Quantitative analysis method for geologic body three-dimensional form surface complexity

Abstract

The invention discloses a geological body three-dimensional form surface complexity quantitative analysis method, and relates to the technical field of mineral exploration. The method comprises the following steps: extracting three-dimensional data on the surface of a geologic body based on existing three-dimensional modeling software; by constructing a calculation process independent of existing three-dimensional modeling software, a three-dimensional geologic modeling technology, differential geometry and Euclidean distance can be effectively combined; the complexity of the surface of the three-dimensional geologic body is evaluated through a curvature concept in differential geometry; and importing the calculation result of the complexity into the three-dimensional modeling software again so as to realize three-dimensional display of the geologic body. According to the method, geological technicians can conveniently carry out further quantitative analysis on the surface morphology complexity of the three-dimensional model, three-dimensional prospecting information is effectively extracted, a deep prospecting target area is rapidly delineated, a deep prospecting breakthrough is obtained, and obvious economic benefits are obtained.

Description

Technical Field

[0001] This application relates to the field of mineral exploration technology, and in particular to a method for quantitative analysis of the surface complexity of three-dimensional geological bodies. Background Technology

[0002] The mining economy is a pillar of the national economy. Currently, after years of mining, most of the shallow ore bodies in many of my country's mines have been exhausted, necessitating deep mineral exploration. Against this backdrop, how to obtain effective deep mineral exploration information to guide deep exploration has become a key focus of current research in this field. Most mineral deposits are controlled by various types of structures, but the occurrence of ore bodies is closely related to specific locations within those structures. A crucial factor determining these specific locations is the complexity of the structural morphology. Generally, the more complex the morphology, the more conducive it is to ore body formation. Therefore, how to determine the location and extent of this complex location in three-dimensional space is a key technical problem facing deep mineral exploration.

[0003] Taking skarn-type deposits as an example, this type of deposit is an important source of metallic minerals such as iron, copper, gold, lead, and zinc in my country. The ore bodies in skarn-type deposits all occur at the contact zone between magmatic intrusions and carbonate strata. However, the more complex the morphology of the contact zone, the more conducive it is to sufficient contact metasomatic reaction, thus facilitating the formation of the ore body. Therefore, quantitatively characterizing the complexity of the three-dimensional morphology of the contact zone has a direct impact on guiding deep mineral exploration and prediction for this type of deposit.

[0004] Currently, 3D geological modeling is widely used in mineral exploration, and 3D geological models have been established for the main geological bodies in mining areas. However, a current research focus is on how to conduct further in-depth analysis of the constructed 3D geological models to extract 3D mineral exploration information and serve as a basis for deep mineral exploration prediction. Although some studies have attempted to combine mathematical morphology with theories such as Euclidean distance transformation to solve the 3D spatial analysis of complex geological bodies, such as extracting geological body trend morphology and geological body contact surfaces, a simple and practical 3D morphological spatial analysis process and technology for geological bodies is still lacking. Summary of the Invention

[0005] Therefore, it is necessary to provide a quantitative analysis method for the three-dimensional morphological surface complexity of geological bodies to address the aforementioned technical problems.

[0006] The following technical solution is adopted in this specification: This specification provides a method for quantitative analysis of the surface complexity of three-dimensional geological bodies, including: A three-dimensional geological model is created for the surface of the target geological body; Extract the three-dimensional point coordinates from the surface of the three-dimensional geological model; Given a point, select the k nearest neighbors of that point according to Euclidean distance to form a local neighborhood. Decenter the local neighborhood and obtain its local tangent plane and normal vector using principal component analysis. Project the neighboring points in the local neighborhood onto the local tangent plane to obtain local two-dimensional coordinates, and the distance of each neighboring point relative to the local tangent plane in the direction of the normal vector, thus obtaining the local three-dimensional coordinates of the three-dimensional point. Based on the local three-dimensional coordinates, fit a quadratic surface using the least squares method. Then, based on differential geometry theory, obtain the curvature of the target three-dimensional geological surface by fitting the second derivative of the quadratic surface. Based on the curvature of the target three-dimensional geological surface, the local bending characteristics of the target three-dimensional geological surface at the three-dimensional points are obtained, thereby constructing geometric quantities to characterize the surface morphology, so as to qualitatively analyze the structural characteristics and distribution of the target geological body.

