CN106934860B - Three-dimensional geological modeling method based on T-spline - Google Patents
Three-dimensional geological modeling method based on T-spline Download PDFInfo
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Abstract
The invention discloses a three-dimensional geological modeling method based on a T spline, which takes the T spline as a spatial data structure of three-dimensional geological modeling, carries out three-dimensional modeling aiming at the complex morphology of a geological object and realizes quantitative depiction of the complexity of a geological structure, and comprises the following steps: integrating multi-source geological data; performing a construction complexity analysis for the geological object based on the geological data; dividing the geological object into two types, and respectively adopting a parameter surface modeling method based on a T spline or a subdivision surface modeling method based on the T spline; and establishing a three-dimensional model of the geological object, and integrating and checking to obtain a final three-dimensional geological model. The method can establish a real form three-dimensional model of geological structures including sedimentary formations, folds, invasion, unconformities, faults and the like, and provides an accurate and reliable initial model for lithology prediction, seepage and grouting simulation, stability analysis and other computer-aided design and numerical simulation analysis.
Description
Technical Field
The invention belongs to the field of three-dimensional visual geological modeling, relates to three-dimensional visual modeling of a complex geological structure, and particularly relates to a three-dimensional geological modeling method based on a T spline.
Background
The three-dimensional geological modeling technology is widely applied to the field of geotechnical engineering at present, and plays an important role in three-dimensional visual analysis and decision in the fields of foundation engineering, slope engineering, tunnel engineering and the like. The practical application of three-dimensional geological models in the aspects of GIS, BIM, CAD/CAE and the like continuously puts higher requirements on the accuracy and reliability of the three-dimensional geological models, however, the existing geological modeling method still faces the challenge of geological structure complexity.
Geologic formation complexity is an important branch of geologic complexity that is of interest to engineering geologists. On the one hand, the natural morphology of geological objects presents an inherent constructive complexity both at the geometric and topological level. On the other hand, geotechnical engineering is moving towards areas where the conditions of geological formations are more and more complex. Therefore, the representation of the complexity of geological structures in three-dimensional geological models is increasingly important for the planning, design, quality and safety aspects of geotechnical engineering. However, existing approaches still have limitations in complexity quantization, spatial data structure, and modeling techniques. Some scholars have studied methods for quantitatively measuring the complexity of geological parameters and geometric elements for geological evaluation in recent years, but quantitative indexes of structural complexity that can be used as input parameters for geological modeling are still under study. The spatial data structure used in three-dimensional geological modeling determines the underlying architecture of the model and the corresponding modeling techniques, but the data structures widely used in geological modeling, such as NURBS (non-uniform rational B-splines), generally do not have sufficient flexibility in characterizing the complexity of geological structures due to the limitations of their mathematical principles.
The spatial data structure suitable for three-dimensional geological modeling differs with different application fields. With the development of computer 3D technology, many different three-dimensional spatial data structures are introduced into geological modeling methods and applied in many different fields, including engineering geology, mineral resource exploration, geothermal resource exploitation, and geological disaster identification, etc. In the field of geotechnical engineering, the B-Rep architecture is one of the most widely adopted data structures for solid modeling of geological objects. The B-Rep has the advantage that flexible modeling can be realized based on a small amount of data, so that the spatial geometry and topological relation of the geological object can be efficiently described. The B-Rep entity is defined by a closed boundary surface whose surface elements can be parametric or discrete. Representative data structures for both forms of surfaces are NURBS and mesh. The non-uniform rational B-spline (NURBS) is a parameter surface which is most widely applied, the topological structure of the non-uniform rational B-spline is defined in a two-dimensional plane parameter space, and a corresponding free-form surface is obtained in a three-dimensional space through analytic calculation. Meshes generate a surface directly from a set of planar polygons connected by common vertices, without parametric definition and the approximation of a smooth surface can only be achieved with limited resolution. In the B-Rep representation method of the geological object, a plurality of NURBS curved surfaces or grid curved surfaces divide the boundary of the geological body so as to enclose a boundary representation entity.
In the engineering field, NURBS has several advantages over grids, including: analytic mathematical expressions, true surface precision and smoothness, vector representation rather than grid representation, compact parameterization, and computational and storage efficiency. NURBS has thus become a standard representation of CAD, CAM and CAE domain curve surfaces and is part of many industry-level standards such as IGES, STEP and PHIGS. In fact, models of engineering objects such as tunnels, dams, bridges, and buildings are typically designed and built using NURBS. The designed models of the engineering object and the natural geological object on the spatial data structure level are unified, so that the compatibility and the convenience of subsequent coupling analysis are facilitated, and the NURBS is more suitable for modeling the geological object in the engineering geological field compared with a grid. A unified data structure method in a three-dimensional unified geological modeling theory uses an NURBS technology and realizes the unified expression of an analytic curved surface of an engineering structure and a free curved surface of a geologic body on the basis of the same mathematical basis.
