Inversion method and system of geological gravity data based on improved diffusion model

Abstract

The present invention relates to the field of geophysical technology, specifically providing a method and system for inverting geophysical gravity data based on an improved diffusion model. The method comprises the following steps: establishing multiple gravity anomaly geological body models based on preset constraints to obtain gravity data; introducing a ResU-Net++ network into the diffusion model's encoder U-shaped structure to obtain a ResDM-net++ network; and, based on the ResDM-net++ network and gravity data, obtaining a three-dimensional physical structure model of the geological body to complete the inversion of the geophysical gravity data. This network primarily leverages ResU-Net++'s high efficiency in image segmentation and feature extraction and its clear structural design to compensate for the shortcomings of the diffusion model in terms of efficiency and interpretability. Furthermore, the diffusion model's denoising process serves as a regularization method to help reduce the risk of overfitting of the ResU-Net++ network with limited data.

Description

Technical Field

[0001] The present invention belongs to the field of geophysical technology, and in particular relates to a geological gravity data inversion method and system based on an improved diffusion model. Background Art

[0002] Gravity inversion is a key technology in geophysical research, widely used to identify geological anomalies, map underground rock structures, and aid in the exploration and extraction of important resources such as oil and minerals. By measuring variations in the Earth's gravity field at the Earth's surface, it is possible to infer the underground density distribution, thereby discovering possible oil and gas reservoirs, mineral veins, and other geological features. This technology not only provides an important scientific basis for resource exploration but also plays a vital role in geological disaster warning and environmental protection.

[0003] In recent years, machine learning techniques have made significant progress in various fields, particularly in image processing and computer vision. Supervised learning, a major category of this approach, uses labeled gravity data to train models, enabling them to make accurate predictions on new gravity data. U-Net, a classic convolutional neural network architecture, falls under the umbrella of supervised learning. U-Net utilizes a symmetrical encoder-decoder structure and excels at extracting semantic information and recovering spatial detail in image segmentation tasks. However, it uniformly weights features of equivalent levels during encoding and decoding, potentially masking key geological features over less important ones. To address this issue, Jha et al. (2019) proposed the ResU-Net++ network. This network, firstly, retains more detailed gravity information by introducing residual connections. Secondly, it uses a compression and excitation module, a lightweight attention mechanism, to significantly enhance the network's ability to discern local and global geophysical features. However, its complex structure and large number of parameters lead to high computational resource requirements, slow training and inference speeds, and a tendency to overfit when data is limited. To improve this situation, the diffusion model proposed by Jascha et al. (2015) can generate samples with rich details, performs well in processing complex data, and has good robustness. It effectively simplifies the complex modules of the ResU-Net++ network and reduces the computational complexity and resource requirements of the overall model. However, it is not as good as the ResU-Net++ network in feature extraction. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention provides a geological gravity data inversion method and system based on an improved diffusion model, which makes use of the high efficiency and clear structural design of ResU-Net++ in feature extraction to make up for the shortcomings of the diffusion model in efficiency and interpretability.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] The inversion method of geological gravity data based on the improved diffusion model includes the following steps:

[0007] Based on preset constraints, multiple gravity anomaly geological body models are established to obtain gravity data; wherein the sizes of the gravity anomaly geological body models include 3x3x3, 4x4x4, 5x5x5, 4x4x2 and 3x3x5;

[0008] Introducing a ResU-Net++ network into the encoder U-shaped structure of a diffusion model to obtain a ResDM-net++ network; wherein the diffusion model includes a forward diffusion process and a reverse diffusion process;

[0009] Based on the ResDM-net++ network and the gravity data, a three-dimensional physical structure model of the geological body is obtained, and the inversion of the geological gravity data is completed.

[0010] Preferably, the gravity data includes gravity component data , , , , , and ;in, is the gravity response simulated by multiple gravity anomaly geological models, denoted as , the vertical component of the gravity field is recorded as :

[0011] ,

[0012] Where γ represents the gravitational constant, represents the density distribution within an underground abnormal domain D, is the corresponding forward linear operator, kernel function , , represents the field point position vector, represents the source position vector, is the field point position vector The vertical coordinate of is the source position vector The vertical coordinate of Represents the volume element at the source point.

