Multi-valued stratigraphic interface three-dimensional automatic modeling method based on multiple constraints of coordinate occurrence

Abstract

A multi-valued stratigraphic interface three-dimensional automatic modeling method based on multiple constraints of coordinate occurrence comprises the following steps: S1, extracting a stratigraphic demarcation point coordinate and a stratigraphic interface trend and an inclination angle at a corresponding demarcation point according to original geological data as basic data for modeling; s2, establishing a stratigraphic boundary NURBS constraint equation based on interpolation points along the trend and the inclination angle; s3, establishing a stratigraphic boundary NURBS constraint equation based on a first-order derivative along the trend and the inclination angle; s4, obtaining an NURBS parameterized dynamic stratum boundary based on coordinate attitude multi-constraint along the trend and the inclination angle; and S5, constructing an NURBS curved surface by using the parameterized dynamic stratum boundary in a tensor product topology mode to obtain a parameterized dynamic stratum interface model based on coordinate attitude multi-constraint. According to the method, the defect that deviation exists between the local stratum trend and the actual situation based on space coordinate trend and dip angle constraint conventionally is overcome.

Description

Technical Field

[0001] The invention relates to the field of three-dimensional geological modeling, and in particular to a three-dimensional automatic modeling method of a multi-valued stratum interface based on multiple constraints of coordinate occurrence. Background Art

[0002] Stratigraphic interface modeling is an important step in the three-dimensional geological modeling process. In existing studies, there are two types of stratigraphic interface modeling methods, namely surface-based modeling methods and grid-based modeling methods. The surface-based modeling method uses mathematical functions to interpolate the original geological data, and uses the interpolated function surface as the modeling method of the three-dimensional geological model. According to the different forms of the function, the surface-based modeling method can be further divided into explicit surface methods and implicit surface methods. Explicit surface methods include Bézier, non-uniform rational B-splines (NURBS), T-splines, local polynomial interpolation (LPI), minimum curvature interpolation (MCI), spline function interpolation, and global polynomial interpolation. Implicit surface methods include discrete smooth interpolation (DSI), moving least squares (MLS), multi-level partition of unity (MPU) and radial basis function (RBF). The advantages of explicit and implicit surface modeling methods are small data volume, strong geometric expression ability, differentiability, and flexible modeling operations such as clipping and combination. However, the disadvantage is that the geological significance of the control parameters is unclear, which leads to the fact that only empirical range values ​​can be taken instead of accurate values, which in turn leads to the modeling results being unable to accurately express the geometric shape and actual distribution range of the stratigraphic layer. For example, the explicit surface modeling method can flexibly model complex stratigraphic layers, but because the connection between the definition domain of the control parameters and the coordinate interval of the geological body distribution is not intuitive, the modeling results are usually not completely consistent with the actual distribution range of the actual geological body, and the multi-valued stratigraphic layer is not fully consistent with the actual distribution range of the geological body. The expression of features and trend mutation features is not accurate enough; the implicit surface modeling method can realize the automatic modeling of a single complex geological body, such as inverted folds and erosional strata with multi-valued features. However, when using implicit surfaces to model multiple geological bodies, boundary inconsistencies such as boundary overlap and local voids will appear at the boundaries of the geological bodies. The reason is that the geological significance of the implicit surface control parameters is not clear, and they can only be valued within an empirical range but not accurately, which leads to deviations between the modeling results and the actual situation. Manual trimming and filling of defective parts are required, so the processing efficiency of multi-geological body modeling tasks is low.Since the surface layer clipping operation requires less manual work and is less difficult to operate than the local cavity filling operation, the explicit surface modeling method is widely used in the field of three-dimensional geological modeling, while the implicit surface modeling method is less used.

