A method for detecting and repairing anomalies in geology survey drilling data

Abstract

The present application relates to geological exploration data processing and three-dimensional geological modeling technical field, disclose a kind of abnormal detection and repair method of geology and mineral exploration drilling data, the method first constructs unstructured three-dimensional Delaunay tetrahedron grid, establishes spatial topology;Using linear unit theory analysis tetrahedron unit internal attribute variation rate, calculate original discrete gradient vector;Based on the curvature of drilling trajectory constructs the geological confidence field reflecting positioning accuracy;By minimizing the component of rotation to optimize gradient field, output the modified gradient field in line with physical conservation;Further calculate local structure tensor, identify stratum direction by eigenvalue decomposition and construct anisotropic diffusion tensor;Finally, establish the anisotropic Poisson equation containing diffusion tensor and the divergence of modified gradient field, solve the equation using confidence screening boundary condition.The present application can effectively remove outlier noise, and maintain stratum bedding structure in repair process, improve geology and mineral data reconstruction accuracy.

Description

Technical Field

[0001] This invention relates to the field of geological exploration data processing and three-dimensional geological modeling technology, specifically a method for anomaly detection and repair of borehole data in geological exploration. Background Technology

[0002] In geological exploration and resource assessment, borehole data is the most direct and crucial source of information for obtaining subsurface geological attributes. Constructing a continuous three-dimensional geological attribute field by interpolating and reconstructing discrete borehole sampling points forms the basis for subsequent reserve calculations, mining planning, and geological structure analysis. However, due to the complexity of the geological environment and engineering limitations of sampling operations, raw borehole data often exhibits sparse spatial distribution, non-uniformity, and accompanying measurement noise, which places extremely high demands on the accuracy of data reconstruction.

[0003] Existing geological data reconstruction methods mostly employ interpolation algorithms based on regular voxel grids, such as inverse distance weighted interpolation or ordinary kriging interpolation. These methods typically require mapping the non-uniformly distributed raw borehole data onto regular grid nodes before processing. Since borehole trajectories are arbitrarily oriented curves in three-dimensional space, the coordinates of their sampling points rarely coincide with regular grid nodes. This forced geometric mapping introduces a significant spatial quantization error. When the grid resolution is insufficient, multiple raw sampling points are merged into the same voxel, leading to the loss of high-precision local fine features; conversely, increasing the grid resolution results in an exponential increase in computational and storage costs, making it difficult to balance accuracy and efficiency.

[0004] Furthermore, raw borehole data inevitably becomes contaminated with non-physical noise during acquisition and transmission. Traditional denoising or smoothing algorithms are mostly based on statistical principles, such as local mean filtering or median filtering. These methods only process scalar attributes at the numerical level, often ignoring the inherent conservation laws that geological attribute fields, as physical fields, should follow. For example, relying solely on statistical laws to smooth data may incorrectly smooth out effective high-frequency signals reflecting geological abrupt changes (such as faults or vein boundaries), or fail to identify outliers that violate physical gradients. This results in the reconstructed attribute field being discontinuous in gradient changes or failing to meet integrability conditions, thus failing to accurately reflect the underground physical state.

[0005] In stratigraphic reconstruction, subsurface media typically exhibit significant anisotropy, meaning that attribute values ​​change slowly along sedimentary bedding directions but drastically along stratigraphic normals. Traditional interpolation reconstruction algorithms often assume that the spatial variability function is isotropic or can only set globally uniform anisotropic parameters. When dealing with complex structures such as folds and bends, this globally set method cannot adapt to the dynamic changes in local bedding directions. This results in overly vague attribute transitions across stratigraphic boundaries in the reconstruction results, while unnatural step effects easily occur along bedding directions, making it impossible to clearly and accurately reconstruct the bedding structure and boundary morphology of complex geological bodies. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for anomaly detection and repair of borehole data in geological and mineral exploration. It aims to solve the problems in existing technologies when reconstructing geological and mineral data, such as loss of original data spatial accuracy due to the use of regular voxel grid mapping, inability to effectively distinguish between non-physical noise and geological abrupt changes due to the lack of physical field conservation constraints, and step effect and stratification ambiguity in the reconstruction results due to the inability to adapt to local stratigraphic changes.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for anomaly detection and repair of geological exploration borehole data, comprising the following steps:

[0008] S1. Obtain the original borehole exploration data set containing three-dimensional spatial coordinates and geological attribute information, directly construct an unstructured three-dimensional Delaunay tetrahedral mesh with the original data points as vertices, and establish the spatial topological connection relationship between the data points.

[0009] S2. Based on the linear element theory, analyze the rate of change of the internal attribute values ​​of each element in the tetrahedral mesh relative to the spatial coordinates, and calculate the original discrete gradient vector of the entire field.

[0010] S3. Quantitatively characterize the geometric shape of the borehole trajectory, calculate the geometric curvature at each sampling point, and construct a geological confidence field;

[0011] S4. Using the geological confidence field as weights, the original discrete gradient vector is weighted and constrained. By minimizing the curl component of the gradient field, a corrected gradient field that conforms to the laws of physical conservation is output.

[0012] S5. Perform second-order statistical integration on the modified gradient field to calculate the local structure tensor, and construct the anisotropic diffusion tensor through eigenvalue decomposition.

[0013] S6. Establish a partial differential equation containing anisotropic diffusion tensor and corrected gradient field divergence within a tetrahedral grid domain. Use the geological confidence field to select high confidence points as boundary conditions, and solve the partial differential equation to obtain the repaired geological and mineral data scalar field.

[0014] Preferably, the construction of the unstructured three-dimensional Delaunay tetrahedral mesh follows the empty circumsphere criterion: that is, for any tetrahedral element in the mesh, its corresponding circumsphere does not contain any other vertices in the original borehole exploration data set, thereby ensuring that all original sampling points are mesh nodes and ensuring that the mesh geometry meets the stability requirements of numerical calculation.

[0015] Preferably, the calculation process of the original discrete gradient vector is as follows: select one vertex of the tetrahedral element as a reference node, and use vector subtraction and scalar subtraction operations to calculate the spatial position difference and attribute value difference of the other three vertices relative to the reference node; construct a system of linear equations describing the relationship between attribute differences and coordinate differences between vertices based on the principle of linear interpolation, and use the product of the inverse matrix of the geometric shape matrix and the attribute difference vector to solve the constant gradient vector inside the tetrahedral element.

[0016] Preferably, the geological confidence field is constructed as follows: using the principle of discrete differential geometry, the current sampling point and its adjacent sampling points are selected to form a local triangular element. The reciprocal of the radius of the circumcircle of the triangular element is calculated using the local geometric curvature calculation formula to obtain the discrete local geometric curvature. A nonlinear decay function is used to establish the mapping relationship between curvature and confidence. Sampling points with high curvature are assigned lower confidence weights, and sampling points with low curvature are assigned higher confidence weights to generate a spatial confidence scalar field.

[0017] Preferably, in the anomaly detection and optimization step, a discrete curl operator is constructed on the unstructured mesh to determine the curl components of the gradient field. Specifically, a loop integration method along the mesh edge is used to construct a closed loop connecting the body centers of all tetrahedral elements sharing the same edge; the tangential integral of the gradient vector along this closed loop is calculated using the discrete curl operator formula, and the integral result is normalized to the circulation density of the dual face around the edge to obtain the discrete curl value at that edge.

