Body-based modeling approach

bBody models are based on the segmentation of body elements in 3D space and the representation of true 3D solids, where the attributes of the body elements can be described and stored independently, thus allowing 3D spatial manipulation and analysis. The body model can be classified into Tetrahedral, Hexahedral, Prismatic and Polyhedral according to the number of faces of the body elements, and also into regular and irregular body elements according to the regularity of the body elements. Regular volume elements include CSG, Voxel, Octree, Needle and Regular Block*** 5 kinds of models. Regular volume elements are usually used for modeling water bodies, pollution and environmental problems, where Voxel and Octree models are a standard segmentation method for continuous space oriented to field substances (e.g., gravity field, magnetic field) without sampling constraints, and Needle and Regular Block can be used for simple geological modeling. Irregular body elements include TEN, Pyramid, TP, Geocelluar, Irregular Block, Solid, 3D Voronoi and GTP***8 models. Irregular body elements are sampling-constrained, solid-oriented 3D models based on geostratigraphic interfaces and geological formations.

Table 2-1 Classification of 3D Spatial Modeling Methods

1. Regular Block Modeling

The research and application of block modeling technology started in the early 1960s, and it is a traditional method of geologic modeling.A number of geologic body simulation systems developed in the 1960s and 1970s used this modeling technique. Some geologic body simulation systems developed in 1960s and 1970s used this modeling technique, the typical ones are OBMS and OPDP system developed by RTZ, Mineval system by Control Data and MEDS system by Minetec. This type of modeling technique involves partitioning the space to be modeled into regular 3D cubic grids called Blocks, each of which is stored in the computer at an address that corresponds to its location in the natural deposit, and each of which is considered to be homogeneous and homogenous, with values for grade or lithological parameters determined by kriging, distance-weighted averaging, or other methods. The model is effective for modeling 3D spaces with gradual attributes (e.g., dipping metalliferous ore bodies), and for modeling sedimentary strata, geologic formations, and excavated spaces with boundary constraints the cell sizes must be continually reduced, which causes a rapid expansion of the data. The solution is to perform localized cell refinement only in the boundary region.

2. Structural solid geometry (CSG) modeling

First of all, we predefine some basic elements with regular shapes, such as cubes, cylinders, spheres, cones, and closed spline surfaces, etc., and geometric transformations and Boolean operations (concatenation, intersection, and difference) can be carried out between these elements, and these regular basic elements can be combined into a single object through operations. The generated 3D object can be represented by a CSG tree.CSG modeling is very effective in describing 3D objects with simple structures, but it is inconvenient and much less efficient for complex irregular 3D features, especially geological bodies.

3.3D Voxel Modeling

This model is essentially a 3D extension of the 2D Grid model, i.e., a set of 3D voxels of regular dimensions (a=b=c) is used to dissect the space to be modeled. A significant advantage of the Voxel-based modeling method is that it can be programmed with implicit positioning techniques to save storage space and computing time. Although the model has a simple structure and is easy to operate, the geometric accuracy of expressing the spatial location is low and it is not suitable for expressing and analyzing the spatial relationship between entities. Of course, the modeling accuracy can be improved by reducing the size of Voxel, but the number of spatial units and the storage capacity will grow by three times.

4. Octree Modeling

Similar to the raster of quadtrees in 2D GIS, the Octree model is essentially a compression improvement of the Voxel model. The method divides the 3D spatial region into 8 quadrants and stores 8 data elements at each node in the tree. When all the voxels in a quadrant are of the same type (i.e., homogeneous voxels), the type value is stored in the corresponding node data element. The non-homogeneous quadrant is then subdivided into quadrants, and the corresponding data element in the node points to the next node in the tree, and so on until the region represented by each node is homogeneous body.Octree model has been successfully applied in the fields of medicine, biology, mechanics and so on, but there are greater limitations in the geological modeling of mineral deposits. Based on Octree, Xiao Lebin et al. proposed a four-layer vectorized Octree hierarchy, and Bian Fuling et al. proposed a goal-oriented data structure.

5. Needle modeling

The principle of this model is similar to the crystalline growth process, in which a set of needle-like columns of different lengths or heights with the same cross-sectional dimensions are used to spatially segment a certain non-regular 3D space, 3D feature or geoid, and the set is used to express the target space, 3D feature or geoid.

6. Tetrahedral Lattice Network (TEN) Modeling

This model is proposed on the basis of 3D Delaunay triangulation research, and it is a 3D vector data model based on point-based TEN. The basic idea is to use mutually non-intersecting straight lines to connect the non-repeating scattered point sets in 3D space two by two to form triangular facets, and then form a tetrahedral lattice network from the mutually non-traversing triangular facets. The tetrahedra (Tetrahedral) are all spatially scattered points as their vertices, and each tetrahedron does not contain any point in the point set.When modeling TEN, the properties of the points inside the tetrahedron can be obtained by the interpolation function, in which the parameters of the interpolation function are determined by the properties of the four vertices, so that after the tetrahedral section interpolation, the 3D data information of the space can be obtained.Although the TEN can describe the solid interior, but cannot represent 3D continuous surface, and it is also more difficult to generate 3D spatial surface with TEN, and the algorithm design is more complicated.

7. Pyramid model

Similar to the TEN model, the pyramid model is formed by four triangular facets and one quadrilateral closure to realize the dissection of spatial data field. It is generally seldom used due to its difficulty in data maintenance and model updating.

