on this, this embodiment introduces a self-attention mechanism in the deepest feature extraction stage of the U-Net branch to enhance the modeling capability of long-range spatial dependencies. The self-attention mechanism architecture is as follows: Figure 4 As shown.

[0038] In multi-attention mechanism fusion neural networks, the self-attention mechanism module first uses a LayerNorm layer to process the input gravity adjoint operator. The features are flattened and reshaped into a sequence form along the three-dimensional space dimension of the gravity adjoint operator to adapt to the input requirements of the multihead attention mechanism; then, through the feedforward neural network and self-attention operation, the global relationship between each position in the three-dimensional space (D×H×W) of the gravity adjoint operator is explicitly modeled. The calculation process of the multihead attention mechanism is shown in Equation (11): (11) In the formula, Q, K, and V represent the query vector, key vector, and value vector, respectively. Let K represent the dimension of the key vector K, T represent the vector transpose, and softmax represent the activation function. After processing by the attention mechanism, the gravity adjoint operator... Next, a feedforward network is used to further enhance the feature representation; (12) In equation (12), Linear is the linear transformation operation, and ReLU() is the activation function. Gravity adjoint operator Finally, the optimized features are output through residual connections and shape recovery.

[0039] (2) K-Net branch.

[0040] To address the issues of insufficient receptive field and redundant feature propagation in the U-Net branch, the K-Net branch employs a more lightweight convolutional module, focusing on preserving the local information of the input 3D adjoint operator data at the boundaries of anomalous regions. Similar to the U-Net branch, the gravity adjoint operator entering the K-Net branch... It also performs three convolutions and two pooling operations, with the following formula: (13) (14) (15) in, ( ) is a linear rectifier unit, which turns all values ​​less than 0 in the input into 0, while keeping the values ​​greater than 0 unchanged, to help the network learn and fit more complex data patterns. For 3D convolutional layers, 1→16 indicates that the layer receives input data from 1 channel and outputs a feature map with 16 channels after convolution; 16→32 indicates that the layer receives input data from 16 channels and outputs a feature map with 32 channels after convolution; 32→64 indicates that the layer receives input data from 32 channels and outputs a feature map with 64 channels after convolution. This further deepens the network structure to capture more complex and global semantic information. `MaxPool3d()` is a 3D max-pooling layer that performs downsampling. Unlike the U-Net branch, the K-Net branch does not introduce channel attention modules or self-attention mechanisms, maintaining the lightweight nature of the path and its ability to preserve details. It is suitable for accurately capturing small-scale, weakly varying density anomaly features (such as small cracks, local salt dome edges, etc.).

[0041] (3) Cross Residual Feature Block (CRFB).

[0042] To fully leverage the complementary features learned by U-Net 3D and K-Net 3D, a multi-attention mechanism fusion neural network introduces Cross-Residual Feature Blocks (CRFBs) at each level of the encoder and decoder. CRFB blocks extract cross-residual features through 3D convolutions and fuse them back into their respective branches, combining multi-scale features to enhance the network's capacity and feature quality. For example, U-Net 3D tends to capture local details in gravity-associated operator fields, while K-Net 3D excels at extracting global context; CRFB blocks integrate the strengths of both through residual connections (such as addition operations). In KiUe-Net3D, CRFB is implemented through interaction layers, with each interaction layer in the encoding phase having the following formula: (16) (17) Similarly, the interaction formula for the decoding phase is: (18) (19) in, This is an interpolation layer, whose function is to increase the spatial dimensions (depth, height, width) of the input feature map. , The representative dimension is preserved, and the current number of channels remains unchanged. Finally, the output feature maps of the two branches are fused by addition, and the stereo prediction result is generated by convolution. The fusion formula is: (20) Here represent The weight of the branch is calculated. Branches and The sum of the weights of the branches is 1. The larger the value, The greater the impact of branch calculation results on the data, the better. The CRFB design not only improves the efficiency of feature fusion, but also alleviates the gradient vanishing problem in deep networks through multi-scale interactions, making the network more stable during training.

