Method for automatic generation of three-dimensional geological model based on contour line and maximum posterior probability

Abstract

This application relates to the field of 3D geological modeling technology and provides an automatic generation method for 3D geological models based on contour lines and maximum posterior probability. The method includes: acquiring the contour lines of the geological body to be modeled within a target area; discretizing the contour lines to obtain a set of 3D discrete points; acquiring the observed values ​​corresponding to the set of 3D discrete points, the variance of the observed value error at the spatial location of each discrete point, and the two-dimensional prior normal vector at each discrete point; constructing an objective function based on the acquired observed values, the variance of the observed value error, and the two-dimensional prior normal vector, with the goal of maximizing the posterior probability distribution of an implicit function; iteratively solving the objective function using the expectation-maximization algorithm to obtain the optimal implicit function; using the gradient of the implicit function to characterize the attitude of the geological body to be modeled; extracting the target isosurface of the optimal implicit function, and using the target isosurface as the 3D geological model of the geological body to be modeled. This application can improve the accuracy of 3D geological modeling.

Description

Technical Field

[0001] This application belongs to the field of three-dimensional geological modeling technology, and in particular relates to an automatic generation method for three-dimensional geological models based on contour lines and maximum a posteriori probability. Background Technology

[0002] In practical geological exploration projects, three-dimensional geological structures are typically inferred and reconstructed from two-dimensional geological profiles (such as exploration profile outlines). Transforming these discrete exploration profile data into continuous three-dimensional geological surfaces is the core step in three-dimensional implicit geological modeling.

[0003] In existing 3D implicit modeling methods, the spatial extension shape of a surface is highly dependent on the constraints of the normal vector (geological attitude) at the sampling point. However, in practical applications, it is difficult to obtain accurate 3D normal vectors, and usually only a rough estimate of the prior normal vectors can be made based on 2D exploration profiles. The main drawback of these estimated normal vectors is that they are restricted to the 2D profile plane, and are normal vectors directly transformed from the 2D plane to 3D space. They do not undergo reasonable spatial deflection between two adjacent contour surfaces in 3D space, resulting in extremely abrupt and unnatural transitions between contour lines of the constructed implicit surface, producing obvious exploration line effects. On the other hand, the direction of these normal vectors on their 2D profiles is often quite accurate, containing important prior geological structural information. Traditional modeling methods usually cannot identify this characteristic, either forcing strict matching, leading to surface distortion and exploration line effects, or completely discarding it, resulting in model distortion.

[0004] In summary, current implicit geological modeling methods suffer from low accuracy in 3D geological modeling. Summary of the Invention This application provides an automatic generation method for three-dimensional geological models based on contour lines and maximum a posteriori probability, which can solve the problem of low accuracy in three-dimensional geological modeling.

[0005] This application provides an embodiment of a method for automatically generating three-dimensional geological models based on contour lines and maximum a posteriori probability, including: Obtain the outline of the geological body to be modeled within the target area, and discretize the outline to obtain a three-dimensional discrete point cloud; the three-dimensional discrete point cloud includes the three-dimensional spatial coordinates of each discrete point obtained by discretization. Obtain the observation values ​​corresponding to the three-dimensional discrete point cloud, the observation error variance of the spatial location of each discrete point, and the two-dimensional prior normal vector at each discrete point; the observation values ​​include the isosurface observation values ​​of the implicit function at each discrete point; Based on the acquired observations, the variance of the observation error, and the two-dimensional prior normal vector, an objective function is constructed to maximize the posterior probability distribution of the implicit function. The expectation-maximization algorithm is then used to iteratively solve the objective function to obtain the optimal implicit function. The gradient of the implicit function is used to characterize the attitude of the geological body to be modeled. Extract the target isosurface of the optimal implicit function and use the target isosurface as a three-dimensional geological model of the geological body to be modeled.

[0006] Optionally, obtain the two-dimensional prior normal vector at each discrete point, including: Based on the morphological characteristics of the contour line in the two-dimensional plane, obtain the two-dimensional prior normal vector at each discrete point.

[0007] Optional, objective function for: ; in, Represents an implicit function. Represents the observed value Implicit functions The posterior probability distribution, Represents the observed value Implicit functions With latent variables The joint posterior probability distribution, latent variables Used to characterize the true three-dimensional spatial attitude of the geological body to be modeled at discrete points. , Indicates the first Latent variables corresponding to discrete points Indicates the number of discrete points. Represents a given implicit function and latent variables Time observations The likelihood term, Represents a given implicit function Latent variables The posterior distribution, Representing implicit functions The global spatial prior distribution, This represents the marginal likelihood of the observed data.