Geological modeling methods based on NURBS have been developed more mature. Fisher and Wales first proposed the theory of applying NURBS to geological modeling in 1992, but the study only stayed in the conceptual stage due to the immaturity of the theoretical development of NURBS itself in its early stages. With the introduction of computer aided geometric design methods, NURBS technology has been greatly enhanced. On the basis, Sprague and de Kemp studied the NURBS geological surface modeling method based on the section control framework and the region structure measurement constraint in 2005. The hybrid data structure of NURBS-TIN-B-REP of three-dimensional geological modeling is proposed in 2006 by Standowa, and the Chinese patent numbers are as follows: CN200610013425.1 discloses a three-dimensional unified model construction method for geological information of hydraulic and hydroelectric engineering, which realizes three-dimensional visual engineering geological analysis of dam bedrock geological structure based on NURBS technology, and the method is widely applied to hydraulic and hydroelectric engineering at home and abroad. Based on the above pioneering studies, NURBS data structures have been widely applied in the field of three-dimensional geological modeling, and recent studies are still further driving the development of this approach.
NURBS has good performance in the aspect of modeling aiming at regular bodies such as tunnels and dams. However, the natural morphology of geological objects differs from the artificial morphology of engineered objects, which possess their particular irregularities and still challenge current NURBS-based geological modeling methods. In the field of geological modeling, NURBS has great limitations in both data structure and modeling techniques. NURBS is defined by the tensor product of a series of B-spline curves whose control points must be distributed in a rectangular array, which limits NURBS surfaces to planar topologies. This defined topology enables NURBS to characterize only a small fraction of real geological formations. The natural morphology of geological objects and the tensor product topology of NURBS are in conflict with three aspects: firstly, the natural geological phenomena commonly have fractal characteristics, namely geological objects have self-similar local details, and control points of NURBS must be distributed over each isoparametric line, so that the NURBS curved surface can only realize uniform detail characteristics; second, intrusive and non-integrated contacts between geobodies can lead to intricate spatial topologies, whereas NURBS surfaces can only follow simple planar topologies; thirdly, geological objects usually have discontinuous features such as faults and fractures, and NURBS can only build internal continuous surfaces due to the definition rule of tensor products.
Meanwhile, a closed entity established based on NURBS must be surrounded by a plurality of NURBS patches. Therefore, the NURBS modeling flow generally requires NURBS surface cropping and splicing technology, and this strategy is suitable for establishing regular geometric morphology, but faces many problems in complex geologic body modeling: firstly, the NURBS curved surface cutting technology is realized by calculating cutting lines and hiding the cut area of the curved surface, and the number and the positions of the control points of the NURBS curved surface are not changed by the algorithm, so that the corresponding control points do not exist on the cutting lines, the cutting is difficult to control, the obtained geological data with complex boundary fitting is obtained, and the accuracy of a geological model is limited; secondly, because two cutting lines for splicing are respectively defined in parameter domains corresponding to the NURBS curved surfaces, and the real intersecting lines of the two curved surfaces are actually respectively approximated by the two cutting lines, gaps are inevitably generated at the splicing positions of the NURBS patches, so that the tightness of a geological entity model is influenced, and the application of geological modeling in subsequent numerical simulation analysis is limited; thirdly, the splicing geometric continuity of the multiple curved surface slices obtained by the NURBS cutting and splicing technology can be damaged in the further editing process, so that a geological model established by the technology is difficult to update along with geological data, and the development of the dynamic geological modeling technology is limited.
Based on the NURBS theory, Sederberg proposed a new generation of parametric surface in 2003, T-splines (non-uniform B-splines with T nodes), and further developed basic algorithms such as simplification and local refinement of T-splines in 2004. In practical applications, the concept of T-splines also includes T-NURCCS (non-uniform rational Catmull-Clark subdivision surfaces with T nodes), which is developed based on subdivision surface theory and introduces the concept of singular points into T-splines. As a superset of the NURBS and the Catmull-Clark subdivision surfaces, the T spline inherits the analytic form of the parameter surface and the flexibility of the subdivision surfaces at the same time, and can realize any NURBS modeling process and Catmull-Clark subdivision surface process under the special condition without T nodes. In the definition of a T-spline, a T-node is a trivalent node at the end of a row or column of control points ending inside a T-grid, and a singular point is a non-tetravalent node other than a T-node. The presence of T-nodes enables the T-splines to have local thinning capability, while the presence of singular points enables the T-splines to implement arbitrary topologies. Furthermore, the T-spline can locally change the geometric continuity by locally inserting multiple nodes with a pitch of 0. These properties of T-splines are of great interest for geological modeling.
Subdivision surface theory is developed based on polygonal meshes. Subdivision surfaces are limit surfaces obtained by recursive subdivision of mesh surfaces on the basis of a rough piecewise linear polygonal mesh. In CAD and GIS implementations, the infinite number of patches resulting from the limit surface definition of the subdivision surface is more difficult to process than the finite number of patches of NURBS. There is currently no industry standard for subdivision and NURBS are not compatible. In fact, subdivision surface techniques are more applicable to the animation and film industries and are rarely applied in the fields of manufacturing and engineering. Therefore, in order to realize the unified modeling of the engineering structure and the geological object, the parametric surface such as the T spline is better to be selected relative to the subdivision surface in the engineering geological modeling.
At present, the T spline technology is mainly applied to organic morphological modeling in the field of industrial design and computer aided design in the field of buildings, but is not introduced into the field of geological modeling. On the aspect of a spatial data structure, the limitation of a tensor product topological structure of the NURBS on the aspect of depicting a complex geological structure is overcome by the arbitrary topological structure of the T spline, and on the aspect of a modeling technology, the T spline modeling technology has the advantages of a parametric surface modeling technology and a subdivision surface modeling technology at the same time, so that the problem caused by a cutting and splicing geological modeling mode of the NURBS can be solved.