[0043] Compared to the U-Net network, the multi-attention mechanism fusion neural network offers significant innovations in receptive field control and feature extraction. Through a dual-branch design and CRFB blocks, it achieves collaborative extraction of multi-scale features. The U-Net 3D branch progressively reduces the resolution through max pooling, while the K-Net 3D branch expands the receptive field through upsampling. The combination of these two effectively balances the capture of local details and global context. Furthermore, all convolutional layers (except the last one) use a 3×3×3 kernel size with a stride and padding of 1, ensuring the stability of feature extraction.

[0044] To verify the effectiveness of the proposed neural network model in the identification and spatial localization of underground gravity anomalies, this embodiment presents examples consisting of a discrete model composed of random cubes and a water droplet model. To verify the accuracy of the prediction results, absolute error E1 and relative error E2 are used to describe the gravity observation loss during training. The specific formulas for calculating the absolute and relative errors are as follows: (twenty one) (twenty two) In the formula, N is the total number of observation points; n represents the numerical index being calculated. This represents the theoretical gravity data from the nth observation. This represents the gravity data for the nth prediction.

[0045] (iv) Comprehensive model research.

[0046] (1) Discrete model.

[0047] The discrete model comprises four spatially separated blocky anomalous bodies, each uniformly assigned a density of 1.0 g / cm³, simulating a typical gravity anomaly source. The entire simulation region covers the horizontal direction. Within a meter range, in 3D visualization, to enhance image resolution and recognition, only areas with a density higher than 0.2 g / cm³ are displayed, thereby highlighting the spatial distribution characteristics and structural morphology of the anomalous body.

[0048] Figure 5 (a) in the image is a 3D representation of the model. Figure 5 (b)-(d) in the figure show its spatial position when cut along three fixed directions: x=1000, y=1800, and z=1600. Figure 6 From left to right, the original discrete model, the multi-attention mechanism fusion neural network, and the prediction results of U-Net and SegVol networks are displayed. The first row shows the field value recovery. The cross-sectional plots in the second to fourth rows express the density difference (Δρ, in g / cm³) in the form of color mapping. The white border represents the boundary of the anomalous body of the real model, which serves as a reference standard for result comparison. Figure 6 Row 1 of (a) is a schematic diagram of the model's three-dimensional position in space. Figure 6 In (a), rows 2-5 show the original gravity field map of the model, the gravity field map predicted by the multi-attention mechanism fusion neural network, U-Net, and the channel attention module gvol network, respectively. Figure 6 In (b), row 1 is a schematic diagram of the position of the tangent plane of model A along x=1000. Figure 6 In (b), rows 2-5 show the original cross section of the model, the cross section prediction results of the multi-attention mechanism fusion neural network, U-Net, and Segvol network, respectively, with the white box lines indicating the edge positions; Figure 6 Row 1 of (c) in the diagram is a schematic diagram of the position of the tangent plane of model A along y=1800. Figure 6 In (c), rows 2-5 show the original cross-section of the model, the cross-section prediction results of the multi-attention mechanism fusion neural network, U-Net, and Segvol network, respectively, with the white box lines indicating the edge positions; Figure 6 In the diagram, row (d) and column 1 represent the position of the model along the tangent plane at z=1600. Figure 6 In the diagram, rows 2-5 of (d) represent the original cross section of the model, the cross section prediction results of the multi-attention mechanism fusion neural network, U-Net, and Segvol network, respectively. The white box lines are the bounding boxes defined by the density volume boundary.

[0049] Analyzing the key dimension of gravity field map reconstruction, the multi-attention mechanism fusion neural network demonstrates superior performance. Numerically, it approximates the numerical features of the original gravity field map with remarkable accuracy. Through its unique convolutional structure and deep feature extraction mechanism, it effectively captures subtle numerical variations in the gravity field map, thus highly restoring the original gravity field map information at the quantization level. In terms of shape, the multi-attention mechanism fusion neural network also performs admirably, achieving near-perfect restoration of the spatial morphology of the gravity field map and accurately reproducing its topological structure and geometric contours. While the Segvol network achieves a relatively close level of numerical restoration, demonstrating its capability in data quantization, likely due to its effective capture and learning of key numerical information during feature extraction, it exhibits significant shortcomings in morphological restoration. The restored gravity field map deviates considerably from the original, failing to accurately recreate the spatial structure and topological features of the field map. This may be due to defects in the network's spatial information processing and integration mechanism, which fails to fully consider the correlation between different parts in three-dimensional space, resulting in deviations in the morphological restoration process.

