A 3D Geological Structure Modeling Method Based on Graph Neural Network

Abstract

The present invention relates to the technical field of geological structure modeling, and specifically discloses a three-dimensional geological structure modeling method based on graph neural networks. The present invention takes the entire geological map as input data. By establishing a new fault coding method, it can automatically identify and simulate the influence of faults on the formation scalar field, especially the discontinuous jump phenomenon of the scalar field at the fault position, avoiding the problem of manually setting fault displacement parameters in traditional methods. It can accurately simulate the fault effect without relying on manual intervention, and solves the problem that the traditional scalar field prediction model based on graph neural networks is difficult to express the discontinuous jump phenomenon of the scalar field at the fault position caused by the influence of the fault effect.

Description

Technical Field

[0001] This application relates to the technical field of geological structure modeling, and specifically discloses a method for three-dimensional geological structure modeling based on graph neural network. Background Art

[0002] The three-dimensional geological structure model is an important model for understanding the geometric shape of underground hidden geological bodies and numerical simulation of geological processes. The construction of the three-dimensional geological structure model can be divided into two categories: explicit modeling and implicit modeling. In the prior art, the implicit modeling method is usually adopted, and the isosurface of the three-dimensional scalar field is used to represent the geological surface.

[0003] With the development of big data, especially the rapid development of the neural network geological modeling method using graph neural network. In the prior art, the graph neural network modeling method consists of a scalar field GNN model and a lithology category GNN model.

[0004] In the scalar field GNN model, by inputting the graph node coordinate matrix and node adjacency matrix to be calculated, under the constraint of the loss function of attitude data and interface attribute data, the model parameters are trained to calculate the scalar field value of unknown nodes and obtain the scalar field value of the nodes.

[0005] In the lithology category GNN model, the lithology category sampling point data is extracted through virtual boreholes in the geological section. The scalar field value predicted by the scalar field GNN can be spliced with the graph node coordinate matrix to form a joint graph feature matrix. Under the constraint of the loss function of lithology category data, the model parameters are trained to calculate the lithology category of unknown nodes and obtain the lithology category of the nodes.

[0006] Through the scalar field GNN model and the lithology category GNN model, the scalar field representing the formation interface to be modeled and the lithology category representing the formation entity can be obtained.

[0007] However, in the current graph neural network modeling method, for the lithology category sampling points, discrete data points are generally taken directly through virtual boreholes in the exploration line profile, and the topological relationship hidden in the map is lost during the sampling process. In addition, in actual modeling applications, the scenario of faults cutting the formation often occurs, and the fault cutting will cause the same formation surface to be discontinuous in space. The current graph neural network scalar field prediction model is difficult to express the problem of discontinuous jump of the scalar field at the fault position caused by the influence of the fault effect.

[0008] The present invention provides a method for three-dimensional geological structure modeling based on graph neural network to solve the above problems. Summary of the Invention

[0009] The object of the present invention is to solve the problem that the traditional scalar field prediction model of graph neural network is difficult to express the phenomenon that the scalar field has discontinuous jumps at fault positions due to the influence of fault effects.

[0010] To achieve the above object, the basic solution of the present invention provides a method for modeling three-dimensional geological structures using graph neural networks, including the following steps:

[0011] Step A1: Obtain a three-dimensional geological map dataset based on the preprocessing of three-dimensional geological maps, and extract scalar field attribute sampling points and lithological unit sampling points from the three-dimensional geological map dataset;

[0012] Step A2: Perform tetrahedral meshing on the point data of the obtained scalar field attribute sampling points and lithological unit sampling points, and generate graph structure data based on the tetrahedral meshing results;

[0013] Step A3: Construct a graph neural network structure based on a dual-task GNN model, where the dual-task GNN model is respectively used to predict the scalar field value of nodes and to classify the lithological categories of nodes;

[0014] Step A4: Input the preprocessed graph structure data into the graph neural network structure, and generate scalar field prediction values and classified lithological categories of nodes by the graph neural network structure;

[0015] Step A5: Based on the scalar field prediction values, extract isosurfaces therefrom through the tetrahedral algorithm as formation interfaces, classify the tetrahedral units through node lithology labels, merge the tetrahedral units of the same lithological category, generate closed three-dimensional entities, and obtain different formation entity models based on different lithological categories.

[0016] Further, the three-dimensional geological maps include plane geological maps, exploration line profiles, and mid-section plane maps.

[0017] Further, in step A2, the graph structure data is represented as:

[0018] G=(V,E);

[0019] In the formula, G represents the graph structure data, G is an undirected graph, V is the set of nodes, including all nodes, V={v1,v2,...,v n}, where each node v i corresponds to a node in the graph, v i ∈V, i = 1, 2, …, n;

[0020] E is the set of edges, representing the connection relationship between nodes, E={(i,j), i,j∈V}, (i,j) represents the edge between node i and node j.