[0013] Preferably, in the diffusion model,

[0014] The forward diffusion process is to add noise to the original gravity data input to the diffusion model. The formula is as follows:

[0015] ,

[0016] in, is in the time step data, is in the time step The noise figure is defined as , is a predefined noise table; is in the time step data, is random noise with the same shape as the input data;

[0017] The reverse diffusion process is to recover the original gravity data from the noisy data. The formula is as follows:

[0018]

[0019] is the output of the diffusion model encoder.

[0020] Preferably, the U-shaped structure of the ResDM-net++ network includes an encoder, a spatial pyramid module and a decoder, wherein the encoder consists of three downsampling modules, each downsampling module includes a residual unit paired with an SE module; the decoder consists of three decoding modules, each decoding module includes an attention mechanism module, an upsampling layer, a feature connection layer and a residual unit.

[0021] Preferably, the SE module uses global pooling to transform the input gravity data Compressed into a vector , the compression formula is as follows:

[0022]

[0023] in, Represents input gravity data , represents the real number domain, H and W represent the number of rows and columns of gravity data extracted by convolution operation in the channel number C, respectively. Represents the row index, Indicates the column index.

[0024] Preferably, the spatial pyramid module performs multi-scale sampling on the gravity data features extracted by the downsampling module by establishing different expansion rates to obtain multi-scale context information of the gravity data features; wherein the expansion rate is equipped with an equivalent convolution kernel, and the size of the equivalent convolution kernel is expressed as follows:

[0025] ,

[0026] Among them, 𝑘 is the original convolution kernel size, is the expansion coefficient.

[0027] The present invention also provides a geological gravity data inversion system based on an improved diffusion model, which is used to implement the method, comprising:

[0028] A gravity data acquisition module is used to establish multiple gravity anomaly geological body models based on preset constraints and acquire gravity data; wherein the sizes of the gravity anomaly geological body models include 3x3x3, 4x4x4, 5x5x5, 4x4x2 and 3x3x5;

[0029] A model improvement module, configured to introduce a ResU-Net++ network into the encoder U-shaped structure of a diffusion model to obtain a ResDM-net++ network; wherein the diffusion model includes a forward diffusion process and a reverse diffusion process;

[0030] The structural inversion module is used to obtain a three-dimensional physical structure model of the geological body based on the ResDM-net++ network and the gravity data, and complete the inversion of the geological gravity data.

[0031] Preferably, the gravity data acquisition module includes:

[0032] A model set construction unit is used to combine multiple individual gravity anomaly geological body models to obtain a model set;

[0033] A model forward modeling unit is used to perform model forward modeling based on the model set to generate the gravity data; the gravity data includes gravity component data , , , , , and ;in, is the gravity response simulated by multiple gravity anomaly geological models, denoted as , the vertical component of the gravity field is recorded as :

[0034] ,

[0035] Where γ represents the gravitational constant, represents the density distribution within an underground abnormal domain D, is the corresponding forward linear operator, kernel function , , represents the field point position vector, represents the source position vector, is the field point position vector The vertical coordinate of is the source position vector The vertical coordinate of Represents the volume element at the source point.

[0036] Compared with existing technologies, the present invention achieves the following benefits: By adding the core ResU-Net++ module to the encoder structure of the diffusion model, a new network (i.e., the ResDM-net++ network) is constructed. This network primarily leverages ResU-Net++'s high efficiency in feature extraction and its clear structural design to address the shortcomings of the diffusion model in terms of efficiency and interpretability. Furthermore, the diffusion model's denoising process serves as a regularization measure, helping to reduce the risk of overfitting in the ResU-Net++ network when using limited data. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0038] Figure 1 These are four arbitrarily selected model sets in the embodiment of the present invention; (a) is model set 1; (b) is model set 2; (c) is model set 3; and (d) is model set 4.

[0039] Figure 2 Schematic diagram of the process of obtaining model forward data and gradient data in an embodiment of the present invention; (a) is the extracted density model; (b) is the gravity forward data Obtaining schematic diagram; (c) is gravity component data Obtaining schematic diagram; (d) is gravity component data Obtaining schematic diagram; (e) is gravity component data Obtaining schematic diagram; (f) is gravity component data Obtaining schematic diagram; (g) is gravity component data Obtaining schematic diagram; (h) is gravity component data Get the schematic diagram;

[0040] Figure 3 This is a theoretical diagram of a diffusion model according to an embodiment of the present invention;