[0007] Furthermore, the establishment of a three-dimensional geological model for the surface of the target geological body includes: The outline of the target geological body on the cross section is constructed by using 3D modeling software, and then the outlines on adjacent cross sections are connected to construct a 3D geological model. By using DXF format files, models constructed by 3D modeling software that does not support the extraction of 3D point coordinates from the surface of 3D geological models are converted to a file format compatible with Leapfrog software.

[0008] Furthermore, the three-dimensional point coordinates on the surface of the three-dimensional geological model represent the east coordinate, north coordinate, and elevation coordinate of the three-dimensional point, respectively.

[0009] Furthermore, the k nearest neighbors, parameter k, are obtained by the point cloud density and the desired smoothness.

[0010] Furthermore, the local neighborhood is decentered, and the local tangent plane and normal vector of the local neighborhood are obtained by principal component analysis, including: Principal component analysis is used to calculate the covariance matrix of the decentralized local neighborhood points, resulting in three eigenvalues. The directions corresponding to the two largest eigenvalues ​​represent the two main directions with the widest distribution of the point cloud, forming a tangent plane. The main direction corresponding to the third eigenvalue represents the direction with the most compact distribution of the point cloud, which is perpendicular to the tangent plane and forms a normal vector.

[0011] Furthermore, the quadratic surface is expressed as: ; Where a, b, c, d, e, and f are constants in the quadratic surface expression; u represents the east coordinate of the three-dimensional point; v represents the north coordinate of the three-dimensional point; and w represents the elevation coordinate of the three-dimensional point.

[0012] Furthermore, the curvature of the target three-dimensional geological surface includes: The Gaussian curvature K is calculated using the following formula: ; The mean curvature H is calculated using the following formula: ; Principal curvature and The calculation formula is: , ; Where a, b, and c are constants in the expression for the quadratic surface. and These represent the maximum and minimum curvature values ​​of the surface at a point along two orthogonal directions, respectively, used to describe the degree of curvature of the surface at that point.

[0013] Furthermore, the principal curvature is measured using five generalization indicators. and The degree of deviation is used to describe the morphological complexity of the three-dimensional curved surface of the geological body, thereby constructing a geometric quantity to characterize the morphology of the curved surface; The five promotion indicators are expressed as follows: ; ; ; ; ; in, , , , and These represent five additional complexity metrics in addition to the mean curvature and principal curvature.

[0014] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: This specification provides a method for quantitatively analyzing the surface complexity of three-dimensional geological bodies. Data is extracted based on existing three-dimensional modeling software, and a calculation process independent of existing three-dimensional modeling software is used to effectively combine three-dimensional geological modeling technology with differential geometry and Euclidean distance. The curvature concept in differential geometry is used to evaluate the complexity of the three-dimensional geological body surface. The technical process established by this invention requires no additional complex operations or calculations. Data extraction can be achieved using current mainstream three-dimensional geological modeling software, and the calculation process provided by this invention can obtain multiple parameter indicators, facilitating further quantitative analysis of the surface morphology complexity of three-dimensional models by geological technicians. This effectively extracts three-dimensional mineral exploration information, rapidly delineates deep mineral exploration target areas, achieves breakthroughs in deep mineral exploration, and yields significant economic benefits.

[0015] Furthermore, the calculation results obtained by the key algorithm established by this invention are in excellent agreement with the actual geological conditions, which can effectively guide mineral exploration in deep mines and generate significant economic value. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0017] Figure 1 This document provides a flowchart illustrating a method for quantitative analysis of the three-dimensional morphological surface complexity of geological bodies. Figure 2 These are schematic diagrams of surfaces with different Gaussian curvatures provided in this specification; wherein, Figure 2 (a) represents negative Gaussian curvature. Figure 2 (b) has zero Gaussian curvature. Figure 2 (c) represents positive Gaussian curvature; Figure 3 This is a schematic diagram of the spatial relationship between the ore-controlling contact zone and the iron ore body at the Daye Iron Mine in Hubei Province, provided in this specification. Figure 4 This document presents the quantitative calculation results of the ore-controlling contact zone complexity of the Daye Iron Mine in Hubei Province and the schematic diagram of the delineation of deep prospecting target areas. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0019] Currently, the main workflow for 3D geological modeling involves using borehole data, exploration profiles, geophysical data, etc., to construct the outline of geological bodies on the profiles, and then connecting the outlines of adjacent profiles to build a 3D geological model for reserve estimation and qualitative analysis of the structural characteristics and distribution of deep geological bodies. However, all current 3D geological modeling software lacks technical modules for further spatial analysis of the constructed 3D geological models, making it impossible to extract further 3D mineral exploration information, which greatly limits the further application of 3D models.

