A finite fault implicit geological modeling method and system based on global background field fusion

Abstract

The application discloses a finite fault implicit geological modeling method and system based on global background field fusion, relates to the technical field of three-dimensional geological modeling, and comprises the following steps: acquiring geological observation data of a modeling area, and establishing a finite fault scalar field and a corresponding ellipsoidal influence range; using data outside the fault influence range to establish a global continuous global background scalar field; dividing the global background into blocks according to a logical sequence of the fault, and establishing a local stratum scalar field in each block; and fusing and evaluating the local stratum scalar field and the global background scalar field through a smooth transition function, extracting a stratum contour surface, and forming a three-dimensional geological model. The application mathematically forces to guarantee the geometric consistency of strata on both sides outside the fault influence range, eliminates common artificial gaps and curvature mutations in the domain segmentation method, and constructs a three-dimensional geological model with high precision and geometric continuity under complex fault conditions.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional geological modeling technology, and in particular to a method and system for implicit geological modeling of finite faults based on global background field fusion. Background Technology

[0002] In the field of 3D geological modeling, implicit modeling, with its high degree of automation and objectivity, has become the mainstream technique for constructing complex geological structures. Among these techniques, domain segmentation is one of the main methods for handling faults. This method uses fault planes to divide the modeling space into several independent subdomains and constructs a stratigraphic scalar field within each subdomain. This method is conceptually intuitive, computationally efficient, and can effectively represent the discontinuity of strata on both sides of a fault, thus it is widely used in industry.

[0003] Domain segmentation methods have an inherent technical bottleneck: ensuring geometric consistency outside the fault's influence zone is difficult. Because each subdomain performs interpolation independently, the scalar fields on both sides of the fault lack a unified reference benchmark in the peripheral regions far from the fault plane. This leads to minor elevation differences or curvature abrupt changes in stratigraphic interfaces that should be smoothly connected when extracting isosurfaces. While existing techniques attempt to mitigate this by setting shared control points, the nonlocality of implicit interpolation makes it difficult to achieve perfect geometric fit between control points. This results in artificial artifacts at fault boundaries that do not conform to geological realities, affecting the accuracy of subsequent numerical simulations. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a finite fault implicit geological modeling method based on global background field fusion and a system to solve the problems of geometric inconsistency outside the fault influence range and artificial artifacts caused by the independent calculation of the scalar fields of each subdomain in the existing domain segmentation method.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] In a first aspect, the present invention provides a finite fault implicit geological modeling method based on global background field fusion, which includes acquiring geological observation data of the modeling area and establishing a finite fault scalar field and the corresponding ellipsoidal influence range.

[0008] Establish a global background scalar field that is continuous across the entire fault zone using data outside the fault's influence area;

[0009] The entire region is divided into blocks according to the fault logic order, and a local stratigraphic scalar field is established in each block;

[0010] By using a smooth transition function to fuse and evaluate the local stratigraphic scalar field with the global background scalar field, stratigraphic isosurfaces are extracted to form a three-dimensional geological model.

[0011] As a preferred embodiment of the implicit geological modeling method for finite faults based on global background field fusion described in this invention, the establishment of the finite fault scalar field and the corresponding ellipsoidal influence range specifically includes:

[0012] For each finite fault, a local coordinate system for the fault is constructed based on the fault orientation and borehole data.

[0013] After normalizing the three scalar fields, the spatial region satisfying |f0|≤1, |f1|≤1, |f2|≤1 is defined as the ellipsoidal influence range of the fault.

[0014] As a preferred embodiment of the implicit geological modeling method for finite faults based on global background field fusion described in this invention, the specific steps for constructing the local coordinate system of the fault include:

[0015] Using the fault plane observation data as constraints, a first scalar field f0 is established, such that the isosurface with f0=0 fits the fault plane.

[0016] Using the observation data of the fault slip direction as a constraint, and with the additional constraint that the gradient ∇f1 of the second scalar field is orthogonal to the gradient ∇f0 of the first scalar field, a second scalar field f1 is established;

[0017] The third scalar field f2 is established by constraining that the gradient ∇f2 of the third scalar field is orthogonal to the gradients of the first two scalar fields;

[0018] Here, gradient ∇f1 represents the direction of the rate of change of the scalar field in space, and orthogonal constraints are used to ensure that the local coordinate systems formed by the first scalar field f0, the second scalar field f1, and the third scalar field f2 are perpendicular to each other.

