An implicit modeling optimization method, system and memory driven by nonlinear constraint coupling

Abstract

The present invention discloses a nonlinear constraint coupling-driven implicit modeling optimization method, system, and memory. The method first obtains nonlinear constraint data for a target geological interface. Then, based on the initial control points of the target geological interface, an initial implicit function representation is generated using a Hermite radial basis function. Next, based on the data type of the nonlinear constraint, a nonlinear coupling-driven optimization objective function for the implicit function representation of the target geological interface is obtained. This objective function is optimized using an implicit gradient flow algorithm to obtain a geological interface reconstruction model and a globally optimized target geological interface model. The present invention also provides a computer-readable memory containing a computer program that implements the aforementioned nonlinear constraint coupling-driven implicit modeling optimization method. The memory is readable and executable, and together with a programmable logic controller and a processor, forms an optimization system. This system achieves high-precision modeling of three-dimensional geological interfaces by fully coupling a large amount of nonlinear constraint data for the geological interface and constraining the implicit modeling framework.

Description

Technical Field

[0001] The present invention relates to an implicit modeling optimization method, in particular to an implicit modeling optimization method, system and memory driven by nonlinear constraint coupling, and belongs to the technical field of three-dimensional geological modeling. Background Art

[0002] Three-dimensional geological interface models can intuitively represent the geometric morphology and spatial distribution characteristics of three-dimensional interfaces, and are of great significance for applications such as geological disaster prediction, engineering design optimization, geological process simulation, mineral resource prediction, and oil and gas exploration. However, current modeling frameworks can only iteratively reconstruct information based on linear constraints. This leads to a large amount of redundant geological, geophysical, and nonlinear constraint information from prior knowledge, making it difficult to constrain the 3D geological modeling process. For 3D geological interfaces with complex morphological features, current modeling methods will lead to significant uncertainty in the modeling results and make it difficult to accurately simulate the actual geological interface. This is particularly evident when detailed features are unclear, resulting in low resolution of model structural features and a high risk of error in subsequent practical exploration applications. Summary of the Invention

[0003] To address the problems of the prior art, the first objective of the present invention is to provide an implicit modeling optimization method driven by nonlinear constraint coupling. This method first obtains nonlinear constraint data for the target geological interface. It then generates an initial implicit function representation using Hermite radial basis functions. Based on the data type of the nonlinear constraints, it then derives a nonlinear coupling-driven optimization objective function for the implicit function representation of the target geological interface. This objective function is then optimized using an implicit gradient flow algorithm to obtain a geological interface reconstruction model and a globally optimized target geological interface model.

[0004] The second object of the present invention is to provide a computer-readable memory containing a computer program for implementing the above-mentioned implicit modeling optimization method driven by nonlinear constraint coupling, which can be read and executed.

[0005] A third objective of the present invention is to provide an implicit modeling optimization system driven by nonlinear constraint coupling. This system achieves high-precision modeling of three-dimensional geological interfaces by fully coupling nonlinear constraint data from a large number of geological interfaces to constrain the implicit modeling framework. This effectively addresses the drawback of existing technologies that geological interface models can only incorporate linear constraint information. Furthermore, the method uses an implicit gradient flow algorithm to transform nonlinear problems into linear least-squares problems, thereby achieving compatibility between nonlinear and linear constraints and significantly improving the accuracy and reliability of geological modeling.

[0006] In order to achieve the above technical objectives, the present invention provides an implicit modeling optimization method driven by nonlinear constraint coupling, comprising:

[0007] Step S1: Acquire nonlinear constraint data of the target geological interface to obtain a modeling constraint database;

[0008] Step S2: extracting exploration control points of the target geological interface based on the exploration data, and generating an initial implicit function representation of the target geological interface through the Hermite radial basis function;

[0009] Step S3: according to the data type in the modeling constraint database, a nonlinear coupling driven optimization objective function expressed by an implicit function of the target geological interface is obtained, and an expression for the relationship between each nonlinear constraint in the objective function and the morphological characteristics of the geological interface is given;

[0010] Step S4: According to the principle of Newton's method, the implicit gradient flow algorithm is used to obtain the model implicit function with an iterative step size, and then the soft linear search algorithm is used to obtain the global optimal target geological interface model;

[0011] Step S5: Substitute the model implicit function of each iteration into the objective function, draw the objective function value change curve, and when the curve oscillation amplitude is within the preset minimum oscillation amplitude range and the error is less than the error threshold, output the current geological interface model as the reconstructed model.

