Geochemical exploration data interpolation method and system under multi-constraint condition and storage medium

Abstract

The invention discloses a geochemical exploration data interpolation method and system under a multi-constraint condition and a storage medium, and the method comprises the steps: obtaining geochemical element sampling information in a research region, and constructing a radial basis function interpolation model; adding a tangent constraint, a gradient constraint and a value domain constraint in the radial basis function interpolation model according to geological information, and constructing a multi-constraint radial basis interpolation model; converting the multi-constraint-condition radial basis interpolation model into a quadratic objective function which takes tangent constraint and gradient constraint as equality constraint and takes value domain constraint as inequality constraint; and solving the quadratic objective function by adopting an iterative interpolation method to obtain a geochemical exploration data interpolation result in the research area. According to the method, a generalized radial basis interpolation method is applied, a general framework in which different types of constraints are added through linear functional is provided, an interpolation result which better conforms to geological laws and expert cognition can be obtained through calculation, and the method has important application value for geochemical exploration mapping based on the interpolation result.

Description

Technical Field

[0001] The present invention relates to the technical field of geochemical data processing, and in particular to a geochemical exploration data interpolation method and system under multiple constraints and a computer-readable storage medium. Background Art

[0002] Interpolation of geochemical element content is the basis of geochemical mapping and a necessary prerequisite for using geochemical means to find mineral targets and predict mineral scale. This is due to the limitations of the actual field environment. Geochemical prospectors can only use limited sampling methods to obtain discrete sampling data at limited spatial locations. In order to obtain more unknown data, known sampling data can be used to predict unknown points using spatial interpolation methods.

[0003] At present, many classical spatial interpolation methods (such as distance weighting method, spline function method, Kriging interpolation and radial basis interpolation method) have been applied to the interpolation of geochemical element content. However, these interpolation methods usually focus on the spatial distribution characteristics of data. In actual geochemical exploration, non-spatial factors such as geological structure and ore body boundary have an important influence on element distribution. Classical methods often cannot consider these constraints at the same time, and the added constraints are single, resulting in deviations in interpolation results. In addition, when the sampling points are sparse and uneven, it is difficult for existing methods to consider the influence of geological structure on element distribution, resulting in changes or distortions in the element distribution characteristics in the interpolation results. At the same time, some classical interpolation algorithms will cause negative values ​​in the interpolation results due to their own algorithm defects. Although some studies have tried to correct this problem by constraining weight coefficients or non-negative constraints, there is still a lack of effective solutions 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, which can use geological bodies, geological structures, water systems, and value ranges as important supplementary constraint information based on the generalized radial basis interpolation method, and perform geochemical element content interpolation together with sampling to obtain interpolation results that are more in line with geological laws and expert cognition, thereby improving the accuracy of the interpolation results. Summary of the invention

[0005] In view of this, the present invention provides a method, system and storage medium for geochemical data interpolation under multiple constraints, so as to solve the technical problems that the existing interpolation methods are difficult to consider multiple types of constraints such as geological data and expert knowledge, resulting in the interpolation results may have changes or distortions in element distribution characteristics, the existence of negative values, and other technical problems that are inconsistent with the actual distribution characteristics.

[0006] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

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

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

[0009] Constructing a radial basis function interpolation model based on the chemical element sampling information;

[0010] According to the geological information, a tangent constraint for indicating the local extension direction of the distribution of geochemical elements, a gradient constraint for reflecting the drastic degree of element concentration change, and a range constraint for ensuring that the range of the interpolation result conforms to the laws of nature are added to the radial basis function interpolation model to obtain a multi-constraint radial basis interpolation model;

[0011] Converting 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;

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

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

[0014] Construct the radial basis function interpolation model of the interpolation surface through all sampling points, expressed as:

[0015]

[0016]

[0017] Among them, s(x) represents the interpolation function, φ(||xx i ||) represents the radial basis function, and the radial basis function value depends on the points x and x i The distance between i , f i} is sample data; x 1 , …, x n is a d-dimensional real space Two different points in the f k Represents the sampling point x k The measured value at is a continuous real value, c i represents real coefficients.