[0050] The U-Net network exhibits a different characteristic. In terms of morphological recovery, the U-Net network can maintain the general shape of the gravity field map relatively well. This is thanks to its classic symmetric network structure and skip connection mechanism, which allows for the effective fusion of shallow and deep features, thus preserving the spatial structure characteristics of the gravity field map to a certain extent. However, in numerical recovery, the U-Net network has limitations. The maximum value of the recovered gravity field map only reaches around 1, which is significantly different from the numerical range of the original gravity field map. This indicates that the U-Net network is insufficient in learning and recovering high-intensity numerical information from the gravity field map. This may be due to factors such as the setting of its convolutional kernel parameters or the selection of activation functions, leading to information loss or bias when processing high numerical features.

[0051] For the model cross-section image, the image boundary range is [200, 3800], the white border represents the boundary position of the original model, and the displayed density range is [0, 1]. From Figure 6The results show that the multi-attention mechanism fusion neural network in this method can accurately reconstruct the geometric contours of the anomalous objects in all three directions. The predicted results are highly consistent with the real boundaries in terms of position, shape, and size, especially in the edge regions, demonstrating good detail recovery and structural fidelity. This is due to its bi-branch symmetric structure and low-level feature reuse mechanism, which effectively enhances the perception of local features. In contrast, although U-Net can maintain the approximation of the overall shape, there is a certain degree of blurring at the boundary transitions, and the prediction results are slightly weakened in intensity, especially in the z=1600 section where the anomalous object position shifts. Although the SegVol network can identify the overall trend, the reconstruction results show obvious diffusion, blurred boundaries, and severe morphological deformation, especially in the x=1000 and y=1800 sections where double centers or "stretching" phenomena occur, indicating that it has certain limitations in the expression of fine structures.

[0052] From the absolute error comparison chart, it can be seen that the multi-attention mechanism fusion neural network... Figure 7 As shown in (a), the absolute error is uniformly distributed throughout the region, with a small error zone only near the center of the anomalous body. The maximum error does not exceed 0.1. This model has a high accuracy in predicting the main structure and also has a certain ability to distinguish the anomalous boundary. U-Net's... Figure 7 As shown in (b), the error exhibits a large-area, high-intensity distribution, with significant error concentration in the core region. The maximum error value is close to 0.3, indicating a significant bias in the model's response to the center of the anomaly, with the recovered value differing considerably from the true value. (SegVol's...) Figure 7 As shown in (c), the error is mainly concentrated in multiple small regions, especially in the edge and near-peripheral region of the target anomaly, forming obvious error clusters. This model is more sensitive to local feature recognition, but its overall structure modeling ability is relatively weaker than that of multi-attention mechanism fusion neural networks.

[0053] From the relative error comparison chart, it can be seen that the multi-attention mechanism fusion neural network... Figure 7 As shown in (d), the relative error remains below 0.05, the error distribution is smooth with no abrupt changes, and the overall prediction-to-true error ratio is well controlled. U-Net's performance is as follows... Figure 7 As shown in (e), the overall relative error is very high, with almost the entire map exhibiting a high error level, particularly severe in the central region, where the maximum relative error approaches 0.2. The predicted results deviate significantly from the true values, especially at locations of strong anomalies, demonstrating weak recovery ability. (SegVol's...) Figure 7 As shown in (f), a local high error region is presented, which is concentrated at the edge of the anomaly and at multiple feature points. Although the average error is not as high as that of U-Net, the error points are distributed in a ring shape. It is more sensitive to changes in the shape of the target but has a tendency to overfit.

