3.1.

ACO-kriging interpolation method

Kriging interpolation has the advantages of high interpolation accuracy and strong uniqueness. It is widely used in reservoirs, reserves prediction and mineral product location estimation⁹. The basic equation is shown in equation (1):

where is the point to be inserted, n is the number of known points, Z(xi) is the i known point, λi is the weight coefficient of the i location the known point and the point to be inserted, the weight λi depends on the known point, the distance and spatial relationship of the point to be interpolated, needs to meet unbiased optimality, namely:

The main steps of ordinary kriging difference are:

Step 1: For the known point data, calculate the distance and semivariance in pairs;

Step 2: Group the distances according to the step length, and calculate the average semivariance of each group;

Step 3: Draw the variogram after grouping;

Step 4: Solve the variogram model parameters and fit the theoretical variogram model;

Step 5: Solve the semivariance from the unknown point to all known points;

Step 6: Use the optimal weight coefficient to weight and sum the attribute values of the known points to obtain the estimated value of the unknown point.

The fitting of the variogram directly affects the accuracy of the interpolation. The ant colony algorithm is used to solve the parameters of the variogram model, and a better fitting model is constructed. The fitting of the variogram model essentially represents the degree of approximation between the experimental variogram and the theoretical variogram⁷, where equation (4) is used as the objective function:

This is the theoretical variance function value, the experimental variance function value, the number of n.

The process of using the ant colony algorithm to solve the objective function is shown in Figure 1:

Figure 1.

Flow chart of ant colony algorithm.

The formula for calculating the probability of state transition is:

Among them, it represents the maximum value of pheromone, represents the pheromone of the i-th ant, and represents the pheromone of ant i in iter times.

The pheromone update formula is:

where is the pheromone volatilization factor, Tau is the pheromone, and f is the objective function value. According to the flowchart of Figure 2, ant colony algorithm, the parameter values of the variogram are solved.

Figure 2.

Line chart of sampling point elevation comparison.

Selecting 50 known sampling data of the C2-2 coal seam of a coal mine as the sample data set, and useing Kriging and ACO-Kriging to perform cross-validation to calculate the theoretical elevation value of the sample, a line chart is obtained comparing the theoretical elevation value and the actual elevation value as shown in Figure 2 shows:

Among them, line A represents the actual elevation value distribution line chart of 50 sample points, and lines B and C represent the theoretical elevation distribution line chart of the corresponding position of the sample calculated according to Kriging and ACO-Kriging, respectively. At the inflection point, the theoretical elevation value obtained by the ACO-Kriging algorithm is closer to the actual elevation value than the Kriging algorithm, so it is feasible to choose the ACO-Kriging method to complete the interpolation of the coal seam elevation attributes.

3.2.

Delaunay triangulated graph

Triangulation is to form a set of discrete points, connect the set of points into triangles, and form a plane plan by these triangles. Delaunay is one of the most widely used triangulation methods in computational geometry, and the triangular network composed of Delaunay methods must satisfy the empty circle properties and maximize the minimal angle properties¹⁰.

3.3.

Generalized triangular prism model

The generalized triprismatic model consists of two not necessarily parallel triangles¹¹, which can represent the minimal three-dimensional spatial unit of the stratigraphic model and can also handle complex geological formations through boundary constraints. The three prisms can be divided into three and four cones under boundary constraints⁵. Three-and four-prism cones can be used to express complex geological structures such as faults, folds, voids, and pinch off.

4.1.

System architecture design

The overall system architecture is mainly divided into user interaction layer, data interface layer, business logic layer, and data persistence layer. The user interaction layer visually displays the functions of the system to users, and at the same time receives user requests and returns system responses. The data interface layer realizes the transmission of messages and completes the interaction between user request messages and the processing results of the business logic layer. The business logic layer processes specific business content by calling the data persistence layer, including two parts: interface and implementation. The data persistence layer is directly connected to the database and manipulates the data according to actual business needs¹².

4.2.

Data table structure design

The system data table includes a drill hole information table for storing information such as drill hole number, coordinates, and coal seam number; a coal seam information table for storing information such as coal seam number and coal seam thickness; a coal seam quality information table for storing coal quality data such as coal ash, water, and calorific value, the coal-bed coal quality range table is used to store the maximum and minimum values of coal thickness and coal quality data; the prediction information table is used to store interpolated borehole coordinates, coal seam information, and coal quality information data; unit information Table user storage unit name, code and other information; user information table user name, password and other information; role information table user storage role name, and its corresponding unit, user ID information.

5.1.

Data preparation

The system conducts unified storage and management of the data required for three-dimensional visualization of coal seam structure, which mainly includes drilling information, basic coal seam information, coal seam quality information and coal seam coal quality range. The ability to add, modify, delete, display these data is implemented, and the need for mass import of excel table data through Java POI technology is realized.

5.2.

Coal seam elevation interpolation prediction

According to the coal seam number, the borehole number in the coal seam information table corresponds to the borehole number in the borehole information table, and the coal seam number, borehole coordinates X and Y, seam floor elevation and coal seam thickness are integrated, using ACO-Kriging interpolation. The method uses the maximum and minimum values of the drilling coordinates X and Y as intervals to supplement the drilling coordinates in the unknown area, and interpolate to obtain the coal seam floor elevation and coal seam thickness of the drilling coordinates, and then the coal seam roof elevation can be obtained. The interpolated data is stored in the database as the basic data for 3D visualization.

5.3.

Three-dimensional visualization of coal seam structure

(1) Three-dimensional visualization of a single coal seam

Based on the interpolated data, Realize the rendering of 3D renderings based on Three.js 3D engine, the Delaunay method connects the discrete data points to obtain a single face model of the coal seam, and the single face model of the coal seam is obtained as shown in Figure 3, using a generalized triangular prism. The model connects the top and floor surfaces of the coal seam, and the three-dimensional model of the coal seam is shown in Figure 4.

Figure 3.

Coal layer model.

Figure 4.

Coal seam model.

Through the method of picking Raycaster object in three.js, a triangular plane that forms the 3D model is obtained with the mouse, according to the coordinates of the triangle, the corresponding coal quality data is queried from the database, and the coal quality data is correlated with the coal seam structure. The results are returned to the front page, as shown in Figure 5. Compared with other 3D visualization software, this system has better interactivity.

Figure 5.

Interaction diagram of coal seam.

(2) Three-dimensional visualization of multiple coal seams

A mine generally contains multiple coal seams. The interpolated drilling coordinates and coal quality data of each coal seam are obtained from the database. According to the coal seam distribution sequence, the Three.js 3D engine, Delaunay method, and generalized triangular prism model are used to obtain the three-dimensional renderings of multiple coal seams, as shown in Figure 6.

Figure 6.

Three-dimensional visualization of coal seams.