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

[0019]

[0020] Among them, s(x) represents the interpolation function, ω j represents the weight coefficient, represents the continuous linear functional acting on the radial basis function Φ(x, x′), p(x) is a (m-1)-order bivariate polynomial, s(x)∈H indicates that the interpolation function belongs to the function space H, N=μ+σ+τ represents the total number of linear functionals, μ, σ and τ represent the number of tangent constraints, gradient constraints and range constraints, respectively.

[0021] Furthermore, in the tangent constraint, the local anisotropy main direction that changes along the linear structure direction is used to indicate the local extension direction of the geochemical element abnormal distribution, and the local extension direction is orthogonal to the gradient direction where the element abnormal distribution changes fastest;

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

[0023]

[0024] Where f(x) is the distribution of geochemical elements, x i is the point position, τ i is the vector representing the principal direction of local anisotropy, is the gradient operator, <·> is the vector dot product operator;

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

[0026]

[0027] in, represents the linear function acting on the radial basis function, represents the point estimate functional, The partial derivative is the second input variable x′ of the radial basis function, ° represents the composite function, t jx and t jy They represent the components of the second-order tensor respectively.

[0028] Furthermore, in the gradient constraint, the gradient direction indicates the direction in which the abnormal distribution of the elements changes fastest, the modulus of the gradient is the unit normal vector, and the establishment condition is:

[0029]

[0030] Among them, f(x i ) is an abnormal distribution, x i is the point position, is the gradient operator, ni is the unit normal vector here;

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

[0032]

[0033] in, is the point estimate functional, The partial derivative is the second input variable x′ of the radial basis function, and ° represents the composite of the function.

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

[0035] The negative value constraint is expressed as: (xi, f(xi))≥0;

[0036] The element content limit range is expressed as: a≤f(x i )≤b;

[0037] Where a and b represent the lower and upper limits of the element content, respectively, and f(xi) is the value of the interpolation function at point xi, indicating 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 constraints 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 quadratic programming problem equation system, which is expressed as:

[0040]

[0041] Among them, ω is the weight coefficient vector, with length L=v+μ+3σ+τ, H is a (L×L) positive definite symmetric matrix, A is a (μ+3σ+τ)×L matrix, F is a (μ+3σ+τ)×L matrix, B is a (v×L) matrix, and I is a zero matrix with length v.

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

[0043] Selecting the center point of the negative value area as the initial inequality constraint point and adding it to the quadratic programming problem equation system;

[0044] Iteratively solving the current quadratic programming problem equation group to obtain newly generated interpolation points, and checking whether the newly generated interpolation points satisfy the range constraint; when the newly generated interpolation points do not satisfy the range constraint, extracting the coordinates of the newly generated interpolation points, and converting the newly generated interpolation points into new inequality constraint points;

[0045] New inequality constraint points are added to the quadratic programming problem equation group for solving until all interpolation results satisfy the range constraint, thereby obtaining the geochemical exploration data interpolation results in the study area.

[0046] In a second aspect, the present invention provides a geochemical exploration data interpolation system under multiple constraints, comprising:

[0047] Acquisition module, used to obtain chemical element sampling information and geological information in the study area;

[0048] A generalized model building module, used for building a radial basis function interpolation model based on the chemical element sampling information;

[0049] A constraint model building module is used to add a tangent constraint for indicating the local extension direction of geochemical element distribution, a gradient constraint for reflecting the drastic degree of element concentration change, and a range constraint for ensuring that the range of the interpolation result conforms to the laws of nature in the radial basis function interpolation model according to the geological information, so as to obtain a multi-constraint radial basis function interpolation model;

[0050] A conversion module, used for converting 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 by adopting an iterative interpolation method to obtain the interpolation result of the geochemical exploration data in the study area.