[0020] Based on this, the present invention establishes a technical process capable of effectively performing quantitative calculations of surface morphology complexity based on existing 3D geological models, including data format, data extraction methods, complexity calculation procedures, calculation results, and the significance of the calculation results. This technical process extracts data based on existing 3D modeling software, but the calculation process is an independent program, separate from the existing 3D modeling software. The calculation results can be imported back into the 3D modeling software and can be displayed in 3D. Figure 3 This facilitates geological personnel in conducting deep mineral exploration analysis and provides an important basis for predicting deep mineral exploration in mines.

[0021] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0022] Figure 1 This is a flowchart illustrating a method for quantitatively analyzing the surface complexity of a three-dimensional geological body, as described in this specification. The method includes the following steps: S101: 3D model preparation and data extraction.

[0023] Currently, mainstream 3D modeling software such as Surpac, Datamine, GOCAD, and Leapfrog can be used to create 3D geological models of ore bodies, rock masses, strata, and faults, which can all be used for surface complexity analysis. Since different software provides 3D model data formats, some software may not support the extraction of 3D point coordinates from the model surface. In such cases, a DXF file format conversion can be used to import the model from other software into Leapfrog, where the coordinates of 3D points on the model surface can be extracted.

[0024] S102: Input the point cloud data into an Excel spreadsheet.

[0025] Extract three-dimensional points from the surface of the three-dimensional geological model at certain intervals. The coordinates of each three-dimensional point are (x, y, z), which represent the east coordinate, north coordinate, and elevation coordinate of the point, respectively. Input all point coordinates into Excel according to the three columns of x, y, and z.

[0026] S103: Estimating the curvature of a 3D surface based on point cloud.

[0027] In geological science, topography or geological interfaces are often obtained as discrete point cloud data, which typically constitute part of an unknown surface. To understand the morphological characteristics of these surfaces, researchers need to use the point cloud to estimate its Gaussian curvature and mean curvature. These two geometric quantities are important indicators for characterizing the local shape of a surface. On a two-dimensional surface, the two principal curvatures at a point (…) and ) represent the maximum and minimum curvature values ​​of the surface at that point along two orthogonal directions, respectively, used to describe the degree of curvature of the surface at that point.

[0028] Gaussian curvature is defined as the product of the two principal curvatures: When the two principal curvatures have the same sign (i.e., both are positive or both are negative), K > 0, indicating that the surface at that point locally exhibits a spherical or elliptical arch, such as... Figure 2 As shown in (c); when one is positive and the other is negative, K < 0, corresponding to a saddle-shaped structure, such as Figure 2 As shown in (a); if one of the principal curvatures is zero, then K = 0, for example, a cylindrical surface, such as... Figure 2 As shown in (b).

[0029] Mean curvature measures the "average" degree of curvature of a surface at a given point, and is defined as the average of the principal curvatures. .

[0030] S104: Since the analytical expression of the surface is unknown, its derivative and curvature cannot be directly calculated. However, a quadratic surface can be fitted in the local neighborhood of each point to approximate the original surface, and then the curvature can be calculated using the fitted surface. This approach has been widely used in computational geometry and shape analysis (e.g., Meyer et al., 2003; Cohen-Steiner & Morvan, 2003).

[0031] The specific steps are as follows: (1) Selecting a local neighborhood: Given a point The k nearest neighbors are selected based on Euclidean distance to form a local neighborhood. The parameter k can be selected based on the point cloud density and the desired smoothness. In this invention, k = 20 is used when calculating curvature.

[0032] (2) Principal Component Analysis (PCA): After decentering the neighborhood points, PCA is used to determine the local tangent plane and normal vector: the tangent plane is formed by the first two principal directions of PCA, and the normal vector is given by the third principal direction with the smallest variance.