[0003] The grid-based modeling method can be summarized as follows: first, the original geological points are calculated according to a certain weighted average method to obtain new interpolation points, and then TIN or quadrilateral grid surfaces are generated based on all interpolation points to represent the stratigraphic surface. Many different interpolation methods have been generated based on different weighted average methods, such as inverse distance weighted interpolation (IDW), natural neighbor interpolation, modified Shepard interpolation, simple Kriging, etc. In addition, there is a special generalized tri-prism (GTP) modeling method based on grid surfaces. This method does not involve the interpolation process, but directly generates the TIN grid surface of the stratigraphic interface based on the actual densely distributed boreholes, and then automatically constructs the GTP to form a three-dimensional geological model through the TIN grid surfaces of different strata. For the grid-based modeling method, the principles of the interpolation methods involved are generally more in line with geological laws, the geological significance of the algorithm control parameters is clear, and the calculation process is simple and fast. However, since the interpolation points are obtained by weighted average calculation of actual geological points, it belongs to a single-value interpolation method and cannot be directly applied to multi-valued stratigraphic layers such as inverted folds and interlayers. When using the grid modeling method to model multi-valued stratigraphic layers, it is necessary to first divide the multi-valued area into several single-valued areas, and then interpolate each single-valued area to obtain the corresponding single-valued stratigraphic layer model, and finally combine all the single-valued stratigraphic layer models to form an overall multi-valued stratigraphic layer model; in addition, the grid surface modeling method is based on discrete points and cannot calculate or express the derivatives of the grid vertices, resulting in the inability to consider the occurrence constraints at each geological point during the modeling process, which may lead to deviations between the local stratigraphic trend of the modeling results and the actual existence.

[0004] Since traditional surface modeling methods and mesh modeling methods require a large amount of human-computer interactive modeling operations when modeling complex multi-valued geometric features of geological bodies, their accuracy and efficiency are low. Therefore, it is necessary to conduct research to improve the existing modeling methods and realize three-dimensional automatic modeling of multi-valued stratigraphic interfaces. Summary of the invention

[0005] The present invention aims to solve the shortcomings of the existing three-dimensional geological modeling methods, that is, the surface modeling method and the grid modeling method require a large number of human-computer interactive modeling operations when modeling the complex multi-valued geometric features of the geological body, and the accuracy and efficiency are low. A three-dimensional automatic modeling method of a multi-valued stratigraphic interface based on multiple constraints of coordinate occurrence is provided. On the basis of the stratigraphic interface NURBS surface modeling method based on coordinate constraints, additional strike and dip constraints are added. The local distribution and extension trend of the stratigraphic layer are described by the strike and dip constraints, so as to realize the automatic modeling of the multi-valued stratigraphic interface.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] The method for three-dimensional automatic modeling of multi-valued stratum interface based on coordinate occurrence multi-constraints includes the following steps:

[0008] S1. Extracting the coordinates of the stratigraphic boundary points and the direction and inclination of the stratigraphic interface at the corresponding boundary points according to the original geological data as the basic data for modeling;

[0009] S2. Taking the coordinates of the stratigraphic boundary point as the basic constraint, NURBS constraint equations of the stratigraphic boundary line based on interpolation points along the strike and along the dip are established. This constraint equation is defined along a p-order NURBS curve as shown in formula (1):

[0010]

[0011] In formula (1), C(t) is a free curve with parameter t; {P i} is the control point set, which contains n+1 control points; {ω i} is the weight factor set; {N i,p (t)} is a p-order B-spline basis function, which is formed by periodic C(a) = C(b) or non-periodic C(a) ≠ C(b), uniform t i+1 -t i =t i -t i-1 or non-uniform t i+1 -t i ≠t i -t i-1 The node vector U of the p-order NURBS curve with m, m=n+p+1 nodes is determined by formula (2): The node set corresponding to the node vector U is {Q k}; Each Q k (k=0,1,…,n) specifies the corresponding parameter value d is {Q k The total length of the polyline formed by {N i,p(t)}, thus the NURBS constraint equation of the stratum boundary line based on the interpolation point can be obtained, as shown in formula (3): And by adding new geological point coordinates to constrain Q new , realize automatic update of stratum boundary line;

[0012] S3. Taking the strike and dip of the stratigraphic boundary point as the basic constraints, the stratigraphic boundary line NURBS constraint equations based on the first-order derivative along the strike and along the dip are established respectively. On the basis of equation (3), the first-order derivative constraint equation is added: Let V k The first-order derivative of the representative curve is obtained, and the NURBS constraint equation of the stratum boundary line based on the first-order derivative can be expressed as formula (4):