[0008] Optional, implicit functions Global spatial prior distribution satisfy: ; in, and All represent weighting coefficients. Representing implicit functions In function space The square of the half-norm of order, Indicates the first Three-dimensional spatial coordinates of a discrete point Representing implicit functions In the The gradient at each discrete point Indicates the first Two-dimensional prior normal vectors at discrete points; Given an implicit function Latent variables posterior distribution Satisfies a Gaussian distribution: ; in, Represents the covariance of latent variables. Representing latent variables Follow the mean Covariance is Gaussian distribution; Given an implicit function and latent variables Time observations Likelihood Item Satisfies a Gaussian distribution: ; in, Indicates the first Isosurface observations of implicit functions at discrete points Indicates the first Implicit function values ​​at discrete points Indicates the first The variance of the observation error of the spatial location of each discrete point Represents isosurface observations Follow the mean variance is The Gaussian distribution.

[0009] Optionally, in the process of iteratively solving the objective function using the expectation-maximization algorithm, the E-step of the expectation-maximization algorithm is in the _____th step. The process of calculating the posterior expectation of the latent variables in the next iteration is as follows: Utilizing the current implicit function Derive the posterior distribution of the latent variables ; Assuming latent variables and observed values Conditional independence, including the posterior distribution of latent variables. Decompose into independent products: ; Representing implicit functions For the current implicit function Latent variables The posterior distribution, Representing implicit functions For the current implicit function Time Latent variables corresponding to discrete points The posterior distribution of; Based on a given implicit function Latent variables posterior distribution If the distribution follows a Gaussian distribution, it can be inferred that the posterior distribution... Next Latent variables corresponding to discrete points posterior expectation for: ; in, Indicates the current implicit function In the The gradient at each discrete point , This indicates the preset maximum number of iterations.

[0010] Optionally, in the process of iteratively solving the objective function using the expectation-maximization algorithm, the E-step of the expectation-maximization algorithm is in the _____th step. Constructed in the next iteration function for: ; in, Represents the combined gradient. , Represents the combined gradient covariance matrix. , This represents the inverse matrix of the combined gradient covariance. , Represents a three-dimensional identity matrix.

[0011] Optionally, in the process of iteratively solving the objective function using the expectation-maximization algorithm, the M-step of the expectation-maximization algorithm is in the 1st step. Execute in the next iteration: for function Find the extreme value, and obtain the first value. The implicit function after the second iteration And update the latent variable covariance to obtain the first... Latent variable covariance after the second iteration .

[0012] Optional, the first The implicit function after the second iteration for: ; in, This represents the scalar coefficients to be solved. Let represent the conditionally positive definite kernel function with respect to the cube of the distance. Represents the three-dimensional spatial coordinates of any point within the target area. Denotes the coefficients of the three-dimensional vector to be solved. This indicates a conditionally positive definite kernel function with respect to the second variable. gradient, Represents the three-dimensional vector coefficients of a polynomial. Represents the scalar coefficients of a polynomial; scalar coefficients , three-dimensional vector coefficients Three-dimensional vector coefficients of polynomials scalar coefficients of polynomials The following system of linear equations was obtained by solving: ; in, , , and All are kernel matrix blocks. and All are polynomial basis matrices. This represents a diagonal matrix of observation error weights. , This represents a diagonal matrix with the elements within the brackets as the main diagonal elements. This represents the gradient covariance block diagonal matrix. , This represents a block diagonal matrix with the matrix within parentheses as the main diagonal matrix block. This represents the column vector of scalar coefficients to be solved. , This represents the column vector of coefficients of the three-dimensional vector to be solved. , This represents a column vector of equality constraint values. , Represents a column vector of latent variables. ; ; ; ; ; ; ; in, Represents the identity matrix. The conditional positive definite kernel function is represented in the th case. discrete points and the discrete points The value at that location, This indicates a conditionally positive definite kernel function with respect to the first variable. Find the three-dimensional row vector obtained by transposing the first-order partial derivative. The conditional positive definite kernel function is defined with respect to the first variable. and the second variable Find the three-dimensional matrix obtained by the second-order mixed partial derivatives, where .

[0013] Optional, the first Latent variable covariance after the second iteration for: ; in, Indicates the first The implicit function after the second iteration In the The gradient at each discrete point Indicates the first The gradient corresponding to the discrete point at the th discrete point is at the th... The latent variable covariance after the next iteration.

[0014] Optionally, when the first The model coefficients in the implicit function after the nth iteration are similar to those of the nth iteration. When the difference in the model coefficients of the implicit function after the nth iteration is less than a preset threshold, the iterative solution is stopped, and the nth iteration is set to the nearest integer. The implicit function after the next iteration is taken as the optimal implicit function; the model coefficients include scalar coefficients. , three-dimensional vector coefficients Three-dimensional vector coefficients of polynomials scalar coefficients of polynomials ; The target isosurface includes all three-dimensional spatial coordinates that make the value of the optimal implicit function equal to the target observation. The set of all geological bodies to be modeled; the three-dimensional geological model of the geological body to be modeled is composed of all the geological bodies in this set. The surfaces formed by corresponding spatial points.