[0052] In a third aspect, the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for interpolating geochemical exploration data under multiple constraints described in any one of the above technical solutions is implemented.

[0053] Compared with the prior art, the method of the present invention: first, construct a radial basis function interpolation model according to the acquired chemical element sampling information; second, in the interpolation process, effectively combine the sampling information and the geological information, and by adding tangent constraints, gradient constraints and range constraints, make the interpolation results fully consider the constraints such as geological structure, and ensure that the interpolation results obtained conform to the actual geological distribution characteristics and natural laws; finally, transform the interpolation model of multiple constraints into a quadratic programming problem, and solve it by iterative interpolation method, which can effectively balance the relationship between the various constraints in the optimization process, find the optimal interpolation result, and maximize the global optimization of the model while ensuring the constraints, so that the interpolation results are more reasonable and accurate in the entire study area. Compared with the traditional spatial interpolation method, the present invention can obtain interpolation results that are more in line with geological laws and expert cognition, can effectively simulate the distribution characteristics of geochemical anomalies, provide a reliable basis for determining the target area, and have important application value in the field of geochemical exploration and mapping. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

[0057] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a 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 used to limit the scope of the present invention.

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

[0059] In geochemical exploration, due to the limitations of the field environment, geochemical explorers can usually only obtain discrete sampling data within a limited spatial range. These sampling data not only include the content values ​​of elements, but may also contain some functional values ​​that are irrelevant to spatial distribution (such as geological structure, ore body boundary and other information). Classical spatial interpolation methods (such as distance weighted method, spline function method, Kriging interpolation method and radial basis interpolation method) usually focus on inferring the value of unknown points through spatial distribution characteristics, but often ignore the influence of non-spatial factors such as geological structure and geological body on element distribution.

[0060] In order 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, linear functionals are introduced to simultaneously add 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] The present invention provides a geochemical exploration data interpolation method under multiple constraints, which is described in detail below.

[0062] See also Figure 1 This embodiment provides a method for geochemical exploration data interpolation under multiple constraints, including:

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

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

[0065] Step S103: Adding a tangent constraint for indicating the local extension direction of geochemical element distribution, a gradient constraint for reflecting the drastic degree of element concentration change, and a range constraint for ensuring that the range of the interpolation result conforms to the laws of nature to the radial basis function interpolation model according to the geological information, so as to obtain a multi-constraint radial basis function interpolation model;

[0066] Step S104: converting 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: using an iterative interpolation method to solve the quadratic objective function to obtain an interpolation result of the geochemical exploration data in the study area.

[0068] The method of this embodiment, first, constructs a radial basis function interpolation model according to the acquired chemical element sampling information; second, in the interpolation process, effectively combines the sampling information and the geological information, and by adding tangent constraints, gradient constraints and range constraints, makes the interpolation results more objectively reflect the spatial distribution law of geochemical elements, avoids over-smoothing or over-changing interpolation results, and ensures that the interpolation results are more in line with the actual geological distribution characteristics; finally, the interpolation model of multiple constraints is transformed into a quadratic programming problem, and is solved by iterative interpolation method, which can effectively balance the relationship between various constraints in the optimization process, find the optimal interpolation result, and maximize the global optimization of the model while ensuring the constraints, so that the interpolation results are more reasonable and accurate in the entire study area. Compared with the traditional spatial interpolation method, the method of this embodiment can obtain interpolation results that are more in line with geological laws and expert cognition, can effectively simulate the distribution characteristics of geochemical anomalies, provide a reliable basis for determining the target area, and have important application value in the field of geochemical exploration and mapping.

[0069] As a preferred embodiment, a scalar function f(x) is used to represent the real distribution of chemical element content in the geochemical field; the distribution of chemical elements in the geochemical field is simulated by interpolation, and represented by an interpolation function s(x). By approximating f(x) with the interpolation function s(x), it can be known from the optimal recovery theory that when the value s* in the space is closest to f(x), we can obtain:

[0070]

[0071] in, represents a function space. This means that in a certain function space Find a function s* that provides the best approximation to f(x) among all possible interpolation functions.

