A method, system, and storage medium for geochemical data interpolation under multiple constraints

Abstract

This invention discloses a method, system, and storage medium for geochemical data interpolation under multiple constraints. The method includes: acquiring geochemical element sampling information within a study area and constructing a radial basis function (RBF) interpolation model; adding tangent constraints, gradient constraints, and range constraints to the RBF interpolation model based on geological information to construct a multi-constraint RBF interpolation model; transforming the multi-constraint RBF interpolation model into a quadratic objective function with tangent and gradient constraints as equality constraints and range constraints as inequality constraints; and solving the quadratic objective function using an iterative interpolation method to obtain the geochemical data interpolation results within the study area. This invention applies a generalized radial basis interpolation method, providing a universal framework for adding different types of constraints through linear functionals. It can calculate interpolation results that better conform to geological laws and expert understanding, and has significant application value for geochemical mapping based on this method.

Description

Technical Field

[0001] This invention relates to the field of geochemical data processing technology, and in particular to a geochemical data interpolation method, system, and computer-readable storage medium under multiple constraints. Background Technology

[0002] Geochemical element interpolation is the foundation of geochemical mapping and a necessary prerequisite for applying geochemical methods to locate mineral targets and predict mineral deposit scale. This is because, due to the limitations of the actual field environment, geochemical researchers can only obtain discrete sampling data in a limited spatial location using limited sampling methods. To obtain more unknown data, spatial interpolation methods can be used to predict unknown points using known sampling data.

[0003] Currently, many classical spatial interpolation methods (such as distance-weighted interpolation, spline function interpolation, kriging interpolation, and radial basis interpolation) are applied to geochemical element content interpolation. However, these interpolation methods typically focus on the spatial distribution characteristics of the data. In actual geochemical exploration, non-spatial factors such as geological structures and ore body boundaries have a significant impact on element distribution. Classical methods often cannot simultaneously consider these constraints, resulting in biased interpolation results due to the addition of only one constraint. Furthermore, when sampling points are sparse and uneven, existing methods struggle to account for the influence of geological structures on element distribution, causing changes or distortions in the element distribution characteristics of the interpolation results. Additionally, some classical interpolation algorithms, due to inherent algorithmic flaws, can produce negative values ​​in the interpolation results. Although some studies have attempted to correct this problem by constraining weighting coefficients or non-negativity constraints, effective solutions are still lacking for numerical ranges with upper and lower limits (such as the concentration range of certain elements).

[0004] Therefore, this application proposes a geochemical data interpolation method under multiple constraints. Based on the generalized radial basis interpolation method, it can use multiple types of information such as geological bodies, geological structures, water systems, and value ranges as important supplementary constraint information, and perform geochemical element content interpolation together with sampling to obtain interpolation results that are more in line with geological laws and expert understanding, thereby improving the accuracy of the interpolation results. Summary of the Invention

[0005] In view of this, the present invention provides a geochemical data interpolation method, system and storage medium under multiple constraints, in order to solve the technical problem that the existing interpolation methods are difficult to consider multiple types of constraints such as geological data and expert knowledge, which may lead to changes or distortions in the element distribution characteristics, negative values ​​and other discrepancies with the true distribution characteristics.

[0006] To achieve the above-mentioned technical objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a geochemical data interpolation method under multiple constraints, comprising:

[0008] Obtain chemical element sampling information and geological information within the study area;

[0009] A radial basis function interpolation model is constructed based on the chemical element sampling information;

[0010] Based on the geological information, a tangent constraint to represent the local extension direction of geochemical element distribution, a gradient constraint to reflect the drastic changes in element concentration, and a range constraint to ensure that the range of interpolation results conforms to natural laws are added to the radial basis function interpolation model to obtain a multi-constraint radial basis interpolation model.

[0011] The multi-constraint radial basis interpolation model is transformed into a quadratic objective function with tangent and gradient constraints as equality constraints and range constraints as inequality constraints.

[0012] The quadratic objective function is solved using an iterative interpolation method to obtain the geochemical data interpolation results within the study area.

[0013] Furthermore, a radial basis function interpolation model is constructed based on the chemical element sampling information, including:

[0014] The interpolation surface is constructed using a radial basis function interpolation model passing through all sampling points, expressed as:

[0015] ;

[0016] ;

[0017] in, Represents the interpolation function. The radial basis function values ​​depend on the point and The distance between them For sample data; ,..., It is a d-dimensional real space Two different points in the middle, , Indicates sampling point The measured values ​​at that location are continuous real values. Represents the real coefficient.