[0019] As a preferred embodiment of the implicit geological modeling method for finite faults based on global background field fusion described in this invention, the implicit interpolation method used to establish the finite fault scalar site is specifically selected from any one or a combination of the following:

[0020] The interpolation method based on radial basis function (RBF) selects thin plate spline kernel, Gaussian kernel or compactly supported radial basis kernel, and obtains the interpolation coefficients by solving a sparse linear system of equations.

[0021] A piecewise linear interpolation method based on the natural neighbor method is used, and linear weight allocation is performed based on the Delaunay triangulation structure.

[0022] The discrete interpolation method based on finite difference solves the Poisson equation numerically by discretizing it and combining it with observation data as hard constraints.

[0023] As a preferred embodiment of the implicit geological modeling method for finite faults based on global background field fusion described in this invention, the process of establishing the global background scalar field uses stratigraphic observation data points located outside the ellipsoidal influence range of all faults. Data points located inside the influence range do not participate in the data fitting of the scalar field, but are extrapolated during the evaluation stage.

[0024] As a preferred embodiment of the implicit geological modeling method for finite faults based on global background field fusion described in this invention, the entire domain is divided into blocks according to the logical order of faults, specifically as follows:

[0025] The cutting sequence is determined based on the relative geological chronology of the faults, with the first fault to occur cutting the entire area first.

[0026] For independent faults that do not intersect, cut them in any order;

[0027] The entire modeling domain is divided into M scalar field blocks using N fault planes, where M≥N+1.

[0028] As a preferred embodiment of the implicit geological modeling method for finite faults based on global background field fusion described in this invention, the fusion evaluation is calculated using the following formula:

[0029] ;

[0030] in, Points to be evaluated The final stratigraphic scalar field value, Let x be the local stratigraphic scalar field value of the block containing point x. The value of the global background scalar field at point x. It is a continuous smooth transition function, taking a value of 0 within the influence range of the fault ellipsoid and a value of 1 outside the fault ellipsoid.

[0031] As a preferred embodiment of the implicit geological modeling method for finite faults based on global background field fusion described in this invention, the smooth transition function is described below. Calculated in the following way:

[0032] Calculate the points to be evaluated Compared to the first Minimum normalized distance of the influence range of each fault ellipsoid ;

[0033] Set transition band width parameter Calculate using the following formula:

[0034] ;

[0035] in, The value ranges from 0.1 to 0.5 times the length of the semi-axis of the corresponding fault ellipsoid.

[0036] As a preferred embodiment of the implicit geological modeling method for finite faults based on global background field fusion described in this invention, the minimum normalized distance is: The calculation method is as follows:

[0037] ;

[0038] in, , and Points In the scalar field values ​​in the local coordinate system of a fault This represents the total number of finite faults within the modeling area;

[0039] When establishing a local stratigraphic scalar field, for stratigraphic observation data located within the influence range of the fault ellipsoid, a data recovery method based on fault kinematics is used to restore the data to its position before fault activity, and then the data is used to participate in the interpolation of the block-based local stratigraphic scalar field.

[0040] This invention provides a finite fault implicit geological modeling system based on global background field fusion, including a data acquisition module for acquiring geological observation data within the modeling area; The fault scalar field establishment module is used to establish a finite fault scalar field and its corresponding ellipsoidal influence range; The global background field creation module is used to create a global background scalar field. The domain segmentation module is used to segment the entire modeling domain into blocks according to the logical order of the fault lines; The Local Stratigraphic Field Establishment Module is used to establish local stratigraphic scalar fields within each block. The fusion evaluation module is used to fuse and evaluate the local scalar field of the formation and the global background scalar field through a smooth transition function; The stratigraphic extraction module is used to extract stratigraphic isosurfaces and generate three-dimensional geological models.