[0054] (2) Water droplet model.

[0055] The main body of the water droplet model is a downward-hanging water droplet. To increase complexity, the edges of the entire model are not smooth and have no regular boundaries. Additionally, a depression is placed at the center of the top of the model to verify the network's ability to learn boundary locations. The entire model anomaly is uniformly assigned a density value of -0.3 g / cm³ to simulate a typical negative density gravity anomaly source. The entire simulation area covers the horizontal direction. Within a meter range, in 3D visualization, to enhance image resolution and recognition, only areas with a density below 0 g / cm³ are displayed, thereby highlighting the spatial distribution characteristics and structural morphology of the anomalous body.

[0056] Figure 8 (a) in the image is a 3D representation of model B. Figure 8 (b)-(d) show the spatial position of the tangent along the three fixed directions x=1200, y=1800, z=1600. Figure 9 From left to right, the original model of the droplet model, the multi-attention mechanism fusion neural network, and the prediction results of the U-Net and SegVol networks are displayed. The first row shows the field value recovery of the model. The cross-sectional plots in the second to fourth rows express the density difference (Δρ, in g / cm³) in the form of color mapping. The white border represents the boundary of the anomalous body of the real model, which serves as a reference standard for result comparison. Figure 9 Row 1 of (a) in the diagram is a schematic diagram of the model's three-dimensional position in space. Figure 9 In (a), rows 2-5 represent the original field map of the model, the field map of the multi-attention mechanism fusion neural network, the prediction result field map of U-Net, and the prediction result field map of Segvol network, respectively. Figure 9 In (b), row 1 is a schematic diagram of the position of the model along the tangent plane at x=1200. Figure 9 In (b), rows 2-5 show the original cross section of the model, the cross section prediction results of the multi-attention mechanism fusion neural network, U-Net, and Segvol network, respectively, with the white box lines indicating the edge positions; Figure 9 In (c), row 1 is a schematic diagram of the position of the tangent plane of model B along y=1800. Figure 9 In (c), rows 2-5 show the original cross-section of the model, the cross-section prediction results of the multi-attention mechanism fusion neural network, U-Net, and Segvol network, respectively, with the white box lines indicating the edge positions; Figure 9 In the diagram, row (d) and column 1 represent the position of the model along the tangent plane at z=1600. Figure 9 In (d), rows 2-5 represent the original model cross section, the density prediction cross section results of the multi-attention mechanism fusion neural network, U-Net, and Segvol network, respectively, with the white box lines indicating the edge positions.

[0057] The results of the recovery from the gravity field diagram ( Figure 9 As shown in (a)), all three networks can reconstruct the centrally symmetric distribution features of gravity anomalies, indicating that they possess a certain spatial structure perception and mapping capability. However, there are significant differences in reconstruction accuracy. The field map recovered by the multi-attention mechanism fusion neural network is closest to the original anomaly distribution in both numerical amplitude and spatial morphology, with accurate anomaly center location and smooth contour distribution. This indicates that its introduced self-attention mechanism module effectively enhances the modeling ability for long-distance spatial dependence, while the channel attention module improves the representation ability between feature channels. Although the SegVol network is relatively close to the original density in terms of maximum anomaly amplitude, the spatial expansion range of low-density anomalies is significantly expanded, the boundaries are blurred, and it is difficult to accurately locate the true contour of the anomaly. In contrast, although U-Net shows better structural consistency in overall morphology, the anomaly values ​​are generally high, lacking sensitivity to low-density negative anomalies. Its minimum recovery value is only about 1 mGal, failing to reflect the low-amplitude characteristics of the original field.

[0058] From the boundary characterization of the 3D volume model ( Figure 9 As shown in (b)-(d)), the original model has obvious irregular concave and convex boundaries, which poses a challenge to the structure perception ability of the neural network. The multi-attention mechanism fusion neural network can restore the edge structure of the model well in 3D slices in all directions, especially in the Y direction, where it can clearly identify concave regions and the density assignment is close to the original minimum value (about -0.3g / cm³), demonstrating strong edge discrimination and detail restoration capabilities. Although SegVol can also approach the minimum density value in some areas, the boundary contours are stretched and offset, and the structure perception ability is slightly insufficient. The U-Net network performs poorly in density assignment and edge discrimination, with blurred boundaries and generally high assignments in low-density regions, but it can still initially identify the existence of low-density anomalies in terms of structure.