[0018] Furthermore, the multi-constraint radial basis interpolation model is expressed as:

[0019] ;

[0020] in, Represents the interpolation function. Indicates the weighting coefficient. Indicates the action on the radial basis functions A continuous linear functional on, It is a (m-1) order bivariate polynomial, and s(x)∈H indicates that the interpolation function belongs to the function space. , This represents the total number of linear functionals. , and These represent the number of tangent constraints, gradient constraints, and range constraints, respectively.

[0021] Furthermore, in the tangent constraint, the principal direction of local anisotropy that varies along the linear structure direction is used to indicate the local extension direction of the geochemical element anomaly distribution, and the local extension direction is orthogonal to the gradient direction of the fastest change in the element anomaly distribution.

[0022] The tangent constraint is expressed by the formula:

[0023] ;

[0024] in, Distribution of geochemical elements, For the point position, Let be the vector representing the principal direction of local anisotropy. For gradient operators, It is a vector dot product operator;

[0025] The tangent constraint acts on the linear function of the radial basis function. The specific form is:

[0026] ;

[0027] in, This represents a linear function acting on radial basis functions. This represents the point estimation functional. , The partial derivative is a function of the second input variable of the radial basis function. ∘ represents the composition of functions. and These represent the components of the second-order tensor.

[0028] Furthermore, in the gradient constraint, the gradient direction indicates the direction of the fastest change in the abnormal distribution of elements, the magnitude of the gradient is a unit normal vector, and the condition for its validity is:

[0029] ;

[0030] in, It is an abnormal distribution. For the point position, For gradient operators, This is the unit normal vector at this location;

[0031] The gradient constraint acts on a linear function of the radial basis function. The specific form is:

[0032] ;

[0033] in, It is a point estimation functional. , The partial derivative is a function of the second input variable of the radial basis function. ∘ represents the composition of functions.

[0034] Furthermore, the value range constraint is obtained based on the geological information of the study area, including negative value constraints that conform to natural laws or the range of regional element content limits;

[0035] The negative value constraint is expressed as: ;

[0036] The specified range for element content is expressed as follows: ;

[0037] in, and These represent the lower and upper limits of the element content, respectively, and f(xi) is the interpolation function at point... The value at that point represents the predicted element content at that point.

[0038] Furthermore, the multi-constraint radial basis interpolation model is transformed into a quadratic objective function with tangent and gradient constraints as equality constraints and range constraints as inequality constraints, including:

[0039] The linear functional is applied to the multi-constraint radial basis interpolation model, and the multi-constraint radial basis interpolation model is transformed into a system of quadratic programming equations, expressed as:

[0040] ;

[0041] Among them, among them, The weight coefficient vector has a length of H is ( A is a positive definite symmetric matrix. ) Matrix, F is ( ) Matrix, B is ( ) matrix, I is the zero matrix, and length is .

[0042] Furthermore, the quadratic objective function is solved using an iterative interpolation method to obtain the geochemical data interpolation results within the study area, including:

[0043] The center point of the negative value region is selected as the initial inequality constraint point and added to the quadratic programming problem equation system;

[0044] Iteratively solve the current quadratic programming problem equation system to obtain newly generated interpolation points, and check whether the newly generated interpolation points satisfy the value range constraint; when the newly generated interpolation points do not satisfy the value range constraint, extract the coordinates of the newly generated interpolation points, and convert the newly generated interpolation points into new inequality constraint points;

[0045] New inequality constraint points are added to the quadratic programming problem equations for solving until all interpolation results satisfy the range constraints, thus obtaining the geochemical data interpolation results within the study area.

[0046] Secondly, the present invention provides a geochemical data interpolation system under multiple constraints, comprising:

[0047] The acquisition module is used to acquire chemical element sampling information and geological information within the study area;

[0048] The generalized model building module is used to construct a radial basis function interpolation model based on the chemical element sampling information;

[0049] The constraint model establishment module is used to add tangent constraints to the radial basis function interpolation model based on the geological information, which represent the local extension direction of the distribution of geochemical elements, gradient constraints to reflect the degree of drastic change in element concentration, and range constraints to ensure that the range of interpolation results conforms to natural laws, so as to obtain a multi-constraint radial basis interpolation model.