[0015] The above-mentioned solution in this application has the following beneficial effects: In the embodiments of this application, a three-dimensional discrete point cloud is obtained by discretizing the contour line of the geological body to be modeled. Based on the observations corresponding to the three-dimensional discrete point cloud, the observation error variance corresponding to each discrete point, and the two-dimensional prior normal vector, an objective function is constructed with the goal of maximizing the posterior probability distribution of the implicit function. Then, the expectation maximization algorithm is used to iteratively solve the objective function to obtain the optimal implicit function. Finally, the three-dimensional geological model of the geological body to be modeled is obtained based on the target isosurface of the optimal implicit function. In this approach, since the gradient of the implicit function is used to characterize the attitude of the geological body to be modeled, the objective function is constructed based on the two-dimensional prior normal vector, the observed values, and the variance of the observed value error. This allows the two-dimensional prior normal vector to provide prior direction and magnitude constraints for the gradient, thereby effectively overcoming the limitation of the two-dimensional prior normal vector lacking deflection ability in three-dimensional space. At the same time, during the solution process, the implicit function is automatically corrected with the goal of maximizing the posterior probability distribution of the implicit function, thereby optimizing the gradient in terms of direction and length. This makes the transition of geological surfaces between contour lines smooth and natural, thus avoiding surface distortion and effectively eliminating the exploration line effect, thereby improving the accuracy of three-dimensional geological modeling. Other beneficial effects of this application will be described in detail in the following detailed description section. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating an embodiment of the automatic generation method for three-dimensional geological models based on contour lines and maximum a posteriori probability provided in this application; Figure 2 This is a schematic diagram of a three-dimensional discrete point cluster of an exploration profile outline in an example of this application; Figure 3 This is a magnified view of the shape of a single contour line before optimization in an example of this application; Figure 4 This is a schematic diagram of the initial three-dimensional geological model constructed using strict interpolation of traditional two-dimensional prior normal vectors in an example of this application; Figure 5 This is a magnified view of the optimized normal vector (gradient) on a single contour line in an example of this application; Figure 6 This is a schematic diagram of a three-dimensional geological model reconstructed using the latent variable gradient optimized in this application, as shown in an example of this application. Detailed Implementation

[0018] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0019] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0020] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0021] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0022] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0023] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0024] To address the issue of low accuracy in current 3D geological modeling, this application provides an automatic 3D geological model generation method based on contour lines and maximum posterior probability. This method discretizes the contour lines of the geological body to be modeled to obtain a set of 3D discrete points. Based on the observed values ​​corresponding to the 3D discrete point set, the variance of the observed value error for each discrete point, and the 2D prior normal vector, an objective function is constructed to maximize the posterior probability distribution of the implicit function. Then, the expected value maximization algorithm is used to iteratively solve the objective function to obtain the optimal implicit function. Finally, the 3D geological model of the geological body to be modeled is obtained based on the target isosurface of the optimal implicit function. In this approach, since the gradient of the implicit function is used to characterize the attitude of the geological body to be modeled, the objective function is constructed based on the two-dimensional prior normal vector, the observed values, and the variance of the observed value error. This allows the two-dimensional prior normal vector to provide prior direction and magnitude constraints for the gradient, thereby effectively overcoming the limitation of the two-dimensional prior normal vector lacking deflection ability in three-dimensional space. At the same time, during the solution process, the implicit function is automatically corrected with the goal of maximizing the posterior probability distribution of the implicit function, thereby optimizing the gradient in terms of direction and length. This makes the transition of geological surfaces between contour lines smooth and natural, thus avoiding surface distortion and effectively eliminating the exploration line effect, thereby improving the accuracy of three-dimensional geological modeling.

[0025] The following describes the automatic generation method for three-dimensional geological models based on contour lines and maximum posterior probability provided in this application, with reference to specific embodiments.

[0026] like Figure 1 As shown in the embodiments of this application, the automatic generation method for three-dimensional geological models based on contour lines and maximum a posteriori probability includes the following steps: Step 11: Obtain the outline of the geological body to be modeled within the target area, and discretize the outline to obtain a three-dimensional discrete point cloud; the three-dimensional discrete point cloud includes the three-dimensional spatial coordinates of each discrete point obtained by discretization.

[0027] The target area mentioned above refers to the region where the geological body to be modeled is located. The geological body to be modeled is the geological body for which a three-dimensional geological model needs to be constructed, such as an iron ore body or a copper ore body. In some embodiments of this application, the outline (i.e., the boundary two-dimensional outline) of the geological body to be modeled can be extracted from exploration data such as geological profile maps and mid-section maps of the target area.

[0028] The three-dimensional discrete point set obtained by discretizing the contour line , Indicates the first Three-dimensional spatial coordinates of a discrete point This indicates the number of discrete points.

[0029] Step 12: Obtain the observation values ​​corresponding to the three-dimensional discrete point cloud, the observation error variance of the spatial location of each discrete point, and the two-dimensional prior normal vector at each discrete point; the observation values ​​include the isosurface observation values ​​of the implicit function at each discrete point.