[0018] Preferably, the modified gradient field is obtained by solving for the global minimum point of the energy functional. The energy functional consists of a curl constraint term and a data fidelity term; wherein, the curl constraint term uses geological confidence weights to weight the square of the modulus of the discrete curl values, constraining the curl to approach zero in the high confidence region; the data fidelity term constrains the modified gradient field to not deviate from the original discrete gradient vector; the energy functional minimization problem is transformed into a large sparse linear equation system for solution through variational derivation.

[0019] Preferably, the calculation and feature decomposition process of the local structure tensor includes: performing an outer product operation on the modified gradient vector in the spatial neighborhood of the tetrahedral cell to obtain the gradient projection matrix; introducing spatial weighting coefficients based on Gaussian function distribution to perform discrete convolution summation to generate the local structure tensor; analyzing the feature system of the structure tensor to extract the principal feature vector indicating the direction of the formation normal and the secondary feature vector indicating the direction of the formation extension surface.

[0020] Preferably, the construction of the anisotropic diffusion tensor follows the principle of smoothing along bedding planes and blocking across bedding planes: based on the principle of spectral decomposition and reconstruction, the tensor is recombined using eigenvectors as local orthogonal bases; a large diffusion coefficient is assigned to eigenvectors indicating the direction of the stratigraphic extension plane, and a minimum diffusion coefficient is assigned to eigenvectors indicating the direction of the stratigraphic normal, wherein the minimum diffusion coefficient is set as a monotonically decreasing function of the principal eigenvalues ​​of the structure tensor or a threshold-based cutoff constant.

[0021] Preferably, the partial differential equation is an anisotropic Poisson equation. The diffusion term on the left-hand side of the equation is formed by the effect of the anisotropic diffusion tensor on the gradient of the scalar field to be solved, introducing directional constraints from the structure tensor; the source term on the right-hand side of the equation is formed by the divergence distribution of the modified gradient field, driving the reconstructed field to approximate the modified gradient field.

[0022] Preferably, the solution process of the partial differential equation includes: selecting points with confidence values ​​greater than a threshold as anchor points based on the geological confidence field, and selecting points with confidence values ​​less than a threshold as points to be repaired; using the Dirichlet boundary condition formula to forcibly constrain the original attribute values ​​of the anchor points to the boundary of the equation solution domain; discretizing the partial differential equation using the finite element method, and calculating the solution vector through a sparse matrix iterative solver.

[0023] This invention provides a method for anomaly detection and repair in geological exploration borehole data. It has the following beneficial effects:

[0024] 1. This invention uses unstructured Delaunay tetrahedral meshes to directly construct spatial topology for discrete borehole data, avoiding spatial quantization errors and data smoothing distortions introduced by traditional regular voxel interpolation methods. By strictly following the empty circumscribed criterion to generate the mesh, it ensures that all original sampling points directly participate in the calculation as computing nodes, maintaining the stability of numerical calculations while preserving the spatial position accuracy and fine geometric features of the original borehole data to the greatest extent.

[0025] 2. This invention introduces a gradient field optimization mechanism based on the law of physical conservation. It uses the geological confidence field constructed by the curvature of the borehole trajectory as a constraint weight. By minimizing the curl component of the gradient field, the original data is corrected. It can distinguish the natural changes of geological properties from non-physical noise from the essence of the physical field. While automatically identifying and repairing abnormal sampling data, it forces the corrected gradient field to satisfy the conservative field property, ensuring the physical integrability of the subsequent scalar field reconstruction.

[0026] 3. This invention utilizes gradient structure tensors to extract stratigraphic bedding features and constructs an anisotropic diffusion model. Data reconstruction is achieved by solving the Poisson equation containing the anisotropic diffusion tensor. This mechanism dynamically adjusts the diffusion coefficient based on the feature decomposition results, realizing smooth diffusion of attribute values ​​along the geological bedding extension direction and barrier preservation across the stratigraphic normal direction. This effectively suppresses the step effect and interface blurring problems commonly found in complex geological modeling, and improves the clarity of stratigraphic boundary reconstruction. Attached Figure Description

[0027] Figure 1 This is a system framework diagram of the present invention;

[0028] Figure 2 This is a schematic diagram of the method flow of the present invention.

[0029] The modules are as follows: 101. Topology construction module; 102. Gradient field calculation module; 103. Confidence assessment module; 104. Anomaly detection and optimization module; 105. Anisotropic modeling module; 106. Reconstruction solution module. Detailed Implementation

[0030] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] See attached document Figure 1 The present invention provides an anomaly detection and repair system for borehole data in geological exploration. The system may include: a topology construction module 101, a gradient field calculation module 102, a confidence assessment module 103, an anomaly detection and optimization module 104, an anisotropic modeling module 105, and a reconstruction solution module 106.

[0032] Topology building module 101 is used to acquire the original borehole exploration data set. This set contains discrete three-dimensional spatial coordinates and corresponding geological attribute values. Topology building module 101 is configured to use the original data points as vertices to construct an unstructured three-dimensional Delaunay tetrahedral mesh, establishing spatial topological connections between data points to preserve the spatial distribution characteristics of the original sampling.

[0033] The gradient field calculation module 102, connected to the topology construction module 101, is used to calculate the discrete gradient vector inside each tetrahedral cell based on the generated tetrahedral mesh. The gradient field calculation module 102 transforms the discrete scalar attribute field into the original gradient vector field on the unstructured mesh by analyzing the attribute difference relationship between the tetrahedral vertices.

[0034] The confidence assessment module 103 is used to analyze the geometry of the borehole trajectory. The confidence assessment module 103 calculates the geometric curvature at each sampling point, quantifies the accuracy of spatial positioning based on the magnitude of the curvature, and constructs a geological confidence field accordingly. This confidence field is used to distinguish between geological abrupt changes and geometric positioning errors in subsequent processing.

[0035] An anomaly detection and optimization module 104 is connected to the gradient field calculation module 102 and the confidence evaluation module 103. The anomaly detection and optimization module 104 combines conservative field theory with the confidence field output by the confidence evaluation module 103 as weights to construct an energy functional containing curl constraint terms. By optimizing this energy functional, non-physical noise in the original gradient vector field is corrected, and a corrected gradient field is output.

[0036] Anisotropic modeling module 105, connected to anomaly detection and optimization module 104, is used to characterize the anisotropic features of the geological medium. Anisotropic modeling module 105 calculates the local structure tensor based on the modified gradient field, identifies the stratigraphic normal direction and extension direction through eigenvalue decomposition of the structure tensor, and constructs anisotropic diffusion tensor.

[0037] The reconstruction solution module 106, connected to the anisotropic modeling module 105, is used for the final reconstruction of the data. The reconstruction solution module 106 constructs anisotropic Poisson equations that include diffusion tensors and modified gradient fields, and uses high-confidence original data points as boundary conditions to obtain the repaired scalar field of geological and mineral data by solving a sparse linear system.