[0021] Furthermore, each node v i has both input features and input attributes. The input features of the node include node coordinate features and fault coding features, and the input attributes of the node include scalar field attributes, attitude attributes, and lithology labels.

[0022] Furthermore, for the i-th node in the graph structure data, i = 1, 2, …, it has both input features and input attributes, and its original input features and input attributes are expressed as follows:

[0023] Feature i ={C i ,F i ,S i ,A i ,L i};

[0024] In the formula, C i represents the coordinate information of the i-th node, and C i ∈R n , R n is an n-dimensional geometric space, F i represents the fault coding feature of the i-th node, and F i ∈{1, 2, …, K f}, K f is the number of faults, S i represents the scalar field attribute of the i-th node, and S i ∈R p , R p is a p-dimensional attribute space, A i represents the attitude attribute of the i-th node, and A i ∈R q , R q is a q-dimensional attribute space, L i represents the lithology label of the i-th node, and L i ∈{1, 2, …, K l}, K l is the number of lithologies.

[0025] Furthermore, for node v i and fault F k , k = 1, 2, …, the expression of its fault coding feature is as follows:

[0026] ;

[0027] In the formula, when node v i is located on the hanging wall of fault F k , then the fault coding feature , when node v i is located on the footwall of fault F k , then the fault coding feature 。

[0028] Further, when node v i is affected by k cross faults, its final fault coding feature F i is:

[0029] ;

[0030] In the formula, is the coding value of node v i on the k-th fault, indicating the position and relative relationship of the node on different faults.

[0031] Further, the graph structure data is divided into continuous data and discrete data. In step A4, the preprocessing operations performed on the graph structure data include performing preprocessing on continuous data by means of range normalization, and performing encoding processing on discrete data by means of One-Hot encoding.

[0032] Further, the dual-task GNN model includes a scalar field GNN model for predicting the scalar field value of nodes and a lithology category GNN model for classifying the lithology categories of nodes. Both the scalar field GNN model and the lithology category GNN model are equipped with three-layer stacked graph attention network modules.

[0033] Further, in step A4, the steps for the graph neural network structure to generate scalar field prediction values and divide the obtained lithology categories of nodes are as follows:

[0034] Step B1, taking the node coordinate features, fault coding features, and edge connection relationships as the feature inputs of the scalar field GNN model, and outputting the scalar field prediction value of each node through the scalar field GNN model equipped with a three-layer stacked graph attention network module.

[0035] Step B2, splicing the scalar field prediction value with the node coordinate features to obtain a feature matrix, taking the spliced feature matrix and the edge connection matrix as the inputs of the lithology category GNN model, and outputting the predicted lithology category of each node through the lithology category GNN model equipped with a three-layer stacked graph attention network module.

[0036] The principle and effect of this solution are as follows:

[0037] 1. Compared with the prior art, the present invention takes the entire geological map as input data. This method significantly enriches the lithology unit sampling point set while maintaining the internal topological relationship of the formation entity, thereby more comprehensively reflecting the geological characteristics.

[0038] 2. Compared with the prior art, the fault encoding method of the present invention can automatically identify and simulate the influence of faults on the scalar field of the formation, especially the discontinuous jump phenomenon of the scalar field at the fault position, avoiding the problem of manually setting fault displacement parameters in the traditional method, and can accurately simulate the fault effect without relying on manual intervention, solving the problem that the traditional scalar field prediction model of the graph neural network is difficult to express the discontinuous jump phenomenon of the scalar field at the fault position caused by the influence of the fault effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present application. For those skilled in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0040] Figure 1 Shows a schematic diagram of a graph neural network three-dimensional geological structure modeling method proposed in an embodiment of the present application;

[0041] Figure 2 Shows the sampling graph proposed in an embodiment of the present application. Among them, (a) is a three-dimensional model, (b) is a cross-sectional view of the three-dimensional model in the A-A' direction, and (c) is a planar geological map of the three-dimensional model in the B-B' direction;

[0042] Figure 3 Shows the sampling difference graph proposed in an embodiment of the present application. Among them, (a) is the sampling graph obtained based on the traditional GNN sampling method, and (b) is the sampling graph obtained based on the sampling method proposed in the present application;

[0043] Figure 4 Shows the schematic diagram of tetrahedral meshing proposed in an embodiment of the present application. Among them, (a) is a schematic diagram of the equidistant interpolation point deletion process, and (b) is a schematic diagram of the boundary and node constraint tetrahedral meshing process;

[0044] Figure 5 Shows the planar geological map of the modeling area proposed in an embodiment of the present application;

[0045] Figure 6 Shows the schematic diagram of the graph data proposed in an embodiment of the present application. Among them, (a) is a three-dimensional view of the modeling graph data, (b) is a three-dimensional view of the sampling data point set, and (c) is a three-dimensional view of the sampling data point set in the east-west direction;