[0012] The method provided by the present invention fully couples a large amount of nonlinear constraint information of the geological interface and, through the constrained modeling process, minimizes the uncertainty of the resulting model. This fundamentally solves the technical problem that the current geological modeling process can only combine linear constraints, thereby greatly improving the accuracy of the reconstructed model and increasing the reliability and accuracy of subsequent exploration applications.

[0013] As a preferred solution, the nonlinear constraint data includes: geological interface continuity constraint data, lithologic spatial distribution constraint data, seismic data reflecting the physical properties of the upper and lower walls of the geological interface, rock physics data, tectonic evolution history constraint data, and sedimentation rate data. To improve the accuracy of the subsequent model, the present invention collects a large amount of nonlinear constraint data on geological interfaces. In 3D geological modeling, all data that can characterize the morphology and spatial distribution characteristics of the 3D geological interface can be used in the modeling workflow.

[0014] As a preferred solution, the process of extracting the exploration control points is: extracting the three-dimensional geological interface boundary from the plan view, cross-section view and drilling record view including the target geological interface, and characterizing the boundary in the form of spatial coordinate points.

[0015] As a preferred solution, the process of obtaining the initial implicit function representation of the target geological interface is as follows:

[0016] Step S2-1, using HRBF modeling method to characterize the initial implicit function of geological interface, that is, in three-dimensional geological space In the 3D interface, the initial implicit function is defined as , representing any point in three-dimensional space Scalar function at , combined with the coordinate constraints of the exploration control points, the initial implicit function of any geological interface is expressed as:

[0017] Formula 1: ;

[0018] Formula 2: ;

[0019] In formula 1 and formula 2, is the number of known points on the geological interface in the three-dimensional geological space, is the linear coefficient expressed by the HRBF function, is the radial basis function, For exploration control points;

[0020] Step S2-2: Substitute the exploration control points into the initial implicit function of the geological interface to make it meet the classification conditions and solve the linear coefficient , the initial implicit function analytical representation of the geological interface is obtained, where the classification conditions are:

[0021] Formula 3: .

[0022] As a preferred solution, the nonlinear coupling driven optimization objective function is constructed based on the data in the modeling constraint database and the initial implicit function representation of the target geological interface.

[0023] As a preferred solution, the data in the modeling constraint database include continuity constraint data, seismic data and sedimentation rate data.

[0024] As a preferred solution, the expression of the nonlinear coupling drive optimization objective function is:

[0025] Formula 4: ;

[0026] In formula 4, is the displacement characteristic on both sides of the three-dimensional geological interface position, Characterizes the number of voxels on both sides of the three-dimensional interface, Represents the coordinates of the spatial voxel with displacement observed in the current geological exploration, Characterize the spatial coordinates of the above voxels during the iteration process, is the seismic wave at the corresponding position of the three-dimensional geological interface, Characterizes the seismic wave velocity value observed at the surface observation point during geophysical exploration, Characterizes the number of discrete points in geological space, Express the sedimentation rate of the corresponding coordinate point in three-dimensional geological space, Represents the sedimentation rate value based on researchers' prior knowledge or geological verification.

[0027] As shown in formula 4, it is mainly obtained by adding three parts, among which the first part It shows that the displacement of the strata on both sides of the three-dimensional interface geometry (such as faults and folds) has nonlinear superposition characteristics and obeys the exponential attenuation law in three-dimensional space. This attenuation form has a great influence on the morphology of the three-dimensional geological interface, so it serves as one of the nonlinear constraints of three-dimensional modeling; the second part is to characterize the physical property distribution on the upper and lower sides of the geological interface. The physical property distribution and the seismic wave velocity show power-law nonlinear characteristics. Therefore, the interface morphology can be adjusted in the subsequent iterative process so that the physical property distribution on the upper and lower sides is more consistent with the geophysical seismic wave velocity observation, thereby exploring the spatial optimal distribution of the three-dimensional geological interface; the third part is that due to the close relationship between the sedimentation rate and the slope of the three-dimensional geological interface in the process of geological structure evolution, a nonlinear relationship can be presented. Therefore, the morphology of the three-dimensional geological interface can be constrained and optimized in combination with this prior knowledge.