[0030] In some embodiments of this application, the variance of the error between the isosurface observation of the implicit function at each discrete point and the observation of the spatial location of each discrete point is set.

[0031] Among them, the observation values ​​corresponding to the three-dimensional discrete point cloud. , Indicates the first The isosurface observations of implicit functions at discrete points. In implicit modeling contexts, the surface containing the boundary of the geological body is typically defined as the target isosurface, and the observation values ​​are set accordingly. Setting the observation error variance is to overcome the accuracy deviation problem in the extraction process of exploration profiles, thereby improving the modeling accuracy. Specifically, the variance constant is assigned to each discrete point based on its data source and reliability. If the discrete point originates from high-precision measured exploration data (such as borehole intersections), its observation error variance is set to a small normal number close to zero to ensure the target isosurface accurately passes through that point. If the discrete point originates from geometric inference or edge sampling of geological profiles, it is set to a relatively large empirical error constant to allow reasonable spatial smoothing of the generated 3D geological surface in that area, thus filtering out local deviations caused by manual contour extraction.

[0032] In some embodiments of this application, the two-dimensional prior normal vector at each discrete point can be obtained based on the morphological characteristics of the contour line in a two-dimensional plane. The specific acquisition method includes: First, along the two-dimensional profile contour line (i.e., the aforementioned contour line), using the coordinate information of the current discrete point and its adjacent discrete points, the local tangent vector at that point is calculated using the central difference method. This tangent vector reflects the local extension direction of the contour line. Second, the local tangent vector is orthogonally rotated 90 degrees in the two-dimensional profile plane to obtain an initial normal vector perpendicular to the contour line. Finally, the initial normal vectors of all discrete points are corrected for orientation consistency, thereby obtaining the final two-dimensional prior normal vector at each discrete point. This two-dimensional prior normal vector is used to characterize the initial local geological occurrence of the boundary of the geological body to be modeled within the two-dimensional profile. Its function is to serve as basic prior information, providing prior direction and magnitude constraints for subsequent latent variables, thereby ensuring that the final generated three-dimensional geological model faithfully reflects the geological trend revealed by the original exploration data and avoids excessive deformation.

[0033] Step 13: Based on the acquired observations, the variance of the observation error, and the two-dimensional prior normal vector, construct an objective function that aims to maximize the posterior probability distribution of the implicit function, and use the expectation-maximization algorithm to iteratively solve the objective function to obtain the optimal implicit function; the gradient of the implicit function is used to characterize the attitude of the geological body to be modeled.

[0034] The aforementioned attitude includes strike, dip, and dip angle. It should be noted that the gradient of the implicit function is a latent variable, and in this application, a two-dimensional prior normal vector is used to provide prior direction and magnitude constraints for the gradient of the implicit function.

[0035] In some embodiments of this application, the above objective function for: ; in, Represents an implicit function. Represents the observed value Implicit functions The posterior probability distribution, Represents the observed value Implicit functions With latent variables The joint posterior probability distribution, latent variables Used to characterize the true three-dimensional spatial attitude of the geological body to be modeled at discrete points. , Indicates the first Latent variables corresponding to discrete points Indicates the number of discrete points. Represents a given implicit function and latent variables Time observations The likelihood term, Used to characterize the extent to which implicit functions and latent variables interpret observed data. Represents a given implicit function Latent variables The posterior distribution, Used to characterize the distribution of the true attitude with respect to the gradient of the function. Representing implicit functions The global spatial prior distribution, Used to introduce smoothness constraints and directional constraints for two-dimensional prior normal vectors. This represents the marginal likelihood of the observed data. Also known as the evidence term, it serves as a normalization factor and is used in optimizing implicit functions. The process is constant.

[0036] In the aforementioned objective function, based on the principle of implicit surface geometry, the interface of a three-dimensional geological body is defined as a continuous implicit function. The target isosurface. According to the geometric meaning of calculus, the gradient vector of an implicit function at any point in space is always perpendicular to the isosurface passing through that point. Therefore, this application characterizes the spatial attitude (normal) of geological interfaces by constraining the gradient direction of the implicit function.

[0037] The above implicit function Global spatial prior distribution satisfy: ; in, and All represent weighting coefficients. and Specifically, these are the weight parameters for adjusting the smoothing weight and the influence of the prior normal vector, which can be set according to the actual situation; Representing implicit functions In function space The square of the half-norm represents the global bending energy of the implicit surface. This term introduces a smooth prior, allowing the surface to maintain its natural extension in the non-sampling region. Indicates the first The three-dimensional spatial coordinates of a discrete point; Representing implicit functions In the Gradient at discrete points; Indicates the first Two-dimensional prior normal vectors at discrete points.

[0038] Given an implicit function Latent variables posterior distribution Satisfies a Gaussian distribution: ; in, Represents the covariance of latent variables. Representing latent variables Follow the mean Covariance is The Gaussian distribution.