[0041] The beneficial effects of this invention are as follows: by introducing a global background scalar field driven only by data outside the fault's influence range, and using a high-order smooth transition function to adaptively fuse it with the local stratigraphic scalar field within each block, the true dislocation details near the fault are preserved, and the geometric consistency of the strata on both sides outside the fault's influence range is mathematically guaranteed. This eliminates the artificial gaps and curvature abrupt changes commonly found in domain segmentation methods, and constructs a three-dimensional geological model with both high accuracy and geometric continuity under complex fault conditions. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a flowchart of a finite fault implicit geological modeling method based on global background field fusion.

[0044] Figure 2 This is a schematic diagram of the local coordinate system f0, f1, and f2 of the fault.

[0045] Figure 3 A schematic diagram of the extraction of fault activity bodies and background data points across the entire region.

[0046] Figure 4 This is a schematic diagram of the segmentation of the fault cutting domain.

[0047] Figure 5 For smooth transition function One-dimensional cross-sectional diagram.

[0048] Figure 6 This is a schematic diagram illustrating the principle of integrated evaluation.

[0049] Figure 7 This is a schematic diagram of the domain partitioning method.

[0050] Figure 8 A schematic diagram of the three-dimensional modeling results of F1 fault, F2 fault, F1 ellipsoid, and F2 ellipsoid.

[0051] Figure 9 Schematic diagram of the three-dimensional modeling results of F1 fault, F2 fault and F1 ellipsoid Detailed Implementation

[0052] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0053] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0054] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0055] Reference Figures 1-9 This is one embodiment of the present invention, which provides a method for implicit geological modeling of finite faults based on global background field fusion, comprising the following steps: Example 1

[0056] For each finite fault, a local coordinate system for the fault is constructed based on the fault orientation and borehole data.

[0057] Furthermore, by constraining the fault plane observation data, a first scalar field is established, and an isosurface with a value of zero for the first scalar field is fitted to the fault plane. Combined with the fault slip direction observation data, a second scalar field is established with the second scalar field gradient being orthogonal to the first scalar field gradient as an additional condition. A third scalar field is then established with the third scalar field gradient being orthogonal to both of the first two scalar field gradients as a constraint. The spatial distribution calculation of the three scalar fields is completed using radial basis function interpolation, natural neighbor method, or finite difference method. The three scalar fields are normalized so that the values ​​within the fault ellipsoidal influence range are within the range of negative one to positive one. Finally, the closed space that simultaneously satisfies that the absolute values ​​of the three scalar fields are all no greater than one is defined as the ellipsoidal influence range of a single fault. The union of the ellipsoidal influence ranges of all faults constitutes the global fault activity body.

[0058] After normalizing the three scalar fields, the spatial region satisfying |f0|≤1, |f1|≤1, and |f2|≤1 is defined as the ellipsoidal influence range of the fault.

[0059] Furthermore, stratigraphic observation data points located outside the active fault body in the entire region are selected for interpolation. A continuous global background scalar field is constructed using radial basis function interpolation, natural neighbor interpolation, or finite difference interpolation. Spatial regions within the active fault body do not participate in data fitting during interpolation but are obtained through scalar field extrapolation in subsequent evaluation stages. The cutting order is determined based on the relative geological time of the faults, with the first-formed faults prioritizing cutting the entire region. Independent faults without intersecting relationships are cut in any order. The fault planes are used to divide the modeled entire region into multiple scalar fields. The field is divided into blocks, and a local stratigraphic scalar field is established within each scalar field block using all stratigraphic observation data points. For stratigraphic observation data located within the influence range of the fault ellipsoid, the fault kinematics restoration method is used to restore them to their positions before fault activity before interpolation. The minimum normalized distance of the point to be evaluated relative to the influence range of each fault ellipsoid is used, and the value of the smooth transition function is determined based on the transition zone width parameter. The local stratigraphic scalar field and the global background scalar field are weighted and fused according to the smooth transition function to obtain the final stratigraphic scalar field. Based on the final stratigraphic scalar field, stratigraphic isosurfaces are extracted to complete the three-dimensional geological modeling.

[0060] Using the fault plane observation data as constraints, a first scalar field f0 is established, such that the isosurface with f0=0 fits the fault plane.