[0028] As a preferred solution, the model implicit function with iterative step size is a solution expression of the geological interface implicit function in the objective function, and its acquisition process is:

[0029] Step S4-1, set the implicit function The iteration step size is , so the above The minimization solution can be converted into an iterative step size The minimization solution is:

[0030] Formula 5: ;

[0031] Step S4-2: To avoid the underdetermination of the objective function during the solution process, a smoothing term is added, and its expression is:

[0032] Formula 6: ;

[0033] Step S4-3: Using the implicit gradient flow algorithm, Taylor expand the function expression obtained in step S4-2 to construct a gradient representation of the implicit function of the geological interface in the objective function, which is expressed as follows:

[0034] Formula 7: ;

[0035] Step S4-4: perform implicit gradient calculation on the gradient representation obtained in step S4-3, and finally obtain the model implicit function with iterative step size, namely:

[0036] Formula 8: ;

[0037] In formulas 5 to 8, Represents corresponding points The initial implicit function value of Characterize the displacement characteristics of the initial observation point, which can be represented as a constant and will be used later To express, represents the weight of the smoothing term, 、 、 The Jacobian matrices representing the geological interface continuity constraint, seismic constraint, and sedimentation rate constraint, respectively, Characterization The implicit function of the model for the iteration, Characterization The step size of the iteration.

[0038] As a preferred solution, the process of globally optimizing the target geological interface model is as follows:

[0039] Step S5-1: Use the weight value of the soft linear search step, and set the iterative step weight to , in the iterative optimization process of the objective function, the weight can be regarded as a constant value, expressed as:

[0040] Formula 9: ;

[0041] Step S5-2: For the initial objective function , which has the form of iterative step size:

[0042] Formula 10: ;

[0043] Formula 11: ;

[0044] Formula 12: ;

[0045] Formula 13: ;

[0046] Step S5-3: According to step S5-1 and step S5-2, the objective function value of each iteration and the weight value of the iteration step are used, that is, the implicit function of the model with the iteration step is expressed as:

[0047] Equation 14: ;

[0048] In formulas 9 to 14, For each iteration The corresponding updated value, is a hyperparameter and needs to satisfy the condition of formula 12. is a hyperparameter and must satisfy the conditions of Formula 13.

[0049] The present invention also provides a computer-readable memory comprising a computer program, wherein the computer program can implement any one of the implicit modeling optimization methods described above.

[0050] The present invention also provides an implicit modeling optimization system driven by nonlinear constraint coupling, comprising: a programmable logic controller, a processor and the above-mentioned readable memory; the programmable logic controller includes a database construction module, an initial model construction module, a model optimization reconstruction module and an optimal model judgment module; the processor reads and executes the computer program on the readable memory according to the programmable logic controller.

[0051] Among them, the database construction module is used to collect nonlinear constraint data related to the three-dimensional geological interface and integrate them to form a standardized database;

[0052] The initial model building module is used to extract exploration control points based on the obtained geological plan, profile, drilling records and other data, and realize the implicit function expression of the three-dimensional geological interface based on the HBRF radial basis function.

[0053] The model optimization and reconstruction module forms the objective function of model optimization and reconstruction based on the obtained nonlinear constraint data type, and uses the proposed implicit gradient flow algorithm to transform the nonlinear optimization problem in the objective function into a linear least squares problem through Taylor expansion and implicit gradient solution. This solves the step size of each iterative optimization and realizes the implicit function expression of the model with step size during the iterative process. In addition, the module adds a soft linear search process to solve the weight of the iterative step size to prevent the optimization model from falling into the local minimum of the objective function.

[0054] The optimal model judgment module is used to draw the objective function value of each iteration, form the objective function change curve, judge the oscillation amplitude of the curve, and stop the model iteration process in time when the minimum oscillation amplitude and the minimum objective function value are reached, and output the implicit function expression of the optimization model.

[0055] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0056] 1) The implicit modeling optimization method provided by the present invention first obtains nonlinear constraint data of the target geological interface, then generates an initial implicit function representation using the Hermite radial basis function. Then, based on the data type of the nonlinear constraint, a nonlinear coupling-driven optimization objective function for the implicit function representation of the target geological interface is obtained. This objective function is then optimized using an implicit gradient flow algorithm to obtain a geological interface reconstruction model and a globally optimized target geological interface model.