[0039] Given an implicit function and latent variables Time observations Likelihood Item Satisfies a Gaussian distribution: ; in, Indicates the first Isosurface observations of implicit functions at discrete points Indicates the first Implicit function values ​​at discrete points Indicates the first The variance of the observation error of the spatial location of each discrete point Represents isosurface observations Follow the mean variance is The Gaussian distribution.

[0040] The following is an illustrative example of the process of iteratively solving the objective function using the Expectation Maximization (EM) algorithm.

[0041] It should be noted that, in the embodiments of this application, when using the EM algorithm for iterative solution, the logic of the traditional EM algorithm is followed (i.e., first the E-step, then the M-step, and so on iteratively until the algorithm converges), and the implicit function at the convergence point is taken as the optimal implicit function. However, in this application, the posterior expectation is calculated in the E-step, and the underlying function is constructed... The function approach and the parameter update method in the M-step differ from the traditional EM algorithm.

[0042] Specifically, in the process of iteratively solving the objective function using the expectation-maximization algorithm, the E-step of the expectation-maximization algorithm is in the _____th step. The process of calculating the posterior expectation of the latent variables in this iteration is as follows: steps 13.1 to 13.3: Step 13.1, utilize the current implicit function Derive the posterior distribution of the latent variables Current implicit function It can be understood as the first The implicit function after the nth iteration, when hour, This is the initial implicit function. This initial implicit function is a three-dimensional continuous function obtained by fitting and solving the three-dimensional discrete points, observations, and two-dimensional prior normal vectors using conventional implicit modeling methods such as radial basis functions.

[0043] Step 13.2, assume latent variables and observed values (i.e., latent variables at discrete points) and observed values ) Items are independent, and the posterior distribution of latent variables is determined. Decompose into independent products: ; Representing implicit functions For the current implicit function Latent variables The posterior distribution, Representing implicit functions For the current implicit function Time Latent variables corresponding to discrete points The posterior distribution.

[0044] Step 13.3, based on the given implicit function Latent variables posterior distribution If the distribution follows a Gaussian distribution, it can be inferred that the posterior distribution... Next Latent variables corresponding to discrete points posterior expectation for: ; in, Indicates the current implicit function In the The gradient at each discrete point , This indicates the preset maximum number of iterations (e.g., 100). Essentially, this involves re-estimating the most reasonable true normal gradient direction at the point cloud based on the current surface geometry.

[0045] It should be noted that, due to latent variables Including it in the joint distribution and not directly observable, leading to a posterior probability Direct maximization is difficult; therefore, the expectation-maximization algorithm is used to construct the joint posterior probability of the logarithm of the complete data in the posterior distribution of the latent variables. The following expectations, namely function As a substitute objective for maximizing the original objective function: ; in, The function mathematically constitutes the logarithmically transformed original objective function. The lower bound is used to approximate the maximization of the original objective by iteratively maximizing this lower bound; the logarithmic terms are expanded and ignored. Irrelevant constant terms Substituting the probability distribution terms into the objective function and taking their negatives, we can transform it into the objective energy functional (i.e., the final one). function That is, in step E (Function). Specifically, in the process of iteratively solving the objective function using the expectation-maximization algorithm, the E-step of the expectation-maximization algorithm is in the _____th step. Constructed in the next iteration function for: ; in, This represents the combined gradient, which incorporates two-dimensional prior constraints. , Let represent the combined gradient covariance matrix. , This represents the inverse matrix of the combined gradient covariance. , Represents a three-dimensional identity matrix.

[0046] In the iterative solution of the objective function using the expectation-maximization algorithm, the M-step of the expectation-maximization algorithm is at the _____th step. Execute in the next iteration: for function Find the extreme value, and obtain the first value. The implicit function after the second iteration And update the latent variable covariance to obtain the first... Latent variable covariance after the second iteration .

[0047] No. The implicit function after the second iteration for: ; in, This represents the scalar coefficients to be solved. Let represent the conditionally positive definite kernel function with respect to the cube of the distance. Represents the three-dimensional spatial coordinates of any point within the target area. Denotes the coefficients of the three-dimensional vector to be solved. This indicates a conditionally positive definite kernel function with respect to the second variable. gradient, Represents the three-dimensional vector coefficients of a polynomial. Represents the scalar coefficients of a polynomial.