[0041] Figure 4 Schematic diagram of the ResDM-net++ network structure according to an embodiment of the present invention; (a) is a schematic diagram of the overall structure of the ResDM-net++ network; (b) is a schematic diagram of the encoding block structure in the ResDM-net++ network; (c) is a schematic diagram of the decoding block structure in the ResDM-net++ network;

[0042] Figure 5 This is a schematic diagram of the SE module according to an embodiment of the present invention;

[0043] Figure 6 This is a schematic diagram of a spatial pyramid module according to an embodiment of the present invention;

[0044] Figure 7 This is a schematic diagram of the attention mechanism module according to an embodiment of the present invention;

[0045] Figure 8 The three-dimensional views and sections of an embodiment of the present invention are shown; (a) is a schematic diagram at Y=1000m; (b) is a schematic diagram at X=2200m;

[0046] Figure 9 The diffusion model under 10% noise in the embodiment of the present invention, the ResU-Net++ and ResDM-net++ networks are combined to invert the geological structure model obtained at Y = 1000m; where (a) is Component; (b) and Component; (c) 、 、 and Component; (d) is 、 、 、 、 、 and Quantity;

[0047] Figure 10 The diffusion model under 10% noise in the embodiment of the present invention, the ResU-Net++ and ResDM-net++ networks are combined to invert the geological structure model obtained at X = 2200m; where (a) is Component; (b) and Component; (c) 、 、 and Component; (d) is 、 、 、 、 、 and Quantity;

[0048] Figure 11The ResDM-net++ network of the embodiment of the present invention combines 7 gravity components under 10% noise conditions, and the observed gravity field, predicted gravity field and fitting difference map of different components; (a) Component; (b) Component; (c) Component; (d) is Quantity;

[0049] Figure 12 The loss curves for network training and verification of the embodiment of the present invention are shown below. (a) is the loss curve for the custom diffusion model; (b) is the loss curve for ResU-Net++; and (c) is the loss curve for ResDM-net++.

[0050] Figure 13 This is a flow chart of a method for inverting geological gravity data based on an improved diffusion model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0052] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] Example 1

[0054] like Figure 13 As shown in FIG, the inversion method of geological gravity data based on the improved diffusion model includes the following steps:

[0055] S1: Based on pre-set constraints, multiple gravity anomaly models are constructed to acquire gravity data. Specifically, achieving accuracy in density, depth, and geological target size attributes requires developing a detailed training sample set encompassing a variety of geomorphic shapes. Therefore, to simulate a variety of geomorphic bodies exhibiting gravity anomalies, we combined multiple individual gravity anomaly models under specific constraints. A model set is constructed by randomly placing 1 to 5 small models in space, with the sizes of 3x3x3, 4x4x4, 5x5x5, 4x4x2, and 3x3x5. Figure 1 Four randomly selected model sets are shown. Figure 1 (a) is model set 1; Figure 1 (b) is model set 2; Figure 1(c) is model set 3; Figure 1 (d) is model set 4; this embodiment generates a total of 10,000 model sets, 8,000 of which are allocated for neural network training and 2,000 for verification purposes.

[0056] A further embodiment is that Figure 2 As shown, in order to add geophysical constraints to deep learning and obtain more realistic prediction data, this embodiment combines the components of gravity gradient data (gravity data), which includes gravity component data , , , , , and ;in, is the gravity response simulated by multiple gravity anomaly geological models, denoted as , the vertical component of the gravity field is recorded as : ,

[0057] Where γ represents the gravitational constant , represents the density distribution within an underground abnormal domain D, is the corresponding forward linear operator, kernel function , , represents the field point position vector, represents the source position vector, is the field point position vector The vertical coordinate of is the source position vector The vertical coordinate of Represents the volume element at the source point. This formula is crucial for calculating the gravitational influence of a specific density distribution on surrounding points in space and is often used in gravity inversion tasks to simulate underground structures. Figure 2 As shown, Figure 2 (a) is the density model, Figure 2 (b) is the gravity forward data Get the schematic diagram; Figure 2 (c) is the gravity component data Get the schematic diagram; Figure 2 (d) is the gravity component data Get the schematic diagram; Figure 2 (e) is the gravity component data Get the schematic diagram; Figure 2 (f) is the gravity component data Get the schematic diagram; Figure 2 (g) is the gravity component data Get the schematic diagram; Figure 2 (h) is the gravity component data Get the schematic.