[0061] Furthermore, stratigraphic observation data points located outside the active fault body in the entire region are selected for interpolation. A continuous global background scalar field is constructed using radial basis function interpolation, natural neighbor interpolation, or finite difference interpolation. Spatial regions within the active fault body do not participate in data fitting during interpolation but are obtained through scalar field extrapolation in subsequent evaluation stages. The cutting order is determined based on the relative geological time of the faults, with the first-formed faults prioritizing cutting the entire region. Independent faults without intersecting relationships are cut in any order. The fault planes are used to divide the modeled entire region into multiple scalar fields. The field is divided into blocks, and a local stratigraphic scalar field is established within each scalar field block using all stratigraphic observation data points. For stratigraphic observation data located within the influence range of the fault ellipsoid, the fault kinematics restoration method is used to restore them to their positions before fault activity before interpolation. The minimum normalized distance of the point to be evaluated relative to the influence range of each fault ellipsoid is used, and the value of the smooth transition function is determined based on the transition zone width parameter. The local stratigraphic scalar field and the global background scalar field are weighted and fused according to the smooth transition function to obtain the final stratigraphic scalar field. Based on the final stratigraphic scalar field, stratigraphic isosurfaces are extracted to complete the three-dimensional geological modeling.

[0062] Using the fault plane observation data as constraints, a first scalar field f0 is established, such that the isosurface with f0=0 fits the fault plane.

[0063] Furthermore, by using fault plane observation data as a hard constraint point set, the spatial discrete points are fitted using radial basis function interpolation or piecewise linear interpolation based on discrete grids to generate a continuously distributed first scalar field f0. The interpolation parameters are adjusted so that the spatial isosurface with the first scalar field f0 value of zero accurately passes through all fault plane observation data points, thereby achieving geometric fitting between the isosurface with the first scalar field f0 value of zero and the fault plane.

[0064] Using the fault slip direction observation data as a constraint, and with the additional constraint that the gradient ∇f1 of the second scalar field is orthogonal to the gradient ∇f0 of the first scalar field, a second scalar field f is established. 1。

[0065] Furthermore, using the vector direction determined by the fault slip direction observation data as an interpolation constraint, additional conditions are applied during the construction of the second scalar field f1, forcing the dot product of the gradient ∇f1 of the second scalar field f1 at any point in space and the gradient ∇f0 of the first scalar field f0 at the same location to be zero. By solving the partial differential equation or constraint optimization problem that satisfies the above gradient orthogonality condition, the second scalar field f1 is generated, ensuring that the numerical change direction of the second scalar field f1 is strictly perpendicular to the fault plane.

[0066] The third scalar field f2 is established by constraining that the gradient ∇f2 of the third scalar field is orthogonal to the gradients of the first two scalar fields;

[0067] Here, gradient ∇f1 represents the direction of the rate of change of the scalar field in space, and orthogonal constraints are used to ensure that the local coordinate systems formed by the first scalar field f0, the second scalar field f1, and the third scalar field f2 are perpendicular to each other.

[0068] Furthermore, the dot product of the gradient ∇f2 of the third scalar field f2 at any point in space with the gradient ∇f0 of the first scalar field f0 and the gradient ∇f1 of the second scalar field f1 is zero, which serves as a double orthogonal constraint. The third scalar field f2 is generated by solving a spatial interpolation or differentiation problem that satisfies the double orthogonal condition. The gradient ∇f1 represents the direction of the rate of change of the second scalar field f1 in space, and the gradient ∇f2 represents the direction of the rate of change of the third scalar field f2 in space. The orthogonal constraint ensures that the three coordinate axes of the local coordinate system formed by the first scalar field f0, the second scalar field f1, and the third scalar field f2 are mutually perpendicular.

[0069] The interpolation method based on radial basis function (RBF) selects thin plate spline kernel, Gaussian kernel or compactly supported radial basis kernel, and obtains the interpolation coefficients by solving a sparse linear system of equations.

[0070] Furthermore, for the interpolation method based on radial basis functions (RBF), a thin plate spline kernel, a Gaussian kernel, or a tightly supported radial basis function kernel is selected as the basis function. The observed data points are taken as the center of the radial basis functions, and an interpolation function form composed of linear combinations of basis functions is constructed. A system of linear equations is listed according to the correspondence between the observed data points and the interpolation function values. The system of linear equations is solved using sparse matrix solving techniques to obtain the interpolation coefficients corresponding to each radial basis function, thus completing the interpolation based on radial basis functions (RBF).