[0057] 2) In the technical solution provided by the present invention, by fully coupling the nonlinear constraint data of a large number of geological interfaces and constraining the implicit modeling framework, high-precision modeling of three-dimensional geological interfaces is achieved, effectively solving the defect in the existing technology that geological interface models can only be combined with linear constraint information. Furthermore, this method also transforms the nonlinear problem into a linear least squares problem through the implicit gradient flow algorithm, thereby achieving compatibility between nonlinear constraints and linear constraints, thereby greatly improving the accuracy and reliability of geological modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram of the standard model and initial model of a simple structure in Example 1 of the present invention;

[0059] in, Figure 1 (a) is a simple structural standard geological interface model, Figure 1 (b) simple structural initial geological model;

[0060] Figure 2 This is a diagram showing the fine reconstruction results of the simple structure model in Example 1 of the present invention;

[0061] Figure 3 illustrative diagrams of the standard model and initial model of a complex salt dome in Example 1 of the present invention;

[0062] in, Figure 3 (a) is the standard geological model of a complex salt dome. Figure 3 (b) is an example of the initial model of a complex salt dome;

[0063] Figure 4 This is a diagram showing the detailed reconstruction results of the complex salt dome model in Example 1 of the present invention. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is further described in detail below with reference to specific embodiments and accompanying drawings. To facilitate understanding of the present invention, the present invention will be described in more comprehensive and detailed form below with reference to the accompanying drawings and preferred embodiments. It should be noted that the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] Example 1

[0066] This embodiment addresses the problem that traditional 3D geological modeling frameworks are difficult to incorporate nonlinear constraints, which makes a large amount of geological and geophysical exploration information and previous prior knowledge redundant. An implicit modeling optimization method driven by nonlinear constraint coupling is provided. The specific process is as follows:

[0067] Step 1: In 3D geological modeling, any data that can characterize the morphology and spatial distribution characteristics of 3D geological interfaces can be used in the modeling workflow. Common data related to the expression of 3D geological interface characteristics can be collected, such as geological interface continuity constraint data and lithologic spatial distribution constraint data in geological exploration; seismic data and rock physics data reflecting the physical properties of the upper and lower walls of the geological interface in geophysical exploration; and tectonic evolution history constraint data and sedimentation rate data related to the morphological evolution characteristics of the geological interface, which are previously recognized by previous researchers during geological process simulation, to form a 3D modeling constraint database.

[0068] Step 2: For the collected intuitive geological plan and cross-section data, as well as the drilling record, extract the 3D geological interface boundary and use the spatial coordinate point form to characterize the boundary, that is, to form the exploration control point. The HRBF modeling method can be used to characterize the initial implicit function of the 3D interface, that is, in the 3D geological space In the 3D interface, the initial implicit function is defined as , representing a scalar function at any point x in three-dimensional space , combined with the coordinate constraints of the exploration control points, the implicit function of any geological interface can be expressed as:

[0069] Formula 1: ;

[0070] Formula 2: ;

[0071] In formula 1 and formula 2, is the number of known points on the geological interface in the three-dimensional geological space, is the linear coefficient expressed by the HRBF function, is the radial basis function, For exploration control points;

[0072] Step S2-2: Substitute the exploration control points into the initial implicit function of the geological interface to make it meet the classification conditions and solve the linear coefficient , the initial implicit function analytical representation of the geological interface is obtained, where the classification conditions are:

[0073] Formula 3: ;

[0074] The implicit modeling optimization method driven by the nonlinear constraint coupling mentioned above is effective for the implicit function of the 3D geological interface model. The linear coefficients can be substituted into the coordinates of the known points on the geological interface in the three-dimensional geological space to make the implicit function equal to 0, thereby solving the linear coefficients. , and obtain the initial implicit function expression;

[0075] Step 3: Based on the implicit function representation of the 3D geological interface, an objective function for reconstructing the 3D geological interface model can be constructed according to the known modeling constraint data. Taking the geological interface continuity constraint data (geological data), seismic data (geophysical data), and sedimentation rate data (prior knowledge) as an example, since the nonlinear constraints are independent of each other, their coupled driving effect can be regarded as the sum of the error mismatch functions between the constraint data and the model forward value. That is, the following objective function is constructed to achieve the optimal reconstruction of the 3D geological interface model:

[0076] Formula 4: ;

[0077] For the first term in the above objective function, Express the displacement characteristics on both sides of the corresponding three-dimensional geological interface position, Characterize the number of voxels on both sides of the three-dimensional interface, Represents the coordinates of the spatial voxel with displacement observed in the current geological exploration, Characterizes the spatial coordinates of the above-mentioned voxels during the iteration process. This term indicates that the displacement of the strata on both sides of the 3D interface geometry (such as faults and folds) has nonlinear superposition characteristics and obeys the exponential decay law in 3D space. This decay form has a significant impact on the 3D geological interface morphology and is therefore used as one of the nonlinear constraints in 3D modeling.