[0058] To reconstruct 3D physical structural models of geological bodies from gravity data, this paper uses the ResDM-net++ network. This network incorporates key modules from the ResU-Net++ network, including residual blocks, Sequencing (SE) modules, spatial pyramid modules, and an attention mechanism, into the U-shaped encoder structure of the diffusion model. This effectively combines the advantages of the diffusion model and the ResU-Net++ network. This innovation significantly improves structural perception and segmentation accuracy during image generation, while enhancing the robustness and accuracy of the generated results.

[0059] S2: Introduce the ResU-Net++ network into the encoder U-shaped structure of the diffusion model to obtain the ResDM-net++ network;

[0060] Among them, Figure 3 As shown, the diffusion model includes a forward diffusion process (i.e., forward propagation) and a reverse diffusion process (i.e., reverse propagation); a further implementation method is that, in the diffusion model,

[0061] The forward diffusion process is to add noise to the original gravity data input to the diffusion model. The formula is as follows:

[0062]

[0063] in, is in the time step data, is in the time step The noise figure is defined as , is a predefined noise table; is in the time step data, is random noise with the same shape as the input data.

[0064] The reverse diffusion process is to recover the original gravity data from the noisy data. The formula is as follows:

[0065]

[0066] is the output of the diffusion model encoder. Encoder ( ) Change the current Encode and convert it into The inverse diffusion formula recovers the original data from the noisy data and attempts to reconstruct the clean signal.

[0067] A further embodiment is that Figure 4 As shown in the figure, the U-shaped structure of the ResDM-net++ network includes an encoder, a spatial pyramid module and a decoder. The encoder consists of three downsampling modules (encoding blocks), each of which includes a residual unit paired with a SE module (Squeeze & Excite). In this embodiment, the residual unit is a residual unit, which includes a Batch Norm & ReLU layer and a Conv2D layer. The decoder consists of three decoding modules (decoding blocks), each of which includes an attention mechanism module, an upsampling layer (UpBlock), a feature connection layer and a residual unit. Figure 4 In (c), the feature connection layer is represented by the connection line between the upsampling layer and the residual unit. These components include residual blocks and attention blocks to enhance detail capture and noise reduction. Figure 4 As shown in (b), each downsampling module includes a residual unit paired with a SE module; Figure 4 As shown in (a), in the ResDM-net++ network, first, the "In Conv" operation applies a 2D convolution with a kernel size of 3x3, a padding of 1, and one input channel to the input gravity data of length 21x21. This operation increases the dimension from 7 channels to 32 channels. The "Out Conv" operation converts the decoding block into a single-channel representation. This layer links the underground geology with the observed gravity changes based on the training of the network on supervised learning labels as the final three-dimensional physical structure model output. The ASPP module and the ASPP output block are both spatial pyramid modules, among which the ASPP module acts as a bridge connection and the ASPP output block acts as an output. The circle with a "+" sign in front of the decoding block indicates that the channel connection is used as a downsampling operation, which doubles the number of channels and reduces the input length by half. The circle with a "+" sign in the encoding block and the decoding block represents the residual connection. Among them, the attention mechanism module is as follows Figure 7 shown.

[0068] like Figure 4 As shown in (a), the ResDM-net++ network includes an "In Conv", three encoding blocks, an ASPP module, an ASPP output block, three decoding blocks, and an "Out Conv". These components include residual blocks and attention blocks to enhance detail capture and noise reduction. The multi-channel information is converted into the required dimension for network input through the "In Conv" and connected to the encoding block. Figure 4 As shown in (b), each encoding block contains a residual unit paired with a SE module. This module enhances key gravity map features by increasing the weight of information channels while reducing irrelevant data, thereby optimizing feature representation. In the decoding block (see Figure 4 (c) ) combines the attention mechanism with the upsampling and concatenation process to retain key information through residual connections, thereby enhancing the network's predictive performance. The purpose of the "upsampling" operation is to reduce the number of channels in the input vector by half while doubling its length. In order to address challenges such as increasing training errors and "gradient dispersion or explosion" associated with deep networks, improved recurrent residual units are used in both the encoder and decoder. These units consist of two consecutive convolutional blocks, including a Batch Norm layer and a ReLU layer, which simplifies the training process and ensures consistent information flow in the network. This structure not only simplifies training, but also improves the network's ability to accurately predict and simulate complex geophysical structures. Finally, the corresponding dimension is output through "Out Conv", thereby connecting the gravity field with the model density information.