[0071] A piecewise linear interpolation method based on the natural neighbor method is proposed, which uses the Delaunay triangulation structure for linear weight allocation.

[0072] Furthermore, for the piecewise linear interpolation method based on the natural neighbor method, the discrete data point set in the modeling region is delaunay triangulated to construct a tetrahedral mesh structure covering the entire modeling space. For any point to be interpolated, the set of natural neighbors of the point to be interpolated in the Delaunay triangulation structure is found. The weight coefficient of each natural neighbor is calculated according to the geometric positional relationship between the point to be interpolated and the natural neighbors. The weight coefficient is inversely proportional to the distance. The observed values ​​of the natural neighbors and the corresponding weight coefficients are linearly weighted and summed to obtain the interpolation result of the point to be interpolated.

[0073] The discrete interpolation method based on finite difference solves the Poisson equation numerically by discretizing it and combining it with observation data as hard constraints.

[0074] Furthermore, for the discrete interpolation method based on finite difference, the modeling region is discretized into regular three-dimensional grid nodes. The partial differential equations of Poisson's equation or Laplace's equation are established according to the physical properties of the scalar field. The partial differential equations are transformed into a system of difference equations on the grid nodes using the finite difference scheme. The observed data points are applied as hard constraints to the system of difference equations. The system of difference equations is numerically solved by an iterative solver to obtain the scalar field values ​​on all grid nodes.

[0075] The process of establishing the global background scalar field uses stratigraphic observation data points located outside the influence range of all fault ellipsoids. Data points located inside the influence range do not participate in the data fitting of the scalar field, but are extrapolated during the evaluation phase.

[0076] Furthermore, all stratigraphic observation data points are screened, and data points located within any fault ellipsoidal influence range are removed. Only data points completely outside all fault ellipsoidal influence ranges are retained as the interpolation input set. Spatial interpolation of this input set is performed using radial basis function interpolation, natural neighbor interpolation, or finite difference interpolation to generate a global background scalar field that is continuous across the entire domain. In the subsequent fusion and evaluation stage, for spatial locations located within the fault ellipsoidal influence range, the generated global background scalar field is directly called for spatial extrapolation to obtain the scalar value for the corresponding location.

[0077] The cutting sequence is determined based on the relative geological time sequence of the faults, with the faults that occurred first cutting the entire area first.

[0078] Furthermore, the geological occurrence and interpenetration of all faults are analyzed to determine the order of their formation. The fault cutting priority is arranged in order from earliest to latest time, with the earliest formed fault having the highest cutting priority and cutting the entire modeled domain first. Subsequent faults are then cut in the subdomains created by the previous faults. The cutting logic is controlled by the relative geological time sequence of the faults to ensure that the fault cutting relationship conforms to the laws of geological evolution.

[0079] For independent faults that do not intersect, cut them in any order.

[0080] Furthermore, the set of independent faults without mutual intersecting relationships within the modeling region is identified, confirming that there are no geometric intersections or mutual cutting phenomena between the independent faults. For the faults in the set of independent faults, the temporal cutting restriction is removed, and the cutting order is arranged according to any selected order. The faults in the set of independent faults cut the remaining modeling domain in turn. The cutting order of the independent faults does not affect the topological correctness of the final geological structure.

[0081] The entire modeling domain is divided into M scalar field blocks using N fault planes, where M≥N+1.

[0082] Furthermore, the geometric data of N fault planes are called sequentially, and the N fault planes are used as cutting planes to perform Boolean segmentation operations on the current modeling domain. Each time a fault plane is used for cutting, the original spatial domain will be divided into two or more new scalar field blocks. After N cutting operations, the initial modeling domain is divided into M independent scalar field blocks. The number of scalar field blocks M is greater than or equal to the number of faults N plus one. Each scalar field block represents an independent geological unit formed after the fault cutting.

[0083] When establishing a local stratigraphic scalar field, for stratigraphic observation data located within the influence range of the fault ellipsoid, a data recovery method based on fault kinematics is used to restore the data to its position before fault activity, and then the data is used to participate in the interpolation of the block-based local stratigraphic scalar field.