[0072] As an accurate interpolation method, the interpolation surface constructed by radial basis function interpolation should pass through all sampling points. A radial basis function interpolation model is constructed based on the chemical element sampling information, including:

[0073] Construct the radial basis function interpolation model of the interpolation surface through all sampling points, expressed as:

[0074]

[0075]

[0076] Among them, s(x) represents the interpolation function, φ(||xx i ||) represents the radial basis function, and the radial basis function value depends on the points x and x i The distance between i , fi} is sample data; x 1 , …, x n is a d-dimensional real space Two different points in the f k Represents the sampling point x k The measured value at is a continuous real value, c i represents real coefficients.

[0077] The above radial basis function interpolation problem can be described as: in d-dimensional space, according to the known sample data Build an interpolation model.

[0078] At the same time, in the generalized radial basis function interpolation, as long as the continuous linear functional ∧ = {λ 1 , …, λ N} are linearly independent, then any type of linear functional is allowed to be added to the interpolation, which can meet the requirements of using multiple types of constraints in geochemical exploration interpolation.

[0079] As a preferred embodiment, a linear functional is introduced to process different constraint information, specifically: according to the geological information, a tangent constraint for indicating the local extension direction of the distribution of geochemical elements, a gradient constraint for reflecting the drastic degree of element concentration change, and a range constraint to ensure that the range of the interpolation result conforms to the laws of nature are added to the radial basis function interpolation model, thereby obtaining a multi-constraint radial basis interpolation model. At this time, the multi-constraint radial basis interpolation model is expressed as:

[0080]

[0081] Among them, s(x) represents the interpolation function, ω j represents the weight coefficient, represents the continuous linear functional acting on the radial basis function Φ(x, x′), p(x) is a (m-1)-order bivariate polynomial, s(x)∈H indicates that the interpolation function belongs to the function space H, N=μ+σ+τ represents the total number of linear functionals, μ, σ and τ represent the number of tangent constraints, gradient constraints and range constraints, respectively.

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

[0083] (1) Tangent constraint

[0084] Affected by hydrothermal activity, the distribution of geochemical elements often manifests itself in the form of spatial distribution along rift zones, faults, stratigraphic bedding, contact zones, foliation and other structures. At the same time, under some special geological backgrounds, the distribution of geochemical elements in geological bodies and water systems often has directional information. Local anisotropy can be directly extracted from linear structural direction data as tangent constraints. Linear structures can be the outline of an object, the direction of a texture, or any structure with obvious directionality.

[0085] The main direction of local anisotropy indicates the local extension direction of geochemical element anomaly distribution, which is orthogonal to the gradient direction where the element anomaly distribution changes fastest.

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

[0087]

[0088] Where f(x) is the distribution of geochemical elements, x i is the point position, τ i is the vector representing the principal direction of local anisotropy, is the gradient operator, <·> is the vector dot product operator;

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

[0090]

[0091] in, represents the linear function acting on the radial basis function, represents the point estimate functional, The partial derivative is the second input variable x′ of the radial basis function, ° represents the composite function, t jx and t jy They represent the components of the second-order tensor respectively.

[0092] (2) Gradient Constraint

[0093] The gradient direction indicates the direction in which the abnormal distribution of elements changes most rapidly. Based on the theory of ore deposits, hydrothermal fluids migrate in a directional manner under the action of percolation and diffusion, and migrate and move under the action of pressure gradients. Under the condition of concentration gradients, they migrate and move from high concentrations to low concentrations. In geochemical interpolation, the gradient direction indicates the direction in which the abnormal distribution of elements changes most rapidly, and the modulus of the gradient is the unit normal vector, that is, the following conditions hold:

[0094]

[0095] Among them, f(x i ) is an abnormal distribution, xi is the point position, is the gradient operator, ni is the unit normal vector here;

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

[0097]

[0098] in, is the point estimate functional, The partial derivative is the second input variable x′ of the radial basis function, and ° represents the composite of the function.