[0038] See attached document Figure 2 This invention provides a method for anomaly detection and repair of borehole data in geological exploration, comprising the following steps:

[0039] S1. Spatial topology construction based on Delaunay tetrahedral meshing: Read the original discrete borehole data containing coordinates and attribute values, abandon regular voxelization, and directly generate tetrahedral meshes with data points as nodes.

[0040] S2. Calculation of unstructured discrete gradient field: Establish a system of linear equations within the tetrahedral element, solve for the rate of change of attribute values ​​relative to spatial coordinates, and obtain the original discrete gradient vector of the entire field.

[0041] S3. Construction of geological confidence field based on trajectory curvature: Calculate the geometric curvature of borehole trajectory at each data point, and generate spatial confidence scalar field using mapping relationship;

[0042] S4. Anomaly detection and optimization of discrete gradient fields: Taking the minimization of the curl of the gradient field as the physical constraint, the gradient field is weighted and corrected by combining the confidence scalar field to remove noise components that do not satisfy the conservative field properties, and the corrected gradient field is obtained.

[0043] S5. Geological anisotropy modeling based on gradient structure tensor: The structure tensor is calculated using a modified gradient field, the main characteristic directions of geological bedding are extracted, and an anisotropic diffusion tensor is constructed accordingly.

[0044] S6. Anisotropic Poisson reconstruction: Establish a partial differential equation in divergence form, which includes the divergence of the diffusion tensor and the corrected gradient field. Solve the equation in combination with boundary conditions and output the anomaly repair data.

[0045] The above steps will be described in detail below with reference to specific embodiments and accompanying drawings.

[0046] The topology building module 101 performs spatial topology building based on Delaunay tetrahedral partitioning. Step S1 aims to establish an unstructured three-dimensional discrete spatial model to solve the accuracy loss problem caused by traditional regular mesh interpolation.

[0047] The topology construction module 101 first acquires the original borehole exploration data set, which consists of discrete sampling points. Each sampling point contains three-dimensional spatial location information and corresponding geological attribute information. For ease of mathematical processing, the input original borehole exploration data set is defined as a discrete point set formula:

[0048] ;

[0049] in, This represents the original set of borehole exploration data; This indicates the total number of sampling points in the dataset; Indicates the index of the sampling point; Indicates the first The three-dimensional spatial coordinate vector of each sampling point is usually represented as: ; Indicates the first Each sampling point corresponds to a geological attribute scalar value, which can be mineral grade, rock density, or apparent resistivity, depending on the actual exploration needs.

[0050] Topology building module 101 reads the above discrete point set Subsequently, instead of resampling or voxelizing the regular mesh, each spatial coordinate in the set is directly mapped. As a vertex of the mesh, a 3D spatial mesh structure is constructed using the Delaunay tetrahedral partitioning algorithm. The output of this process is the tetrahedral set formula:

[0051] ;

[0052] in, This represents the generated set of unstructured tetrahedral meshes; This represents the total number of tetrahedral elements in the set; Indicates the first Each tetrahedral element consists of a discrete set of points. It consists of four non-coplanar vertices.

[0053] In generating tetrahedral sets During the process, topology building module 101 strictly follows the empty circumsphere criterion. For sets Any tetrahedral unit in Its corresponding circumsphere does not contain a set of discrete points. Any other vertex in the grid. This criterion ensures that the generated mesh is geometrically optimal, avoiding the generation of elongated tetrahedrons, thus guaranteeing the numerical stability of subsequent gradient calculations.

[0054] In the above manner, the unstructured mesh constructed by the topology building module 101 ensures that all original sampling points are protected. All nodes are grid nodes, and the positions of the data points are not shifted or interpolated smoothly. This processing method not only preserves the full spatial accuracy of the original data, but also establishes spatial topological adjacency relationships between data points, providing a precise geometric basis for the subsequent differential operations performed by the gradient field calculation module 102 in discrete space. The specific algorithm implementation logic for the Delaunay tetrahedral subdivision is well-known in this field and will not be elaborated here.

[0055] After the topology construction module 101 completes the construction of the three-dimensional spatial partitioning structure, the gradient field calculation module 102 executes step S2, which is the calculation step of the unstructured discrete gradient field. This step aims to transform the discretely distributed scalar attribute data into vector field data with physical meaning, thereby capturing the changing trends and directional characteristics of geological attributes in three-dimensional space, and providing a data foundation for subsequent gradient domain-based anomaly detection.

[0056] The gradient field calculation module 102 is based on the linear element theory in finite element analysis, and calculates the tetrahedral set generated in step S1. Each tetrahedral element in the set is analyzed independently. For any tetrahedral element in the set... Assuming its internal geological properties It exhibits a linear transformation relative to spatial coordinates (x, y, z). Based on this linear assumption, the gradient vector inside the tetrahedral element... This is a constant vector. To solve for this constant vector, the gradient field calculation module 102 selects tetrahedral elements. Given four vertices, one of which is designated as a reference node. Vector subtraction and scalar subtraction are used to calculate the spatial position difference and attribute value difference of the other three vertices relative to the reference node.

[0057] Define tetrahedral elements The four vertex indices are 0, 1, 2, and 3, and their corresponding spatial coordinate vectors are respectively , , , The corresponding attribute value is , , , The gradient field calculation module 102, based on the principle of linear interpolation, establishes a system of linear equations describing the relationship between attribute differences and coordinate differences between vertices:

[0058] ;

[0059] in, The geometric shape matrix representing a tetrahedral element is a... The matrix is ​​composed of edge vectors pointing from the reference vertex to the other three vertices, specifically in the form of... ; This represents the constant gradient vector inside the tetrahedral element to be solved, containing the gradient of that element in... Partial derivative components in three directions; Represents the attribute difference vector, which is a The column vector is obtained by subtracting the attribute value of the reference vertex from the attribute values ​​of the other three vertices, specifically in the form of: .

[0060] Because the Delaunay partitioning algorithm was used in step S1 and the empty circumsphere criterion was followed, the generated tetrahedral elements... All are non-degenerate units, which guarantees the geometric shape matrix. It is neither singular nor reversible.

[0061] The gradient field calculation module 102 solves the above linear equation system formulas, that is, it calculates... Alternatively, Gaussian elimination can be used to obtain the unique gradient vector within the tetrahedral element. .

[0062] Gradient field calculation module 102 traverses the tetrahedron set Repeat the above calculation process for all elements in the dataset to ultimately generate the original discrete gradient field covering the entire exploration area. For clarity, this output result is defined as the original gradient field set formula:

[0063] ;

[0064] in, This represents the original unstructured discrete gradient field obtained from the full-field calculation; Corresponding to the Gradient vectors of tetrahedral elements; This represents the total number of tetrahedral elements. This is the original discrete gradient field. This directly reflects the local rate of change of the original borehole data in three-dimensional space, and also includes gradient anomaly information caused by sampling errors or geological abrupt changes. This information will be further identified and processed in subsequent steps. For the specific numerical solution algorithm of the linear equation system, those skilled in the art can use existing matrix operation libraries, which are well-known techniques in the field and will not be elaborated upon here.