[0069] A further embodiment is that the SE module enhances key gravity data features by increasing the weights of information channels while reducing irrelevant data, thereby optimizing feature representation.

[0070] like Figure 5 As shown in Figure 2, the SE module plays a central role in accurately recalibrating the weights of channel features when processing gravity data. The module amplifies important features by adding weights to information channels, while shrinking noise and insignificant features by reducing the corresponding weights. This increase and decrease in weights improves the network's operational efficiency and its ability to identify complex patterns in gravity data - a key aspect of geophysical analysis. The SE module pools the input gravity data through global pooling. Compressed into a vector , the compression formula is as follows:

[0071]

[0072] in, Represents input gravity data , represents the real number domain, H and W represent the number of rows and columns of gravity data extracted by convolution operation in the channel number C, respectively. Represents the row index, Indicates the column index.

[0073] To identify channel-level correlations, an excitation operation is used during feature extraction to give amplified weights to key feature maps within a feature channel, emphasizing critical information while reducing unimportant information. This operation generates a weight value for each feature channel through two fully connected layers. The resulting output is obtained by multiplying each channel by its associated channel weight. The output of this mapping operation is shown in the following formula:

[0074] ,

[0075] in, Represents a mapping operation, a two-dimensional tensor Represented as input information of An element of represents the field of real numbers, and Represents the sigmoid function. Weight The matrix is represented as and The SE block is able to identify channel correlations, thereby increasing sensitivity to key channels, while suppressing redundant or irrelevant information. This irrelevant information may appear as noise, thus affecting the prediction performance of the network.

[0076] Classic pooling mechanisms used in CNNs, including max pooling and average pooling, are widely used to reduce the spatial dimensionality of feature maps, enabling the model to understand more abstract and high-level features. However, these operations can lead to a reduction in spatial resolution and the loss of complex details, while computational resources limit the number and dimensionality of convolution kernels. This can cause significant difficulties in identifying elongated, narrow, and belt-like formations (such as narrow geological formations, faults, and fractures), which are common in geophysical data.

[0077] A further embodiment is that, in order to solve the above problem, the present invention uses a spatial pyramid module to read contextual information of different scales in the data, so that the original input resolution is maintained without losing information during the geophysical inversion process. Figure 6 As shown in the figure, the spatial pyramid module establishes different expansion rates and combines the gravity data features extracted by the downsampling module at different ratios for multi-scale sampling, effectively increasing the size of the convolution kernel and obtaining multi-scale contextual information of the gravity data features. Among them, the expansion rate is equipped with an equivalent convolution kernel (receptive field), and the size of the equivalent convolution kernel is expressed as follows:

[0078] ,

[0079] Among them, 𝑘 is the original convolution kernel size, is the expansion coefficient. The output size after convolution is defined as:

[0080] ,

[0081] in Indicates the output size, Indicates the input size. Indicates the length of the stride. Padding ( ) operation solves the problem of information loss near the image boundaries after each convolution operation. This is achieved by replacing the missing boundary parts with zeros.

[0082] In the decoder, the attention mechanism is combined with the upsampling and concatenation process to retain key information through residual connections, enhancing the network's predictive performance. The purpose of the "upsampling" operation is to reduce the number of channels in the input vector by half while doubling its length. To address challenges such as increasing training errors and "gradient dispersion or explosion" associated with deep networks, improved recurrent residual units are used in both the encoder and decoder. These units consist of two consecutive convolutional blocks, including a BatchNorm layer and a ReLU layer, which simplifies the training process and ensures consistent information flow in the network. This structure not only simplifies training but also improves the network's ability to accurately predict and simulate complex geophysical structures.

[0083] The decoder consists of three decoding modules, each of which consists of an attention mechanism, an upsampling process, a feature connection layer, and a residual unit. The attention mechanism (i.e., Convolutional Block Attention Module, CBAM) is integrated into the gravity network model because the model contains a large number of parameters. By introducing CBAM, the model can focus on key features in the channel dimension and spatial dimension respectively, improve the expression ability of important information, and suppress redundant features. This mechanism enhances the effectiveness of the model, optimizes information retention, and thus improves training efficiency and prediction accuracy. The input of CBAM is the encoder feature map and decoder feature maps , both come from the same layer in the U-Net structure and have the same dimensions. The difference is that represents low-resolution data, while Represents high-resolution data. The output of CBAM is defined as , which achieves efficient information extraction by enhancing features related to the current task and highlighting the key areas of gravity anomalies. Specifically, Figure 7 As shown, the output is the input feature and attention weights The element-by-element multiplication of is as follows:

