A gravity anomaly three-dimensional inversion method based on multi-scale feature fusion

Abstract

The application belongs to the technical field of geophysical inversion, and relates to a gravity anomaly three-dimensional inversion method based on multi-scale feature fusion, comprising the following steps: randomly generating density anomaly bodies with different number, density, size and shape to obtain a three-dimensional density model of underground medium; forward modeling the three-dimensional density model of underground medium to obtain two-dimensional gravity anomaly data of the ground surface; training a multi-scale feature fusion model with the three-dimensional density model of underground medium as output and the two-dimensional gravity anomaly data as input, wherein the multi-scale feature fusion model comprises a two-dimensional encoder and a three-dimensional decoder, and a dimension converter and a multi-scale feature fusion device located between the two-dimensional encoder and the three-dimensional decoder; inputting the measured two-dimensional gravity anomaly data into the trained multi-scale feature fusion model to obtain a three-dimensional density body constrained by a physical range through inversion. The application enhances the expression capability of multi-scale features of underground structures, and can relieve the multi-solution problem of inversion and the problem of resolution decline in deep parts.

Description

Technical Field

[0001] This application belongs to the field of geophysical inversion technology, specifically, it relates to a three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion. Background Technology

[0002] Gravity exploration technology is a non-contact, efficient, and economical geophysical exploration technique widely used in mantle dynamics research, mineral resource exploration, hydrogeological surveys, and disaster monitoring. With the development of high-precision gravity detection instruments, its application scope and value will be further expanded and enhanced. Gravity anomaly inversion is a key technology in the interpretation of gravity exploration data. It infers subsurface density distribution and geological structural characteristics through changes in the surface gravity field. Its reliability directly affects the accuracy of geological interpretation. The core challenge lies in reducing the ambiguity of the inversion and constructing a reasonable and stable subsurface density model to achieve an accurate interpretation of geological structures.

[0003] In recent years, the rapid development of deep learning technology has provided new ideas to overcome the limitations of traditional gravity anomaly inversion methods. Unlike traditional gravity anomaly inversion methods, deep learning-based gravity anomaly inversion methods can directly learn high-dimensional features from gravity anomaly data by constructing a data-driven nonlinear mapping model. This effectively captures the complex correspondence between underground density structure and surface gravity field, significantly reducing the dependence of the inversion process on the initial model and effectively alleviating the problem of multiple solutions.

[0004] However, due to the unique spatial distribution characteristics of geophysical potential field data, and the fact that traditional convolutional neural networks rely on local convolutional kernels for feature extraction, it is difficult to fully capture long-range dependencies, which limits the spatial resolution of the inversion results. Summary of the Invention

[0005] This application provides a three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion, which solves the problem that traditional convolutional neural networks rely on local convolutional kernels for feature extraction, making it difficult to fully capture long-range dependencies and thus limiting the spatial resolution of the inversion results.

[0006] A three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion according to an embodiment of this application includes:

[0007] Density anomalies with different quantities, densities, sizes and shapes are randomly generated to obtain a three-dimensional density model of the subsurface medium;

[0008] Forward modeling of the three-dimensional density model of the subsurface medium yields two-dimensional gravity anomaly data of the Earth's surface;

[0009] A multi-scale feature fusion model is trained using a three-dimensional density model of underground medium as output and two-dimensional gravity anomaly data as input. The multi-scale feature fusion model includes a two-dimensional encoder and a three-dimensional decoder, as well as a dimension converter and a multi-scale feature fusion unit located between the two-dimensional encoder and the three-dimensional decoder.

[0010] The measured two-dimensional gravity anomaly data is input into the trained multi-scale feature fusion model to invert and obtain a three-dimensional density volume constrained by physical range.

[0011] Furthermore, the two-dimensional encoder employs multiple cascaded sub-coding modules. Each sub-coding module sequentially includes a first two-dimensional convolutional layer, a first channel attention mechanism module, a first residual module, and a second two-dimensional convolutional layer, which are used to focus on channels with important information, perform attention weighting on the channels, and map the data into high-dimensional, low-resolution deep features.