[0065] After the gradient field calculation module 102 outputs the original discrete gradient field for the entire field, the confidence assessment module 103 begins to execute step S3, namely, the construction of the geological confidence field. The first step in this process is to quantitatively characterize the geometric shape of the borehole trajectory. Due to the influence of formation stress and drill string weight during deep geological drilling, the actual borehole trajectory is often not an ideal straight line, but exhibits varying degrees of spatial curvature. In order to accurately distinguish whether the data gradient anomaly is due to a real geological abrupt change or a positioning deviation caused by borehole curvature, the confidence assessment module 103 needs to calculate the local geometric curvature at each sampling point based on continuous sampling points within the same borehole.

[0066] The confidence assessment module 103 first identifies the trajectory affiliation of the sampling points in the original borehole exploration data set, sorting all sampling points according to their borehole number and depth value to construct several discrete spatial polyline trajectories. For each sampling point within a trajectory, the confidence assessment module 103 uses the circumcircle geometry principle from discrete differential geometry to select the sampling point and its adjacent sampling points to form a local triangular element. The discrete curvature of the point is determined by calculating the reciprocal of the radius of the circumcircle of the triangular element.

[0067] For any non-endpoint sampling point on the borehole trajectory, let its index be... The confidence assessment module 103 constructs a local geometric curvature calculation formula based on the spatial coordinates of the sampling point and its preceding and subsequent sampling points, as follows:

[0068] ;

[0069] in, Indicates the first The discrete local geometric curvature at each sampling point; the larger the value, the greater the degree of curvature of the borehole at that location. Indicates the first The three-dimensional spatial coordinate vector of each sampling point; Indicates the location along the borehole depth direction at the th The three-dimensional spatial coordinate vector of the adjacent sampling points before each sampling point; Indicates the location along the borehole depth direction at the th The three-dimensional spatial coordinate vector of the adjacent sampling points after the sampling point; The cross product operation represents vectors and is used to calculate the area vector of the parallelogram formed by two vectors. The Euclidean norm of a vector is used to calculate the magnitude of the vector.

[0070] Through the above calculations, the confidence assessment module 103 obtains the curvature value at each sampling point. For the beginning and end points of the borehole trajectory, since there is a lack of complete neighborhood points, the confidence assessment module 103 uses the curvature value of its nearest neighbor or directly sets its curvature value to zero.

[0071] The full-field curvature data generated in this step can objectively reflect the degree of geometric distortion of the borehole trajectory in three-dimensional space, providing a direct numerical basis for the subsequent construction of confidence weights based on physical morphology. For the specific numerical calculations of the vector cross product and norm, those skilled in the art can use existing linear algebra algorithm libraries, which are well-known techniques in the field and will not be elaborated upon here.

[0072] After obtaining the discrete local geometric curvature at each sampling point, the confidence assessment module 103 further establishes a numerical mapping relationship between geometric shape and data confidence. The physical logic followed by this mapping process is as follows: when the borehole trajectory is approximately straight, i.e., the curvature approaches zero, the spatial positioning accuracy of the drilling tool in deep strata is high. At this time, the gradient abrupt change detected in the data is judged as a reflection of the real geological interface and should be given a high confidence level. Conversely, when the borehole trajectory is significantly curved, i.e., the curvature is large, the spatial position coordinates of the probe are often accompanied by a large cumulative measurement error. At this time, the gradient anomaly in the data may be due to coordinate geometric distortion rather than changes in the geological entity, and should be given a low confidence level to suppress its weight in the subsequent reconstruction process.

[0073] To mathematically express the above logic and construct continuous field data, the confidence assessment module 103 uses a nonlinear decay function to construct a spatial confidence scalar field. For each sampling point, the corresponding confidence weight value is calculated using its curvature data, specifically based on the confidence mapping formula as follows:

[0074] ;

[0075] in, Indicates the first The confidence scalar value at each sampling point, the range of which is: The closer the value is to 1, the more reliable the spatial positioning of the data point is, which corresponds to a strong constraint in subsequent optimization. This indicates that the first step calculated in the preceding steps... Discrete local geometric curvature at each sampling point; This represents the error tolerance adjustment coefficient, which is a preset constant greater than zero.

[0076] In this formula, the adjustment coefficient Used to control the sensitivity of the confidence level to changes in curvature. When a larger value is set... When the value is specified, the confidence function exhibits high sensitivity to trajectory curvature; even a small increase in curvature can lead to a decrease in confidence. Rapid attenuation makes this configuration suitable for detailed reconnaissance scenarios requiring extremely high spatial positioning accuracy; when a smaller setting is used... When the value is set, the system exhibits a high tolerance for trajectory curvature, allowing a high confidence weight to be maintained within a certain curvature range. This configuration is suitable for exploration scenarios where the impact of positioning errors is relatively small.

[0077] Given that the discrete gradient field in step S2 is a constant vector field defined inside the tetrahedral element, and the confidence level calculated at this time... It is a scalar attribute defined on the mesh vertices, i.e., the original sampling points. The confidence evaluation module 103 performs a spatial mapping operation from vertices to cells. For tetrahedral sets... Any tetrahedral unit in The confidence assessment module 103 extracts the confidence values ​​of the four vertices constituting the unit and calculates the overall confidence of the unit by arithmetic average. The overall confidence level This constitutes a discrete confidence field covering the entire exploration area. As a spatial weighting coefficient in subsequent energy functional optimization, it directly determines the degree to which the original gradient data in this area is retained during the anomaly detection and repair process, thereby realizing the transformation of the physical geometric constraints of the borehole trajectory into statistical weights in the mathematical optimization model.

[0078] After the confidence assessment module 103 completes the mapping of the geometric confidence weights across the entire field, the anomaly detection and optimization module 104 executes step S4, which verifies the physical properties of the original gradient field based on conservative field theory. The core logic of this verification is that the gradient field of any scalar physical quantity (such as geological properties) is mathematically irrotational, meaning its curl is zero everywhere.

[0079] To quantize the original gradient field To determine the degree of deviation from this physical constraint, the anomaly detection and optimization module 104 needs to construct a discrete curl operator on the unstructured mesh.

[0080] Unlike the finite difference calculation based on coordinate axes in regular meshes, the anomaly detection and optimization module 104 uses a loop integration method along the mesh edges to define discrete curl in a tetrahedral mesh topology. For any common edge within the mesh, it is shared by several tetrahedral elements surrounding this edge. The anomaly detection and optimization module 104 constructs a closed loop connecting the centers of these shared tetrahedral elements; this loop forms the boundary of the dual mesh face. Based on the discrete form of Stokes' theorem, the anomaly detection and optimization module 104 obtains the discrete curl value at the edge by calculating the tangential integral of the gradient vector along this closed loop, specifically based on the discrete curl operator formula. (See below.)

[0081] ;

[0082] in, Indicates the first in the grid The discrete curl scalar value (or circulation density) calculated at the edge of the stripe reflects the degree of nonconservatism of the gradient field in that local region. Indicates surrounding the first The area of ​​the dual face of a ridge edge, i.e. the area of ​​the polygon formed by the body centers of all tetrahedrons surrounding that ridge edge, is used to normalize circulation to curl density. Indicates sharing the first The total number of tetrahedral units with striped edges; The index of the tetrahedral element surrounding this edge; Indicates the first The constant gradient vector inside each tetrahedral element; Indicates from the first The body center of the tetrahedron points to the adjacent first... The displacement vectors of the body center of a tetrahedron constitute the line elements of a closed integral path. Represents the dot product operation of vectors; This indicates the calculation of the constant gradient vector inside the first tetrahedral element, accumulated to the th tetrahedral element. The constant gradient vector inside each tetrahedral unit.