[0050] The transformation module is used to transform the multi-constraint radial basis interpolation model into a quadratic objective function with tangent constraints and gradient constraints as equality constraints and range constraints as inequality constraints.

[0051] The calculation module is used to solve the quadratic objective function using an iterative interpolation method to obtain the geochemical data interpolation results within the study area.

[0052] Thirdly, the present invention also provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, it implements the geochemical data interpolation method under multiple constraints described in any of the above technical solutions.

[0053] Compared to existing technologies, the method of this invention involves: first, constructing a radial basis function interpolation model based on the acquired chemical element sampling information; second, effectively combining sampling and geological information during the interpolation process by incorporating tangent constraints, gradient constraints, and range constraints to ensure that the interpolation results fully consider geological structural constraints and conform to actual geological distribution characteristics and natural laws; and finally, transforming the multi-constraint interpolation model into a quadratic programming problem and solving it using an iterative interpolation method. This effectively balances the relationships between various constraints during the optimization process, finding the optimal interpolation result. While ensuring the constraints are met, it maximizes the global optimization of the model, making the interpolation results more reasonable and accurate throughout the study area. Compared to traditional spatial interpolation methods, this invention can obtain interpolation results that better conform to geological laws and expert understanding, effectively simulate the distribution characteristics of geochemical anomalies, provide a reliable basis for determining target areas, and has significant application value in the field of geochemical mapping. Attached Figure Description

[0054] Figure 1 A schematic diagram of the geochemical data interpolation method under multiple constraints provided by the present invention;

[0055] Figure 2 This is a schematic diagram of the main technical route provided by the present invention;

[0056] Figure 3 This is a schematic diagram of the geochemical data interpolation system under multiple constraints provided by the present invention. Detailed Implementation

[0057] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0058] Before describing the embodiments of the present invention, the design concept of the present invention will be introduced first.

[0059] In geochemical exploration, due to the limitations of the field environment, geochemical researchers can typically only obtain discrete sampling data within a limited spatial range. This sampling data includes not only elemental abundance values ​​but may also contain functional values ​​unrelated to spatial distribution (such as information on geological structures and ore body boundaries). Classical spatial interpolation methods (such as distance-weighted methods, spline function methods, kriging interpolation, and radial basis interpolation) usually focus on estimating values ​​at unknown points based on spatial distribution characteristics, but often neglect the influence of non-spatial factors such as geological structures and geological bodies on elemental distribution.

[0060] To overcome this problem, this application incorporates functional information into the interpolation process to improve the accuracy of the interpolation method. Based on the general framework of the generalized radial basis interpolation method, a linear functional is introduced to simultaneously incorporate multiple types of constraints. By conditionalizing the radial basis interpolation, spatial data can be effectively integrated with non-spatial factors such as geology and ore bodies, thereby significantly improving the accuracy of the interpolation results.

[0061] This invention provides a geochemical data interpolation method under multiple constraints, which will be described in detail below.

[0062] Please see Figure 1 This embodiment provides a geochemical data interpolation method under multiple constraints, including:

[0063] Step S101: Obtain chemical element sampling information and geological information within the study area;

[0064] Step S102: Construct a radial basis function interpolation model based on the chemical element sampling information;

[0065] Step S103: Based on the geological information, add tangent constraints to the radial basis function interpolation model to represent the local extension direction of geochemical element distribution, gradient constraints to reflect the degree of drastic change in element concentration, and range constraints to ensure that the range of interpolation results conforms to natural laws, to obtain a multi-constraint radial basis interpolation model.

[0066] Step S104: Transform the multi-constraint radial basis interpolation model into a quadratic objective function with tangent constraints and gradient constraints as equality constraints and range constraints as inequality constraints;

[0067] Step S105: Solve the quadratic objective function using the iterative interpolation method to obtain the geochemical data interpolation results within the study area.