[0013]

[0014] S4. Combining the NURBS constraint equations of the stratum boundary line based on the interpolation point and the NURBS constraint equations of the stratum boundary line based on the interpolation point, we can obtain a 2(n+1)×2(n+1) linear equation system. The corresponding unknowns are 2(n+1) control points {P i}, and solve the equation system, as shown in equation (5),

[0015] The NURBS parameterized dynamic stratum boundary function is obtained as shown in formula (6): u and v are parameters, S(u,v) is the ground plane with the longitudinal parameter u and the transverse parameter v as control parameters; {P i,j} is the set of control points that form the control grid in two directions; {N i,p (u)} and {N j,q (v)} are the p-order and q-order non-rational B-spline basis functions defined in the u and v directions, respectively; n and m are the total number of segmentations of the parameter interval in the u and v directions, respectively;

[0016] S5. The NURBS parameterized dynamic stratum boundary line is constructed into a NURBS surface in a tensor product topology manner to obtain a parameterized dynamic stratum boundary interface model based on multiple constraints of coordinate occurrence.

[0017] The multi-valued feature expression and updating of multi-valued stratigraphic interfaces are automatically achieved through parameterized adjustment of coordinates, strike and dip parameters.

[0018] The three-dimensional automatic modeling method of multi-valued stratigraphic interfaces based on coordinate occurrence multi-constraints can be applied to the modeling of multi-valued stratigraphic interfaces such as inverted folds and interlayers, as well as the modeling of conventional single-valued stratigraphic interfaces.

[0019] The beneficial effects of the present invention are as follows: the method of the present invention makes up for the deficiency that the conventional discretized stratigraphic interface modeling method based on weighted interpolation of spatial coordinates cannot calculate and express the derivatives at the grid vertices, that is, the strike and dip constraints, which leads to the deviation between the local stratigraphic strike and the actual existence; the automatic modeling of multi-valued stratigraphic interfaces can be realized, instead of the conventional modeling method which requires firstly manually dividing the multi-valued area into a number of single-valued areas, then interpolating each single-valued area to obtain the corresponding single-valued stratigraphic surface model, and finally combining all the single-valued stratigraphic surface models to form an overall multi-valued stratigraphic surface model; BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Characteristic diagram of the NURBS curve of the present invention, ((a) and (b) reflect that the division method of the parameter interval does not affect the geometric shape of the curve, (c) and (d) reflect the characteristics of the single-valued vector function of the NURBS curve);

[0021] Figure 2 The automatically updated map of NURBS stratum boundaries of the present invention;

[0022] Figure 3 It is a NURBS stratigraphic boundary line map based on coordinate occurrence multi-constraints of the present invention;

[0023] Figure 4 This is a result diagram of automatic modeling of a NURBS stratum surface based on multiple constraints of coordinate occurrence according to the present invention;

[0024] The following is a detailed description of the embodiments of the invention with reference to the accompanying drawings. DETAILED DESCRIPTION

[0025] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0026] The method for three-dimensional automatic modeling of multi-valued stratum interface based on coordinate occurrence multi-constraints is characterized by comprising the following steps:

[0027] S1. Extracting the coordinates of the stratigraphic boundary points and the direction and inclination of the stratigraphic interface at the corresponding boundary points according to the original geological data as the basic data for modeling;

[0028] S2. Taking the coordinates of the stratigraphic boundary point as the basic constraint, NURBS constraint equations of the stratigraphic boundary line based on interpolation points along the strike and along the dip are established. This constraint equation is defined along a p-order NURBS curve as shown in formula (1):

[0029]