[0099] (3) Range Constraints

[0100] Based on the geological background, regional geological structure, element co-occurrence rules, etc., industry experts give a threshold range for the element content in the region or perform statistical analysis on the sampled data in the study area to obtain the element content range threshold, which includes: negative value constraint ((xi, f(xi)) ≥ 0}) or expert-estimated regional element content limit range a ≤ f(x i )≤b;

[0101] Where a and b represent the lower and upper limits of the element content, respectively, and f(xi) is the value of the interpolation function at point xi, indicating the predicted element content at that point.

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

[0103]

[0104] in, is the point estimate functional, The partial derivative refers to the second input variable x′ of the radial basis function.

[0105] This linear functional Applied to the generalized radial basis interpolation formula, the following equation for interpolation s(x) is obtained after expansion:

[0106]

[0107] Among them, the weight coefficient aj is related to the known sampling point data Related, the weight vector is b k =(b, c, d) and gradient condition Correlation, weight coefficient el and tangent data Weight coefficient g s Related to the m-1 order polynomial. Differential operator is the second input variable x to the radial basis μ+k =(x μ+k ,y μ+k ), x μ+σ+l =(x μ+σ+l ,y μ+σ+l ) to perform differential operations.

[0108] Therefore, the generalized radial basis interpolation problem will eventually be transformed into the problem of solving the linear equation system Αx=b (where A=φ(r), b=Φ(x, x′)).

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

[0110] 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 quadratic programming form, which is expressed as:

[0111]

[0112] Among them, ω is the weight coefficient vector, with length L = v + μ + 3σ + τ, H is a (L×L) positive definite symmetric matrix, A is a (μ+3σ+τ)×L matrix, F is a (μ+3σ+τ)×L matrix, B is a (v×L) matrix, and I is a zero matrix with length v.

[0113] The matrix and optimized vector details are summarized as follows:

[0114]

[0115]

[0116] like Figure 2 As shown, Figure 2 A schematic diagram of the main technical route of this method is shown.

[0117] Since the range constraint is for a large number of points to be estimated in the entire region, and the inequality constraint solving method itself is time-consuming, these factors may lead to complex calculations. As a preferred embodiment, the idea of ​​iterative interpolation is used to gradually add a number of range constraint points in the iterative interpolation process until all the values ​​of the points to be estimated meet the range constraint, and it is expected that reasonable results can be obtained quickly.

[0118] The specific steps of iterative interpolation are as follows:

[0119] Step S201: preliminarily select one (or several) inequality points, preferably the center point of the negative value area, and add them to the interpolation framework of the generalized radial basis as inequality constraints to construct a quadratic programming problem for solution.

[0120] Step S202: construct an interpolation model, obtain the interpolation result of the point to be solved, extract the coordinates of the point that does not meet the range constraint in the interpolation result, convert the point into an inequality constraint, and reconstruct the equation for solving.

[0121] Step S203: Repeat step S202 until all interpolation results in the grid fall within the value range, stop calculating and output the final interpolation result.

[0122] like Figure 3 As shown, the embodiment of the present invention further provides a geochemical exploration data interpolation system 300 under multiple constraints, including:

[0123] An acquisition module 301 is used to acquire chemical element sampling information and geological information in a study area;

[0124] A generalized model building module 302 is used to build a radial basis function interpolation model based on the chemical element sampling information;

[0125] The constraint model building module 303 is used to add a tangent constraint for indicating the local extension direction of the distribution of geochemical elements, a gradient constraint for reflecting the degree of drastic change in element concentration, and a range constraint for ensuring that the range of the interpolation result conforms to the laws of nature in the radial basis function interpolation model according to the geological information, so as to obtain a multi-constraint radial basis function interpolation model;

[0126] A conversion module 304 is used to convert 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;

[0127] The calculation module 305 is used to solve the quadratic objective function by adopting an iterative interpolation method to obtain the interpolation result of the geochemical exploration data in the study area.