[0059] For the comparison chart of absolute error distribution, multi-attention mechanism fusion neural network (such as...) Figure 10 The reconstruction accuracy of (a) shown in the figure is extremely high. Its absolute error is mainly concentrated at the anomalous boundary, with a peak error of only about 0.04, and the deviation in the core region is almost zero, fully demonstrating its strong structural recovery capability. In contrast, U-Net (such as Figure 10 As shown in (b)), the absolute error distribution range is wider, especially in the core region of the anomaly, where the cumulative error reaches as high as 0.35, reflecting its poor ability to handle low-density anomalies. SegVol (as shown in (b)) Figure 10 Although the performance of (c) is slightly better than U-Net, the edge error is obvious and the uncertainty is high in the blurred boundary, resulting in the overall reconstruction performance being inferior to the multi-attention mechanism fusion neural network.

[0060] For the comparison map of relative error distribution, the multi-attention mechanism fusion neural network (such as...) Figure 10 The relative error distribution of (d) is best controlled, with error values ​​mostly below 0.08. The error is only relatively significant at abrupt boundary changes, while deviations are minimal in other regions, demonstrating excellent global fitting ability. In contrast, U-Net (as shown in (d)) exhibits... Figure 10 As shown in (e), a large area of ​​high error exists throughout the entire anomaly region, with a relative error peak exceeding 2.5, and the error is also significant in the low-amplitude region. SegVol (as shown in...) Figure 10 Although the relative error distribution pattern shown in (f) is similar to that of the multi-attention mechanism fusion neural network, the error profile is more chaotic, with a maximum relative error of about 1.4, indicating that in some areas, the predicted value still deviates significantly from the true value.

[0061] To verify the robustness of the neural network based on the fusion of two-branch and multi-attention mechanisms, SmoothL1Loss was selected as the loss function during training. SmoothL1Loss is a hybrid loss function combining L1 and L2 losses, widely used in regression tasks. Its definition is: (twenty three) When prediction error At that time, the loss was ;when At that time, the loss was , β It is a threshold parameter that controls the shape of the loss function, and it is the default value in PyTorch. β =1.0, where x is the model's predicted value and y is the actual value. For small errors, the squared form of L2 loss provides smooth gradients and fast convergence; for large errors, the linear L1 loss reduces the impact of outliers and enhances robustness. Compared to mean squared error (MSE, defined as...) Excessive sensitivity to outliers and mean absolute error (MAE, defined as...) The lack of differentiability at zero may lead to unstable optimization, while SmoothL1Loss combines the advantages of both.

[0062] For the same training set and with the same training parameters, the training and validation losses of the three models—multi-attention mechanism fusion neural network, U-Net, and Segvol—show different trends over epochs. The multi-attention mechanism fusion neural network performs best, with its training and validation losses rapidly decreasing from 0.012 to 0.004, converging in only about 20 epochs, and the difference between the two is minimal, demonstrating excellent stability and generalization ability. U-Net is second, with its training loss decreasing from 0.010 to 0.004, and its validation loss decreasing slightly slower to 0.005, stabilizing after about 150 epochs. It exhibits slight overfitting but overall good performance. Segvol's training loss decreases from 0.025 to below 0.005, and its validation loss eventually hovers around 0.010. Although it fluctuates slightly after 200 epochs, it eventually stabilizes.