[0030] In formula (1), C(t) is a free curve with parameter t; {P i} is the control point set, which contains n+1 control points; {ωi} is the weight factor set; {N i,p (t)} is a p-order B-spline basis function, which is formed by periodic C(a) = C(b) or non-periodic C(a) ≠ C(b), uniform t i+1 -t i =t i -t i-1 or non-uniform t i+1 -t i ≠t i -t i-1 The node vector U of the p-order NURBS curve with m, m=n+p+1 nodes is determined by formula (2): The node set corresponding to the node vector U is {Q k}; For any NURBS curve, you can move the control point P i Or change the weight factor ω i The local geometry of the curve is modified by changing the parameter interval division method (i.e. the parameter value of the node Qk) and does not have any effect on the geometry of the curve. Figure 1 (a, b), (a) and (b) reflect that the division of the parameter interval does not affect the geometric shape of the curve, (c) and (d) reflect the characteristics of the single-valued vector function of the NURBS curve; the curve C(t) is a single-valued vector function of the parameter t; based on this characteristic, assuming that all ownership factors are equal to 1, the parameter interval is (0,1), and the geological point coordinate constraints are taken as the node set {Q k}, and for each Q k (k=0,1,…,n) specifies the corresponding parameter value d is {Q k The total length of the polyline formed by {N i,p (t)}, thus the NURBS constraint equation of the stratum boundary line based on the interpolation point can be obtained, as shown in formula (3): And Q can be constrained by adding new geological point coordinates new , to achieve automatic update of stratum boundaries, such as Figure 2 As shown;

[0031] S3. Taking the strike and dip of the formation boundary point as the basic constraints, the NURBS constraint equations of the formation boundary line based on the first-order derivative along the strike and along the dip are established respectively. Considering that the occurrence constraint is essentially a first-order derivative constraint, a first-order derivative constraint equation is added on the basis of equation (3): Let V k The first-order derivative of the representative curve is obtained, and the NURBS constraint equation of the stratum boundary line based on the first-order derivative can be expressed as formula (4):

[0032] S4. Combine the two constraint equations, the NURBS constraint equation of the stratum boundary line based on the interpolation point and the NURBS constraint equation of the stratum boundary line based on the interpolation point, and combine equations (3, 4) in an alternating manner to obtain a 2(n+1)×2(n+1) linear equation system. The corresponding unknown quantity is 2(n+1) control points {P i}, and solve the equation system, as shown in equation (5), The NURBS parameterized dynamic stratum boundary function is obtained as shown in formula (6): u and v are parameters, S(u,v) is the ground plane with the longitudinal parameter u and the transverse parameter v as control parameters; {P i,j} is the set of control points that form the control grid in two directions; {N i,p (u)} and {N j,q (v)} are p-order and q-order non-rational B-spline basis functions defined in the u and v directions respectively; n and m are the total number of segmentations of the parameter interval in the u and v directions respectively, such as Figure 3 As shown;

[0033] S5. After obtaining the NURBS parametric dynamic stratigraphic boundary line, the stratigraphic interface is modeled in the tensor product topology of the vertical and horizontal stratigraphic boundary lines in the modeling area. Since the NURBS stratigraphic boundary line is a single-valued vector function of the parameter t, the NURBS stratigraphic interface is a single-valued vector function of the parameters u and v. By parametrically adjusting the occurrence constraint, the parametric control of the stratigraphic interface in the u and v directions is achieved, and the multi-valued stratigraphic surface can be quickly modeled, and the automatic modeling of the multi-valued stratigraphic interface based on the coordinate occurrence multi-constraints is realized, such as Figure 4 As shown. The multi-valued feature expression and update of the multi-valued stratigraphic interface are automatically realized by parametrically adjusting the coordinate, strike and dip parameters. The three-dimensional automatic modeling method of the multi-valued stratigraphic interface based on the coordinate occurrence multi-constraint can be applied to the modeling of multi-valued stratigraphic interfaces such as inverted folds and interlayers, as well as the modeling of conventional single-valued stratigraphic interfaces.

[0034] In the description of the invention, it is to be understood that the terms “center”, “longitudinal”, “lateral”, “length”, “width”, “thickness”, “up”, “down”, “front”, “back”, “left”, “right”, “vertical”, “horizontal”, “top”, “bottom”, “inside”, “outside”, “clockwise”, “counterclockwise”, “axial”, “radial”, “circumferential”, etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the invention.