[0046] Figure 7 Shows the schematic diagram of cross-fault encoding proposed in an embodiment of the present application. Among them, (a) is a schematic diagram of the fault, (b) is the new fault feature, (c) is the old fault feature, and (d) is the final fault feature;

[0047] Figure 8 Shows a schematic diagram of the three-dimensional formation scalar field model with fault effect proposed in the embodiment of the present application. Among them, (a) is the three-dimensional formation scalar field model with fault effect, (b) is section 1 of the three-dimensional formation scalar field, (c) is section 2 of the three-dimensional formation scalar field, and (d) is section 3 of the three-dimensional formation scalar field;

[0048] Figure 9 Shows a schematic diagram of the three-dimensional lithology category model with fault effect proposed in the embodiment of the present application. Among them, (a) is the three-dimensional lithology category model with fault effect, (b) is section 1 of the three-dimensional lithology category model, (c) is section 2 of the three-dimensional lithology category model, and (d) is section 3 of the three-dimensional lithology category model;

[0049] Figure 10 Shows a schematic diagram of the three-dimensional formation model with fault effect proposed in the embodiment of the present application. Among them, (a) is the superimposed display of the fault plane and the formation model, and (b) is the superimposed display of the formation isosurface and the formation model. Detailed implementation manners

[0050] To further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following combines the accompanying drawings and preferred embodiments to detail the specific implementation manners, structures, features and their effects of the present invention as follows.

[0051] A method for three-dimensional geological structure modeling based on graph neural network, as shown in the embodiments Figure 1 shown, includes the following steps:

[0052] Step A1: Obtain a three-dimensional geological map dataset based on the preprocessing of three-dimensional geological maps, and extract sampling points based on the three-dimensional geological map dataset. The sampling points include scalar field attribute sampling points and lithology unit sampling points.

[0053] The three-dimensional geological maps include plane geological maps, exploration line profiles and mid-section plane maps.

[0054] For the processing of three-dimensional geological maps, it includes vectorization processing of two-dimensional maps: plane geological maps, exploration line profiles and mid-section plane maps, and two-dimensional to three-dimensional mapping according to spatial control points to generate a three-dimensional geological map dataset.

[0055] Specifically, as shown in Figure 2 the sampling map shown, extract formation boundaries, fault boundaries and formation surfaces based on the three-dimensional geological map dataset. For formation boundaries and fault boundaries, extract scalar field attribute sampling points at equal intervals on the line.

[0056] Perform Delaunay triangulation on the ground layer and extract the nodes of the triangulation: The nodes of the triangular mesh are used as the sampling points of the lithology units. As Figure 3 shown in the sampling difference diagram, Figure 3 in (a) is the sampling diagram obtained based on the traditional GNN sampling method, Figure 3 in (b) is the sampling diagram obtained based on the sampling method proposed in this application. As Figure 3 in (a), the use of virtual boreholes for lithology sampling results in the loss of topological information. Compared with the traditional lithology sampling method of first extracting several lithology unit sampling points through virtual boreholes in the exploration profile and then performing triangulation, in this embodiment, uniform sampling is performed throughout the exploration line profile. As Figure 3 shown in (b), the original topological relationship of the exploration line profile is retained, and at the same time, the sampling data volume of the lithology units is increased.

[0057] Step A2: Perform tetrahedral meshing on the point data of the obtained scalar field attribute sampling points and lithology unit sampling points, and generate graph structure data based on the tetrahedral meshing result.

[0058] Specifically, in the present invention, as Figure 4 shown in the tetrahedral meshing schematic diagram, during the process of performing tetrahedral meshing on the point data of the obtained scalar field attribute sampling points and lithology unit sampling points, the modeling space range and the DEM surface are used as the boundary constraint surfaces for tetrahedral meshing, and the cleaned equidistant interpolation encrypted points and sampling points are used as the nodes for tetrahedral meshing to ensure that the graph structure data is consistent with the modeling area space range, includes all known sampling points, and additionally adds encrypted control meshing points.

[0059] Specifically, the input modeling space range is used as the bottom boundary and side boundary for tetrahedral meshing;

[0060] The DEM surface is used as the top boundary constraint boundary for tetrahedral meshing;

[0061] All sampling points are used as the nodes for tetrahedral meshing, and since the lithology unit sampling points are directly obtained from the triangular mesh of the geological map, the topological relationship of the sampling points is retained during tetrahedral meshing;

[0062] Equidistant interpolation encrypted points are generated according to the specified modeling resolution, and when the generated equidistant interpolation encrypted points coincide with the sampling points and DEM points, the coincident encrypted points are deleted.

[0063] In this embodiment, the graph structure is defined by the node set V and the edge set E, and the graph structure data generated based on the tetrahedral meshing result is expressed as:

[0064] G=(V,E);

[0065] Wherein, G represents graph-structured data, G is an undirected graph, V is a set of nodes, including all nodes, V = {v1, v2,..., v n}, where each node v i corresponds to a node in the graph, v i ∈V, i = 1, 2,..., n;

[0066] E is a set of edges, representing the connection relationship between nodes, E = {(i, j), i, j ∈ V}, (i, j) represents the edge between node i and node j. And each node v i ∈V has input features and input attributes, and the edge (i, j) ∈ E represents the connection relationship between node i and node j.