[0083] Based on the operator definition above, the anomaly detection and optimization module 104 can traverse every edge in the grid and calculate its corresponding discrete curl value. If the original data fully conforms to geophysical laws, the curl value at all edges should be approximately zero; however, when there is non-physical random noise or measurement error in the data, the closed-loop integral of the gradient vector in space will produce a significant non-zero residual. This discrete curl operator effectively transforms the anomaly detection problem into a problem of measuring the non-conservative components of the gradient field, providing direct mathematical operator support for the subsequent construction of energy optimization functionals based on physical constraints.

[0084] Based on the aforementioned discrete curl operator, the anomaly detection and optimization module 104 further constructs an energy functional for global optimization, aiming to find a corrected gradient field that both conforms to the conservation laws of geophysics and preserves the original measurement information to the maximum extent. According to the variational principle, this module transforms the denoising problem of the gradient field into a mathematical optimization problem of minimizing an energy function. This energy functional consists of two parts: a curl constraint term representing physical constraints and a data fidelity term representing data fitting; these two are linearly weighted and combined to form the total energy of the entire field.

[0085] The energy functional formula constructed by the anomaly detection and optimization module 104 is as follows:

[0086] ;

[0087] in, This represents the total energy value to be optimized; this value is a scalar. This represents the set of corrected gradient fields to be solved, which contains the corrected gradient vectors within all tetrahedral elements; This indicates the total number of edges in the grid; Edge index; Indicates the first The geological confidence weight at the edge of the strip is obtained by mapping the confidence values ​​of the vertices constituting the edge through an arithmetic mean or weighted average, and is used to adjust the intensity of physical constraints on the local area. Indicates the first The discrete curl value at the edge of the strip is calculated using the modified gradient field, and its calculation method is consistent with the aforementioned discrete curl operator. The balance coefficient representing the data fidelity term is a preset, positive constant used to adjust the weight ratio between physical constraints and data fitting. This represents the total number of tetrahedral units; Index for tetrahedral elements; Indicates the first The corrected gradient vector within each tetrahedral cell is the unknown variable in this optimization problem; Indicates the first The original gradient vector within each tetrahedral element, i.e., the calculation result in step S2; This indicates taking the square of the magnitude of a vector or scalar.

[0088] In the above energy functional formula, the first term on the right-hand side of the equation is the curl constraint term. This term uses the sum of squares of the weights to force the curl of the correction gradient to approach zero. Here, a geological confidence weight is introduced. It played a crucial adaptive adjustment role: in the high-confidence region where the borehole trajectory was straight ( Approaching 1), the energy functional imposes a high penalty on the curl residual, forcing the correction gradient field. Strictly satisfying the irrotational conservative field properties, thus eliminating noise that violates physical laws; and in the low-confidence region where borehole curvature is severe ( (Smaller) The energy functional reduces the penalty weight on the curl term, allowing the modified gradient field to retain a certain non-zero curl, thus tolerating data fluctuations that seem to violate physical conservation due to geometric positioning errors, and avoiding the mistakenly treating geometric errors as noise and forcibly smoothing them out.

[0089] The second term on the right side of the equation is the data fidelity term. This term represents the gradient vector after constraint correction. The gradient vector should not deviate excessively from the original observations. Balance coefficient The settings determine the system's level of trust in the raw data; a larger... Values ​​tend to retain more original details, smaller The value tends to yield a smoother field distribution that conforms to physical conservation. By minimizing this energy functional... The anomaly detection and optimization module 104 can automatically balance physical conservation and data authenticity across the entire field, providing a high-quality gradient data foundation for subsequent anisotropic modeling.

[0090] After constructing the energy functional including curl constraints and data fidelity terms, the anomaly detection and optimization module 104 iteratively calculates the global minimum point of the functional to obtain the optimal gradient field distribution after denoising. Due to the aforementioned energy functional... Regarding the unknown variable, namely the modified gradient vector field to be solved, it is mathematically represented as a positive definite quadratic function. Therefore, this optimization problem is a typical unconstrained convex optimization problem with a unique global optimum. The anomaly detection and optimization module 104 uses the least squares method to transform the energy minimization problem into solving a large-scale sparse linear equation system through variational derivation.

[0091] Specifically, the anomaly detection and optimization module 104 measures the total energy of the entire field. Regarding the corrected gradient vector within each tetrahedral unit The partial derivatives of each component are calculated separately, and all partial derivatives are set to zero. This mathematical operation, based on the extremum theorem, transforms the original energy minimization logic into an algebraic equation solving logic. The gradient components of all tetrahedral elements are coupled together through a shared edge curl term, forming a linear system formula of the following form:

[0092] ;

[0093] in, The system matrix (or stiffness matrix) representing the optimization problem is a large sparse symmetric positive definite matrix, whose elements consist of the geometric coefficients of the discrete curl operator and the confidence weights from step S3. Together, they constitute the matrix, whose structure reflects the topological connectivity of the unstructured mesh. The unknown vector to be solved is represented by the corrected gradient vector of all tetrahedral elements in the entire field. The components are connected in series, and the dimension is ( (total number of tetrahedrons); This represents the data payload vector, which is derived from the original discrete gradient field. The vector data in the middle is multiplied by the balance parameter The subsequent structure represents the data anchor points in the optimization process.

[0094] The anomaly detection and optimization module 104 uses a numerical linear algebra solver to solve the above linear system formula. Given the system matrix... Due to the sparsity of the problem, the solution process typically employs efficient algorithms such as the conjugate gradient method or the Cholesky decomposition method.

[0095] After the solution is completed, the anomaly detection and optimization module 104 will obtain the solution vector. Remapping back to the corresponding tetrahedral elements yields the complete corrected gradient field. This modified gradient field, while preserving the main trends of the original data, effectively smooths out non-physical curl noise caused by borehole curvature, guided by confidence weights. This provides a high-quality vector data foundation that conforms to physical conservation laws for subsequent extraction of geological structure tensors. The specific numerical solution for the sparse linear equation system can be implemented using existing mathematical libraries, which are well-known techniques in the field and will not be elaborated upon here.

[0096] The gradient field, corrected for physical conservation constraints, is obtained in the anomaly detection and optimization module 104. Subsequently, the anisotropic modeling module 105 executes step S5, namely, geological anisotropic modeling based on gradient structure tensors. The core purpose of this step is to extract the implicit spatial structural features of geological bodies from simple gradient vector data, such as the bedding direction, fold morphology, and sedimentary trend of strata, thereby constructing anisotropic parameters that can guide subsequent data reconstruction.