[0048] scalar coefficients , three-dimensional vector coefficients Three-dimensional vector coefficients of polynomials scalar coefficients of polynomials The following system of linear equations was obtained by solving: ; in, , , and All are kernel matrix blocks. and All are polynomial basis matrices. This represents a diagonal matrix of observation error weights. , This represents a diagonal matrix with the elements within the brackets as the main diagonal elements. This represents the gradient covariance block diagonal matrix. , This represents a block diagonal matrix with the matrix within parentheses as the main diagonal matrix block. This represents the column vector of coefficients of the three-dimensional vector to be solved. , This represents the column vector of coefficients of the three-dimensional vector to be solved. , This represents a column vector of equality constraint values. , Represents a column vector of latent variables. ; ; ; ; ; ; ; in, Represents the identity matrix. The conditional positive definite kernel function is represented in the th case. discrete points and the discrete points The value at that location, This indicates a conditionally positive definite kernel function with respect to the first variable. Find the three-dimensional row vector obtained by transposing the first-order partial derivative. The conditional positive definite kernel function is defined with respect to the first variable. and the second variable Find the three-dimensional matrix obtained by the second-order mixed partial derivatives, where .

[0049] No. Latent variable covariance after the second iteration for: ; in, Indicates the first The implicit function after the second iteration In the The gradient at each discrete point Indicates the first The gradient corresponding to the discrete point at the th discrete point is at the th... The latent variable covariance after the next iteration Specifically, the first The gradient at discrete points on the th... The latent variable covariance after the nth iteration. hour, The initial latent variable covariance is typically set as a constant diagonal matrix to represent the fundamental uncertainty of the two-dimensional prior normal vector in the initial stage of algorithm iteration.

[0050] It is worth mentioning that by using the above formula to update the latent variable covariance, it is possible to automatically identify and suppress normal inconsistencies in exploration data, guide the normal vector to deflect reasonably in three-dimensional space, and eliminate the "exploration line effect".

[0051] It should be noted that during the update process of the latent variable covariance, terms related to the covariance are extracted from the target energy functional, and the latest obtained implicit function is fixed. By taking the partial derivative of the latent variable covariance matrix and setting it to zero, the update formula for the latent variable covariance is derived.

[0052] In some embodiments of this application, when the first The model coefficients in the implicit function after the nth iteration are similar to those of the nth iteration. When the difference in the model coefficients of the implicit function after the nth iteration is less than a preset threshold, the iterative solution is stopped, and the nth iteration is set to the nearest integer. The implicit function after the next iteration is taken as the optimal implicit function. The model coefficients here include scalar coefficients. , three-dimensional vector coefficients Three-dimensional vector coefficients of polynomials scalar coefficients of polynomials When comparing the differences between model coefficients, the comparison is performed separately for each type of coefficient. The iterative solution stops only when the difference between each type of coefficient is less than a preset threshold (i.e., ).

[0053] Understandably, if, when the maximum number of iterations is reached, the difference between the model coefficients in the implicit function after the last iteration and the model coefficients in the implicit function after the previous iteration is still greater than or equal to a preset threshold, then the implicit function after the last iteration is taken as the optimal implicit function.

[0054] Step 14: Extract the target isosurface of the optimal implicit function and use the target isosurface as the three-dimensional geological model of the geological body to be modeled.

[0055] In some embodiments of this application, the target isosurface includes all three-dimensional spatial coordinates that make the value of the optimal implicit function equal to the target observation. The set of all geological bodies to be modeled; the three-dimensional geological model of the geological body to be modeled is composed of all the geological bodies in this set. The model consists of surfaces formed by corresponding spatial points. These points constitute the model of the geological body to be modeled because the observed values ​​of discrete points on the contour lines are the constraint values ​​of the target isosurface. Therefore, extracting the isosurfaces whose implicit functions are equal to the constraint values ​​ensures that the generated surfaces accurately pass through all contour lines, thus closing in three-dimensional space to form the physical boundary of the target geological body. Specifically, the Dual Marching Cubes algorithm can be used to mesh the isosurfaces whose optimal implicit functions are equal to the target values, ultimately generating a smooth, continuous, and realistic three-dimensional geological body boundary surface model (i.e., the three-dimensional geological model of the geological body to be modeled). It should be noted that the specific values ​​of the target observed values ​​can be set according to the actual situation (e.g., set to 0). Furthermore, the target observed values ​​are consistent with the isosurface observed values ​​of the previously obtained discrete points.

[0056] To more intuitively demonstrate the 3D modeling effect of this application based on maximum a posteriori probability inference and EM algorithm iteration, the effect of the method in this application is illustrated below with specific experimental data.

[0057] like Figure 2 The image shows a three-dimensional discrete point set of the exploration profile outline extracted from a two-dimensional geological profile. In traditional implicit modeling, the prior normal vector is usually calculated directly from this two-dimensional outline. Combined with... Figure 3 As can be seen from the enlarged view before optimization, the traditional prior normal vector is strictly confined to its own two-dimensional profile plane, and the normal vector length at each point is uniform, lacking the ability to adapt to spatial topology. For example... Figure 4 As shown, if such a forced two-dimensional prior normal vector is directly used to construct a geological model, the normal vector cannot be reasonably deflected between adjacent contour surfaces, which will cause obvious grooves, step-like stretching and sharp concave-convex distortions on the generated initial model surface, i.e., the typical exploration line effect 401.