[0068] The method in this embodiment first constructs a radial basis function interpolation model based on the acquired chemical element sampling information. Second, during the interpolation process, the sampling information and geological information are effectively combined by incorporating tangent constraints, gradient constraints, and range constraints. This ensures that the interpolation results more objectively reflect the spatial distribution patterns of geochemical elements, avoiding overly smoothed or overly varied interpolation results and guaranteeing that the interpolation results better match the actual geological distribution characteristics. Finally, the multi-constraint interpolation model is transformed into a quadratic programming problem and solved using an iterative interpolation method. This effectively balances the relationships between various constraints during the optimization process, finding the optimal interpolation result. While ensuring the constraints are met, it maximizes the global optimization of the model, making the interpolation results more reasonable and accurate throughout the study area. Compared with traditional spatial interpolation methods, the method in this embodiment can obtain interpolation results that better conform to geological laws and expert understanding, effectively simulating the distribution characteristics of geochemical anomalies, providing a reliable basis for determining target areas, and has significant application value in the field of geochemical mapping.

[0069] As a preferred embodiment, scalar functions are used. To represent the actual distribution of chemical elements in a geochemical field; to simulate the distribution of chemical elements in a geochemical field using interpolation methods, using interpolation functions. Represented using interpolation functions. Approaching According to optimal recovery theory, the value s* in this space is the closest approximation. At that time, we can obtain:

[0070]

[0071] in, This represents the function space. It means that in a certain function space... Find a function This function provides the most suitable interpolation function among all possible interpolation functions. The best approximation.

[0072] Radial basis function interpolation, as an accurate interpolation method, requires the constructed interpolation surface to pass through all sampling points. Based on the chemical element sampling information, a radial basis function interpolation model is constructed, including:

[0073] The interpolation surface is constructed using a radial basis function interpolation model passing through all sampling points, expressed as:

[0074] ;

[0075] ;

[0076] in, Represents the interpolation function. The radial basis function values ​​depend on the point and The distance between them For sample data; ,..., It is a d-dimensional real space Two different points in the middle, , Indicates sampling point The measured values ​​at that location are continuous real values. Represents the real coefficient.

[0077] The radial basis function interpolation problem described above can be described as follows: In d-dimensional space, based on known sample data... , , , Construct an interpolation model.

[0078] Meanwhile, in generalized radial basis function interpolation, as long as the continuous linear functional... If the functions are linearly independent, then any type of linear functional can be incorporated into the interpolation, which can be applied to the need for multiple types of constraints in geochemical interpolation.

[0079] In a preferred embodiment, a linear functional is introduced to handle different constraint information. Specifically, based on the geological information, tangent constraints representing the local extension direction of geochemical element distribution, gradient constraints reflecting the drastic changes in element concentration, and range constraints ensuring that the interpolation result range conforms to natural laws are added to the radial basis function interpolation model, resulting in a multi-constraint radial basis interpolation model. At this time, the multi-constraint radial basis interpolation model is expressed as:

[0080] ;

[0081] in, Represents the interpolation function. Indicates the weighting coefficient. Indicates the action on the radial basis functions A continuous linear functional on, It is a (m-1) order bivariate polynomial, and s(x)∈H indicates that the interpolation function belongs to the function space. , This represents the total number of linear functionals. , and These represent the number of tangent constraints, gradient constraints, and range constraints, respectively.

[0082] In this embodiment, the various types of constraints used in geochemical interpolation mainly consider tangent constraints, gradient constraints, and range constraints. These are explained below.

[0083] Tangent constraint

[0084] Influenced by hydrothermal activity, the distribution of geochemical elements often exhibits morphological characteristics along structural features such as breccia zones, faults, stratigraphic bedding, contact zones, and foliation. Furthermore, under certain geological contexts, the distribution of geochemical elements within geological bodies and drainage systems often displays directional information. Local anisotropy can be directly extracted from linear structural directional data as tangent constraints. Linear structures can be the contours of objects, the direction of textures, or any structure with a clear directionality.

[0085] The principal direction of local anisotropy indicates the local extension direction of geochemical element anomalies, which is orthogonal to the gradient direction in which the element anomalies change the fastest.

[0086] The tangent constraint is expressed by the formula:

[0087] ;

[0088] in, Distribution of geochemical elements, For the point position, Let be the vector representing the principal direction of local anisotropy. For gradient operators, It is a vector dot product operator;

[0089] The tangent constraint acts on the linear function of the radial basis function. The specific form is:

[0090]

[0091] in, This represents a linear function acting on radial basis functions. This represents the point estimation functional. , The partial derivative is a function of the second input variable of the radial basis function. ∘ represents the composition of functions. and These represent the components of the second-order tensor.