[0067] The input features of the nodes include node coordinate features and fault coding features, and the input attributes of the nodes include scalar field attributes, occurrence attributes, and lithology labels. The node coordinate features are obtained when generating the nodes. The fault coding feature value is determined by the relative position of the node and the fault. The relative position of the node and the fault includes being on the hanging wall of the fault and being on the footwall of the fault. The scalar field attribute of the node is based on the top surface formation of the modeled formation as the reference plane, and scalar field values are assigned to different formation interfaces according to the cumulative formation thickness. Occurrence sampling points are extracted near the formation and fault lines, and unit vector calculations are performed according to the dip angle and dip direction of the occurrence points. The occurrence point data of the node is represented by the unit normal vector as the occurrence attribute. The lithology label of the node is represented by different integers.

[0068] For node v i , its original input features and input attributes are expressed as follows:

[0069] Feature i ={C i ,F i ,S i ,A i ,L i};

[0070] Wherein, C i represents the coordinate information of the i-th node, and C i ∈R n , R n is an n-dimensional geometric space, F i represents the fault coding feature of the i-th node, and F i ∈{1, 2,..., K f}, K f is the number of faults, S i represents the scalar field attribute of the i-th node, and S i ∈R p , R p is a p-dimensional attribute space, Ai represents the attitude attribute of the \(i\)-th node, and \(A\) i \(\in R\) q , where \(R\) q is a \(q -\)dimensional attribute space, and \(L\) i represents the lithology label of the \(i\)-th node, and \(L\) i \(\in\{1,2,\cdots,K\) l}\), where \(K\) l is the number of lithologies.

[0071] In this embodiment, a fault coding method is established based on the relative relationship between nodes and faults: The fault coding feature \(F\) of each node i represents the spatial relative relationship between this node and different faults. For node \(v\) i and fault \(F\) k , \(i = 1,2,\cdots,k = 1,2,\cdots\), the expression of its fault coding feature is as follows:

[0072] ;

[0073] In the formula, when node \(v\) i is located on the hanging wall of fault \(F\) k , then the fault coding feature , when node \(v\) i is located on the footwall of fault \(F\) k , then the fault coding feature .

[0074] When there are cross - faults, the final fault coding of the node can be represented as a vector, integrating the influence of multiple faults. When node \(v\) i is affected by \(k\) cross - faults, its final fault coding feature \(F\) i is:

[0075] ;

[0076] In the formula, is the coding value of node \(v\) i on the \(k -\)th fault, indicating the position and relative relationship of this node on different faults.

[0077] Specifically, a node located on the footwall of a fault is assigned a value of 0, a node located on the hanging wall of a fault is assigned a value of 1, and for cross - faults, the partition fault coding values of different faults are superimposed as the final fault coding feature value of a certain node.

[0078] In this embodiment, the constructed graph structure data is divided into continuous data and discrete data. The continuous data includes coordinate features, scalar field attributes, and occurrence attributes, and the discrete data includes fault coding and lithology coding (lithology labels). When the graph structure data is input as training data, it is necessary to preprocess the graph structure data, including preprocessing the continuous data by range normalization to accelerate the training convergence of the subsequent graph neural network structure, and encoding the discrete data by the One-Hot encoding method. Specifically:

[0079] For the coordinate features, scalar field attributes, and occurrence attributes that belong to continuous data, the input features of each graph node are the normalized spatial coordinates of the nodes located in the three-dimensional space and the fault coding features.

[0080] Normalized spatial coordinates: The calculation method of Cartesian coordinates is to readjust the range of each node feature according to the maximum coordinate range and center it around 0. The calculation process of the normalized spatial coordinates coordinates is as follows:

[0081] ;

[0082] ;

[0083] ;

[0084] ;

[0085] where x v , y v , z v are the unnormalized x, y, and z coordinates of the node respectively, , , are the central values of the x, y, and z direction coordinates respectively, x max , y max , z max are the maximum coordinate values in the x, y, and z directions respectively, x min , y min , z min are the minimum coordinate values in the x, y, and z directions respectively, and x, y, z are the scaling factors in the x, y, and z directions. In the present invention, the coordinate range is scaled between [-1, 1], and for the scalar field attributes, it is scaled between [-1, 1].

[0086] For the fault coding and lithology coding belonging to discrete data, One-Hot coding is used for processing. The principle is to convert the categorical variable into a binary vector, where each category corresponds to a unique position, and only the corresponding position of that category is assigned a value of 1, and the values of other positions are 0. In this embodiment, Var is a categorical variable with n possible values. For the category value c i ∈c, its One-Hot coding vector v i ∈{0,1} n has the i-th component as 1, and other components as 0, that is:

[0087] v i =[0,0,…,1,…,0];

[0088] In the formula, 1 appears in the i-th position, indicating the existence of this category.