[0012] Furthermore, the input two-dimensional gravity anomaly data is convolved through the first two-dimensional convolutional layer and processed by a non-linear activation function before being input into the first channel attention mechanism module together with the input two-dimensional gravity anomaly data.

[0013] The first channel attention mechanism module adaptively calibrates the input data using global average pooling of the channels, and then weights it through the first and second fully connected layers to assign higher weights to the features of important channels in high-dimensional data.

[0014] The first residual module and the second two-dimensional convolutional layer output high-dimensional and low-resolution deep features.

[0015] Furthermore, the dimension converter includes a third two-dimensional convolutional layer, a dimension conversion layer, and a first three-dimensional convolutional layer from input to output, thereby upgrading the data output by the two-dimensional encoder from two-dimensional data feature dimensions to three-dimensional data feature dimensions.

[0016] Furthermore, the dimension transformation layer upscales the two-dimensional features through channel expansion and reshapes them into three-dimensional tensors. The spatial correlation of the three-dimensional tensors is then established through the first three-dimensional convolutional layer.

[0017] Furthermore, the multi-scale feature fusion unit includes, from input to output, a second three-dimensional convolutional layer, a second residual module, and a three-dimensional hollow spatial pyramid pooling module, which are used to fuse multi-scale spatial features.

[0018] Furthermore, the three-dimensional void space pyramid pooling module includes a 3D void convolution branch, global average pooling, and feature fusion operations. The 3D void convolution branch uses four parallel branches with different void ratios to extract multi-scale spatial features. Global average pooling extracts global features for each feature channel. The multi-scale spatial features are fused with the global features to output a feature map after feature fusion.

[0019] Furthermore, the 3D decoder adopts a progressive 3D upsampling structure, including multiple decoding modules. Each decoding module includes an upsampling layer, a 3D residual module convolutional unit, a second channel attention module, and a third 3D convolutional layer. The multiple decoding modules are used to establish a large-scale structural framework for multi-scale spatial features and then gradually recover the small- and medium-scale boundaries.

[0020] Furthermore, the upsampling layer uses trilinear interpolation to increase the spatial resolution of the feature map. After the interpolation stage, a three-dimensional residual convolutional unit is applied to refine the feature map, and a second-channel attention module is used to enhance the inter-channel correlation of the feature map.

[0021] Furthermore, the loss function of the multi-scale feature fusion model is constrained by both a data loss term and a physical loss term, wherein the data loss term is expressed as: ,in For the number of datasets, Indicates the first Inversion results for each dataset For the three-dimensional density model of the underground medium corresponding to the dataset;

[0022] The physical loss term is represented as: , Indicates the first The gravity response obtained by forward modeling after inversion of the datasets. Indicates the first Two-dimensional gravity anomaly data corresponding to each dataset.

[0023] Compared with existing technologies, the advantages of this application are as follows: This invention proposes a method suitable for three-dimensional inversion of gravity anomalies, improving the neural network architecture from the perspectives of dimension transformation, multi-scale feature fusion, and three-dimensional reconstruction. This enhances the network's spatial resolution and strengthens its ability to express multi-scale features of underground structures, thus alleviating the problems of multiple solutions and decreased resolution in deep areas. Furthermore, this method introduces both data loss and physical loss as loss functions to constrain the model, combining traditional forward modeling techniques with data-driven deep learning techniques to achieve efficient and high-resolution three-dimensional inversion of gravity anomalies. Attached Figure Description

[0024] Figure 1A flowchart of a three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion provided in this application embodiment;

[0025] Figure 2 A schematic diagram of the framework structure of a three-dimensional gravity anomaly inversion model based on multi-scale feature fusion for implementing the inversion method provided in this application embodiment;

[0026] Figure 3 A schematic diagram of the frame structure of a two-dimensional encoder provided in an embodiment of this application;

