Non-structural grid pearson coefficient geophysical joint inversion constraint method

Abstract

The application belongs to the technical field of multi-parameter joint inversion of geophysical exploration, and more particularly to a non-structure grid Pearson coefficient geophysical joint inversion constraint method, aiming at the technical problems of gradient solving difficulty of existing cross gradient constraint under non-structure grid, traditional Pearson constraint only adapting to regular grid, poor stability and weak universality of conventional constraint method, the application defines a non-structure grid self-adaptive local sub-domain, extracts a physical parameter sequence and calculates a local Pearson correlation coefficient, constructs a joint constraint term, meanwhile introduces a standard deviation weighting coefficient to eliminate invalid constraints, finally incorporates the constraint term into an inversion objective function to complete joint inversion; the application does not need gradient operation, can self-adapt to complex topography and structure scene, effectively improves inversion stability and precision, supports joint inversion of multiple types of physical parameters, has strong universality and adapts to complex geological exploration operation.

Description

Technical Field

[0001] This application belongs to the field of multi-parameter joint inversion technology in geophysical exploration, and more specifically, it relates to a geophysical joint inversion constraint method for unstructured grid Pearson coefficients. Background Technology

[0002] Geophysical inversion is a core technology that infers the distribution of physical properties and structural morphology of subsurface geological bodies from surface observation data. It is widely used in mineral exploration, geological structure detection, and resource exploration. However, inversion based on single geophysical data suffers from significant ambiguity and limitations, resulting in low accuracy and poor reliability of the inversion results. To overcome the shortcomings of single inversion technology, multi-parameter joint inversion technology has emerged. By fusing two or more geophysical observation data and introducing model constraints to narrow the inversion solution space, it can effectively reduce the ambiguity of inversion and improve the accuracy of subsurface structural imaging. It is currently the mainstream core technology in the field of geophysical exploration.

[0003] Existing geophysical joint inversion techniques are mainly divided into two categories based on different constraint principles: joint inversion methods based on rock physical relationships and joint inversion methods based on structural similarity. Both types of methods have inherent technical defects and are difficult to adapt to the high-precision inversion requirements of complex exploration scenarios.

[0004] Among them, the joint inversion method based on rock physics relationships relies on rock physics experiments to establish empirical functional relationships between different physical property parameters such as resistivity, density, magnetization, and wave velocity, which are then used as constraints to achieve joint inversion. However, this method is highly dependent on the rock physical property characteristics of the sampling area. The physical property correlation laws of different exploration areas and different lithological strata vary greatly, making it impossible to form a universal and unified physical property relationship function. This characteristic leads to extremely poor adaptability and generalizability of the method, which can only be applied to small-scale exploration scenarios with single lithology. It cannot meet the joint inversion needs of large-scale and complex geological areas, and its application is significantly limited.

[0005] Joint inversion methods based on structural similarity are currently the most widely used joint inversion techniques. They utilize the spatial structural similarity of different physical property models to construct constraints, without relying on fixed rock property relationships, thus offering greater versatility. Among these methods, the cross-gradient constraint method is the mainstream core technology. It constrains the structural change trends of different physical property models to remain consistent by performing a cross product operation on the gradients of two physical property models and minimizing the cross product result, thereby achieving structural similarity constraints. However, this method has an unavoidable technical bottleneck: the prerequisite for cross-gradient calculation is the accurate acquisition of model gradients. In unstructured grid exploration scenarios, grid cell shapes are irregular, and cell adjacency relationships are complex and disordered, making it impossible to effectively solve for model gradients and joint gradient terms. At the same time, when the underground geological structure is complex and the structural consistency of a single inversion result is poor, the constraint effect of cross-gradients will be significantly weakened, resulting in serious deficiencies in stability and adaptability, making it difficult to adapt to inversion operations in undulating terrain and complex tectonic regions.