[0128] In summary, the geochemical exploration data interpolation method under multiple constraints provided by the present invention has the following advantages:

[0129] (1) Aiming at the anisotropic characteristics of element content distribution in geochemical fields, this method extracts directional information from special geological bodies (dykes, special rock formations, etc.), geological structures (folds, faults), and water systems, and converts them into local anisotropic constraints to participate in the interpolation process to constrain the distribution and direction of anomalies. Experiments show that after adding local anisotropic constraints, the accuracy of the interpolation results is improved due to the inclusion of more geological knowledge in the interpolation process.

[0130] (2) Due to the defects of some classic interpolation algorithms (such as radial basis function interpolation) or the local uneven spatial distribution of sampling points, the interpolation results may not conform to natural laws (such as negative values) or be too large or too small. In view of this situation, this method converts the threshold range of element content given by experts in the region by combining geological background, regional geological structure, element association law, etc. into inequality constraints and adds them to the geochemical exploration interpolation process, so that the interpolation results are more in line with geological laws and expert cognition.

[0131] (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 a cross-validation method to quickly find the optimal parameters that minimize the error of the radial basis interpolation model.

[0132] (4) In order to improve the computational efficiency, this method uses the idea of ​​iterative interpolation. By gradually adding a number of range constraint points during the iterative interpolation process until all the values ​​of the points to be estimated meet the range constraints, a reasonable result can be obtained quickly.

[0133] Compared with traditional spatial interpolation methods, this method can obtain interpolation results that are more in line with geological laws and expert cognition, can effectively simulate the distribution characteristics of geochemical anomalies, provide a reliable basis for determining target areas, and has important application value for geochemical exploration mapping based on this.

[0134] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A geochemical exploration data interpolation method under multiple constraints, characterized in that: include: Obtain chemical element sampling information and geological information in the study area; Constructing a radial basis function interpolation model based on the chemical element sampling information; According to the geological information, a tangent constraint for indicating the local extension direction of the distribution of geochemical elements, a gradient constraint for reflecting the drastic degree of element concentration change, and a range constraint for ensuring that the range of the interpolation result conforms to the laws of nature are added to the radial basis function interpolation model to obtain a multi-constraint radial basis interpolation model; Converting 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 quadratic objective function is solved by using an iterative interpolation method to obtain the interpolation results of the geochemical exploration data in the study area.

2. The geochemical exploration data interpolation method under multiple constraints according to claim 1 is characterized in that: Constructing a radial basis function interpolation model based on the chemical element sampling information includes: Construct the radial basis function interpolation model of the interpolation surface through all sampling points, expressed as: Among them, s(x) represents the interpolation function, φ(||xx i ||) represents the radial basis function, and the radial basis function value depends on the point x i and x i The distance between i , f i } is sample data; x1,…,x n is a d-dimensional real space Two different points in the f k Represents the sampling point x k The measured value at is a continuous real value, c i represents real coefficients.

3. The geochemical exploration data interpolation method under multiple constraints according to claim 2 is characterized in that: The multi-constraint radial basis interpolation model is expressed as: Among them, s(x) represents the interpolation function, ω j represents the weight coefficient, represents the continuous linear functional acting on the radial basis function Φ(x, x′), p(x) is a (m-1)-order bivariate polynomial, s(x)∈H indicates that the interpolation function belongs to the function space H, N=μ+σ+τ represents the total number of linear functionals, μ, σ and τ represent the number of tangent constraints, gradient constraints and range constraints, respectively.