[0027] Figure 4 This is a schematic diagram of the framework structure of the dimension converter provided in the embodiments of this application;

[0028] Figure 5 A schematic diagram of the framework structure of the multi-scale feature fusion device provided in the embodiments of this application;

[0029] Figure 6 This is a schematic diagram of the framework structure of the 3D decoder provided in the embodiments of this application;

[0030] Figure 7 A schematic diagram of the framework structure of the first channel attention mechanism module provided in the embodiments of this application;

[0031] Figure 8 A schematic diagram of the framework structure of the three-dimensional void space pyramid pooling module provided in the embodiments of this application;

[0032] Figure 9 This is a schematic diagram of the framework structure of the residual module provided in an embodiment of this application. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0034] See Figure 1 Combination Figure 2 As shown, a three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion includes the following steps:

[0035] S1 randomly generates density anomalies with different quantities, densities, sizes, and shapes to obtain a three-dimensional density model of the subsurface medium; in one example, density anomalies with different quantities, densities, sizes, and shapes are randomly generated in a 32×32×16 grid area to obtain a three-dimensional density model of the subsurface medium.

[0036] S2 performs forward modeling of the three-dimensional density model of the subsurface medium to obtain two-dimensional gravity anomaly data of the surface; based on ,in, For gravity forward modeling kernel matrix operator, A three-dimensional density model of the subsurface medium was used to calculate two-dimensional gravity anomaly data at the surface. A dataset was established using two-dimensional gravity anomaly data and the corresponding three-dimensional density model of underground medium. The dataset was divided into training set, validation set and test set in a ratio of 16:3:1 for use during training.

[0037] S3 uses a three-dimensional density model of underground medium as output and two-dimensional gravity anomaly data as input to train a multi-scale feature fusion model. The multi-scale feature fusion model includes a two-dimensional encoder and a three-dimensional decoder, as well as a dimension converter and a multi-scale feature fusion unit located between the two-dimensional encoder and the three-dimensional decoder.

[0038] S4 inputs the measured two-dimensional gravity anomaly data into the trained multi-scale feature fusion model to invert and obtain a three-dimensional density volume constrained by the physical range.

[0039] See Figure 2 As shown, the multi-scale feature fusion model based on this application includes a two-dimensional encoder and a three-dimensional decoder, as well as a dimension converter and a multi-scale feature fusion unit located between the two-dimensional encoder and the three-dimensional decoder.

[0040] A multi-scale feature fusion model was trained using a training set, with two-dimensional gravity anomaly data as input samples and the corresponding three-dimensional density model as the network model's output label. The mapping relationship between the input two-dimensional gravity anomaly data and the output three-dimensional density model was established. During training, the loss function included data loss and physical loss terms, and the network parameters were continuously optimized until the loss function converged and stabilized, resulting in the three-dimensional gravity anomaly inversion model. In the testing phase, the accuracy of the inversion results of the multi-scale feature fusion model was tested using a test set.

[0041] In one embodiment, the two-dimensional encoder employs multiple cascaded sub-encoding modules, see [link to documentation]. Figure 3 As shown, each sub-encoding module sequentially includes a first two-dimensional convolutional layer, a first channel attention mechanism module, a first residual module, and a second two-dimensional convolutional layer. The overall function of the two-dimensional encoder is to use the output of one sub-encoding module as the output of another sub-encoding module, thereby reducing the resolution step by step and extracting features of important channels.

[0042] Specifically: In the 2D encoder, the first 2D convolutional layer is responsible for extracting preliminary spatial features from the input 2D gravity anomaly data. The number of output feature channels is controlled by setting the number of convolutional kernels. The first channel attention mechanism module evaluates the importance of each feature channel, enhances feature channels with high information content, and suppresses unimportant or redundant feature channels to achieve the extraction of important channel features. The first residual module learns deep features through nonlinear transformation without losing the original information. The second 2D convolutional layer fuses and refines the features output by the first residual module and passes them to the next cascaded sub-encoding module.