[0089] Step A3: Construct a graph neural network structure based on a dual-task GNN model, where the dual-task GNN model is respectively used to predict the scalar field value of nodes and to classify the lithology categories of nodes.

[0090] Specifically, the dual-task GNN model includes a scalar field GNN model for predicting the scalar field value of nodes and a lithology category GNN model for classifying the lithology categories of nodes.

[0091] The scalar field GNN model generates scalar field prediction values for each graph node based on scalar field sampling point data (stratigraphic boundary scalar field value points S i 、stratigraphic attitude points A i 、fault feature coding F i etc.) as input for subsequent stratigraphic interface extraction.

[0092] The lithology category GNN model uses the prediction result from the scalar field GNN model: the scalar field prediction value as input to classify the lithology categories of nodes.

[0093] Both the scalar field GNN model and the lithology category GNN model include three-layer stacked graph attention network modules.

[0094] The scalar field GNN model includes an input layer, three-layer stacked graph attention network modules, a PReLU activation function, a linear layer, and an output layer, and the scalar field prediction value is output by the output layer.

[0095] The lithology category GNN model includes an input layer, three-layer stacked graph attention network modules, a PReLU activation function, a linear layer, and a Softmax classification layer.

[0096] Step A4: Input the preprocessed graph structure data into the graph neural network structure, and generate scalar field prediction values and the classified node lithology categories by the graph neural network structure.

[0097] Input the graph structure data into the graph neural network structure, including node attributes (coordinates, fault codes, attitude vectors, lithology categories, formation scalar values) and edge connection relationships.

[0098] After receiving the preprocessed graph structure data, the processing procedures of the scalar field GNN model and the lithology category GNN model incorporated in the graph neural network structure include the following steps:

[0099] Step B1, take the node coordinate features, fault code features and edge connection relationships as the feature inputs of the scalar field GNN model, embed the input features into high-dimensional vectors through a three-layer stacked graph attention network module, perform non-linear transformation through the PReLU activation function, and use a linear layer to reduce the dimensions of the features. Construct a joint loss function through the scalar field loss function and the attitude vector loss function, and adjust the network parameters iteratively in the backpropagation process in combination with the GradNorm loss weight adjustment strategy to output the scalar field prediction value of each node.

[0100] Step B2, splice the scalar field prediction value with the node coordinate features to obtain a feature matrix, take the spliced feature matrix and the edge connection matrix as the inputs of the lithology category GNN model, embed the input features into high-dimensional feature vectors through a three-layer stacked graph attention network module, use a linear layer to reduce the dimension to the number of lithology categories, use the Softmax function to take the lithology category with the highest predicted probability as the predicted lithology formation category of the current node, and use the formation category label loss function based on the cross-entropy loss function to iteratively update the network parameters. After the lithology category GNN model converges, output the predicted lithology category of each node.

[0101] Specifically, after inputting the preprocessed graph structure data, each layer of the neural network calculates the convolution operation of its neighborhood at each node v i to generate a new node embedding. The node v i embedding high-dimensional feature h i is initialized as the node feature x i and used as the input of the first layer of the network. In this way, the graph neural network can gradually update the node embeddings to better capture the spatial relationships and graph structure information between nodes.

[0102] Such as Figure 5As shown in the figure, in view of the particularity of geological modeling, the GAT belonging to the spatial domain convolution is selected as the method for node embedding and representation in the present invention. The spatial domain convolution directly performs convolution between the nodes of the graph, and uses the connection relationship between the nodes to perform weighted fusion on the features of each node neighbor. In the present invention, a neighbor aggregation strategy based on the self-attention mechanism is used.

[0103] Specifically, for node v i and its neighbor node v j , calculate the attention coefficient α ij , which reflects the importance of node v j to the information transfer of node v i . The calculation formula is as follows:

[0104] ;

[0105] In the formula, a is the learned attention parameter, || represents the concatenation operation of feature vectors, W is the weight matrix, h i and h j are the high-dimensional feature representations of node v i and node v j respectively.

[0106] For complex graph learning tasks, a multi-head attention mechanism is introduced. The embedding of each node is calculated through multiple attention heads. Each attention head independently aggregates the features of its neighbors and learns through different weight matrices. The final node representation is the concatenation or average of the outputs of all heads. When there are K attention heads, the output of the multi-head attention is:

[0107] ;

[0108] In the formula, the output of the k-th self-attention head, through the formula:

[0109] ;

[0110] Each self-attention head independently learns a set of attention coefficients and the weight matrix W k .

[0111] In this embodiment, according to the type of network prediction (such as continuous variables, discrete classes) and learning objectives, and based on the different characteristics of the regression and classification tasks of the scalar field GNN model and the lithology class GNN model and the data input situation, different loss functions are designed specifically.