[0035] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0036] In the invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be fixedly connected, detachably connected, or integrated; it can be mechanically connected, electrically connected, or able to communicate with each other; it can be directly connected, or indirectly connected through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0037] The invention is described above by way of example in conjunction with the accompanying drawings. It is obvious that the specific implementation of the invention is not limited to the above-mentioned method. As long as various improvements are made using the method concept and technical solution of the invention, or they are directly applied to other occasions without improvement, they are all within the scope of protection of the invention.

Claims

1. A three-dimensional automatic modeling method of multi-valued stratum interface based on multiple constraints of coordinate occurrence, characterized in that: The following steps are involved: S1. Extracting the coordinates of the stratigraphic boundary points and the direction and inclination of the stratigraphic interface at the corresponding boundary points according to the original geological data as the basic data for modeling; S2. Taking the coordinates of the stratigraphic boundary point as the basic constraint, NURBS constraint equations of the stratigraphic boundary line based on interpolation points along the strike and along the dip are established. This constraint equation is defined along a p-order NURBS curve as shown in formula (1): In formula (1), C(t) is a free curve with parameter t; {P i } is the control point set, which contains n+1 control points; {ω i } is the weight factor set; {N i,p (t)} is a p-order B-spline basis function, which is formed by periodic C(a) = C(b) or non-periodic C(a) ≠ C(b), uniform t i+1 -t i =t i -t i-1 or non-uniform t i+1 -t i ≠t i -t i-1 The node vector U of the p-order NURBS curve with m, m=n+p+1 nodes is determined by formula (2): The node set corresponding to the node vector U is {Q k }; Each Q k (k=0,1,…,n) specifies the corresponding parameter value d is {Q k The total length of the polyline formed by {N i,p (t)}, thus the NURBS constraint equation of the stratum boundary line based on the interpolation point can be obtained, as shown in formula (3): And Q can be constrained by adding new geological point coordinates new , realize automatic update of stratum boundary line; S3. Taking the strike and dip of the stratigraphic boundary point as the basic constraints, the stratigraphic boundary line NURBS constraint equations based on the first-order derivative along the strike and along the dip are established respectively. On the basis of equation (3), the first-order derivative constraint equation is added: Let V k The first-order derivative of the representative curve is obtained, and the NURBS constraint equation of the stratum boundary line based on the first-order derivative can be expressed as formula (4): S4. Combining the NURBS constraint equations of the stratum boundary line based on the interpolation point and the NURBS constraint equations of the stratum boundary line based on the interpolation point, we can obtain a 2(n+1)×2(n+1) linear equation system. The corresponding unknowns are 2(n+1) control points {P i }, and solve the equation system, as shown in equation (5), Parameterized dynamic stratum boundary function, as shown in formula (6), u and v are parameters, S(u,v) is the ground plane with the longitudinal parameter u and the transverse parameter v as control parameters; {P i,j } is the set of control points that form the control grid in two directions; {N i,p (u)} and {N j,q (v)} are the p-order and q-order non-rational B-spline basis functions defined in the u and v directions, respectively; n and m are the total number of segmentations of the parameter interval in the u and v directions, respectively; S5. The NURBS parameterized dynamic stratum boundary line is constructed into a NURBS surface in a tensor product topology manner to obtain a parameterized dynamic stratum boundary interface model based on multiple constraints of coordinate occurrence.

2. The method for three-dimensional automatic modeling of multi-valued stratum interfaces based on coordinate occurrence multi-constraints according to claim 1 is characterized in that: The multi-valued feature expression and updating of multi-valued stratigraphic interfaces are automatically achieved through parameterized adjustment of coordinates, strike and dip parameters.

3. The method for three-dimensional automatic modeling of multi-valued stratum interfaces based on coordinate occurrence multi-constraints according to claim 2 is characterized in that: The three-dimensional automatic modeling method of multi-valued stratigraphic interfaces based on coordinate occurrence multi-constraints can be applied to the modeling of multi-valued stratigraphic interfaces such as inverted folds and interlayers, as well as the modeling of conventional single-valued stratigraphic interfaces.

Images