[0092] (2) Gradient constraints

[0093] The gradient direction indicates the direction of the most rapid change in elemental anomaly distribution. Based on mineral deposit theory, hydrothermal fluids undergo directional migration through seepage and diffusion, moving under the influence of pressure gradients and from high concentration to low concentration under concentration gradients. In geochemical interpolation, the gradient direction indicates the direction of the most rapid change in elemental anomaly distribution, and the magnitude of the gradient is a unit normal vector, meaning the following conditions hold:

[0094] ;

[0095] in, It is an abnormal distribution. For the point position, For gradient operators, This is the unit normal vector at this location;

[0096] The gradient constraint acts on a linear function of the radial basis function. The specific form is:

[0097] ;

[0098] in, It is a point estimation functional. , The partial derivative is a function of the second input variable of the radial basis function. ∘ represents the composition of functions.

[0099] (3) Range constraint

[0100] Based on industry experts' analysis of geological background, regional geological structure, and elemental association patterns, threshold ranges for elemental content within a region are provided, or threshold ranges for elemental content are obtained through statistical analysis of sampled data within the study area. These thresholds can take the form of negative value constraints. }) or the range of regional element content estimated by experts. ;

[0101] in, and Let f(xi) represent the lower and upper limits of the element content, respectively, and f(xi) be the interpolation function at point x. The value at that point represents the predicted element content at that point.

[0102] Combining the aforementioned tangent constraints, gradient constraints, and range constraints, the generalized radial basis function interpolation method incorporates multiple types of independent geological constraints when processing different constraint information by deriving each linearly independent functional. When processing element-sampled data (i.e., range constraints), tangent data, and gradient data, the linear function acting on the radial basis function... They are respectively:

[0103]

[0104] in, It is a point estimation functional, ( , The partial derivative is a function of the second input variable of the radial basis function. In other words.

[0105] This linear functional When applied to the generalized radial basis interpolation formula and expanded, the following equation for the interpolation s(x) is obtained:

[0106] ;

[0107] Among them, the weighting coefficient Compared with known sampling point data Correlation, weight vector is With gradient condition Correlation, weighting coefficient With tangent data Weighting coefficients and Dependent on order polynomials. Differential operators. It is the second input variable for the radial basis. , Perform differentiation operations.

[0108] Therefore, the generalized radial basis interpolation problem will ultimately be transformed into solving a system of linear equations. (where A= b= The problem to be solved.

[0109] In a preferred embodiment, the multi-constraint radial basis interpolation model is transformed into a quadratic objective function with tangent and gradient constraints as equality constraints and range constraints as inequality constraints, including:

[0110] Applying the linear functional to the multi-constraint radial basis interpolation model, the multi-constraint radial basis interpolation model is transformed into a quadratic programming form, expressed as:

[0111] ;

[0112] in, The weight coefficient vector has a length of H is ( A is a positive definite symmetric matrix. ) Matrix, F is ( ) Matrix, B is ( ) matrix, I is the zero matrix, and length is .

[0113] The details of the matrices and optimized vectors are summarized below:

[0114]

[0115] ;

[0116]

[0117] like Figure 2 As shown, Figure 2 A schematic diagram illustrating the main technical route of this method is shown.

[0118] Since the range constraint applies to a large number of points to be estimated across the entire region, and the inequality constraint solution method itself is time-consuming, these factors can lead to computational complexity. As a preferred embodiment, an iterative interpolation approach is used, gradually adding several range constraint points during the iterative interpolation process until all points to be estimated satisfy the range constraint, which is expected to quickly yield reasonable results.

[0119] The specific steps of iterative interpolation are as follows:

[0120] Step S201: Initially select one (or several) inequality points, prioritizing the center point of the negative value region, and add them as inequality constraints to the interpolation framework of the generalized radial basis to construct a quadratic programming problem for solution.

[0121] Step S202: Construct the interpolation model, obtain the interpolation results of the points to be solved, extract the coordinates of the points in the interpolation results that do not meet the range constraints, convert the points into inequality constraints, and reconstruct the equations for solution.

[0122] Step S203: Repeat step S202 until all interpolation results in the grid fall within the range of values, then stop the calculation and output the final interpolation result.