[0063] 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 method for predicting the density of salt ore bodies based on a bi-branch and multi-attention mechanism, characterized in that, Includes the following steps: A three-dimensional density model dataset was constructed based on gravity observation surface data and gravity field potential field migration theory. A multi-attention mechanism fusion neural network for dual-path feature fusion is constructed and trained and optimized using the aforementioned 3D density model dataset. The multi-attention mechanism fusion neural network adopts a dual-branch architecture, including a U-Net branch and a K-Net branch. The U-Net branch embeds a channel attention module, a self-attention mechanism module, and a cross-resolution residual feature block. The gravity data of the salt ore body to be predicted is converted into the corresponding three-dimensional volume adjoint operator, and then processed by a trained and optimized multi-attention mechanism fused neural network to obtain the salt ore body density prediction result.

2. The salt ore body density prediction method based on bi-branch and multi-attention mechanism according to claim 1, characterized in that, The process of constructing a 3D density model dataset includes: Based on the gravity field potential field migration theory, the adjoint operator based on the stable transformation of gravity observation surface data is calculated. Combined with the edge data difference recovery technology, the gravity observation surface data is converted into a three-dimensional volume adjoint operator with the same dimension as the underground density as the input data, and the corresponding three-dimensional density model is constructed as the label to obtain the three-dimensional density model dataset.

3. The salt ore body density prediction method based on bi-branch and multi-attention mechanism according to claim 2, characterized in that, The adjoint operator formula obtained based on the theory of potential field migration in a gravitational field is as follows: ； in, It is gravity observation data. The spatial distance between the observation point and the underground grid. For kernel function, x, y, and z represent the horizontal, vertical, and longitudinal coordinates of the underground space, respectively. It is gravity observation data. The spatial distance between the observation point and the underground grid. This indicates that the horizontal, vertical, and longitudinal coordinates of the observation point and the underground grid are taken separately and the difference is calculated. S is the area integral operator.

4. The salt ore body density prediction method based on bi-branch and multi-attention mechanism according to claim 1, characterized in that, After the 3D volume adjoint operator is input into the U-Net branch, features are extracted from the input 3D volume adjoint operator through continuous 3D convolution operations. Each convolution is followed by a max pooling operation to extract multi-scale feature information and reduce the feature map size, thereby obtaining a multi-scale feature map.

5. The salt ore body density prediction method based on bi-branch and multi-attention mechanism according to claim 4, characterized in that, The multi-scale feature map is input into the channel attention module, which performs global average pooling on the multi-scale feature map to obtain the global feature representation of each channel. The global feature representation is learned through two fully connected layers to obtain the weight coefficient of each channel; the obtained weight coefficients are multiplied with the corresponding channels of the original feature map to complete the channel recalibration of the feature map.

6. The salt ore body density prediction method based on bi-branch and multi-attention mechanism according to claim 4, characterized in that, The U-Net branch introduces a self-attention mechanism module, which dynamically models the global dependencies between different scales and semantic levels through a multi-head self-attention mechanism. The self-attention mechanism module normalizes the input feature map; divides the normalized feature map into multiple heads, and calculates the query vector, key vector, and value vector for each head. The weight relationship between features is calculated through the self-attention mechanism; and a non-linear transformation is performed on the feature map after the self-attention operation to obtain a global dependency enhancement feature map.

7. The salt ore body density prediction method based on bi-branch and multi-attention mechanism according to claim 6, characterized in that, The K-Net branch performs three convolutions and two pooling operations on the input 3D volume adjoint operator to obtain lightweight local features.

8. The salt ore body density prediction method based on bi-branch and multi-attention mechanism according to claim 7, characterized in that, Cross-resolution residual feature blocks are embedded in each stage of the encoder and decoder of the U-Net and K-Net branches; during the encoding stage, the cross-resolution residual feature blocks are used to extract cross-residual features from the feature maps of the two branches through three-dimensional convolution operations and then fused back into their respective branches. In the decoding stage, the feature maps of the two branches are fused through residual connections; the output feature maps of the U-Net branch and the K-Net branch are fused by addition, and the salt ore body density prediction result is generated by convolution.

9. The method for predicting the density of salt ore bodies based on a bi-branch and multi-attention mechanism according to claim 1, characterized in that, The training optimization employs the SmoothL1Loss loss function, which is obtained by combining absolute error and relative error.

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