4. The geochemical exploration data interpolation method under multiple constraints according to claim 3 is characterized in that: In the tangent constraint, the local anisotropy main direction that changes along the linear structure direction is used to indicate the local extension direction of the abnormal distribution of geochemical exploration elements, and the local extension direction is orthogonal to the gradient direction where the abnormal distribution of elements changes fastest; The tangent constraint is expressed by the formula: Where f(x) is the distribution of geochemical elements, x i is the point position, τ i is the vector representing the principal direction of local anisotropy, is the gradient operator, <·> is the vector dot product operator; The tangent constraint acts on a linear function of the radial basis function. The specific form is: in, represents the linear function acting on the radial basis function, δ' xj x′ represents the point estimate functional, δ' xj x′ Φ(x, x′)=Φ(x, x j ), The partial derivative is the second input variable x′ of the radial basis function, represents the composition of functions, t jx and t jy They represent the components of the second-order tensor respectively.

5. The geochemical exploration data interpolation method under multiple constraints according to claim 3 is characterized in that: In the gradient constraint, the gradient direction indicates the direction in which the abnormal distribution of the elements changes fastest. The modulus of the gradient is the unit normal vector, and the establishment condition is: Among them, f(x i ) is an abnormal distribution, x i is the point position, is the gradient operator, ni is the unit normal vector here; The gradient constraint acts on a linear function of the radial basis function The specific form is: Among them, δ' xj x′ is the point estimate functional, δ' xj x′ Φ(x, x′)=Φ(x, x j ), The partial derivative is the second input variable x′ of the radial basis function, Represents the composition of functions.

6. The geochemical exploration data interpolation method under multiple constraints according to claim 3 is characterized in that: 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 a limited range of regional element content obtained based on expert experience; The negative value constraint is expressed as: (xi, f(xi))≥0; The element content limit range is expressed as: a≤f(x i )≤b; Where a and b represent the lower and upper limits of the element content, respectively, and f(xi) is the value of the interpolation function at point xi, indicating the predicted element content at that point.

7. The geochemical exploration data interpolation method under multiple constraints according to claim 1, characterized in that: The multi-constraint radial basis interpolation model is converted into a quadratic objective function with tangent constraints 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 quadratic programming problem equation system, which is expressed as: Among them, ω is the weight coefficient vector, with length L = v + μ + 3σ + τ, H is a (L×L) positive definite symmetric matrix, A is a (μ+3σ+τ)×L matrix, F is a (μ+3σ+τ)×L matrix, B is a (v×L) matrix, and I is a zero matrix with length v.

8. The geochemical exploration data interpolation method under multiple constraints according to claim 7 is characterized in that: The quadratic objective function is solved by using an iterative interpolation method to obtain the interpolation results of the geochemical exploration data in the study area, including: Selecting the center point of the negative value area as the initial inequality constraint point and adding it to the quadratic programming problem equation system; Solving the current quadratic programming problem equation group to obtain newly generated interpolation points, and checking whether the newly generated interpolation points satisfy the range constraint; when the newly generated interpolation points do not satisfy the range constraint, extracting the coordinates of the newly generated interpolation points, and converting the newly generated interpolation points into new inequality constraint points; New inequality constraint points are added to the quadratic programming problem equation group for iterative solution until all interpolation results satisfy the range constraint, thereby obtaining the geochemical exploration data interpolation results in the study area.

9. A geochemical exploration data interpolation system under multiple constraints, characterized in that: include: Acquisition module, used to obtain chemical element sampling information and geological information in the study area; A generalized model building module, used for building a radial basis function interpolation model based on the chemical element sampling information; A constraint model building module is used to add a tangent constraint for indicating the local extension direction of geochemical element distribution, a gradient constraint for reflecting the drastic degree of element concentration change, and a range constraint for ensuring that the range of the interpolation result conforms to the laws of nature in the radial basis function interpolation model according to the geological information, so as to obtain a multi-constraint radial basis function interpolation model; A conversion module, used for converting 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 by adopting an iterative interpolation method to obtain the interpolation result of the geochemical exploration data in the study area.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for interpolating geochemical exploration data under multiple constraints as described in any one of claims 1 to 8 is implemented.

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