[0033] (3) Establish a local coordinate system and project it: Project the neighborhood points onto the tangent plane, construct a local two-dimensional coordinate system (u, v), and record the "height" w (i.e., the distance in the normal direction) of each point relative to the plane, thereby transforming the three-dimensional points into a local coordinate system (u, v). .

[0034] (4) Fitting a local quadratic surface: Fit a quadratic surface in the local coordinate system using the least squares method: ; Extracting curvature information: According to differential geometry theory, the second derivative of the fitted surface can be used to estimate the curvature of the original surface.

[0035] The Gaussian curvature, mean curvature, and principal curvature are as follows: ; ; , ; (4) Result characterization: Gaussian curvature and mean curvature characterize the principal curvature from different perspectives. k 1 and k 2 The degree of deviation from 0 reflects the local curvature of the surface at that point. Similarly, we can measure the degree of deviation of the principal curvature in other ways to construct geometric quantities to characterize the surface morphology. Here are five generalized indices we propose:

[0036] ; ; ; ; ; The invention establishes a simple and practical technical process for analyzing the three-dimensional morphological surface complexity of geological bodies using equal-quantity analysis, providing an important basis for deep mineral exploration prediction in mines. It represents a significant advancement in creativity, novelty, and practicality.

[0037] Creativity: The quantitative analysis process for the three-dimensional morphological surface complexity of geological bodies established in this invention effectively combines three-dimensional geological modeling technology with differential geometry and Euclidean distance, and uses the concept of curvature in differential geometry to evaluate the complexity of the three-dimensional geological body surface, which is innovative; Novelty: The technical process constructed in this invention can be used to analyze three-dimensional geological bodies constructed by current mainstream three-dimensional geological modeling software, and to perform calculations according to the calculation method established in this invention. The calculation results can be imported back into the three-dimensional geological modeling software for three-dimensional visualization, making it convenient for geological technicians to use. Practicality: The technical process established by this invention does not require additional complex operations and calculations. Data extraction can be achieved in existing mainstream 3D geological modeling software. Then, calculations can be performed in the program provided by this invention to obtain the results. Furthermore, multiple parameter indicators are provided to characterize the results, making it convenient for geological technicians to select different parameters for result evaluation.

[0038] Furthermore, taking the Daye Iron Mine in Huangshi, Hubei Province as an example, this specification is described in detail in the embodiments.

[0039] The Daye Iron Mine in Huangshi, Hubei Province, is one of the most typical skarn-type iron-copper deposits in my country. After years of mining, the shallow ore bodies have been almost completely depleted, leading to a crisis in the mining industry.

[0040] As a typical skarn-type deposit, the ore body occurs at the contact zone between quartz diorite and Daye Group carbonate rocks. The three-dimensional morphology of this contact zone and the iron ore body is as follows: Figure 3 As shown. The discovered ore bodies in this deposit are relatively shallow, with some directly exposed at the surface; therefore, open-pit mining is the primary method. We conducted systematic three-dimensional geological modeling of this deposit, obtaining the three-dimensional morphology of the contact zone and ore bodies. Based on this, using the technical process constructed in this invention, we quantitatively calculated the complexity of the contact zone, such as... Figure 4 As shown. Using absolute Gaussian curvature as a characterization, it can be seen that existing ore bodies are all found in areas with high absolute Gaussian curvature, meaning they are all found in complex parts of the contact zone. This is completely consistent with existing geological understanding, demonstrating the effectiveness of the technical process constructed in this invention. Moving deeper, based on calculations of absolute Gaussian curvature, it can be seen that the deep morphology on both sides of the contact zone tends to be simpler, while the deep section in the middle of the contact zone still has a significant high-value area. This indicates that the deep morphology in the middle section of the contact zone remains highly complex, thus allowing for the delineation of deep prospecting target areas (…). Figure 4 Deep engineering verification also shows that there are still good iron ore bodies in the middle section of the contact zone, while the mineralization on both sides is significantly poor.

[0041] The above examples illustrate that the technical process established by this invention can provide an effective solution for deep mineral exploration prediction, helping geological technicians to quickly obtain deep mineral exploration information, thereby delineating deep mineral exploration target areas and achieving breakthroughs in deep mineral exploration.