Reference documents:
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[2]Fisher,T.R.,&Wales,R.Q.(1992),Three dimensional solid modeling of geo-objects using Non-Uniform Rational B-Splines(NURBS),In Three-dimensional modeling with geoscientific information systems(pp.85-105),SpringerNetherlands.
[3]Liu,L.,Zhang,Y.J.,&Wei,X.(2015),Weighted T-splines with application in reparameterizing trimmed NURBS surfaces,Computer Methods inApplied Mechanics and Engineering,295,108-126.
[4]Li,X.,Chen,F.,Kang,H.,&Deng,J.(2016).A survey on the local refinable splines.Science China Mathematics,59(4),617-644.
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Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a three-dimensional geological modeling method based on T splines, introduces a T spline data structure and a modeling technology into the field of three-dimensional geological modeling, realizes the quantitative control of the geometric morphology of a T spline surface by using the structural complexity and simultaneously ensures higher model precision. The method can establish a real form three-dimensional model of geological structures including sedimentary formations, folds, invasion, unconformities, faults and the like, and provides an accurate and reliable initial model for lithology prediction, seepage and grouting simulation, stability analysis and other computer-aided design and numerical simulation analysis.
The purpose of the invention is realized by the following technical scheme:
a three-dimensional geological modeling method based on T splines is characterized in that the T splines are used as a spatial data structure of three-dimensional geological modeling, three-dimensional modeling is carried out aiming at the complex morphology of a geological object, and quantitative depiction of the complexity of a geological structure is realized, and the method comprises the following steps:
integrating multi-source geological data;
performing a construction complexity analysis for the geological object based on the geological data; dividing the geological object into two types, and respectively adopting a parameter surface modeling method based on a T spline or a subdivision surface modeling method based on the T spline;
the parameter surface modeling method based on the T spline adopts geometric-topological modeling logic: in the geometric stage, fitting a T spline surface to geological data based on geological data boundary constraint, and establishing an open T spline surface to represent the geological surface; in the topological stage, performing T spline Boolean operation according to the topological relation of the geological curved surface to obtain a geological object established by the closed T spline geological entity representation;
the subdivision surface modeling method based on the T spline adopts topological-geometric modeling logic: in a topological stage, a topological structure of a T spline is constructed according to complex characteristics of geological data to obtain a closed space T grid representation geologic body; in the geometric stage, according to geological data boundary constraint, surface fitting of a geological object is achieved by calculating T spline control points, a T spline surface corresponding to a T grid is established, and the geological object established by closed T spline geological entity representation is obtained;
and establishing a three-dimensional model of the geological object, and integrating and checking to obtain a final three-dimensional geological model.
The process of performing a construction complexity analysis on a geological object comprises the following two steps:
step 1, carrying out structural complexity analysis on three aspects of fractal geometric complexity, arbitrary genus topological complexity and discontinuous complexity of a geological object based on geological data;
step 2, dividing geological objects with small construction complexity into a class, and modeling by adopting a parameter surface method based on T splines, wherein the method comprises the following steps: the geological structure comprises a terrain, a layered sediment structure, a fold structure, a weathered and unloaded interface geological structure; dividing geological objects with larger structural complexity into another type and modeling by adopting a subdivision surface method based on T splines, wherein the subdivision surface method comprises the following steps: quaternary blanket, unconformity contact configuration, intrusion configuration, pinch-out configuration, and fault configuration.
The T-spline-based parametric surface modeling method specifically comprises the following steps:
(1) and (3) establishing a released T-spline surface in a geometric stage and fitting, wherein the method comprises the following three steps:
step 1, carrying out boundary surface division on a geological object according to an earth surface outcrop line, a drilling data point and section line geological data, and determining the number of boundary surfaces and an initial T spline surface of each boundary;
step 2, local thinning is carried out on the geological data neighborhood part of the initial T spline;
step 3, fitting the initial T spline surface after local thinning to corresponding geological data to generate a group of boundary T spline surfaces of the geological object;
(2) constructing a topological relation among the T spline surfaces in a topological stage to obtain a closed T spline surface, and the method comprises the following three steps:
step 1, analyzing the intersection relation of the boundary surfaces of the geological object, calculating the intersection lines between the T spline surfaces, and calculating the cutting line of each T spline surface;
step 2, adjusting the topological structure of the T mesh corresponding to the T spline surface in the neighborhood of the cutting line, deleting the cut area of the T spline, and establishing a curved surface boundary line which is close to the cutting line in the reserved area to obtain a group of non-cutting T spline geological curved surfaces with mutually matched boundaries;
and 3, splicing the geological boundary curved surfaces with the boundaries matched with each other into a closed T-spline curved surface, and adjusting the geometric continuity of the positions of the splicing lines according to the actual condition to finally obtain a geological object entity based on the closed T-spline curved surface.
The subdivision surface modeling method based on the T spline specifically comprises the following steps:
(1) constructing a space topological structure of a closed T grid in a topological stage, comprising the following three steps:
step 1, mapping earth surface outcrop lines, drilling data points and section line geological data from a three-dimensional physical space to a two-dimensional parameter space;
step 2, in a two-dimensional parameter space, controlling a topological structure of the T grid primitive on a geological data neighborhood by utilizing a quantized structural complexity index based on geological boundary constraint obtained by mapping;
step 3, remapping the T grid original image after the re-topology to a three-dimensional physical space to generate a closed space T grid corresponding to the geological object;
(2) establishing a T spline surface corresponding to the T mesh in a geometric stage and fitting, wherein the method comprises the following three steps:
step 1, defining a node vector on the basis of a three-dimensional space topology of a T grid and generating a T spline mixed function;
step 2, fitting the boundary constraint between geologies by the T spline surface is achieved by calculating the three-dimensional physical space position of the T spline control point;
and 3, generating a corresponding T spline surface based on the closed space T grid, the node vector, the mixing function and the control point coordinates, and finally obtaining the geological object entity based on a closed T spline surface.