[0078] For the second term in the above objective function: Express the seismic wave velocity at the corresponding position of the three-dimensional geological interface, Characterizes the seismic wave velocity value observed at the surface observation point during geophysical exploration, Represents the number of discrete points in geological space. This target function characterizes the distribution of physical properties above and below the geological interface. The relationship between the physical property distribution and seismic velocity exhibits a power-law nonlinearity. Therefore, the interface morphology can be adjusted in subsequent iterations to make the physical property distribution above and below more closely match geophysical seismic velocity observations, thereby exploring the optimal spatial distribution of the three-dimensional geological interface.

[0079] For the third term in the objective function: Express the sedimentation rate of the corresponding coordinate point in three-dimensional geological space, It represents the sedimentation rate value based on researchers' prior knowledge or geological verification. Since the sedimentation rate is closely related to the slope of the three-dimensional geological interface during the evolution of geological structures and can present a nonlinear relationship, the morphology of the three-dimensional geological interface can be constrained and optimized in combination with this prior knowledge.

[0080] Based on the above objective function, the error between the three-dimensional geological interface and various types of exploration data can be expressed in the form of an implicit function. By solving and minimizing the above objective function, the reconstructed three-dimensional geological interface can be made close to the actual observation value, thereby obtaining a high-precision three-dimensional geological interface model.

[0081] In the implicit modeling optimization method driven by nonlinear constraint coupling described in the above embodiment of the present invention, for the displacement characteristics on both sides of the geological interface position in the first term of the objective function, the displacement of the geological interface in a uniform elastic medium is considered, and the displacement can be calculated by dislocation theory. The analytical solution can be determined by the dislocation and the geometric parameters of the geological interface, that is:

[0082] Formula 5: ;

[0083] In formula 5, and is the elastic constant tensor of the medium, is the distance from the observation point to the geological interface, is the integral variable. It can be seen from this formula that the displacement on both sides of the geological interface has a nonlinear relationship with the geometric characteristics of the geological interface. Therefore, this data can be used to constrain the geometric shape of the geological interface, making the modeling results more accurate.

[0084] For the second seismic wave velocity data constraint in the objective function, it can be known from the empirical correlation formula that the seismic wave velocity Physical properties on both sides of the geological interface It has a nonlinear relationship, which can be expressed as:

[0085] Formula 6: ;

[0086] In formula 6, and is an empirical constant. Based on the geophysical interface inversion hypothesis, during the iterative reconstruction of the model, constant physical parameters are set on both sides of the 3D geological interface. By adjusting the position of the geological interface, the voxels on both sides of the geological interface have different physical parameters, thereby generating different seismic velocity forward responses. The forward model that best fits the observed seismic velocity values ​​is then used as the optimal model for iterative reconstruction, thereby constraining the 3D geological modeling framework.

[0087] Regarding the prior knowledge of the third term of the objective function, which is the sedimentation rate, previous studies have shown that the sedimentation rate is closely related to the undulation of the geological interface. The sedimentation rate can be obtained from the diffusion equation. and interface slope The relationship between:

[0088] Formula 7: ;

[0089] In formula 7, is the diffusion coefficient, is a nonlinear exponent. The above formula can demonstrate the nonlinear relationship between sedimentation rate and the slope of the 3D geological interface. Therefore, the sedimentation rate obtained from geological observations and simulation information in the target study area can be incorporated into the 3D geological modeling framework and constrain the iterative optimization direction of the model.

[0090] Nonlinear constraint information is closely related to the morphology and physical properties of the 3D geological interface. These spatial morphology and physical property distribution characteristics can be represented using the implicit function of the 3D geological interface. Ultimately, from the perspective of the implicit function, an association expression between the 3D geological interface and the nonlinear constraint information can be established, thereby realizing the objective function expression of the reconstruction optimization model.

[0091] Step 4: To obtain the implicit function expression of the optimized surface, an implicit gradient flow algorithm is proposed to solve the above objective function. The optimal value of , since the constraint data in the modeling process are all nonlinear constraints, we refer to the basic principle of Newton's method and set the implicit function The iteration step size is , so the above The minimization solution can be converted into an iterative step size The minimization solution is:

[0092] Formula 8: ;

[0093] In formula 8, Represents corresponding points The initial implicit function value of Characterize the displacement characteristics of the initial observation point, which can be represented as a constant and will be used later To express;

[0094] In order to avoid the underdetermination of the objective function during the solution process, a smoothing term is added here to ensure the smoothness of the reconstructed three-dimensional geological interface and to ensure the overdetermination of the objective function. After adding the smoothing term, the objective function can be expressed as:

[0095] Formula 9: ;

[0096] Then, the implicit gradient flow algorithm is used to Taylor expand the above objective function to construct the gradient representation of the implicit function of the three-dimensional geological interface:

[0097] Formula 10: ;

[0098] In Equations 9 and 10, represents the weight of the smoothing term, 、 、 The Jacobian matrices that represent the continuity constraints, seismic constraints, and sedimentation rate constraints of the geological interface are mathematically expressed as the first-order derivative form of the corresponding nonlinear function expression. Its specific form can be derived through the nonlinear relationship between the above nonlinear constraint data and the three-dimensional geological interface. Subsequently, the Taylor expansion of the above objective function is implicitly calculated to solve the objective function as a nonlinear least squares problem for each iteration, and finally the expression of the iterative step length is solved. Since the above nonlinear relationships can all be represented by nonlinear analytical expressions, the expression of the solved iterative step length can also be expressed as an analytical function form. Finally, the reconstructed three-dimensional geological interface can be represented as an implicit function representation with an iterative step length, that is:

[0099] Formula 11: ;

[0100] In formula 11, Characterize the number of iterations, Characterization The implicit function of the model for the iteration, Characterization The step size of the iteration;

[0101] In the implicit modeling optimization method driven by nonlinear constraint coupling described in this embodiment, for the Jacobian matrices corresponding to the geological interface continuity constraint, the seismic constraint, and the sedimentation rate constraint, an analytical expression for the nonlinear relationship between the implicit function and the constraint information can be constructed through the nonlinear relationship between the constraint information and the geological interface distribution represented in the specific implementation scheme of step 4. The analytical expression of the Jacobian matrix can be obtained through the first-order derivative of the analytical expression. Subsequently, the Taylor expansion of the objective function ε(f(x)) can be derived, and the derivative function can be equal to 0 to obtain the minimum value of the objective function under different nonlinear constraints.

[0102] For the nonlinear constraints in the objective function, we can obtain the following by taking the derivative:

[0103] Formula 12: ;

[0104] In order to realize the analytical function representation of implicit gradient flow, DiracDelta function is used to express the discrete voxels in its implicit function, namely:

[0105] Formula 13: ;

[0106] To find the minimum value of the objective function, solve The analytical expression of the iterative step size when , can obtain the form of the solution with the spatial influence kernel function as a linear combination, that is:

[0107] Equation 14: ;

[0108] Step 5: To avoid the iterative process from falling into the local minimum of the objective function during the objective function solution, a weighted step size is used for iterative optimization of the objective function, and a soft linear search step size weight value is used. That is, the function is expressed as:

[0109] Equation 15: ;

[0110] In formula 15, is the iterative step weight. During the iterative optimization of the objective function, this weight can be regarded as a constant value, that is:

[0111] Equation 16: ;

[0112] This constant will not affect the implicit gradient flow solution algorithm under nonlinear constraints, so the focus will be on the value of the step weight after each iteration;

[0113] For the initial objective function , which can be written with the iteration step as:

[0114] Equation 17: ;

[0115] This function must satisfy:

[0116] ;

[0117] in:

[0118] ;

[0119] ;

[0120] By satisfying the above conditions, it is ensured that It is necessary to ensure that the objective function value decreases effectively in each iteration, and It needs to be large enough to ensure that the step size is large enough to jump out of the local minimum range. Therefore, the weight value of the iteration step is obtained through soft linear search through the objective function value of each iteration to represent the final implicit function expression of the optimization model;

[0121] Step 6: Substitute the implicit function representation of the 3D geological interface for each iteration into the objective function to obtain the corresponding objective function value. A curve of the objective function value during the iteration is plotted. When the oscillation amplitude of the curve is within the preset minimum oscillation amplitude range and the error is less than the error threshold, the current geological interface model is output as the reconstructed model.

[0122] Based on the above optimization method, this embodiment further provides a computer-readable memory, which contains a computer program for implementing the above nonlinear constraint coupling driven implicit modeling optimization method, which can be read and executed;

[0123] This embodiment also provides an implicit modeling optimization system driven by nonlinear constraint coupling, comprising: a programmable logic controller, a processor and the above-mentioned readable memory; the programmable logic controller includes a database construction module, an initial model construction module, a model optimization reconstruction module and an optimal model judgment module; the processor reads and executes the computer program on the readable memory according to the programmable logic controller.