[0112] For the scalar field GNN model, a scalar field loss function for formation interface sampling points, a scalar field loss function for lithology unit sampling points, and an attitude vector loss function are established as follows:

[0113] Scalar field loss function for formation interface sampling points:

[0114] The predicted value of the scalar field is generated by each graph node v of the scalar field GNN module and is constrained by the interface data points in the formation and tectonic directions (dip angle, dip direction). Represented in three-dimensional space as a scalar function f(p), where f represents the burial depth value of the formation relative to a certain formation surface at the position of point p in three-dimensional space (in this invention, the latest modeled geological surface is selected as the reference surface). For a series of H formation interfaces in space, it can be expressed as:

[0115] ;

[0116] where f1 and f H are the scalar field values of the oldest and latest formations respectively.

[0117] During the geological structure modeling process, by extracting the scalar field isosurfaces of two adjacent formations and using the adjacent isosurfaces as constraints, different formation models can be obtained.

[0118] In a given formation surface I sampled under the constraint of the scalar field f v , the subset of graph nodes v can be expressed by the following formula:

[0119] I = {v ∈ V | s v = f v}

[0120] The difference between the scalar field value s v at the formation interface sampling point and the scalar field value predicted by the network can be measured by the loss function L interface :

[0121] ;

[0122] Scalar field loss function for lithology unit sampling points:

[0123] The lithology unit sampling points are sampled in the formation between two formation interfaces, and the scalar field value of the lithology unit sampling points should also be between the scalar field values of the two formation interfaces. In this invention, R(L v ) is a function that depends on the lithology label L v :

[0124] R(L v ) = [a v , b v ​

[0125] wherein, a v is the minimum scalar field value corresponding to the lithology label L v , a v =R(L v ) min , and b v is the maximum scalar field value corresponding to the lithology label L v , b v =R(L v ) max . For the scalar field loss function at a sampling point of a certain lithology unit, it can be defined as:

[0126] ;

[0127] wherein, is the scalar value of the node with the true lithology label predicted by the current network. For the node with the lithology label L v , the maximum value of its scalar value is R(L v ) max , and the minimum value is R(L v ) min . The correct scalar value should be between the two ranges. When >R(L v ) max or <R(L v ) min , it indicates that there is a deviation between the scalar field value predicted by the current network and the range of the true field value. Then, the absolute value of the deviation is used as the loss value L litho of the sampling point of the current lithology unit.

[0128] For all sampling point sets of lithology units in the whole graph, the final total loss function L sum_litho can be expressed as:

[0129] ;

[0130] Attitude vector loss function:

[0131] Nodes containing attitude data can be obtained from the geological map, representing the true change of the surface near this point. To measure the angular error between the sampling point and the predicted node, it is necessary to estimate the gradient of the predicted scalar field on these map nodes. In the present invention, by performing a first-order Taylor series approximation on the scalar field value within the first-order neighborhood range of the node where the gradient is to be obtained, the directional derivative of the predicted scalar field is obtained for least squares fitting, as shown in the following formula:

[0132] ;

[0133] wherein, is the estimated gradient of the scalar field at node v, matrix P v and S v are given by:

[0134] ;

[0135] ;

[0136] where, , , are the normalized spatial coordinates of the fixed nodes, and the estimated angle between the predicted scalar field gradient and the known direction vector α v at node v is:

[0137] ;

[0138] This angle is used to measure the angular error of the predicted angle and the observed angle (true angle) constraint . For a given angle constraint , the loss function is:

[0139] ;

[0140] However, for normal data , its loss function is:

[0141] ;

[0142] For tangent data , its loss function is:

[0143] ;

[0144] During the training process of the scalar field GNN model, both L interface and L orientation are used as loss functions. According to the learning objectives, different weights are given to the loss functions. Different loss functions may have inconsistent units and numerical ranges, resulting in unbalanced gradient updates. The present invention introduces the idea of GradNorm (Gradient Normalization) to optimize the training process. It adaptively adjusts the weights of the loss functions of each task, thereby ensuring that the gradients of each task have a similar scale during the training process, and then improving the stability and efficiency of the training.

[0145] For the lithology category GNN model, a formation category label loss function is established as follows:

[0146] In the practice of modeling, the data of geological boundary sampling points is relatively scarce. To make full use of the data of geological maps, the sampling points of lithologic units are incorporated into the modeling data in the form of a formation category loss function.

[0147] Establish a measured data set R of lithologic units, which contains N class possible lithologic categories related to a subset of graph nodes. Each measured data point of a lithologic unit is assigned a one-hot encoded vector label v , indicating the class to which it belongs. A one-hot encoded vector is a vector in which all components are 0 except for one given component with a value of 1.