[0058] In contrast, this application introduces the real 3D gradient as a latent variable and continuously optimizes its posterior expectation and normal covariance during the iteration of the EM algorithm. Combined with... Figure 5 As can be seen from the optimized local magnified image, after optimization by the algorithm in this application, the normal vector (i.e., the latent variable gradient) breaks through the limitations of the two-dimensional plane and undergoes a natural deflection in three-dimensional space, pointing to the direction that best conforms to the global smooth prior. Simultaneously, the optimized gradient vector exhibits a regular adaptive change in length (magnitude): in areas with gentle geological interfaces and low curvature, the gradient vector length is longer, indicating high confidence and reliability of the normal vector at that location; while in areas with sharp interfaces, high curvature, or data conflicts, the gradient vector length automatically shortens, indicating higher error tolerance at that location.

[0059] Benefiting from the aforementioned three-dimensional adaptive deflection and dynamic confidence adjustment of the latent variable normal, such as Figure 6 As shown, the three-dimensional geological model reconstructed using the optimization method of this application completely eliminates the stepped exploration line effect. The surface achieves an extremely smooth and natural transition between each exploration contour line, accurately restoring the true spatial morphology of the three-dimensional geological body. It is evident that this application, through adaptive optimization of surface morphology and hyperparameters, achieves maximum a posteriori probability reconstruction from a noisy two-dimensional contour profile to the boundary of a three-dimensional geological body.

[0060] In summary, the automatic generation method for 3D geological models based on contour lines and maximum a posteriori probability provided in this application has the following advantages: First, it effectively eliminates the exploration line effect, overcomes the limitation of the lack of deflection ability of the two-dimensional prior normal in three-dimensional space, and uses the three-dimensional gradient as a latent variable for adaptive correction, realizing the optimization of the gradient in direction and length, so that the geological surface transition between contour lines is smooth and natural.

[0061] Second, by continuously optimizing the posterior expectation and covariance of the gradient latent variables, the normal constraints that can accommodate point cloud position noise and automatically correct anomalies are able to ensure the continuity and accuracy of the reconstructed geological body boundary.

[0062] Third, by finding the extreme values, the optimal implicit function analytical expression and the latent variable covariance update expression are naturally derived, eliminating the dependence on repeated manual adjustment of weights, realizing fully adaptive optimization of modeling parameters, and improving modeling efficiency.

[0063] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principles described in this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for automatically generating three-dimensional geological models based on contour lines and maximum a posteriori probability, characterized in that, include: Obtain the outline of the geological body to be modeled within the target area, and discretize the outline to obtain a three-dimensional discrete point cloud; the three-dimensional discrete point cloud includes the three-dimensional spatial coordinates of each discrete point obtained by discretization. The observed values ​​corresponding to the three-dimensional discrete point cloud, the observed value error variance of the spatial location of each discrete point, and the two-dimensional prior normal vector at each discrete point are obtained; the observed values ​​include the isosurface observed values ​​of the implicit function at each discrete point; Based on the acquired observations, the variance of the observation error, and the two-dimensional prior normal vector, an objective function is constructed to maximize the posterior probability distribution of the implicit function. The objective function is then iteratively solved using the expectation-maximization algorithm to obtain the optimal implicit function. The gradient of the implicit function is used to characterize the attitude of the geological body to be modeled. Extract the target isosurface of the optimal implicit function and use the target isosurface as the three-dimensional geological model of the geological body to be modeled.

2. The method for automatically generating a three-dimensional geological model according to claim 1, characterized in that, Obtain the two-dimensional prior normal vector at each discrete point, including: Based on the morphological characteristics of the contour line in the two-dimensional plane, obtain the two-dimensional prior normal vector at each discrete point.

3. The method for automatically generating a three-dimensional geological model according to claim 1, characterized in that, objective function for: ； in, Represents an implicit function. Represents the observed value Implicit functions The posterior probability distribution, Represents the observed value Implicit functions With latent variables The joint posterior probability distribution, latent variables Used to characterize the true three-dimensional spatial attitude of the geological body to be modeled at discrete points. , Indicates the first Latent variables corresponding to discrete points Indicates the number of discrete points. Represents a given implicit function and latent variables Time observations The likelihood term, Represents a given implicit function Latent variables The posterior distribution, Representing implicit functions The global spatial prior distribution, This represents the marginal likelihood of the observed data.

4. The method for automatically generating a three-dimensional geological model according to claim 3, characterized in that, Implicit functions Global spatial prior distribution satisfy: ； in, and All represent weighting coefficients. Representing implicit functions In function space The square of the half-norm of order, Indicates the first Three-dimensional spatial coordinates of a discrete point Representing implicit functions In the The gradient at each discrete point Indicates the first Two-dimensional prior normal vectors at discrete points; Given an implicit function Latent variables posterior distribution Satisfies a Gaussian distribution: ； in, Represents the covariance of latent variables. Representing latent variables Follow the mean Covariance is Gaussian distribution; Given an implicit function and latent variables Time observations Likelihood Item Satisfies a Gaussian distribution: ； in, Indicates the first Isosurface observations of implicit functions at discrete points Indicates the first Implicit function values ​​at discrete points Indicates the first The variance of the observation error of the spatial location of each discrete point Represents isosurface observations Follow the mean variance is The Gaussian distribution.