8. Tri-Prism (TP) Modeling

This model is a commonly used and simple spatial modeling technique for D geodesy. Zhang Yu et al. gave the definition of TP body elements, as well as the related cutting and sectioning algorithms, and listed the related applications of digital stratigraphic model based on this model. Since the premise of the TP model is that the three prongs are parallel to each other, it is not possible to construct a true 3D geology based on actual skewed boreholes, and it is difficult to deal with complex geological formations. On the other hand, Dai Wujiao et al. discussed the data structure, topology establishment, topology checking and spatial interpolation of the irregular TP network model (TPN) with irregular TP as the basic unit, but lacked in-depth discussion on the geologic applications.

9. Geocellular model

In essence, it is a variant of the Voxel model, i.e., it is still a standard Grid section in the xy plane, while in the z direction, it is actually partitioned based on the type of data field or stratigraphic interface changes, which results in a 3D voxel spatial section that approximates the actual interface.

10. Irregular Block Modeling

The difference between Irregular Block and Regular Block is that the scales (a, b, and c) in the three directions of Regular Block are not equal to each other, but are kept constant (e.g., in the OBMS system); whereas, the scales (a, b, and c) in the three directions of Irregular Block are not only unequal to each other, but also are not constant. The advantage of the non-regular block modeling method is that it can be simulated according to the actual changes in the stratigraphic spatial interfaces, and thus the accuracy of spatial modeling can be improved.

11. Solid modeling

Solid modeling is a modeling method developed in the 1980s, which initially used polygonal grids (wireframe models) to describe the geometric boundaries of the geologic body, and traditional block models to describe the distribution of grade or mass within the geologic body. Solid modeling techniques have matured over time and are typified by the solid modeling techniques provided in the Canadian Lynx system. This technique models a geologic body by constructing a Component from the boundary lines of the geologic body in three parallel sections and their connecting lines. A Component represents not only a closed body, but also the properties within the body. A simple geoid consists of such a series of Components. The property changes inside the geoid are still modeled by the traditional block-segment model. In simulating the property changes inside the geoid with the traditional block segment model, the boundaries of the geoid are generally used as constraints, which involves the problem of generating a 3D raster model of the geoid from a wireframe model or a body-element model, which has been solved in the existing commercialized software. The main advantages of the solid modeling method are: (i) modeling with profiles not only conforms to the way of geological work, but also allows the modeler to interpret and deduce the available information; (ii) not only can it accurately express the geometrical forms of various irregular geologic bodies, but also describe the attributes of the geologic bodies; (iii) the geometrical model of geologic bodies is easy to be modified; and (iv) this modeling method is also applicable to the expression of the boundaries of the extractive engineering. Its main shortcomings are: ① Lack of description of necessary topological relationships between various geological bodies of different complexity and between geometric elements of geological bodies, thus the boundaries of adjacent geological bodies have to be digitized repeatedly, and the querying of geological boundaries, geological interfaces and geological bodies, as well as the topological spatial analysis of geological objects can not be carried out. ② The workload of manual interaction is huge.

Hou Enke conducted an in-depth study on the shortcomings of the model and proposed a new object-oriented metadata model for irregular bodies according to the characteristics of the object-oriented method, the special requirements of computerized geologic modeling, and the irregularity of geologic body geometries as well as the diversity of production characteristics. The geological objects are abstracted into four major categories: point, line, surface and body, and the geological body is divided into four object types: complex body, complicated body, simple body and body element. The body element is the basic voxel constituting the geoid, which can be defined in the local coordinate system and described by five basic object classes: point, arc segment, connecting line, body element profile polygon (including the front, middle and back three profile polygon boundaries) and body element surface. The spatial relationship between each object type can be described by 12 topological relationships. Based on these 12 topological relationships, the data structure of the irregular body metadata model is defined.

12.3D Voronoi diagram model

3D Voronoi diagram is a 3D extension of 2D Voronoi diagram. In essence, it is based on a set of discrete sampling points, forming a set of face-to-face neighboring polyhedra without crossing each other (overlapping) in the constraint space, and completing the seamless segmentation of the target space with this set of polyhedra. The model first originated in the field of computer graphics, and in recent years, people have begun to study its feasibility in the field of geosciences in an attempt to find applications in the modeling of oceans, pollution, water bodies, and metallic ore bodies.

13. Generalized Tri-Prism (GTP) Modeling

Aiming at the characteristics of geologic drilling, especially deep drilling deflection, Wu Lixin et al. put forward a method of modeling ATP (Analogical Tri-Prism) which can be unrestricted by the limitation of parallelism of tri-prism prisms i.e. (verticality of drilling holes), which was later developed into the Generalized Tri-Prism (GTP) modeling. Generalized Tri-Prism (GTP) and referred to TP modeling as its special case. Moreover, based on the TIN side degeneration and TIN face degeneration, Pyramid model and TEN model can be derived from GTP.The principle of GTP modeling is that the TIN faces composed of the set of triangles on the upper and lower bottom surfaces of the GTP are used to express the different stratigraphic levels, and then the spatial quadrilateral faces on the sides of the GTP are used to describe the spatial relations between the levels, and the GTP columns are used to express the internal relationships among the levels. entities. It is characterized by fully integrating the borehole data and using the different stratification of the borehole data to simulate the stratified entities of the stratum and express the morphology of the stratum level. Eight groups of topological relationships are defined based on points, TIN edges, side edges, TIN faces, sides and GTP, according to which spatial adjacency and spatial proximity query and analysis can be easily realized. Moreover, the GTP data structure is easy to expand, when there is a new borehole data added, only the generation of TIN is modified locally and the generation of GTP is modified locally without changing the structure of the whole body, which makes the local refinement and dynamic maintenance of the GTP very convenient.