[0097] The anisotropic modeling module 105 first calculates the local structure tensor for each element in the tetrahedral set. Since a single gradient vector can only indicate the direction of maximum change at the current point, it is highly susceptible to local residual noise and cannot stably represent macroscopic geological textures. Therefore, the anisotropic modeling module 105 introduces a tensor analysis method, constructing a structure tensor matrix by performing second-order statistical integration of gradient information within the local neighborhood. For any tetrahedral element, the calculation of its local structure tensor follows the structure tensor construction formula, as follows:

[0098] ;

[0099] in, Indicates the first The local structure tensor at each tetrahedral element is a A symmetric positive semidefinite matrix; Indicates the first The spatial neighborhood set of a tetrahedral unit, which is usually composed of the first tetrahedral unit. The unit is the center and the radius is It consists of all tetrahedral units within the sphere's range; The index of the tetrahedral cell in the neighborhood; Represents the spatial weighting coefficients (corresponding to the convolution kernel) The discrete form of the expression, whose value is usually calculated based on the Gaussian function distribution, is given by the following formula:

[0100] ;

[0101] in, and They represent the first The central unit and the first The geometric center coordinates of each neighboring unit; The preset spatial scale parameter is used to control the smoothing range; neighboring units closer to the central unit have a greater weight; Indicates the number of neighbors within the neighborhood. The corrected gradient vector of each tetrahedral element; This represents the outer product operation of vectors; This represents an exponential function with the real number e as its base.

[0102] In the above calculation process, the outer product operation Map the three-dimensional gradient vector to The matrix form of the gradient vector. Geometrically, this matrix projects the direction information of the gradient vector, and its magnitude is proportional to the square of the gradient magnitude. This is achieved by introducing weighting coefficients. By performing weighted summation within the neighborhood (i.e., discrete convolution operation on the unstructured mesh), the anisotropic modeling module 105 smooths and integrates local geological strike information. This processing method effectively suppresses isolated gradient direction abrupt changes, enhances the signal intensity of the main geological bedding directions, and ensures the generation of structural tensors. It can robustly reflect the dominant geological structural trends in the local area.

[0103] Obtaining the structure tensor of each element in the entire field Subsequently, the anisotropic modeling module 105 further performs eigenvalue decomposition on the tensor matrix to analyze the three-dimensional spatial attitude of the geological body. Because It is a symmetric positive semi-definite matrix, which necessarily has three non-negative real eigenvalues ​​and three mutually orthogonal eigenvectors. The anisotropy modeling module 105 solves the characteristic equation using a numerical algorithm, obtains the eigenvalue decomposition results, and arranges the eigenvalues ​​in order of magnitude, specifically described as the eigensystem formula:

[0104] ;

[0105] in, , , Represents the structure tensor The three eigenvalues ​​quantify the average contrast or rate of change of local image texture along the corresponding feature vector direction; , , These represent the corresponding normalized eigenvectors, which together form an orthogonal coordinate system describing local geological anisotropy.

[0106] Anisotropy modeling module 105 analyzes the geological meaning based on the above feature system: corresponding to the largest eigenvalue. Main eigenvectors It indicates the direction of the most drastic changes in geological properties; in layered geological structures, this direction is the normal direction of the strata; corresponding to smaller eigenvalues. and secondary eigenvectors and This forms a plane perpendicular to the normal, which indicates the direction of least change in geological properties, i.e., the extension surface or bedding plane of the strata.

[0107] Through this eigenvalue decomposition mechanism, this invention can automatically identify and extract the dip and strike information of strata at any location in three-dimensional space without human interaction, providing accurate geometric guidance for the subsequent construction of anisotropic diffusion models that are conductive along the bedding direction and blocked along the normal direction. The specific algorithms for matrix eigenvalue decomposition (such as the QR algorithm or the Jacobi iteration method) are well-known technologies in this field and will not be elaborated upon here.

[0108] After obtaining the eigenvectors and eigenvalues ​​indicating geological occurrence through eigenvalue decomposition, the anisotropic modeling module 105 further executes the construction step of the anisotropic diffusion tensor. This step aims to transform the feature system describing the geometric structure into a mathematical operator that controls the propagation of physical properties, thereby achieving precise control over the data smoothing direction in the subsequent reconstruction process.

[0109] The anisotropic modeling module 105, based on the principle of spectral decomposition and reconstruction, uses the eigenvectors obtained in the preceding steps as local orthogonal basis to recombine and generate anisotropic diffusion tensors. For any tetrahedral element... Its diffusion tensor is constructed based on the diffusion tensor spectral decomposition formula:

[0110] ;

[0111] in, Indicates the first The anisotropic diffusion tensor at each tetrahedral unit is a A symmetric positive definite matrix; , , The three normalized eigenvectors calculated in step S5 above represent the formation normal direction, the main extension direction and the secondary extension direction of the formation, respectively. This represents the outer product operation of vectors; , , These represent the diffusion coefficients (or eigenvalues) of the diffusion tensor along the corresponding eigenvector directions. The values ​​of these coefficients are determined by the eigenvalues ​​of the structure tensor. It is determined together with the preset anisotropic strategy.

[0112] Determining the diffusion coefficient When calculating the numerical values, the anisotropy modeling module 105 follows the construction principles of smoothing along bedding planes and blocking across bedding planes to achieve edge-preserving filtering. Specifically, for the eigenvector direction representing the stratigraphic extension surface... and The system assigns it a large diffusion coefficient (e.g., sets it to a certain value). This allows geological attribute values ​​to be fully diffused and averaged along the geological bedding direction, thereby filling sampling gaps and smoothing noise within the layer.

[0113] Conversely, for the eigenvector representing the direction of the formation normal... The anisotropic modeling module 105 imparts a very small diffusion coefficient. This coefficient is typically designed as the principal eigenvalue of the structure tensor. In a specific embodiment, the monotonically decreasing function is constructed using the following exponential decay function:

[0114] ;

[0115] Alternatively, threshold truncation can be used directly: when At that time, set (in For a very small positive number, such as (used to maintain numerical stability), otherwise set ; This represents the contrast control constant, used to control the diffusion coefficient. The decay rate as structural strength changes;

[0116] With this assignment strategy, when there is a significant gradient in the normal direction of the data (i.e., across different geological layers), the conductivity of the diffusion tensor in the normal direction is significantly suppressed, thereby effectively blocking the non-physical smoothness of attribute values ​​across geological interfaces and ensuring that clear boundary features between different lithologies or mineralization zones are preserved.

[0117] Finally, the diffusion tensor field generated by the anisotropic modeling module 105 It is a spatially non-uniformly distributed tensor field. In flat geological areas, this tensor tends to be isotropic; while in areas with obvious bedding or structural features, the tensor exhibits strong anisotropy, with its principal axis always adaptively aligned with the local geological texture. This mathematical construction provides a decisive coefficient matrix for establishing the anisotropic Poisson equation in the subsequent step S6, ensuring that the data reconstruction process strictly follows the physical structural laws of the geological body.

[0118] After the anisotropic modeling module 105 constructs a full-field anisotropic diffusion tensor field based on geological bedding characteristics, the data reconstruction module 106 executes step S6, namely the final repair and reconstruction of anomalous data. This step aims to transform the physically denoised and optimized gradient vector field back into a scalar attribute field through numerical integration methods, thereby obtaining a three-dimensional borehole data model that eliminates measurement noise while preserving clear geological boundaries.