[0043] The first residual module includes the main road and branch roads, see [link / reference]. Figure 9 The schematic diagram of the residual module shown shows that the main path includes multiple convolutional layers, such as in one embodiment... Figure 9 The three convolutional layers learn deep features by nonlinear transformation of the features output by the first channel attention mechanism module, and pass the features output by the first channel attention mechanism module through branches without any operation. Finally, the features of the branches and the main path are added together. In this way, the features output by the first channel attention mechanism module are preserved.

[0044] See Figure 7 As shown, the input data is adaptively calibrated by using global average pooling of the channels through the first channel attention mechanism module, and then weighted by the first and second fully connected layers respectively, so that the features of important channels of high-dimensional data are given higher weights.

[0045] When the data passes through the first channel attention mechanism module, the... The layer output can be represented as:

[0046] ,in, For the weights of the first fully connected layer, For the weights of the second fully connected layer, For activation function, For scaling functions, To use global average pooling of channels, for The output of the layer, after being weighted by the first and second fully connected layers, is fed into the scaling function along with the input of the first channel attention mechanism module. This process adaptively calibrates the data, making the network pay more attention to the features of important channels in high-dimensional data.

[0047] In one embodiment, see Figure 4As shown, the dimension converter, from input to output, sequentially includes a third 2D convolutional layer, a dimension transformation layer, and a first 3D convolutional layer, which upscales the data output from the 2D encoder from a 2D data feature dimension to a 3D data feature dimension. Specifically, the third 2D convolutional layer removes redundant information within the 2D plane by increasing or decreasing the number of channels; the dimension transformation layer upscales the 2D data features through channel expansion and reshapes them into a 3D tensor; and the first 3D convolutional layer establishes the spatial correlation of the 3D tensor.

[0048] Specifically, when the data passes through a dimension transformer, the first... The layer output can be represented as:

[0049] ,

[0050] in, For dimension reorganization operation, This represents the activation function. and These are two-dimensional convolution operations and three-dimensional convolution operations, with convolution kernel dimensions of two and three dimensions, respectively. The data is transformed from two-dimensional to three-dimensional data feature space through a dimension converter.

[0051] In one embodiment, see Figure 5 As shown, the second 3D convolutional layer is used to uniformly transform and integrate the input features, adjusting the number of channels of the input features to a dimension suitable for subsequent processing. After the output of the second 3D convolutional layer, a second residual module is used to ensure stable training and prevent gradient vanishing and other problems caused by subsequent complex multi-scale calculations. The second residual module has the same structure as the first residual module, including a main path and branches. The main path includes multiple convolutional layers, which learn deep features by nonlinearly transforming the features output by the second 3D convolutional layer. The features output by the second 3D convolutional layer are then passed through branches, which do not perform any operations. Finally, the features of the branches and the main path are added together. In this way, the features output by the second 3D convolutional layer are preserved. The 3D hollow spatial pyramid pooling module effectively alleviates the problem of information loss during dimensional transformation and enhances the modeling ability for complex structures through multi-scale spatial feature fusion.

[0052] For details, see Figure 8 As shown, the 3D void space pyramid pooling module contains two core paths: one is four parallel 3D void convolution branches with different void ratios, used to capture multi-scale spatial features; the other is to provide global context after global average pooling, 1x1 convolution transformation and upsampling to restore size, and finally fuse the features of different paths for output.

[0053] The data is processed through a 3D hollow space pyramid pooling module, the first... The layer output can be represented as:

[0054] ,

[0055] in, , To determine the dilation rate, four parallel 3D dilated convolution branches are used, with dilation rates of [missing information]. , This represents a dilated convolution operation, equivalent to a dilation rate. The three-dimensional convolution operation, namely .

[0056] ,

[0057] in, For upsampling, This is a global average pooling operation. This is after global average pooling and upsampling operations. This indicates a fusion operation.