[0148] For a data set with category N class = 3, the one-hot encoded vectors for the corresponding categories a, b, and c are respectively:

[0149] ;

[0150] ;

[0151] ;

[0152] The loss function used for one-hot encoding is the cross-entropy loss function L rockunit :

[0153] ;

[0154] In the formula, is the probability value of predicting a certain category obtained from the following formula. The calculation formula of

[0155] ;

[0156] In the formula, is the predicted value of the lithologic category corresponding to the i-th element of the vector . The Softmax function is commonly used in the field of machine learning to normalize the network output into a probability distribution over N class categories.

[0157] Step A5: Based on the scalar field prediction value, extract an isosurface therefrom through the tetrahedron algorithm as the formation interface, classify the tetrahedral elements through the node lithology label, merge the tetrahedral elements of the same lithologic category, generate a closed three-dimensional entity, and use different lithologic categories as different formation entity models.

[0158] An example of modeling is as Figure 5 shown, Figure 5It is a planar geological map of the modeling area. The strata exposed in the area from old to new are the Xiaomuping Formation (Pt x ) and the Madiyi Formation (Pt m ) of the Banxi Group, the Tongtawan Formation (Pt t ), the Cretaceous System (K) and the Quaternary System (Q). According to the thickness ranges of each stratum in the comprehensive stratigraphic columnar section, the burial depth values of each geological interface relative to the top surface of the Quaternary System were determined, and these relative burial depth values were used as the field values for the stratum boundary node attributes.

[0159] The planar geological map and the sectional geological map were triangulated, and combined with the determined spatial range, tetrahedral meshed map data was generated, as Figure 6 shown.

[0160] As Figure 7 shown in (a), the new fault F1 runs through the whole area and cuts off the old fault F2, dividing the area into three parts. Figure 7 In (b), the area is divided into two regions of 1 and 0 according to the uplift and subsidence of the fault. P1, P2, and P3 are three points at different positions in the area, and F is the coded fault feature. For example, it represents that the fault feature code of the F1 fault at point P2 is 1. In Figure 7 (c), since the old fault is cut by the new fault, the right side of the F2 fault is the 1 region, and other regions are the 0 region. The fault code of point P2 is , Figure 7 In (d), the coded features of the intersecting faults are fused, so F2 = [1,0] represents that the final fault feature code of point P2 is [1,0].

[0161] After preparing the map data for modeling, the model was trained according to the following model parameters. The network depth of the model was set to 3 layers. A shallower network depth helps to avoid overfitting and reduce the problem of gradient disappearance at the same time.

[0162] The initial learning rate was set to 0.01. During the training process, the learning rate adaptive decay strategy was used. If the loss function decrease value was less than 0.01 every 10 epochs, the learning rate was decayed by 50%. The PReLU (Parametric ReLU) activation function was selected. The embedding dimension was selected as 128, and the number of attention heads was set to 2. Then, the scalar field GNN model and the lithology category GNN model were trained respectively to predict the scalar field values and lithology categories of the nodes.

[0163] After the training was completed, based on the above-generated scalar field GNN model and lithology category GNN model, the stratum interface and the stratum entity model were extracted. For the scalar field, the marching tetrahedron algorithm was used to extract different isosurfaces as the stratum interface, and different lithology categories were directly extracted as different stratum entity models. The method of the present invention constructs asFigure 8 The three-dimensional stratigraphic scalar field model with fault effect shown, such as Figure 9 the three-dimensional lithology category model with fault effect shown, and such as Figure 10 the three-dimensional stratigraphic model with fault effect shown.

[0164] Compared with the traditional graph neural network that only uses virtual borehole data as input, the present invention innovatively uses the entire geological map as input data. While maintaining the internal topological relationship of the stratigraphic entities, this method significantly enriches the sampling point set of lithology units, thus more comprehensively reflecting the geological characteristics. During the tetrahedral meshing process, the present invention introduces the digital elevation model (DEM) surface as the upper boundary surface constraint of the graph structure, considering the influence of the DEM topological relationship on the model, so that not only the surface characteristics of the strata are retained during the meshing process, but also the local geological topological information can be reflected, thereby enhancing the model's ability to capture local changes and details.

[0165] In addition, the present invention proposes a fault coding method, through which the influence of faults on the stratigraphic scalar field can be automatically identified and simulated, especially the discontinuous jump phenomenon of the scalar field at the fault position, avoiding the problem of manually setting fault displacement parameters in the traditional method, and enabling the accurate simulation of fault effects without relying on manual intervention.

[0166] Based on the graph neural network, the present invention also constructs a scalar field GNN model and a lithology category GNN model stacked based on three-layer stacked graph attention network modules (GAT), and introduces self-attention mechanism and multi-head attention mechanism respectively, which can dynamically adjust the weight difference according to the importance of each node, thereby enhancing the model's expression ability in complex geological environments. At the same time, the appropriate GNN model can be selected according to different data types, such as continuous or discrete, expanding the applicability of the modeling data. In terms of multi-task learning, the present invention constructs a multi-task loss function including scalar field, attitude vector, stratigraphic category, etc., and introduces the GradNorm algorithm to automatically adjust the weights of different loss functions during training to achieve adaptive loss balance. This mechanism avoids the cumbersome process of manually setting loss weights in the traditional method and significantly improves the learning performance and stability of the model.