[0119] Based on the principle of variational method, the data reconstruction module 106 transforms the process of recovering the scalar field from the gradient field into a boundary value problem of solving partial differential equations. To organically combine the physically conserved corrected gradient field obtained in step S4 with the diffusion tensor reflecting the geological structure obtained in step S5, the data reconstruction module 106 establishes an anisotropic Poisson equation in divergence form within a tetrahedral grid domain. This equation describes the flux balance relationship between the scalar field to be solved and the known vector field, specifically based on the anisotropic reconstruction equation formula:

[0120] ;

[0121] in, This represents the divergence operator, used to calculate the source and sink densities of a vector field; The anisotropic diffusion tensor field generated in step S5 is used as the diffusion coefficient matrix of the equation to control the direction and intensity of the propagation of attribute information in space. The scalar field of the restored geological properties (such as the restored grade or density value) to be solved is the unknown solution of the equation; This represents the gradient vector of the scalar field to be solved; This represents the denoised and optimized corrected gradient field output from step S4, which serves as the driving source term of the equation.

[0122] In this partial differential equation, the source term on the right-hand side of the equation Representing the divergence distribution of the modified gradient field, it physically reflects the accumulation or dissipation characteristics of geological properties in local areas, forcing the final reconstructed scalar field. The changing trend should approximate the optimized gradient field as closely as possible. The diffusion term on the left-hand side of the equation. This introduces the constraint effect of the structure tensor. Due to the diffusion tensor Exhibiting anisotropic characteristics (large coefficient along the bedding direction and small coefficient along the normal direction), this term forces the property fluid to preferentially propagate along the geological bedding direction during mathematical solution, while inhibiting its diffusion across bedding interfaces. This mechanism ensures that numerical errors or residual noise are smoothed out along the stratigraphic extension direction during integral reconstruction, while the steep boundaries between strata are fully preserved, thus achieving the technical effect of enhancing geological structural features while restoring data.

[0123] The anisotropic Poisson equation established above only mathematically determines the scalar field. To obtain an absolute numerical solution with clear physical meaning, appropriate boundary conditions must be applied to eliminate the uncertainty of the solution (i.e., constant term drift). The data reconstruction module 106 uses Dirichlet boundary conditions and utilizes highly reliable sampling points in the original borehole data to lock in the numerical range of the equations.

[0124] The data reconstruction module 106 first uses the spatial confidence scalar field generated in step S3 to reconstruct the original discrete point set. Reliability screening is performed on each sampling point. A confidence threshold is set. (e.g., 0.8), for any index of The original sampling points, if their corresponding confidence values If the value is greater than the threshold, the point is determined to be an "anchor point," meaning that the original measurement value at that point was not significantly affected by borehole curvature and can be directly used as a known condition; if If the value is less than the threshold, the point is determined to be a "point to be repaired", and its value will be determined by the solution of the equation.

[0125] For the selected set of anchor points, the data reconstruction module 106 forces the original attribute values ​​to the solution domain boundary of the equation, constructing the Dirichlet boundary condition formula in the following form:

[0126] ;

[0127] in, Indicates spatial location The attribute value to be solved at the location; This represents the original observed attribute value at the same location; This indicates that all confidence levels are greater than or equal to the threshold. The set of sampling point indices.

[0128] By applying this boundary condition, the data reconstruction module 106 effectively constrains the reconstructed data field to the original observation points with high confidence, ensuring the consistency of the repair results with the actual geological conditions on a macroscopic scale. For low-confidence areas (such as severely curved borehole sections), since no mandatory constraints are applied, the equations will automatically calculate estimated values ​​that conform to the laws of geological continuity based on the information of surrounding anchor points and the guidance of the gradient field, thereby realizing implicit correction of anomalous data. Subsequently, the process of transforming the partial differential equation with boundary conditions into a system of linear equations for numerical solution can be implemented by those skilled in the art using the finite element method (FEM) or the finite volume method (FVM), which are well-known techniques in the field and will not be elaborated here.

[0129] After determining the mathematical form of the anisotropic Poisson equation and the corresponding Dirichlet boundary conditions, the data reconstruction module 106 uses the finite element method to discretize the continuous partial differential equations into a system of linear equations in algebraic form. This process is based on the Galerkin weighted residual principle, projecting the infinite-dimensional function space onto a finite-dimensional space defined by a tetrahedral mesh. The data reconstruction module 106 defines a set of basis functions, which are non-zero in the local neighborhood of each tetrahedral node. By integrating and weakening the governing equations, the differential operators are transformed into matrix operation forms, constructing a global sparse linear system formula describing the interactions between all nodes in the field:

[0130] ;

[0131] in, The global stiffness matrix is ​​a... Large sparse symmetric matrices ( (Total number of mesh vertices) This matrix is ​​assembled from the local stiffness matrices of all tetrahedral elements. Its value depends not only on the geometry and topological connectivity of the mesh, but also incorporates the anisotropic diffusion tensor generated in step S5. The distribution information determines the weight of attribute values ​​being transferred between grids; This represents the global node attribute vector to be solved, which contains the geological attribute scalar values ​​at all vertices in the mesh, corresponding to the aforementioned anisotropic reconstruction equation. Discrete solutions; This represents the global load vector, which is generated by the corrected gradient field output in step S4. The projection integrals on the basis functions at each node are used to calculate the source force that drives the change in the attribute field.

[0132] In constructing the aforementioned system, the data reconstruction module 106 directly substitutes the Dirichlet boundary conditions determined in step S6.2 into the system of equations. For high-confidence nodes marked as "anchor points," the system assigns their corresponding unknowns to vectors. The values ​​are fixed at the original observation values, and the stiffness matrix is ​​adjusted accordingly. Rows and columns and load vectors The corresponding elements are used to embed the constraints into the linear system. This operation ensures that the solution to the system of equations is strictly equal to the observed value at the known point, while eliminating the singularity of the stiffness matrix and ensuring the existence of a unique solution.

[0133] Given that the generated 3D tetrahedral mesh typically contains tens of thousands to millions of nodes, resulting in a global stiffness matrix... It exhibits extremely high sparsity. The data reconstruction module 106 employs an efficient sparse matrix iterative solver to numerically solve this linear system, obtaining the unknown vector. The numerical solution is obtained; the sparse matrix iterative solver can specifically use the conjugate gradient method, the biconjugate gradient stabilization method, or the generalized minimum residual method. This solution vector represents the final three-dimensional geological property field after geometric correction, physical denoising, and structural enhancement. By mapping this vector data back to three-dimensional spatial coordinates, the system ultimately outputs a new dataset that precisely corresponds to the original borehole location but has corrected bending errors and measurement noise. Specific solution algorithms for large sparse linear equation systems (such as the preprocessed conjugate gradient method or the algebraic multigrid method) are well-known techniques in this field and will not be elaborated upon here.