The process of controlling the topological structure of the T grid primitive according to the geological structure complexity index comprises the following steps:
step 1, analyzing fractal geometric characteristics, any defect topology and discontinuity of a geological object represented by parameter space geological data, and quantizing by using a fractal dimension, a defect number and a continuity order respectively;
and 2, respectively quantizing and controlling local thinning parameters of the T-spline according to the fractal dimension, quantizing and controlling any topological parameters of the T-spline according to the deficiency number and quantizing and controlling variable continuity parameters of the T-spline according to the continuity order by inserting and removing cross nodes, T nodes, singular points and multiple nodes in the geological data neighborhood of the T-grid original image in the parameter space.
The process of integrating and verifying a three-dimensional model of a geological object comprises the steps of:
step 1, combining two types of geological objects obtained by a parameter surface modeling method based on a T spline and a subdivision surface modeling method based on the T spline into the same space coordinate system;
step 2, analyzing spatial position relations and topological relations among the mutually contacted geological objects, integrating all the geological objects into a regional integral geological model by utilizing T spline entity Boolean operation, and adjusting Boolean logic sequence by considering the relative size of construction complexity in the process;
step 3, integrally checking the reliability and the rationality of the geological structure model from the structural geology angle;
and 4, obtaining a final engineering region three-dimensional geological model.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. the T-spline-based three-dimensional geological modeling method provided by the invention realizes the refined expression of a three-dimensional model of a complex geological structure, utilizes the flexibility of the T-spline in the aspects of local refinement, arbitrary topology and variable continuity, describes the complexity of the geological structure based on a quantification method, overcomes the problem that the existing CAD method based on the NURBS is difficult to quantitatively describe the complex form of a geological object, inherits the accuracy of the NURBS method, keeps the compatibility with the NURBS, and realizes the unification of three-dimensional modeling technologies in the engineering field and the geological field.
2. The method disclosed by the invention is used for realizing characteristic quantification modeling on the engineering geological structure, and can assist engineering personnel to more accurately master and research the regional engineering geological condition; meanwhile, the method can provide accurate and reliable model foundation for lithology prediction, seepage, stability analysis and the like, and provides powerful technical means for geological problem analysis in engineering survey, design and construction under complex geological conditions.
Drawings
FIG. 1 is a flow chart of the T-spline-based geological modeling of the present invention;
FIG. 2 is a schematic illustration of the present invention for controlling T-spline parameters using construction complexity quantization;
FIG. 3 is a schematic diagram of a T-spline topology under complex boundary constraints according to the present invention;
FIG. 4 is a schematic illustration of modeling a sedimentary formation body;
FIG. 5 is a schematic diagram of modeling a quaternary overlay local detail and spatially interleaved contact features;
FIG. 6 is a schematic diagram of modeling pinch-out characteristics of a sandwiched geologic body;
FIG. 7 is a schematic diagram of modeling positive fault cracking and dislocation characteristics;
FIG. 8 is a schematic view of a forward fault control point topology;
FIG. 9 is a three-dimensional geological model of an actual hydroelectric project area constructed by the method of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention provides a three-dimensional geological modeling method based on a T spline, which takes the T spline as a spatial data structure of three-dimensional geological modeling, carries out three-dimensional fine modeling aiming at the complex morphology of a geological object and realizes the quantitative depiction of the complexity of a geological structure, and comprises the following steps (shown in figure 1):
firstly, integrating multi-source geological data;
carrying out construction complexity analysis on the geological object based on geological data, wherein the analysis process comprises the following two steps:
step 1, carrying out structural complexity analysis on three aspects of fractal geometric complexity, arbitrary genus topological complexity and discontinuous complexity of a geological object based on geological data;
step 2, on the basis of structural complexity analysis, dividing geological objects with smaller structural complexity into a class, and modeling by adopting a parameter surface method based on T splines, wherein the method comprises the following steps: geological structures such as terrain, layered sediment structure, fold structure, weathered and unloaded interface and the like; dividing geological objects with larger structural complexity into another type and modeling by adopting a subdivision surface method based on T splines, wherein the subdivision surface method comprises the following steps: quaternary overlay, unconformity contact configuration, intrusion configuration, pinch-out configuration, fault configuration, and the like.
Dividing the geological object into two types, and respectively adopting a parameter surface modeling method based on a T spline or a subdivision surface modeling method based on the T spline;
the T spline-based parameter surface geological modeling method comprises the following steps:
(1) establishing a released T-spline surface in a geometrical stage and fitting, wherein the method comprises the following three steps:
step 1, carrying out boundary surface division on a geological object according to geological data such as an earth surface outcrop line, a drilling data point, a section line and the like, and determining the number of boundary surfaces and an initial T spline surface of each boundary;
step 2, local thinning is carried out on the geological data neighborhood part of the initial T spline;
and 3, fitting the initial T spline surface after local thinning to the corresponding geological data to generate a group of boundary T spline surfaces of the geological object.