[0084] Further identification of stratigraphic observation data points within the influence range of the fault ellipsoid; determination of the corresponding fault slip direction and slip parameters based on the scalar field block to which the stratigraphic observation data points belong; inverse coordinate transformation of the stratigraphic observation data points along the opposite slip direction based on the principle of fault kinematics; restoration of the stratigraphic observation data points from their deformed positions after fault activity to their original positions before fault activity; use of the restored stratigraphic observation data points to participate in the local stratigraphic scalar field interpolation within the corresponding scalar field block; elimination of the interference of fault displacement on the continuity of the local stratigraphic scalar field.

[0085] Example 2: Layered deposition modeling with two intersecting layers

[0086] Step S1: Obtain the modeling region Geological observation data within the area includes: 12 fault data points exposed by boreholes, located on faults F1 and F2 respectively;

[0087] Surface fault outcrop data: F1 outcrop consists of 15 points, and F2 outcrop consists of 12 points.

[0088] Field fault attitude data: 4 groups of F1 attitudes and 3 groups of F2 attitudes;

[0089] The stratigraphic observation data includes 50 points of stratigraphic location data and 10 sets of stratigraphic attitude data, distributed across multiple observation points within the modeling area.

[0090] A fault scalar field is established based on observational data of fault F1 using the radial basis function (RBF) interpolation method. ,make The isosurface of fault F1 is fitted; similarly, the scalar field of fault F2 is established. .

[0091] Step S2: Establish a local coordinate system for fault F1:

[0092] S2.1: Using the observation data of the F1 fault plane as constraints, establish ,make Fitting the isosurface to the F1 fault plane;

[0093] S2.2: Based on field observations of the slip direction of the F1 fault (dipping at 95° and dip angle at 60°), establish... Additional constraints ;

[0094] S2.3: Based on field observations of the slip direction of the F2 fault (dipping at 25° and dip angle at 70°), establish... ,constraint At the same time with , Orthogonal;

[0095] S2.4: Normalize the three scalar fields, and set the ellipsoidal influence range of F1 as follows: , , After normalization, the values ​​are all in the range of [-1, 1].

[0096] Similarly, establish a local coordinate system for F2, and set its ellipsoidal influence range as follows: , , .

[0097] The union of the influence ranges of the two fault ellipsoids constitutes a global fault active body. .

[0098] Step S3: Extract the data located in the stratigraphic observation data. External data points. In this embodiment, 30 of the 50 ground plane location points are located in... In addition, 6 out of 10 sets of stratigraphic attitude data are located in Externally, using only these 30 points and 6 sets of attitude data, a global background scalar field was established using FDI interpolation. Covering the entire modeling area .

[0099] Step S4: Based on the relative timing of F1 and F2 (F1 is earlier than F2), first use the F1 sectional plane to divide the modeling global domain into Block1 and Block2; then use the F2 sectional plane to cut Block2 separately, finally obtaining 3 scalar field blocks Block-1, Block-2-1, and Block-2-2.

[0100] Step S5: Establish a local stratigraphic scalar field independently for each block:

[0101] For the stratigraphic observation data within Block-1 (including data located within the influence range of the F1 or F2 ellipsoid), the local stratigraphic scalar field of Block-1 is established using FDI interpolation. ;

[0102] Similarly, establish , .

[0103] Step S6: Perform a fusion evaluation on any point x to be evaluated within the modeling region:

[0104] S6.1: Calculate the normalized distance d1(x) of x relative to the F1 ellipsoid and the normalized distance d2(x) relative to the F2 ellipsoid;

[0105] S6.2: Calculate d(x) = min(d1(x), d2(x));

[0106] S6.3: Set the transition band width parameter ε = 0.3, and calculate according to the C² smooth transition function. :

[0107] If d(x) ≤ 0 (i.e. x is located within at least one fault ellipsoid), = 0;

[0108] If d(x) ≥ 0.3, = 1;

[0109] If 0 < d(x) < 0.3, let t = d(x) / 0.3. ;

[0110] Step S7: Generate a regular sampling grid (e.g., 100×100×50) within the modeling area, and calculate for each grid point. The formation isosurface is extracted using Marching Cubes or MT algorithm and output in OBJ format.