[0123] like Figure 3 As shown, this embodiment of the invention also provides a geochemical data interpolation system 300 under multiple constraints, comprising:

[0124] The acquisition module 301 is used to acquire chemical element sampling information and geological information within the study area;

[0125] Generalized model building module 302 is used to construct a radial basis function interpolation model based on the chemical element sampling information;

[0126] The constraint model establishment module 303 is used to add tangent constraints to the radial basis function interpolation model based on the geological information, to represent the local extension direction of geochemical element distribution, gradient constraints to reflect the degree of drastic change in element concentration, and range constraints to ensure that the range of interpolation results conforms to natural laws, so as to obtain a multi-constraint radial basis interpolation model.

[0127] The transformation module 304 is used to transform the multi-constraint radial basis interpolation model into a quadratic objective function with tangent constraints and gradient constraints as equality constraints and range constraints as inequality constraints.

[0128] The calculation module 305 is used to solve the quadratic objective function using an iterative interpolation method to obtain the geochemical data interpolation results within the study area.

[0129] In summary, the geochemical data interpolation method under multiple constraints provided by this invention has the following advantages:

[0130] (1) To address the anisotropic characteristics of elemental distribution in geochemical fields, this method extracts directional information from special geological bodies (dikes, special strata, etc.), geological structures (folds, faults), and drainage systems, converting it into local anisotropic constraints to participate in the interpolation process, thereby constraining the distribution and orientation of anomalies. Experiments show that after adding local anisotropic constraints, the accuracy of the interpolation results is improved due to the incorporation of more geological knowledge.

[0131] (2) Due to inherent defects in some classic interpolation algorithms (such as radial basis function interpolation), or due to local unevenness in the spatial distribution of sampling points, interpolation results may appear that do not conform to natural laws (such as negative values), or the interpolation results may be too large or too small. To address this, this method transforms the threshold range of element content in the region given by experts in combination with geological background, regional geological structure, and element association laws into inequality constraints and incorporates them into the geochemical interpolation process, making the interpolation results more consistent with geological laws and expert understanding.

[0132] (3) Since the shape parameters of the radial basis function determine the quality of the interpolation model, this method uses an improved grid search method and cross-validation to quickly find the optimal parameters that minimize the error of the radial basis interpolation model.

[0133] (4) In order to improve computational efficiency, this method uses the idea of ​​iterative interpolation. By gradually adding several range constraint points during the iterative interpolation process until all the values ​​to be estimated meet the range constraints, reasonable results can be obtained quickly.

[0134] Compared with traditional spatial interpolation methods, this method can obtain interpolation results that are more consistent with geological laws and expert understanding. It can effectively simulate the distribution characteristics of geochemical anomalies, provide a reliable basis for determining target areas, and has important application value for geochemical mapping based on this method.

[0135] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A geochemical data interpolation method under multiple constraints, characterized in that, include: Obtain chemical element sampling information and geological information within the study area; Based on the chemical element sampling information, a radial basis function interpolation model is constructed. The interpolation surface passes through all sampling points in the radial basis function interpolation model, expressed as: ； ； in, Represents the interpolation function. This represents the radial basis functions, whose values ​​depend on the points. and The distance between them For sample data; ,..., It is a d-dimensional real space Two different points in the middle, , Indicates sampling point The measured values ​​at that location are continuous real values. Represents real coefficients; Based on the geological information, a tangent constraint to represent the local extension direction of geochemical element distribution, a gradient constraint to reflect the drastic changes in element concentration, and a range constraint to ensure that the range of interpolation results conforms to natural laws are added to the radial basis function interpolation model to obtain a multi-constraint radial basis interpolation model. The multi-constraint radial basis interpolation model is transformed into a quadratic objective function with tangent and gradient constraints as equality constraints and range constraints as inequality constraints. The quadratic objective function is solved using an iterative interpolation method to obtain the geochemical data interpolation results within the study area.

2. The geochemical data interpolation method under multiple constraints according to claim 1, characterized in that, The multi-constraint radial basis interpolation model is expressed as follows: ； in, Represents the interpolation function. Indicates the weighting coefficient. Indicates the action on the radial basis functions A continuous linear functional on, It is a (m-1) order bivariate polynomial, and s(x)∈H indicates that the interpolation function belongs to the function space. , This represents the total number of linear functionals. , and These represent the number of tangent constraints, gradient constraints, and range constraints, respectively.