(2) Constructing a topological relation among the T spline surfaces in a topological stage to obtain a closed T spline surface, and comprising the following three steps of:
step 1, analyzing the intersection relation of the boundary surfaces of the geological object, calculating the intersection lines between the T spline surfaces, and further calculating the cutting line of each T spline surface;
step 2, adjusting the topological structure of the T mesh corresponding to the T spline surface in the neighborhood of the cutting line, deleting the cut area of the T spline, and establishing a curved surface boundary line which is close to the cutting line in the reserved area to obtain a group of non-cutting T spline geological curved surfaces with mutually matched boundaries;
and 3, splicing the geological boundary curved surfaces with the boundaries matched with each other into a closed T-spline curved surface, and adjusting the geometric continuity of the positions of the splicing lines according to the actual condition to finally obtain a geological object entity based on the closed T-spline curved surface.
The subdivision surface geological modeling process based on the T spline comprises the following steps:
(1) constructing a space topological structure of a closed T grid in a topological stage, comprising the following three steps:
step 1, mapping geological data such as an earth surface outcrop line, a drilling data point, a section line and the like from a three-dimensional physical space to a two-dimensional parameter space;
step 2, in a parameter space, controlling a topological structure of the T grid primitive on a geological data neighborhood by utilizing a quantized structural complexity index based on geological boundary constraint obtained by mapping; the method specifically comprises the following steps:
a) analyzing fractal geometric characteristics, any genus topology and discontinuity of the represented geological objects of the parametric spatial geological data, and quantizing by using fractal dimension, genus number and continuity order respectively;
b) and respectively quantizing and controlling local thinning parameters of the T-spline according to fractal dimension, quantizing and controlling any topological parameters of the T-spline according to the deficiency number and quantizing and controlling variable continuity parameters of the T-spline according to the continuity order by inserting and removing cross nodes, T nodes, singular points and multiple nodes in the geological data neighborhood of the T-grid original image in the parameter space.
And 3, remapping the T grid original image after the re-topology to a three-dimensional physical space to generate a closed space T grid corresponding to the geological object.
(2) Establishing a T spline surface corresponding to the T mesh in a geometric stage and fitting, wherein the method comprises the following three steps:
step 1, defining a node vector on the basis of a three-dimensional space topology of a T grid and generating a T spline mixed function;
step 2, fitting the boundary constraint between geologies by the T spline surface is achieved by calculating the three-dimensional physical space position of the T spline control point;
and 3, generating a corresponding T spline surface based on the closed space T grid, the node vector, the mixing function and the control point coordinates, and finally obtaining the geological object entity based on a closed T spline surface.
Fourthly, integrating and checking the three-dimensional model of the geological object established in the previous step to obtain a final three-dimensional geological model, wherein the integration and checking process comprises the following four steps:
step 1, combining two types of geological objects obtained by the T-spline-based parameter surface modeling method and the T-spline-based subdivision surface modeling method into the same spatial coordinate system;
step 2, analyzing spatial position relations and topological relations among the mutually contacted geological objects, integrating all the geological objects into a regional integral geological model by utilizing T spline entity Boolean operation, and adjusting Boolean logic sequence in consideration of the relative size of construction complexity in the process;
step 3, integrally checking the reliability and the rationality of the geological structure model from the structural geology angle;
and 4, obtaining a final engineering region three-dimensional geological model.
According to the method, the complexity of the geological structure is quantized from three aspects of fractal geometric features, any defect topology and discontinuity, and local refinement parameters, any topology parameters and variable continuity parameters of the T-spline surface are controlled in a quantization mode, and the method is shown in figure 2. The quantitative control relationship can be summarized as the following three points:
1) and quantizing the fractal geometric complexity of the geological structure by using the fractal dimension, and further controlling the local thinning parameters of the T spline based on the T node elements. Local detail geometry of a geological formation can be described using fractal theory and quantified using fractal dimensions. The fractal dimension describes the degree of space filling of a fractal object and reflects its ability to self-resemble copies. For a geologic body, the local fractal dimension distribution of different regions on the geologic surface is not uniform, i.e., some regions have relatively higher fractal complexity and local details.
2) And quantizing the topology complexity of any defect of the geological structure by using the defect number, and further controlling any topological parameter of the T spline based on the singular point elements. Spatially interleaved contact features of a geological formation can be topologically described and quantified by a genus number. For a geologic model, the number of defects is generally equivalent to the number of holes it penetrates. Holes are widely existing phenomena in rock and soil body forms, so that the topological structure of a geological object usually shows a higher defect number.
3) The discontinuous complexity of the geological structure is quantified using the geometric continuity order, which in turn controls the variable continuity parameters of the T-spline based on the multiple node elements. Fracture and fracture characteristics of a geological formation can be described using geometric continuity analysis theory and quantified using geometric continuity order. The different geometrical continuity representations are as follows: c-1 continuous indicates discontinuous surface separation, C0 continuous indicates continuous position, C1 continuous indicates continuous first derivative, and C2 continuous indicates continuous first and second derivatives. In tectonic geology, the key features that distinguish geologic objects from engineered objects are geological discontinuities, including the pinch-out feature of C0 and the fracture feature of C-1.