[0111] Example 3: Modeling of a splay fault system

[0112] For a branched fault system, the main fault Fmain and the branched fault Fsplay share geometry at the tangent line. The implementation process of this embodiment is similar to that of Embodiment 1, but in step S2, the scalar field f0 of the branched fault Fsplay is solved in the neighborhood of the tangent line with the corresponding equivalent constraint of the main fault Fmain as a hard constraint, ensuring that the geometry of the two faults is strictly consistent at the tangent line.

[0113] Example 4: Modeling of Complex Structures with Folds

[0114] For scenarios where faults cut through folds, in step S5, the local stratigraphic scalar field of each block is interpolated using an interpolation method combined with the fold coordinate system, which can accurately characterize the fold geometry after fault cutting. The remaining steps are the same as in Example 2.

[0115] Key Parameter Selection Guide The choice of the transition band width parameter ε needs to strike a balance between strict seamlessness in the far field and smooth transition:

[0116] When ε is too small (e.g., < 0.1): the transition band is too narrow, and the transition region is too narrow. Large gradient changes may produce visible curvature changes at the edges of the transition zone;

[0117] When ε is too large (e.g., > 0.5): the transition zone is too wide, and the fault dislocation effect will extend to a region far beyond the influence range of the ellipsoid, weakening the dislocation accuracy at the fault.

[0118] The recommended value for ε is [0.2, 0.4], which corresponds to an actual transition zone width of 20% to 40% of the length of the fault ellipsoid's semi-axis.

[0119] In practical engineering, ε can be adjusted based on visual inspection of the smoothness of the isosurface near the fault or quantitative indicators (such as the continuity of isosurface curvature).

[0120] Algorithm Time Complexity Analysis Let P be the total number of observation points in the modeling area, N be the number of faults, and M = N + 1 be the number of blocks (in the case of no intersection).

[0121] Global background scalar field establishment: approximately O(Pα), where α depends on the specific interpolation algorithm (2~3 for RBF, 1~2 for piecewise linear). The local scalar field of each block is established as follows: approximately M×O((P / M)α) ≤ O(Pα), and can be implemented in parallel. Integration assessment: O(K), where K is the number of assessment points; The overall complexity is lower than that of the pure kinematic restoration method (O(Pα) for solving a single large scalar field), and it has the advantage of parallelization.

[0122] In summary, this invention introduces a global background scalar field driven solely by data outside the fault's influence range, and adaptively fuses it with the local stratigraphic scalar fields within each block using a high-order smooth transition function. This preserves the true dislocation details near the fault, mathematically enforces the geometric consistency of the strata on both sides outside the fault's influence range, and eliminates artificial gaps and curvature abrupt changes commonly found in domain segmentation methods. This allows for the construction of a three-dimensional geological model with both high accuracy and geometric continuity under complex fault conditions.

[0123] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A finite fault implicit geological modeling method based on global background field fusion, characterized in that: This includes acquiring geological observation data of the modeling area and establishing a finite fault scalar field and its corresponding ellipsoidal influence range; Establish a global background scalar field that is continuous across the entire fault zone using data outside the fault's influence area; The entire region is divided into blocks according to the fault logic order, and a local stratigraphic scalar field is established in each block; By using a smooth transition function to fuse and evaluate the local stratigraphic scalar field with the global background scalar field, stratigraphic isosurfaces are extracted to form a three-dimensional geological model.

2. The implicit geological modeling method for finite faults based on global background field fusion as described in claim 1, characterized in that: The establishment of the finite fault scalar field and the corresponding ellipsoidal influence range specifically includes: For each finite fault, a local coordinate system for the fault is constructed based on the fault orientation and borehole data.