[0058] In one embodiment, the 3D decoder employs a progressive 3D upsampling structure, which refers to the use of multiple cascaded decoding modules, performing decoding step by step. (See [link to previous document]). Figure 6 As shown, each decoding module includes an upsampling layer, a 3D residual module convolutional unit, a second channel attention module, and a third 3D convolutional layer. Multiple cascaded decoding modules are used to process the input multi-scale spatial features. First, a large-scale structural framework of the multi-scale spatial features is constructed, and then the small- and medium-scale geometric boundaries are restored step by step. This progressive process improves the spatial resolution step by step while refining the geometric details simultaneously, and finally outputs a high-resolution 3D density volume. The whole process is a coarse-to-fine process. The first-level decoding module performs coarse extraction and constructs a large-scale structural framework. The second-level and subsequent decoding modules refine the details step by step. This can be explained as follows: the first-level decoding module outlines an overall large-scale structural framework, and the second-level and subsequent decoding modules gradually restore and refine the geometric details within the large-scale structural framework in a step-by-step manner.

[0059] In the 3D decoder, a combination of trilinear interpolation and residual convolution is used. Specifically, in the upsampling layer, trilinear interpolation is used to uniformly enlarge the input feature map in three spatial dimensions (depth, height, and width) to obtain a feature map with a larger spatial size. At this point, the feature map is relatively blurry. After the upsampling layer, a 3D residual convolution unit is used to deblur and restore the geometric information that should be present at this resolution, thus achieving spatial dimension refinement. The second channel attention module optimizes in the channel dimension. It dynamically focuses on the feature channels most useful for the current reconstruction stage (restoring the large-scale structural framework or refining geometric details), suppressing noise or redundant channels, thereby improving the efficiency and robustness of feature representation. Finally, in the third 3D convolutional layer, a 1×1×1 3D convolution is used to compress the feature map to a single channel, and then the Sigmoid function is used to normalize each feature value of the feature map to the [0,1] interval, thereby outputting a probabilistic 3D density volume that can be directly used for 3D reconstruction.

[0060] In this application, the three-dimensional residual convolutional unit has the same structure as the first residual module, containing a main path of two or three convolutional layers, and a branch path that directly connects the input of the three-dimensional residual convolutional unit to its output. The core is to add the input of the three-dimensional residual convolutional unit to the output of the main path through this shortcut connection. When the input and output dimensions do not match, the input needs to be linearly projected to adjust the dimensions, so that the three-dimensional residual convolutional unit focuses on learning the residual mapping between the input and the output, and can effectively alleviate the gradient vanishing problem of deep networks.

[0061] In one embodiment, the loss function of the multi-scale feature fusion model is constrained by both a data loss term and a physical loss term. The data loss term is expressed as: ,in For the number of datasets, Indicates the first Inversion results for each dataset For the three-dimensional density model of the underground medium corresponding to the dataset;

[0062] The physical loss term is represented as: , Indicates the first The gravity response obtained by forward modeling after inversion of the datasets. Indicates the first Two-dimensional gravity anomaly data corresponding to each dataset.

[0063] The final loss function is: ,in, , These are the weights for the data loss term and the physical loss term, respectively.

[0064] During training, the parameter set is iteratively updated through backpropagation until the loss function converges, thus completing the training of the multi-scale feature fusion model.

[0065] When in use, the measured two-dimensional gravity anomaly data is input into the trained multi-scale feature fusion model to invert and obtain a three-dimensional density volume constrained by the physical range.

[0066] This application proposes a method that uses deep learning to invert a three-dimensional density distribution model of an underground study area from observed gravity anomaly data. Compared with the standard convolutional neural network commonly used in deep learning, this method is specifically designed for the task characteristics of gravity anomaly inversion. It introduces a cross-dimensional and multi-scale feature fusion mechanism to integrate feature information at different scales, effectively model the global information of potential field data, improve the characterization and recovery capabilities of complex geological structures, and is expected to improve the ability to distinguish deep anomalies.