[0084] ,

[0085] in, It can be expressed as:

[0086] ,

[0087] in, After batch normalization, ReLU activation function, a two-dimensional convolution and maximum pooling (MaxPool), the first single-channel attention weight is generated ; After batch normalization (BatchNorm), ReLU activation function and a two-dimensional convolution, the second single-channel attention weight is generated . compared to The only missing calculation process is the maximum pooling process. (...) Representatives will After batch normalization, ReLU activation function and a two-dimensional convolution, we get .

[0088] The CBAM module selectively highlights task-relevant gravity anomaly features while suppressing redundant or irrelevant information by combining attention mechanisms in both the channel and spatial dimensions. It captures global correlations between features in the channel dimension and precisely locates the distribution of anomalies in the spatial dimension. This effectively addresses the complex features and information redundancy inherent in gravity anomaly data, thereby enhancing the effectiveness of feature representation and significantly improving the accuracy and efficiency of gravity inversion tasks.

[0089] In order to verify the robustness of the network, this paper uses the fitting error E to describe the gravity observation loss. The specific calculation formula of this loss is as follows:

[0090]

[0091] Where N is the total number of observation points; represents theoretical observational gravity data; Represents predicted gravity data.

[0092] S3: Based on the ResDM-net++ network and gravity data, the three-dimensional physical structure model of the geological body is obtained, and the inversion of the geological gravity data is completed.

[0093] Example 2

[0094] The present invention also provides a geological gravity data inversion system based on an improved diffusion model, which is used to implement a method, including:

[0095] A gravity data acquisition module is used to establish multiple gravity anomaly geological body models based on preset constraints and acquire gravity data; wherein the sizes of the gravity anomaly geological body models include 3x3x3, 4x4x4, 5x5x5, 4x4x2 and 3x3x5;

[0096] The model improvement module is used to introduce the ResU-Net++ network into the encoder U-shaped structure of the diffusion model to obtain the ResDM-net++ network; the diffusion model includes the forward diffusion process and the reverse diffusion process;

[0097] The structural inversion module is used to obtain the three-dimensional physical structure model of the geological body based on the ResDM-net++ network and gravity data, and complete the inversion of the geological gravity data.

[0098] In a further embodiment, the gravity data acquisition module includes:

[0099] A model set construction unit is used to combine multiple individual gravity anomaly geological body models to obtain a model set;

[0100] Model forward modeling unit, used to perform model forward modeling based on the model set and generate gravity data; gravity data includes gravity component data , , , , , and ;in, is the gravity response simulated by multiple gravity anomaly geological models, denoted as , the vertical component of the gravity field is recorded as : ,

[0101] Where γ represents the gravitational constant , represents the density distribution within an underground abnormal domain D, is the corresponding forward linear operator, kernel function , , represents the field point position vector, represents the source position vector, is the field point position vector The vertical coordinate of is the source position vector The vertical coordinate of Represents the volume element at the source point.

[0102] Example 3

[0103] In order to evaluate the effectiveness of the network in feature detection, the present invention extracts a set of models from the test set. Figure 8 (a) and Figure 8(b) shows a visual description of the model and views at different sections for predictive analysis. The models are all uniformly dense at 1.0 g / cm³. The observation field spans from 0 m to 4000 m along the x-axis and from 0 m to 4000 m along the y-axis, with a data point spacing of 200 m, a total of 441 data points, and the vertical component of gravity is calculated. The space is divided into 8000 cubic units (20m × 20m × 20m), each with a side length of 200 meters. To improve readability, the density of all 3D perspective parts exceeds 0.5 g / cm 3 .

[0104] Figure 9 and Figure 10 The inversion slice results of the model at Y=1000m and X=2200m are shown respectively. The three columns in the figure show the comparison of the results of the custom diffusion model, ResU-Net++ and ResDM-net++ networks. Figure 9 (a) and Figure 10 (a) shows three network usages Component prediction; Figure 9 (b) and Figure 10 (b) Describes three network combinations and Component prediction; Figure 9 (c) and Figure 10 (c) Describes three network combinations 、 、 and Component prediction; Figure 9 (d) and Figure 10 (d) Describes three types of network associations 、 、 、 、 、 and Component prediction.