3. The implicit geological modeling method for finite faults based on global background field fusion as described in claim 2, characterized in that: The specific steps for constructing a local coordinate system for a fault include: After normalizing the three scalar fields, the spatial region satisfying |f0|≤1, |f1|≤1, |f2|≤1 is defined as the ellipsoidal influence range of the fault. Using the fault plane observation data as constraints, a first scalar field f0 is established, such that the isosurface with f0=0 fits the fault plane. Using the observation data of the fault slip direction as a constraint, and with the additional constraint that the gradient ∇f1 of the second scalar field is orthogonal to the gradient ∇f0 of the first scalar field, a second scalar field f1 is established; The third scalar field f2 is established by constraining that the gradient ∇f2 of the third scalar field is orthogonal to the gradients of the first two scalar fields; Here, gradient ∇f1 represents the direction of the rate of change of the scalar field in space, and orthogonal constraints are used to ensure that the local coordinate systems formed by the first scalar field f0, the second scalar field f1, and the third scalar field f2 are perpendicular to each other.

4. The implicit geological modeling method for finite faults based on global background field fusion as described in claim 3, characterized in that: The implicit interpolation method used to establish the finite fault scalar location is specifically selected from any one or a combination of the following: The interpolation method based on radial basis function (RBF) selects thin plate spline kernel, Gaussian kernel or compactly supported radial basis kernel, and obtains the interpolation coefficients by solving a sparse linear system of equations. A piecewise linear interpolation method based on the natural neighbor method is used, and linear weight allocation is performed based on the Delaunay triangulation structure. The discrete interpolation method based on finite difference solves the Poisson equation numerically by discretizing it and combining it with observation data as hard constraints.

5. The implicit geological modeling method for finite faults based on global background field fusion as described in claim 4, characterized in that: The process of establishing the global background scalar field uses stratigraphic observation data points located outside the influence range of all fault ellipsoids. Data points located inside the influence range do not participate in the data fitting of the scalar field, but are extrapolated during the evaluation phase.

6. The implicit geological modeling method for finite faults based on global background field fusion as described in claim 1, characterized in that: The entire domain is divided into blocks according to the logical order of the fault lines, specifically as follows: The cutting sequence is determined based on the relative geological chronology of the faults, with the first fault to occur cutting the entire area first. For independent faults that do not intersect, cut them in any order; The entire modeling domain is divided into M scalar field blocks using N fault planes, where M≥N+1.

7. The implicit geological modeling method for finite faults based on global background field fusion as described in claim 6, characterized in that: The fusion assessment is calculated using the following formula: ;in, The final stratigraphic scalar field value for point X to be evaluated. Let x be the local stratigraphic scalar field value of the block containing point x. The value of the global background scalar field at point x. It is a continuous smooth transition function, taking a value of 0 within the influence range of the fault ellipsoid and a value of 1 outside the fault ellipsoid.

8. The implicit geological modeling method for finite faults based on global background field fusion as described in claim 7, characterized in that, Smooth transition function Calculated in the following way: Calculate the minimum normalized distance of the influence range of the point X to be evaluated relative to the i-th fault ellipsoid. ; Set transition band width parameter Calculate using the following formula: ； in, The value ranges from 0.1 to 0.5 times the length of the semi-axis of the corresponding fault ellipsoid.

9. The implicit geological modeling method for finite faults based on global background field fusion as described in claim 8, characterized in that, minimum normalized distance The calculation method is as follows: ； in, , and , where are the scalar field values ​​of point X in the local coordinate system of the i-th fault, and N represents the total number of finite faults in the modeling region; When establishing a local stratigraphic scalar field, for stratigraphic observation data located within the influence range of the fault ellipsoid, a data recovery method based on fault kinematics is used to restore the data to its position before fault activity, and then the data is used to participate in the interpolation of the block-based local stratigraphic scalar field.

10. A finite fault implicit geological modeling system based on global background field fusion, based on the finite fault implicit geological modeling method based on global background field fusion as described in any one of claims 1 to 9, characterized in that: This includes a data acquisition module, used to acquire geological observation data within the modeling area; The fault scalar field establishment module is used to establish a finite fault scalar field and its corresponding ellipsoidal influence range; The global background field creation module is used to create a global background scalar field. The domain segmentation module is used to segment the entire modeling domain into blocks according to the logical order of the fault lines; The Local Stratigraphic Field Establishment Module is used to establish local stratigraphic scalar fields within each block. The fusion evaluation module is used to fuse and evaluate the local formation scalar field and the global background scalar field through a smooth transition function; The stratigraphic extraction module is used to extract stratigraphic isosurfaces and generate three-dimensional geological models.

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