[0124] In order to more fully illustrate the excellent technical effects of the technical solution of the present invention, the present invention also adopts the implicit modeling optimization method driven by nonlinear constraint coupling described in the above embodiment to perform three-dimensional modeling of complex salt domes. During the construction process, a nonlinear coupling driven optimization objective function is constructed for the nonlinear constraints of the custom model, and the implicit gradient flow algorithm is used to solve the objective function. In this process, the solution process is prevented from falling into a local minimum, and finally a fine three-dimensional geological interface reconstruction model is obtained. As shown in the example, Figure 1 (a) and (b) are relatively simple standard geological interface models and the initial input model of the algorithm, respectively. Based on the stratum displacement constraints, physical property distribution constraints, and slope constraints on both sides of the geological interface, an implicit model reconstruction objective function driven by nonlinear constraint coupling is constructed. Through iterative optimization, the fine reconstruction of the closed geological interface model is achieved. The reconstruction results are shown in Figure 2. Figure 2 In addition, the present invention also performs nonlinear constraint coupling driven reconstruction on the salt dome model to illustrate the applicability of the method of the present invention to the reconstruction of geological interfaces with complex morphology, wherein Figure 3 (a) and (b) are the standard model of the salt dome model and the initial input model of the algorithm, respectively. From the reconstruction results of the above two examples, it can be seen that the selected initial models are all ideal, uniform, simple closed surface models, such as spheres and ellipsoids. Under the implicit modeling framework driven by nonlinear constraint coupling, the nonlinear data constraints closely related to the morphology can be combined to achieve the fine reconstruction of any complex and smooth model. For simple geological interface models, Figure 2 The reconstruction results clearly show that, driven by nonlinear constraint coupling, the reconstructed model is restored to the standard model morphology. Furthermore, for salt dome models with complex morphology and numerous local details, even if the initial input model does not have any surface morphological fluctuations, the reconstructed model can still restore its surface morphological details while also considering the smoothness of the salt dome model surface, demonstrating high accuracy and reliability.

[0125] pass Figures 1 to 4It can be seen that the implicit modeling optimization method driven by nonlinear constraint coupling provided by the present invention realizes the coupling of different types of nonlinear constraint information, can be applied to the three-dimensional modeling framework of any type of information, breaks through the limitation that traditional modeling frameworks are difficult to combine nonlinear constraint information, and can directly extract the features related to the three-dimensional geological interface morphology and spatial distribution from multivariate nonlinear information, and use this to constrain the modeling process, thereby enhancing the accuracy and effectiveness of the three-dimensional geological interface reconstruction model.

[0126] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. An implicit modeling optimization method driven by nonlinear constraint coupling, characterized in that: include: Step S1: Acquire nonlinear constraint data of the target geological interface to obtain a modeling constraint database; Step S2: extracting exploration control points of the target geological interface based on the exploration data, and generating an initial implicit function representation of the target geological interface through the Hermite radial basis function; Step S3: according to the data type in the modeling constraint database, a nonlinear coupling driven optimization objective function expressed by an implicit function of the target geological interface is obtained, and an expression for the relationship between each nonlinear constraint in the objective function and the morphological characteristics of the geological interface is given; Step S4: According to the principle of Newton's method, the implicit gradient flow algorithm is used to obtain the model implicit function with an iterative step size, and then the soft linear search algorithm is used to obtain the global optimal target geological interface model; Step S5: Substitute the model implicit function of each iteration into the objective function, draw the objective function value change curve, and when the curve oscillation amplitude is within the preset minimum oscillation amplitude range and the error is less than the error threshold, output the current geological interface model as the reconstructed model.

2. The implicit modeling optimization method driven by nonlinear constraint coupling according to claim 1, characterized in that: The nonlinear constraint data include: geological interface continuity constraint data, lithologic spatial distribution constraint data, seismic data reflecting the physical properties of the upper and lower walls of the geological interface, rock physics data, tectonic evolution history constraint data and sedimentation rate data.

3. The implicit modeling optimization method driven by nonlinear constraint coupling according to claim 1, characterized in that: The extraction process of the exploration control points is as follows: extracting the three-dimensional geological interface boundary from the plan view, cross-section view and drilling record view including the target geological interface, and characterizing the boundary in the form of spatial coordinate points.