Claims

1. A method for anomaly detection and repair of borehole data in geological exploration, characterized in that, Includes the following steps: S1. Spatial topology construction based on Delaunay tetrahedral subdivision: Obtain the original borehole exploration data set containing three-dimensional spatial coordinates and geological attribute information, directly use the original data points as vertices to construct an unstructured three-dimensional Delaunay tetrahedral mesh, and establish the spatial topological connection relationship between the original data points. S2. Calculation of unstructured discrete gradient field: Based on linear element theory, the rate of change of the internal attribute value of each tetrahedral element in the tetrahedral mesh relative to the spatial coordinates is analyzed, and the discrete scalar attribute field is transformed into the original discrete gradient vector of the entire field. S3. Construction of geological confidence field based on trajectory curvature: The geometric shape of the borehole trajectory is quantitatively characterized, the geometric curvature at each sampling point is calculated, and a geological confidence field reflecting the accuracy of spatial positioning of the data is constructed accordingly. S4. Anomaly detection and optimization of discrete gradient field: Conservative field theory is introduced, and the geological confidence field is used as a weight to constrain the original discrete gradient vector. By minimizing the curl component of the gradient field, a corrected gradient field that conforms to the physical conservation law is output. S5. Geological anisotropy modeling based on gradient structure tensor: The modified gradient field is subjected to second-order statistical integration and the local structure tensor is calculated. The stratigraphic normal direction and extension direction are identified through feature decomposition, and anisotropic diffusion tensor is constructed. S6. Anisotropic Poisson Reconstruction: Within the tetrahedral grid domain, a partial differential equation containing the anisotropic diffusion tensor and the modified gradient field divergence is established. High confidence points are selected as boundary conditions using the geological confidence field. The partial differential equation is solved to obtain the repaired geological and mineral data scalar field. The partial differential equation is specifically the anisotropic Poisson equation, including: The anisotropic Poisson equation describes the flux balance between the scalar field to be solved and the known vector field; The left-hand side of the anisotropic Poisson equation is a diffusion term, which is formed by the effect of the anisotropic diffusion tensor on the gradient of the scalar field to be solved, and is used to introduce the directional constraint of the structure tensor. The right-hand side of the anisotropic Poisson equation is the source term, which is composed of the divergence distribution of the modified gradient field and is used to drive the trend of the reconstructed field to approximate the optimized gradient field. Solving the aforementioned partial differential equation specifically includes: Based on the geological confidence field, the original sampling points are screened, and points with confidence values ​​greater than the confidence threshold are identified as anchor points, while points with confidence values ​​less than the confidence threshold are identified as points to be repaired. The original attribute values ​​of the anchor points are forcibly constrained to the solution domain boundary using the Dirichlet boundary condition formula. The partial differential equation with boundary conditions is discretized into a sparse linear system using the finite element method, and the solution vector of all mesh vertex attribute values ​​is solved by a sparse matrix iterative solver.

2. The method for anomaly detection and repair of geological exploration borehole data according to claim 1, characterized in that, In step S1, the process of constructing the unstructured three-dimensional Delaunay tetrahedral mesh strictly follows the empty circumsphere criterion, which is defined as follows: For any tetrahedral cell in the tetrahedral mesh, the circumsphere corresponding to the tetrahedral cell does not contain any other vertices in the original borehole exploration data set, and the mesh generated by the empty circumsphere criterion ensures that all original sampling points are nodes of the mesh, and the spatial topological connectivity satisfies the numerical stability requirements of subsequent gradient calculations.

3. The method for anomaly detection and repair of geological exploration borehole data according to claim 1, characterized in that, In step S2, the specific calculation process of the original discrete gradient vector of the entire field includes: Select one vertex of the tetrahedral unit as a reference node, and use vector subtraction and scalar subtraction to calculate the spatial position difference and attribute value difference of the other three vertices relative to the reference node; Based on the principle of linear interpolation, a system of linear equations is constructed to describe the relationship between attribute differences and coordinate differences between vertices. The system of linear equations includes a geometric shape matrix composed of spatial position differences, a gradient vector to be solved, and an attribute difference vector composed of attribute value differences. By multiplying the inverse of the geometric shape matrix with the attribute difference vector, the unique constant gradient vector inside the tetrahedral unit is calculated, and the field composed of the original discrete gradient vector is formed by traversing all the tetrahedral units.

4. The method for anomaly detection and repair of geological exploration borehole data according to claim 1, characterized in that, In step S3, constructing the geological confidence field specifically refers to: Using the principle of discrete differential geometry, a local triangular element is formed by selecting the current sampling point and the sampling points adjacent to the current sampling point. The reciprocal of the radius of the circumcircle of the triangular element is calculated using the local geometric curvature calculation formula to obtain the discrete local geometric curvature at the current sampling point. A nonlinear decay function is used to establish a mapping relationship between curvature and confidence. Using the confidence mapping formula, the sampling points with larger curvature are assigned lower confidence weights, and the sampling points with curvature close to zero are assigned higher confidence weights. The confidence defined by the vertex is then mapped to the tetrahedral unit to generate a spatial confidence scalar field.

5. The method for anomaly detection and repair of geological exploration borehole data according to claim 1, characterized in that, In step S4, the curl component is determined by constructing a discrete curl operator on an unstructured mesh. The specific construction process of the discrete curl operator includes: A closed loop connecting the body centers of all tetrahedral elements sharing the same edge is constructed by using the loop integration method along the mesh edge. The tangential integral of the gradient vector along the closed loop is calculated using the discrete curl operator formula, and the result of the tangential integral is normalized to the circulation density of the dual surface around the edge of the grid to obtain the discrete curl value at the edge of the grid, and the degree of nonconservatism of the gradient field in the local region is quantified.

6. The method for anomaly detection and repair of geological exploration borehole data according to claim 5, characterized in that, In step S4, the modified gradient field is obtained by solving for the global minimum point of the energy functional, which consists of a curl constraint term and a data fidelity term. The curl constraint term uses geological confidence weights to weight the square of the modulus of the discrete curl values, forcing the curl to approach zero in the high confidence region. The data fidelity term constrains the modified gradient field to not deviate from the original discrete gradient vector. The problem of minimizing the energy functional is transformed into a large sparse linear equation system through variational derivation. Solving the large sparse linear equation system yields the corrected gradient vector of all tetrahedral elements in the entire field.

7. The method for anomaly detection and repair of geological exploration borehole data according to claim 6, characterized in that, In step S5, the calculation and eigenvalue decomposition of the local structure tensor includes: Perform an outer product operation on the modified gradient vectors in the spatial neighborhood of the tetrahedral unit to obtain the gradient projection matrix; By introducing spatial weighting coefficients calculated based on Gaussian function distribution, discrete convolution summation is performed on the gradient projection matrix in the neighborhood to generate a symmetric positive semidefinite local structure tensor. The feature system of the local structure tensor is analyzed, and three orthogonal normalized feature vectors and their corresponding feature values ​​are extracted. The principal feature vector indicates the direction of the stratum normal where the geological properties change most drastically, and the secondary feature vector indicates the direction of the stratum extension surface.

8. The method for anomaly detection and repair of geological exploration borehole data according to claim 7, characterized in that, In step S5, the construction of the anisotropic diffusion tensor follows the principle of smoothing along bedding planes and blocking across bedding planes. Specifically, this principle includes: Based on the principle of spectral decomposition and reconstruction, the eigenvectors are used as local orthogonal bases to recombine and generate tensors. For feature vectors indicating the direction of formation extension, a larger diffusion coefficient is assigned to promote property smoothing within the formation; For the eigenvector indicating the direction of the stratum normal, a very small diffusion coefficient is assigned to suppress the propagation of cross-layer properties. The diffusion coefficient is set as a monotonically decreasing function of the principal eigenvalues ​​of the structure tensor, specifically an exponential decay function.

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