[0105] from Figure 9 It can be seen that under the condition of 10% noise, the models predicted by different components of the three networks basically restore the shape and density of the test model from the slice. Figure 9 As can be seen from the three columns, as the types of training gravity components increase, the slices of the same network prediction model show better results in terms of boundaries and density, and adding other components helps to identify the x, y, and z directions; Figure 9 (a)- Figure 9(d) As can be seen, the slice prediction model of the ResDM-net++ network outperforms the custom diffusion model and the ResU-Net++ network in both boundary and density dimensions. Therefore, the present invention concludes that the ResDM-net++ network predicts clear slice boundaries when combining the seven gravity components prediction model, and the density restoration range and size are close to the test model, which also verifies the network's robustness to noise in the model.

[0106] Similarly, Figure 10 It can be seen that under the condition of 10% noise, the models predicted by different components of the three networks basically restore the shape and density of the test model from the slice. Figure 10 As can be seen from each column, as the types of training gravity components increase, the slices of the same network prediction model show better results in terms of boundaries and density, and the addition of other components helps to identify the x, y, and z directions; Figure 10 (a)- Figure 10 (d) As can be seen, the slices predicted by the ResDM-net++ network model outperform the custom diffusion model and the ResU-Net++ network in both boundary and density dimensions. Therefore, we conclude that the ResDM-net++ network achieves clear slice boundary predictions in the combined seven gravity component prediction model, and the density restoration range and size are close to the test model, which also verifies the network's robustness to noise in the model.

[0107] Based on the previous analysis of the slicing effect of different networks combined with different components to predict the model and the reasons for the length of the article, Figure 11 Only the ResDM-net++ network combined with the four gravity components under 10% noise conditions is shown, and the observed gravity field, predicted gravity field and fitting difference map of different components are shown. Figure 11 (a)- Figure 11 (d) Display separately 、 、 and As can be seen from the figure, the shape and field value of the predicted field are basically consistent with the observed field, and the fitting error is less than 5%, which is in line with the error range. The inversion result is credible. In addition, combined with the situation not shown, the ResDM-net++ network combines the four gravity components to predict the smallest fitting error and the best effect.

[0108] Figure 12 (a)- Figure 12(c) Plots the mean squared error (MSE) loss curves for the custom diffusion model, ResU-Net++, and ResDM-net++ networks. The loss functions clearly converge as training progresses. Notably, the loss functions of all three networks exhibit convergence. This convergence indicates that the difference between the predicted and actual values is minimized, indicating that the network models have reached a stable state during training.

[0109] Table 1 shows the memory usage, GPU utilization, training time, and number of training grids for the custom diffusion model, ResU-Net++, and ResDM-net++ networks. A comparison shows that ResDM-net++ achieves 99% GPU utilization. Training time is relatively short for the custom diffusion model due to its simple structure and fewer parameters. ResU-Net++ takes the longest, with ResDM-net++ falling somewhere in between. The number of training grids for all three networks is 8,000. To fully understand the network configuration, Table 2 details the hyperparameters used during network training.

[0110] Table 1

[0111]

[0112] Table 2

[0113]

[0114] To more quantitatively evaluate the inversion results of the three networks, we calculated the field map fitting error of each network. Here, we only show the fitting error of the combined seven components, as shown in Table 3. As can be seen from the table, ResDM-net++ has the smallest fitting error and the best results.

[0115] Table 3

[0116]