4. The implicit modeling optimization method driven by nonlinear constraint coupling according to claim 3, characterized in that: The process of obtaining the initial implicit function representation of the target geological interface is as follows: Step S2-1, using HRBF modeling method to characterize the initial implicit function of geological interface, that is, in three-dimensional geological space In the 3D interface, the initial implicit function is defined as , representing any point in three-dimensional space Scalar function at , combined with the coordinate constraints of the exploration control points, the initial implicit function of any geological interface is expressed as: Formula 1: ; Formula 2: ; In formula 1 and formula 2, is the number of known points on the geological interface in the three-dimensional geological space, is the linear coefficient expressed by the HRBF function, is the radial basis function, For exploration control points; Step S2-2: Substitute the exploration control points into the initial implicit function of the geological interface to make it meet the classification conditions and solve the linear coefficient , the initial implicit function analytical representation of the geological interface is obtained, where the classification conditions are: Formula 3: .

5. The implicit modeling optimization method driven by nonlinear constraint coupling according to claim 1, characterized in that: The nonlinear coupling driven optimization objective function is constructed based on the data in the modeling constraint database and the initial implicit function representation of the target geological interface; The data in the modeling constraint database include continuity constraint data, seismic data and sedimentation rate data.

6. The implicit modeling optimization method driven by nonlinear constraint coupling according to claim 5, characterized in that: The expression of the nonlinear coupling drive optimization objective function is: Formula 4: ; In formula 4, is the displacement characteristic on both sides of the three-dimensional geological interface position, Characterize the number of voxels on both sides of the three-dimensional interface, Represents the coordinates of the spatial voxel with displacement observed in the current geological exploration, Characterize the spatial coordinates of the above voxels during the iteration process, is the seismic wave at the corresponding position of the three-dimensional geological interface, Characterizes the seismic wave velocity value observed at the surface observation point during geophysical exploration, Characterizes the number of discrete points in geological space, Express the sedimentation rate of the corresponding coordinate point in three-dimensional geological space, Represents the sedimentation rate value that the researcher has a priori knowledge or has been verified by geology, is an implicit function.

7. The implicit modeling optimization method driven by nonlinear constraint coupling according to claim 6, characterized in that: The model implicit function with iterative step size is the solution expression of the geological interface implicit function in the objective function, and its acquisition process is: Step S4-1, set the implicit function The iteration step size is , so the above The minimization solution can be converted into an iterative step size The minimization solution is: Formula 5: ; Step S4-2: To avoid the underdetermination of the objective function during the solution process, a smoothing term is added, and its expression is: Formula 6: ; Step S4-3: Using the implicit gradient flow algorithm, Taylor expand the function expression obtained in step S4-2 to construct a gradient representation of the implicit function of the geological interface in the objective function, which is expressed as follows: Formula 7: ; Step S4-4: perform implicit gradient calculation on the gradient representation obtained in step S4-3, and finally obtain the model implicit function with iterative step size, namely: Formula 8: ; In formulas 5 to 8, Represents corresponding points The initial implicit function value of Characterize the displacement characteristics of the initial observation point, which can be represented as a constant and will be used later To express, represents the weight of the smoothing term, 、 、 The Jacobian matrices representing the geological interface continuity constraint, seismic constraint, and sedimentation rate constraint, respectively, Characterization The implicit function of the model for the iteration, Characterization The step size of the iteration.

8. The implicit modeling optimization method driven by nonlinear constraint coupling according to claim 7, characterized in that: The process of global optimization of the target geological interface model is: Step S5-1: Use the weight value of the soft linear search step, and set the iterative step weight to , in the iterative optimization process of the objective function, the weight can be regarded as a constant value, expressed as: Formula 9: ; Step S5-2: For the initial objective function , which has the form of iterative step size: Formula 10: ; Formula 11: ; Formula 12: ; Formula 13: ; Step S5-3: According to step S5-1 and step S5-2, the objective function value of each iteration and the weight value of the iteration step are used, that is, the implicit function of the model with the iteration step is expressed as: Equation 14: ; In formulas 9 to 14, For each iteration The corresponding updated value, is a hyperparameter and needs to satisfy the condition of formula 12. is a hyperparameter and must satisfy the conditions of Formula 13.

9. A computer-readable memory comprising a computer program, characterized in that: The computer program can implement the implicit modeling optimization method described in any one of claims 1 to 8.

10. An implicit modeling optimization system driven by nonlinear constraint coupling, characterized in that: include: A programmable logic controller, a processor and a readable memory as described in claim 9; the programmable logic controller includes a database construction module, an initial model construction module, a model optimization and reconstruction module and an optimal model judgment module; the processor reads and executes the computer program on the readable memory according to the programmable logic controller.

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