Fig. 3 illustrates a method for quantization control of T-spline parameters based on different kinds of construction complexity by a normalization algorithm. The figure shows five pairs of T mesh original images in two-dimensional parameter space and T spline surfaces corresponding to the T mesh original images and using cube formalization, and the initial T mesh original image 3012 corresponding to the initial T spline cube 3011 is respectively characterized by four different structural complexities through four transformations: the fractal geometric characteristics of the geological structure are described through the local thinning T grid primitive image 3021, and a T node of the corresponding local thinning T spline cube 3022 is framed by a circle; the high-deficiency T mesh primitive 3031 is used for depicting any deficiency topology of a geological structure, one singular point in a corresponding high-deficiency T spline cube 3032 is framed by a rectangle, the deficiency set for simplifying explanation in the embodiment is 1, and any deficiency can be realized by using the singular point of a T spline in actual modeling; depicting pinch-out characteristics in discontinuity of a geological structure through a local C0 continuous T grid original image 3041, and a corresponding pinch-out edge in a local C0 continuous T spline cube 3042 is indicated by a thickened line; fracture characteristics in the discontinuity of the geological structure are described through the local C-1 continuous T grid primitive 3051, and singular points introduced in the process of generating the internal boundary of the corresponding local C-1 continuous T spline cube 3052 are outlined by rectangles in the figure.
The technical scheme adopted by the three-dimensional geological modeling method based on the T spline mainly comprises three-dimensional fine modeling of the engineering geological structure based on multi-source geological data.
1. Engineering geological data space integration of coupled multi-source survey data comprises the following specific steps:
spatially integrating surface data acquired from an engineered geological survey with subsurface data, wherein the surface data comprises: topographic control points and contour lines obtained by total station or satellite positioning measurement, outcrop boundary occurrence of geological structure obtained by outcrop surveying and mapping, digital terrain obtained by aerial remote sensing and the like; subsurface data includes: the geological data comprises geological attribute space coordinates obtained by vertical drilling and horizontal hole probing, sampling analysis data, drilling video, a footrill display map, geological data obtained by geophysical exploration and analysis and the like. And performing spatial integration analysis on the multi-source geological data to generate a section, checking the consistency and reliability of geological information, and providing objective and accurate basic data for three-dimensional geological modeling.
2. The method comprises the following steps of finely modeling a three-dimensional model of the complex geological structure:
according to the multi-source survey integrated data, analyzing the complexity of different geological structure objects (terrain, covering layer, fault, interlayer and the like), and dividing and selecting data required by modeling; and carrying out three-dimensional modeling based on the T spline data structure.
(1) And modeling the T spline parametric surface of the sedimentary geological structure.
The sedimentary geological structure presents a more regular layered contact characteristic, and a parameter surface modeling method based on a T spline is adopted. Generating an initial terrain curved surface according to data such as surface contour lines, terrain point clouds and the like, generating an initial stratum boundary curved surface according to data such as drilling holes and profiles, locally thinning a geological data neighborhood part of an initial T spline, fitting the locally thinned initial T spline curved surface to corresponding geological data, and generating an open T spline curved surface to represent a terrain surface and a stratum boundary curved surface, as shown in a left side diagram of FIG. 4. Analyzing the intersection relation between the terrain curved surface and the stratum boundary curved surface on the basis, calculating the intersection line between the T spline curved surfaces, and further calculating the cutting line of each T spline curved surface; adjusting the topological structure of the T mesh corresponding to the T spline surface in the neighborhood of the cutting line, deleting the cut area of the T spline, and establishing a surface boundary line which is close to the cutting line in the reserved area to obtain a group of non-cutting T spline geological surfaces with mutually matched boundaries; and splicing the geological boundary curved surfaces with the boundaries matched with each other into a closed T-spline curved surface, adjusting the geometric continuity of the position of the splicing line according to the actual condition, and finally obtaining a sedimentary structure stratum body model expressed by local thinning of the T-spline, as shown in the right side diagram of FIG. 4.
(2) And modeling the T spline subdivision surface of the covering layer.
Local details of the outcrop line of the boundary of the covering layer show a certain degree of fractal geometrical characteristics, and the complex invasion contact relationship of the outcrop line and the bedrock below the outcrop line enables the geologic body to have any genus topological characteristics.
The covering layer object shows higher fractal complexity and any defect topological complexity, a subdivision surface modeling method based on T-spline is adopted, fractal dimension and defect number of geological data are used as a structure complexity quantization index, and the T-spline local refinement parameters and any topological parameters are quantized and controlled by adjusting the distribution of T nodes and singular points in a space T grid in a topological stage; in the geometric stage, the T grid is converted into a corresponding T spline surface, and geological boundaries such as earth surface outcrop constraint, terrain constraint, section line constraint and the like are fitted. The finally obtained overburden geologic body model is built only by using a closed T spline surface and can be subsequently converted into a B-Rep entity or a tetrahedral mesh entity based on non-cutting NURBS for subsequent analysis. Fig. 5 shows an overlay layer model established based on the above method, and shows the positions and topology structures of a T node and a singular point on a T-spline surface in an enlarged manner.
In the modeling method based on NURBS, a large number of NURBS patches are required to be used for simulating fractal geometric characteristics and any defect topology of a geological object through complex cutting and splicing operation, on one hand, the strategy has low feasibility, on the other hand, a large number of gaps are introduced to a geological object entity at patch splicing positions, and a plurality of problems are brought to subsequent numerical simulation analysis. On the contrary, the T-spline converts the modeling problem of the multiple curved surfaces into the control point and topological structure control problem in the single curved surface, a quantification method can be introduced to depict fractal geometric complexity and any defect topological complexity, and the surface of the established complex geological object has a uniform T-spline parameter domain without gaps. Therefore, the geological modeling method based on the T spline breaks through the limitation of the traditional NURBS method in depicting the complex local detail and space invasion relationship of the geological object.