[0042] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A method for quantitative analysis of the surface complexity of a three-dimensional geological body, characterized in that, include: A three-dimensional geological model is created for the surface of the target geological body; Extract the three-dimensional point coordinates from the surface of the three-dimensional geological model; Given a point, select the k nearest neighbors of that point according to Euclidean distance to form a local neighborhood. Decenter the local neighborhood and obtain its local tangent plane and normal vector using principal component analysis. Project the neighboring points in the local neighborhood onto the local tangent plane to obtain local two-dimensional coordinates, and the distance of each neighboring point relative to the local tangent plane in the direction of the normal vector, thus obtaining the local three-dimensional coordinates of the three-dimensional point. Based on the local three-dimensional coordinates, fit a quadratic surface using the least squares method. Then, based on differential geometry theory, obtain the curvature of the target three-dimensional geological surface by fitting the second derivative of the quadratic surface. Based on the curvature of the target three-dimensional geological surface, the local bending characteristics of the target three-dimensional geological surface at the three-dimensional points are obtained, thereby constructing geometric quantities to characterize the surface morphology, so as to qualitatively analyze the structural characteristics and distribution of the target geological body.

2. The method for quantitative analysis of the three-dimensional morphological surface complexity of a geological body as described in claim 1, characterized in that, The process of establishing a three-dimensional geological model of the target geological body surface includes: The outline of the target geological body on the cross section is constructed by using 3D modeling software, and then the outlines on adjacent cross sections are connected to construct a 3D geological model. By using DXF format files, models constructed by 3D modeling software that does not support the extraction of 3D point coordinates from the surface of 3D geological models are converted to a file format compatible with Leapfrog software.

3. The method for quantitative analysis of the three-dimensional morphological surface complexity of a geological body as described in claim 1, characterized in that, The coordinates of the three-dimensional points on the surface of the three-dimensional geological model represent the east coordinate, north coordinate, and elevation coordinate of the three-dimensional points, respectively.

4. The method for quantitative analysis of the three-dimensional morphological surface complexity of a geological body as described in claim 1, characterized in that, The k nearest neighbors are obtained by taking the parameter k from the point cloud density and the desired smoothness.

5. The method for quantitative analysis of the three-dimensional morphological surface complexity of a geological body as described in claim 1, characterized in that, The local neighborhood is decentralized, and the local tangent plane and normal vector of the local neighborhood are obtained by principal component analysis, including: Principal component analysis is used to calculate the covariance matrix of the decentralized local neighborhood points, resulting in three eigenvalues. The directions corresponding to the two largest eigenvalues ​​represent the two main directions with the widest distribution of the point cloud, forming a tangent plane. The main direction corresponding to the third eigenvalue represents the direction with the most compact distribution of the point cloud, which is perpendicular to the tangent plane and forms a normal vector.

6. The method for quantitative analysis of the three-dimensional morphological surface complexity of a geological body as described in claim 1, characterized in that, The quadratic surface is expressed as: ； Where a, b, c, d, e, and f are constants in the quadratic surface expression; u represents the east coordinate of the three-dimensional point; v represents the north coordinate of the three-dimensional point; and w represents the elevation coordinate of the three-dimensional point.

7. The method for quantitative analysis of the three-dimensional morphological surface complexity of a geological body as described in claim 1, characterized in that, The curvature of the target three-dimensional geological surface includes: The Gaussian curvature K is calculated using the following formula: ； The mean curvature H is calculated using the following formula: ； Principal curvature and The calculation formula is: ， ； Where a, b, and c are constants in the expression for the quadratic surface. and These represent the maximum and minimum curvature values ​​of the surface at a point along two orthogonal directions, respectively, used to describe the degree of curvature of the surface at that point.

8. The method for quantitative analysis of the three-dimensional morphological surface complexity of a geological body as described in claim 7, further comprising: The principal curvature is measured using five generalization metrics. and The degree of deviation is used to describe the morphological complexity of the three-dimensional curved surface of the geological body, thereby constructing a geometric quantity to characterize the morphology of the curved surface; The five promotion indicators are expressed as follows: ； ； ； ； ； in, , , , and These represent five additional complexity metrics in addition to the mean curvature and principal curvature.

Images