5. The method for automatically generating a three-dimensional geological model according to claim 4, characterized in that, In the iterative solution of the objective function using the expectation-maximization algorithm, the E-step of the expectation-maximization algorithm is at the [missing information]th step. The process of calculating the posterior expectation of the latent variables in the next iteration is as follows: Utilizing the current implicit function Derive the posterior distribution of the latent variables ; Assuming latent variables and observed values Conditional independence, including the posterior distribution of latent variables. Decompose into independent products: ; Representing implicit functions For the current implicit function Latent variables The posterior distribution, Representing implicit functions For the current implicit function Time Latent variables corresponding to discrete points The posterior distribution of; Based on a given implicit function Latent variables posterior distribution If the distribution follows a Gaussian distribution, it can be inferred that the posterior distribution... Next Latent variables corresponding to discrete points posterior expectation for: ； in, Indicates the current implicit function In the The gradient at each discrete point , This indicates the preset maximum number of iterations.

6. The method for automatically generating a three-dimensional geological model according to claim 5, characterized in that, In the iterative solution of the objective function using the expectation-maximization algorithm, the E-step of the expectation-maximization algorithm is at the [missing information]th step. Constructed in the next iteration function for: ； in, Represents the combined gradient. , Represents the combined gradient covariance matrix. , This represents the inverse matrix of the combined gradient covariance. , Represents a three-dimensional identity matrix.

7. The method for automatically generating a three-dimensional geological model according to claim 6, characterized in that, In the iterative solution of the objective function using the expectation-maximization algorithm, the M-step of the expectation-maximization algorithm is in the... Execute in the next iteration: for function Find the extreme value, and obtain the first value. The implicit function after the second iteration And update the latent variable covariance to obtain the first... Latent variable covariance after the second iteration .

8. The method for automatically generating a three-dimensional geological model according to claim 7, characterized in that, No. The implicit function after the second iteration for: ； in, Denotes the scalar coefficients to be solved. Let represent the conditionally positive definite kernel function with respect to the cube of the distance. Represents the three-dimensional spatial coordinates of any point within the target area. Denotes the coefficients of the three-dimensional vector to be solved. This indicates a conditionally positive definite kernel function with respect to the second variable. gradient, Represents the three-dimensional vector coefficients of a polynomial. Represents the scalar coefficients of a polynomial; scalar coefficients , three-dimensional vector coefficients Three-dimensional vector coefficients of polynomials scalar coefficients of polynomials The following system of linear equations was obtained by solving: ； in, , , and All are kernel matrix blocks. and All are polynomial basis matrices. This represents a diagonal matrix of observation error weights. , This represents a diagonal matrix with the elements within the brackets as the main diagonal elements. This represents the gradient covariance block diagonal matrix. , This represents a block diagonal matrix with the matrix within parentheses as the main diagonal matrix block. This represents the column vector of scalar coefficients to be solved. , This represents the column vector of coefficients of the three-dimensional vector to be solved. , This represents a column vector of equality constraint values. , Represents a column vector of latent variables. ; ； ； ； ； ； ； in, Represents the identity matrix. This indicates that the conditional positive definite kernel function is in the th... discrete points and the discrete points The value at that location, This indicates that the conditional positive definite kernel function applies to the first variable. Find the three-dimensional row vector obtained by transposing the first-order partial derivative. This indicates that the conditional positive definite kernel function applies to the first variable. and the second variable Find the three-dimensional matrix obtained by the second-order mixed partial derivatives, where .

9. The method for automatically generating a three-dimensional geological model according to claim 8, characterized in that, No. Latent variable covariance after the second iteration for: ； in, Indicates the first The implicit function after the second iteration In the The gradient at each discrete point Indicates the first The gradient corresponding to the discrete point at the th discrete point is at the th... The latent variable covariance after the next iteration.

10. The method for automatically generating a three-dimensional geological model according to claim 9, characterized in that, When the The model coefficients in the implicit function after the nth iteration are similar to those of the nth iteration. When the difference in the model coefficients of the implicit function after the nth iteration is less than a preset threshold, the iterative solution is stopped, and the nth iteration is set to the nearest integer. The implicit function after the next iteration is taken as the optimal implicit function; the model coefficients include scalar coefficients. , three-dimensional vector coefficients Three-dimensional vector coefficients of polynomials scalar coefficients of polynomials ; The target isosurface includes all three-dimensional spatial coordinates that make the value of the optimal implicit function equal to the target observation value. The set of all geological bodies to be modeled, whose three-dimensional geological models are composed of all the geological bodies in the set. The surfaces formed by corresponding spatial points.

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