[0167] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments of equivalent changes within the scope of the technical solution of the present invention by using the above-disclosed technical content. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A graph neural network three-dimensional geological structure modeling method, characterized in that: The steps include: Step A1: obtaining a three-dimensional geological map data set based on three-dimensional geological map preprocessing, and extracting scalar field attribute sampling points and lithology unit sampling points based on the three-dimensional geological map data set; Step A2: tetrahedroning the point data of the obtained scalar field attribute sampling points and lithology unit sampling points, and generating graph structure data with the tetrahedroning results; In step A2, the graph structure data is represented as: G = (V, E); In the formula, G represents graph structure data, G is an undirected graph, V is a node set, including all nodes, V={v1,v2,...,v n }, where each node v i Corresponding to a node in the graph, v i ∈V, i=1,2,…,n; E is a set of edges, which represents the connection relationship between nodes. E={(i,j), i,j∈V}, (i,j) represents the edge between node i and node j; Each node v i They all have input features and input attributes. The input features of nodes include node coordinate features and fault coding features. The input attributes of nodes include scalar field attributes, occurrence attributes, and lithology labels. For the i-th node in the graph structure data, i=1,2,…, all have input features and input attributes, and their original input features and input attributes are expressed as follows: Feature i ={C i ,F i ,S i ,A i ,L i }; In the formula, C i represents the coordinate information of the i-th node, and C i ∈R n , R n is an n-dimensional geometric space, F i represents the fault coding feature of the i-th node, and F i ∈{1,2,…,K f }, K f is the number of faults, S i represents the scalar field property of the ith node, and S i ∈R p , R p is a p-dimensional attribute space, A i represents the occurrence attribute of the i-th node, and A i ∈R q , R q is a q-dimensional attribute space, L i represents the lithology label of the i-th node, and L i ∈{1,2,…,K l }, K l is the number of lithology; Step A3: constructing a graph neural network structure based on a dual-task GNN model, wherein the dual-task GNN model is used to predict the scalar field value of the node and to classify the lithology category of the node; Step A4: inputting the preprocessed graph structure data into the graph neural network structure, and generating the scalar field prediction value and the node lithology category obtained by the division by the graph neural network structure; Step A5: Based on the predicted value of the scalar field, isosurfaces are extracted from it by the tetrahedron algorithm as the stratigraphic interface, the tetrahedron units are classified by the node lithology labels, the tetrahedron units of the same lithology category are merged to generate a closed three-dimensional entity, and different stratigraphic entity models are obtained based on different lithology categories.

2. A graph neural network three-dimensional geological structure modeling method according to claim 1, characterized in that: The three-dimensional geological map includes a plan geological map, an exploration line profile map and a mid-section plan map.

3. A graph neural network three-dimensional geological structure modeling method according to claim 1, characterized in that: For node v i and fault F k , k=1,2,…, the expression of its fault coding characteristics is as follows: ； In the formula, when the node v i Located on fault F k When the upper wall of , when node v i Located on fault F k When the footwall is .

4. A graph neural network three-dimensional geological structure modeling method according to claim 3, characterized in that: When node v i When affected by k cross faults, the final fault coding feature F i for: ； In the formula, For node v i The encoding value on the kth fault indicates the position and relative relationship of the node on different faults.

5. The method for three-dimensional geological structure modeling using a graph neural network according to claim 1, characterized in that: The graph structure data is divided into continuous data and discrete data. In step A4, the preprocessing operation performed on the graph structure data includes preprocessing the continuous data by range normalization and encoding the discrete data by One-Hot encoding.

6. A graph neural network three-dimensional geological structure modeling method according to claim 1, characterized in that: The dual-task GNN model includes a scalar field GNN model for predicting the scalar field value of a node and a lithology category GNN model for classifying the lithology category of the node. Both the scalar field GNN model and the lithology category GNN model are equipped with a three-layer stacked graph attention network module.

7. A graph neural network three-dimensional geological structure modeling method according to claim 6, characterized in that: In step A4, the steps of generating scalar field prediction values ​​and node lithology categories obtained by the graph neural network structure are as follows: Step B1, taking the node coordinate features, fault coding features and edge connection relationships as feature inputs of the scalar field GNN model, and outputting the scalar field prediction value of each node through the scalar field GNN model equipped with a three-layer stacked graph attention network module; In step B2, the scalar field prediction value is concatenated with the node coordinate feature to obtain a feature matrix, and the concatenated feature matrix and edge connection matrix are used as the input of the lithology category GNN model. The lithology category GNN model equipped with a three-layer stacked graph attention network module outputs the predicted lithology category of each node.

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