(3) And modeling the T spline subdivision surface of the interlayer body.
The ubiquitous unconformity of contact relationships in the formation results in the pinch-out morphology characteristic of the geologic volume, i.e., the thickness of the formation gradually thins as it extends and disappears at the boundaries. Describing this non-integration is also a key link in geological modeling.
The interlayer body geological object shows high discontinuous complexity, a subdivision surface modeling method based on T splines is adopted, the continuity order of geological data is used as a structure complexity quantization index, and in a topological stage, a local pinch-out edge with C0 position continuity is established by locally inserting multiple nodes with the node spacing of 0; in the geometric phase, the control points on the local pinch-out edge are fitted to the pinch-out line in the geological data by calculating their spatial positions. The finally obtained interlayer lens body model is formed by a closed T spline surface and can be subsequently converted into a B-Rep entity or a tetrahedral mesh entity based on non-cutting NURBS for subsequent analysis. Fig. 6 shows a sandwich lens body with two pinch-out boundaries established based on the above method, and shows the form of one of the pinch-out boundaries in an enlarged manner.
In the NURBS-based method, pinch-out edges are mainly established by clipping and splicing two NURBS patches, but because there is no control point on the pinch-out edges established by the algorithm and further deformation of the pinch-out edges may cause splicing failure of the NURBS patches, the pinch-out edges cannot be controlled to fit to geological data. On the contrary, the T spline can locally change the geometric continuity, and the T spline modeling technology can establish a local sharp edge and fit the local sharp edge to geological constraints, so that the geological modeling method based on the T spline provided by the invention is more effective in processing the problem of unconformity contact of the geological body.
(4) And modeling the T spline subdivision surface of the fault layer body.
Faults divide a continuous layered sedimentary earth formation into discrete regions. Fault modeling is a key link in geological modeling, and a fault dislocation process is also a difficulty of geological modeling.
The fault geological object shows higher discontinuous complexity, a subdivision surface modeling method based on T splines is adopted, and the continuity order of geological data is used as a structure complexity quantization index. Fig. 7 is a positive fault model established based on a T-spline, and a pre-dislocation fault structure 701 and a post-dislocation fault structure 702 respectively show dislocation of an upper disc and a lower disc of a fault layer in an enlarged manner from two angles of a cross section and a perspective view, wherein a cross section view 7011 of the pre-dislocation fault and a cross section view 7021 of the post-dislocation fault contrast illustrate a fault-layer dislocation distance, and a perspective view 7012 of the pre-dislocation fault and a perspective view 7022 of the post-dislocation fault contrast illustrate a spatial relationship between a non-penetrating fault and a stratum interface.
In the NURBS-based modeling method, the fracture characteristics of the fault need to be realized by using a clipping operation. Because the cutting boundary obtained by the NURBS cutting algorithm has no control point, the fault boundary is difficult to control to simulate the fault dislocation process, and the dislocation form can be established only aiming at the fault which is explored to obtain dislocation distance data. Instead, a T-spline surface may establish internal boundaries and simulate the fault slip process by moving control points on the fault boundaries. Fig. 8 shows the topology of the T-spline control points near the fault, and shows a T-node and a singular point in an enlarged manner. The T node is inserted into a T grid near a fault, control points of the boundary of an upper disc and a lower disc are separated and move under the constraint of a fault plane so as to simulate the fault dislocation process, and singular points are generated at two ends of the termination of stratum fracture concomitantly. In conclusion, the geological modeling method based on the T-spline can better support the simulation of fault dislocation.
3. The three-dimensional geological model integration and inspection method comprises the following specific steps:
combining various geological objects obtained by the T-spline-based parametric surface modeling method and the T-spline-based subdivision surface modeling method into the same spatial coordinate system; analyzing the spatial position relationship and the topological relationship between the mutually contacted geological objects, adjusting the Boolean logic sequence by considering the relative size of the construction complexity, integrating all the geological objects into a regional integral geological model by utilizing T spline entity Boolean operation, and integrally checking the reliability and the rationality of the geological structure model from the structural geological angle to obtain a final engineering regional three-dimensional geological model, as shown in figure 9.