[0117] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. The inversion method of geological gravity data based on the improved diffusion model is characterized by: The following steps are involved: Based on preset constraints, multiple gravity anomaly geological body models are established to obtain gravity data; wherein the sizes of the gravity anomaly geological body models include 3x3x3, 4x4x4, 5x5x5, 4x4x2 and 3x3x5; Introducing a ResU-Net++ network into the encoder U-shaped structure of a diffusion model to obtain a ResDM-net++ network; wherein the diffusion model includes a forward diffusion process and a reverse diffusion process; Based on the ResDM-net++ network and the gravity data, a three-dimensional physical structure model of the geological body is obtained, and the inversion of the geological gravity data is completed; The gravity data includes gravity component data 、 、 、 、 、 and ;in, is the gravity response simulated by multiple gravity anomaly geological models, denoted as , the vertical component of the gravity field is recorded as : ， Where γ represents the gravitational constant, represents the density distribution within an underground abnormal domain D, is the corresponding forward linear operator, kernel function , , represents the field point position vector, represents the source position vector, is the field point position vector The vertical coordinates of is the source position vector The vertical coordinate of Represents the volume element at the source point; The forward diffusion process is to add noise to the original gravity data input to the diffusion model. The formula is as follows: in, is in the time step data, is in the time step The noise figure is defined as , is a predefined noise table; is in the time step data, is random noise with the same shape as the input data; The reverse diffusion process is to recover the original gravity data from the noisy data. The formula is as follows: ， is the output of the diffusion model encoder; The U-shaped structure of the ResDM-net++ network includes an encoder, a spatial pyramid module, and a decoder. The encoder consists of three downsampling modules, each of which includes a residual unit paired with an SE module; the decoder consists of three decoding modules, each of which includes an attention mechanism module, an upsampling layer, a feature connection layer, and a residual unit. The decoder consists of three decoding modules, each of which consists of an attention mechanism, an upsampling process, a feature connection layer, and a residual unit. The attention mechanism is integrated into the gravity network model. By introducing the attention mechanism, the model focuses on key features in the channel dimension and spatial dimension respectively, improving the expression ability of important information while suppressing redundant features. This mechanism enhances the effectiveness of the model, optimizes information retention, and improves training efficiency and prediction accuracy. The input of the attention mechanism is the encoder feature map. and decoder feature map , both come from the same layer in the U-Net structure and have the same dimension; represents low-resolution data, while represents high-resolution data; the output of the attention mechanism is defined as ; Output is input features and attention weights The element-by-element multiplication of is as follows: ， in, Expressed as: ， in, After batch normalization, ReLU activation function, a two-dimensional convolution and maximum pooling, the first single-channel attention weight is generated ; After batch normalization, ReLU activation function and a two-dimensional convolution, the second single-channel attention weight is generated ; ( ) Representatives will After batch normalization, ReLU activation function and a two-dimensional convolution, we get ; The fitting error E is used to describe the loss of gravity observations. The specific calculation formula of the loss is as follows: Where N is the total number of observation points; represents theoretical observational gravity data; Represents predicted gravity data.

2. The method according to claim 1, characterized in that The SE module uses global pooling to transform the input gravity data Compressed into a vector , the compression formula is as follows: ， in, Represents input gravity data , represents the real number domain, H and W represent the number of rows and columns of gravity data extracted by convolution operation in the channel number C, respectively. Represents the row index, Indicates the column index.

3. The method according to claim 1, characterized in that The spatial pyramid module performs multi-scale sampling on the gravity data features extracted by the downsampling module by establishing different expansion rates to obtain multi-scale context information of the gravity data features; wherein the expansion rate is equipped with an equivalent convolution kernel, and the equivalent convolution kernel The size is expressed as follows: ， Among them, 𝑘 is the original convolution kernel size, is the expansion coefficient.

4. A geological gravity data inversion system based on an improved diffusion model, used to implement the method according to any one of claims 1 to 3, characterized in that: include: A gravity data acquisition module is used to establish multiple gravity anomaly geological body models based on preset constraints and acquire gravity data; wherein the sizes of the gravity anomaly geological body models include 3x3x3, 4x4x4, 5x5x5, 4x4x2 and 3x3x5; A model improvement module, configured to introduce a ResU-Net++ network into the encoder U-shaped structure of a diffusion model to obtain a ResDM-net++ network; wherein the diffusion model includes a forward diffusion process and a reverse diffusion process; The structural inversion module is used to obtain a three-dimensional physical structure model of the geological body based on the ResDM-net++ network and the gravity data, and complete the inversion of the geological gravity data.

5. The system according to claim 4, characterized in that The gravity data acquisition module includes: A model set construction unit is used to combine multiple individual gravity anomaly geological body models to obtain a model set; A model forward modeling unit is used to perform model forward modeling based on the model set to generate the gravity data; the gravity data includes gravity component data , , , , , and ;in, is the gravity response simulated by multiple gravity anomaly geological models, denoted as , the vertical component of the gravity field is recorded as : ， Where γ represents the gravitational constant, represents the density distribution within an underground abnormal domain D, is the corresponding forward linear operator, kernel function , , represents the field point position vector, represents the source position vector, is the field point position vector The vertical coordinate of is the source position vector The vertical coordinate of Represents the volume element at the source point.

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