[0067] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion, characterized in that, include: Density anomalies with different quantities, densities, sizes and shapes are randomly generated to obtain a three-dimensional density model of the subsurface medium; Forward modeling of the three-dimensional density model of the subsurface medium yields two-dimensional gravity anomaly data of the Earth's surface; A multi-scale feature fusion model is trained using a three-dimensional density model of underground medium as output and two-dimensional gravity anomaly data as input. The multi-scale feature fusion model includes a two-dimensional encoder and a three-dimensional decoder, as well as a dimension converter and a multi-scale feature fusion unit located between the two-dimensional encoder and the three-dimensional decoder. The measured two-dimensional gravity anomaly data is input into the trained multi-scale feature fusion model to invert and obtain a three-dimensional density volume constrained by the physical range. The multi-scale feature fusion unit consists of a second 3D convolutional layer, a second residual module, and a 3D hollow spatial pyramid pooling module from input to output, which are used to fuse multi-scale spatial features. The loss function of the multi-scale feature fusion model is constrained by both a data loss term and a physical loss term. The data loss term is expressed as: ,in For the number of datasets, Indicates the first Inversion results for each dataset, For the three-dimensional density model of the underground medium corresponding to the dataset; The physical loss term is represented as: , Indicates the first The gravity response obtained by forward modeling after inversion of the datasets. Indicates the first Two-dimensional gravity anomaly data corresponding to each dataset.

2. The three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion according to claim 1, characterized in that, The two-dimensional encoder employs multiple cascaded sub-coding modules. Each sub-coding module sequentially includes a first two-dimensional convolutional layer, a first channel attention mechanism module, a first residual module, and a second two-dimensional convolutional layer. The output of one sub-coding module of the two-dimensional encoder is used as the output of another sub-coding module. The resolution is reduced step by step, and the features of important channels are extracted.

3. The three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion according to claim 2, characterized in that, The input two-dimensional gravity anomaly data is convolved through the first two-dimensional convolutional layer and processed by a non-linear activation function before being input into the first channel attention mechanism module along with the input two-dimensional gravity anomaly data. The first channel attention mechanism module adaptively calibrates the input data using global average pooling of the channels, and then weights it through the first and second fully connected layers to assign higher weights to the features of important channels in high-dimensional data. The first residual module and the second two-dimensional convolutional layer output high-dimensional and low-resolution deep features.

4. The three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion according to claim 1, characterized in that, The dimension converter includes a third two-dimensional convolutional layer, a dimension conversion layer, and a first three-dimensional convolutional layer from input to output, which improves the data output by the two-dimensional encoder from two-dimensional data feature dimension to three-dimensional data feature dimension.

5. The three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion according to claim 4, characterized in that, The dimension transformation layer upscales the two-dimensional features through channel expansion and reshapes them into three-dimensional tensors. The spatial correlation of the three-dimensional tensors is then established through the first three-dimensional convolutional layer.

6. The method for three-dimensional inversion of gravity anomalies based on multi-scale feature fusion according to claim 1, characterized in that, The three-dimensional void space pyramid pooling module includes a 3D void convolution branch, global average pooling, and feature fusion operations. The 3D void convolution branch uses four parallel branches with different void ratios to extract multi-scale spatial features. Global average pooling extracts global features for each feature channel. The multi-scale spatial features are fused with the global features to output a feature map after feature fusion.

7. The three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion according to claim 1, characterized in that, The 3D decoder adopts a progressive 3D upsampling structure, which includes multiple decoding modules. Each decoding module includes an upsampling layer, a 3D residual module convolutional unit, a second channel attention module, and a third 3D convolutional layer. The multiple decoding modules are used to establish a large-scale structural framework for multi-scale spatial features and then gradually recover the small and medium-scale boundaries.

8. The three-dimensional inversion method for gravity anomalies based on multi-scale feature fusion according to claim 7, characterized in that, The upsampling layer uses trilinear interpolation to increase the spatial resolution of the feature map. After the interpolation stage, a three-dimensional residual convolutional unit is applied to refine the feature map, and a second-channel attention module is used to enhance the inter-channel correlation of the feature map.

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