The present invention is not limited to the above-described embodiments. The foregoing description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention, and the above specific embodiments are merely illustrative and not restrictive. Those skilled in the art can make many changes and modifications to the invention without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (4)
1. A three-dimensional geological modeling method based on T splines is characterized in that the T splines are used as a spatial data structure of three-dimensional geological modeling, three-dimensional modeling is carried out aiming at the complex morphology of a geological object, and quantitative depiction of geological structure complexity is realized, and the method comprises the following steps:
integrating multi-source geological data;
performing a construction complexity analysis for the geological object based on the geological data; dividing the geological object into two types, and respectively adopting a parameter surface modeling method based on a T spline or a subdivision surface modeling method based on the T spline;
the process of performing a construction complexity analysis on a geological object comprises the following two steps:
carrying out structural complexity analysis on three aspects of fractal geometric complexity, arbitrary genus topological complexity and discontinuous complexity of a geological object based on geological data;
dividing geological objects with small construction complexity into a class, and modeling by adopting a parameter surface method based on T splines, wherein the method comprises the following steps: the geological structure comprises a terrain, a layered sediment structure, a fold structure, a weathered and unloaded interface geological structure; dividing geological objects with larger structural complexity into another type and modeling by adopting a subdivision surface method based on T splines, wherein the subdivision surface method comprises the following steps: a quaternary overlay, unconformity contact configuration, intrusion configuration, pinch-out configuration, and fault configuration;
the parameter surface modeling method based on the T spline adopts geometric-topological modeling logic: in the geometric stage, fitting a T spline surface to geological data based on geological data boundary constraint, and establishing an open T spline surface to represent the geological surface; in the topological stage, performing T spline Boolean operation according to the topological relation of the geological curved surface to obtain a geological object established by the closed T spline geological entity representation;
the subdivision surface modeling method based on the T spline adopts topological-geometric modeling logic: in a topological stage, a topological structure of a T spline is constructed according to complex characteristics of geological data to obtain a closed space T grid representation geologic body; in the geometric stage, according to geological data boundary constraint, surface fitting of a geological object is achieved by calculating T spline control points, a T spline surface corresponding to a T grid is established, and the geological object established by closed T spline geological entity representation is obtained;
establishing a three-dimensional model of a geological object, integrating and checking to obtain a final three-dimensional geological model, and specifically comprising the following steps:
step 1, combining two types of geological objects obtained by a parameter surface modeling method based on a T spline and a subdivision surface modeling method based on the T spline into the same space coordinate system;
step 2, analyzing spatial position relations and topological relations among the mutually contacted geological objects, integrating all the geological objects into a regional integral geological model by utilizing T spline entity Boolean operation, and adjusting Boolean logic sequence by considering the relative size of construction complexity in the process;
step 3, integrally checking the reliability and the rationality of the geological structure model from the structural geology angle;
and 4, obtaining a final engineering region three-dimensional geological model.
2. The T-spline-based three-dimensional geological modeling method according to claim 1, characterized in that the T-spline-based parametric surface modeling method specifically comprises the following steps:
(1) and (3) establishing a released T-spline surface in a geometric stage and fitting, wherein the method comprises the following three steps:
step 1, carrying out boundary surface division on a geological object according to an earth surface outcrop line, a drilling data point and section line geological data, and determining the number of boundary surfaces and an initial T spline surface of each boundary;
step 2, local thinning is carried out on the geological data neighborhood part of the initial T spline;
step 3, fitting the initial T spline surface after local thinning to corresponding geological data to generate a group of boundary T spline surfaces of the geological object;
(2) constructing a topological relation among the T spline surfaces in a topological stage to obtain a closed T spline surface, and the method comprises the following three steps:
step 1, analyzing the intersection relation of the boundary surfaces of the geological object, calculating the intersection lines between the T spline surfaces, and calculating the cutting line of each T spline surface;
step 2, adjusting the topological structure of the T mesh corresponding to the T spline surface in the neighborhood of the cutting line, deleting the cut area of the T spline, and establishing a curved surface boundary line which is close to the cutting line in the reserved area to obtain a group of non-cutting T spline geological curved surfaces with mutually matched boundaries;
and 3, splicing the geological boundary curved surfaces with the boundaries matched with each other into a closed T-spline curved surface, and adjusting the geometric continuity of the positions of the splicing lines according to the actual condition to finally obtain a geological object entity based on the closed T-spline curved surface.
3. The T-spline-based three-dimensional geological modeling method according to claim 1, characterized in that the T-spline-based subdivision surface modeling method specifically comprises the following steps:
(1) constructing a space topological structure of a closed T grid in a topological stage, comprising the following three steps:
step 1, mapping earth surface outcrop lines, drilling data points and section line geological data from a three-dimensional physical space to a two-dimensional parameter space;
step 2, in a two-dimensional parameter space, controlling a topological structure of the T grid primitive on a geological data neighborhood by utilizing a quantized structural complexity index based on geological boundary constraint obtained by mapping;
step 3, remapping the T grid original image after the re-topology to a three-dimensional physical space to generate a closed space T grid corresponding to the geological object;
(2) establishing a T spline surface corresponding to the T mesh in a geometric stage and fitting, wherein the method comprises the following three steps:
step 1, defining a node vector on the basis of a three-dimensional space topology of a T grid and generating a T spline mixed function;
step 2, fitting the boundary constraint between geologies by the T spline surface is achieved by calculating the three-dimensional physical space position of the T spline control point;
and 3, generating a corresponding T spline surface based on the closed space T grid, the node vector, the mixing function and the control point coordinates, and finally obtaining the geological object entity based on a closed T spline surface.
4. The T-spline-based three-dimensional geological modeling method according to claim 3, characterized in that the topological structure process of the T-mesh protograph is controlled according to the geological structure complexity index, and the method comprises the following steps:
step 1, analyzing fractal geometric characteristics, any defect topology and discontinuity of a geological object represented by parameter space geological data, and quantizing by using a fractal dimension, a defect number and a continuity order respectively;
and 2, respectively quantizing and controlling local thinning parameters of the T-spline according to the fractal dimension, quantizing and controlling any topological parameters of the T-spline according to the deficiency number and quantizing and controlling variable continuity parameters of the T-spline according to the continuity order by inserting and removing cross nodes, T nodes, singular points and multiple nodes in the geological data neighborhood of the T-grid original image in the parameter space.
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