3. The geochemical data interpolation method under multiple constraints according to claim 2, characterized in that, In the tangent constraint, the principal direction of local anisotropy that varies along the linear structure direction is used to indicate the local extension direction of the geochemical element anomaly distribution, and the local extension direction is orthogonal to the gradient direction of the fastest change in the element anomaly distribution. The tangent constraint is expressed by the formula: ； in, Distribution of geochemical elements, For the point position, Let be the vector representing the principal direction of local anisotropy. For gradient operators, It is a vector dot product operator; The tangent constraint acts on the linear function of the radial basis function. The specific form is: ； in, This represents a linear function acting on radial basis functions. This represents the point estimation functional. , The partial derivative is a function of the second input variable of the radial basis function. ∘ represents the composition of functions. and These represent the components of the second-order tensor.

4. The geochemical data interpolation method under multiple constraints according to claim 2, characterized in that, In the gradient constraint, the gradient direction indicates the direction of the fastest change in the abnormal distribution of elements, the magnitude of the gradient is a unit normal vector, and the condition for its validity is: ； in, It is an abnormal distribution. For the point position, For gradient operators, This is the unit normal vector at this location; The gradient constraint acts on a linear function of the radial basis function. The specific form is: ； in, It is a point estimation functional. , express Direction and y Two independent linear functionals in the direction , respectively corresponding to and , The partial derivative is a function of the second input variable of the radial basis function. ∘ represents the composition of functions.

5. The geochemical data interpolation method under multiple constraints according to claim 2, characterized in that, The value range constraints are obtained based on the geological information of the study area, including negative value constraints that conform to natural laws or the range of regional element content limits obtained based on expert experience; The negative value constraint is expressed as: ; The specified range for element content is expressed as follows: ; in, and These represent the lower and upper limits of the element content, respectively, and f(xi) is the interpolation function at point... The value at that point represents the predicted element content at that point.

6. The geochemical data interpolation method under multiple constraints according to claim 1, characterized in that, The multi-constraint radial basis interpolation model is transformed into a quadratic objective function with tangent and gradient constraints as equality constraints and range constraints as inequality constraints, including: The linear functional is applied to the multi-constraint radial basis interpolation model, and the multi-constraint radial basis interpolation model is transformed into a system of quadratic programming equations, expressed as: ； in, The weight coefficient vector has a length of H is ( A is a positive definite symmetric matrix. ) Matrix, F is ( ) Matrix, B is ( ) matrix, I is the zero matrix, and length is .

7. The geochemical data interpolation method under multiple constraints according to claim 6, characterized in that, The quadratic objective function is solved using an iterative interpolation method to obtain the geochemical data interpolation results within the study area, including: The center point of the negative value region is selected as the initial inequality constraint point and added to the quadratic programming problem equation system; Solve the current quadratic programming problem equations to obtain newly generated interpolation points, and check whether the newly generated interpolation points satisfy the value range constraints; when the newly generated interpolation points do not satisfy the value range constraints, extract the coordinates of the newly generated interpolation points, and convert the newly generated interpolation points into new inequality constraint points; New inequality constraint points are added to the quadratic programming problem equations for iterative solution until all interpolation results satisfy the range constraints, thus obtaining the geochemical data interpolation results within the study area.

8. A geochemical data interpolation system under multiple constraints, characterized in that, include: The acquisition module is used to acquire chemical element sampling information and geological information within the study area; The generalized model building module is used to construct a radial basis function interpolation model based on the chemical element sampling information; the radial basis function interpolation model with the interpolation surface passing through all sampling points is constructed as follows: ； ； in, Represents the interpolation function. This represents the radial basis functions, whose values ​​depend on the points. and The distance between them For sample data; ,..., It is a d-dimensional real space Two different points in the middle, , Indicates sampling point The measured values ​​at that location are continuous real values. Represents real coefficients; The constraint model establishment module is used to add tangent constraints to the radial basis function interpolation model based on the geological information, which represent the local extension direction of the distribution of geochemical elements, gradient constraints to reflect the degree of drastic change in element concentration, and range constraints to ensure that the range of interpolation results conforms to natural laws, so as to obtain a multi-constraint radial basis interpolation model. The transformation module is used to transform the multi-constraint radial basis interpolation model into a quadratic objective function with tangent constraints and gradient constraints as equality constraints and range constraints as inequality constraints. The calculation module is used to solve the quadratic objective function using an iterative interpolation method to obtain the geochemical data interpolation results within the study area.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the geochemical data interpolation method under multiple constraints as described in any one of claims 1-7.

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