[0006] To address the challenge of gradient calculation in cross-gradient constraints, the industry has gradually introduced Pearson correlation coefficients from statistics into geophysical joint inversion. This method constructs structural constraints by calculating the linear correlation between different physical property parameters, eliminating the need for gradient and derivative calculations and effectively avoiding the inherent limitations of cross-gradient methods. Local Pearson correlation coefficient constraint techniques can accurately characterize the correlation characteristics of physical property parameters in local areas, significantly improving the accuracy of model constraints and becoming an important development direction for joint inversion techniques. However, all current joint inversion constraint techniques based on Pearson correlation coefficients suffer from the following drawbacks: Existing technologies can only perform correlation calculations and constraint construction based on regular grids. Regular grids have a regular structure and fixed neighborhood relationships, and the calculation logic is simple, but they cannot meet the grid discretization requirements of undulating terrain and complex geological structures in actual exploration. On the other hand, unstructured grids can adaptively divide grid units according to terrain features and geological structure complexity, and can accurately adapt to complex exploration scenarios. They are the mainstream grid form for high-precision geophysical inversion. Existing Pearson correlation coefficient constraint technology cannot adapt to the irregular unit distribution and lack of adjacency relationships of unstructured grids, making it difficult to complete local correlation calculations and joint constraint construction under the framework of unstructured grids.

[0007] In summary, the current field of geophysical joint inversion lacks a local correlation constraint method that is adaptable to structural grids, highly stable, accurate, and widely applicable. This method cannot meet the industry's demand for stable and accurate joint inversion of multiple physical parameters under undulating terrain and complex tectonic conditions. There is an urgent need to develop a new joint inversion constraint technology to solve the above-mentioned technical pain points. Summary of the Invention

[0008] To overcome the technical problem that current geophysical joint inversion methods cannot satisfy the stable and accurate inversion of multiple physical parameters under undulating terrain and complex tectonic conditions, this invention provides a non-structured grid Pearson coefficient geophysical joint inversion constraint method, including the following steps: Construct an unstructured network model corresponding to the geophysical joint inversion. For each grid cell in the unstructured network model, match the corresponding local subdomain. Adaptively determine the coverage of each local subdomain based on the geological characteristics of the exploration area and the grid density. Based on the determined local subdomains, two sets of physical property parameter datasets corresponding to each local subdomain are extracted in batches from the two types of geophysical property models to be inverted. The amount of data in each dataset is consistent with the number of grid cells in the corresponding local subdomain. For each local subdomain, two sets of physical property parameter datasets are used to analyze the discrete characteristics and overall trend characteristics of the data sets. Based on the statistical results, the corresponding local Pearson correlation coefficient is calculated to quantify the linear correlation between the two sets of physical property parameters. Based on the local Pearson correlation coefficients of each local subdomain, a joint inversion local structure constraint term is constructed. The constraint weights of the constraint term are inversely corresponding to the strength of the local correlation of the physical property parameters, thereby realizing the model structure similarity constraint. Based on the dispersion values ​​of two sets of physical property parameter datasets, a weighted filtering rule is set. By setting a threshold, effective constraint subdomains and invalid constraint subdomains are identified. The local structural constraint terms are then weighted and corrected to eliminate interference from undisputed constraints. The weighted and corrected local structural constraint terms are introduced into the joint inversion objective function along with the preset constraint weights. The minimum value of the objective function is then solved iteratively using an optimization algorithm to complete the stable joint inversion of multiple physical property parameters under unstructured grids.

[0009] Preferably, the local subdomain corresponding to any grid cell is composed of that grid cell and its multiple neighboring grid cells. The number of neighboring grid cells is adjusted according to the geological structure and grid density. The more complex the geological structure or the denser the grid, the smaller the number of neighboring cells. The simpler the geological structure or the sparser the grid, the larger the number of neighboring cells.

[0010] Preferably, the two types of geophysical property models to be inverted are resistivity models and magnetization models, and the corresponding two sets of property parameter datasets are resistivity parameter datasets and magnetization parameter datasets, respectively.

[0011] Preferably, the quantification of the linear correlation between the two sets of physical property parameters is based on the following rule: A local Pearson correlation coefficient approaching 1 indicates a strong positive correlation, approaching -1 indicates a strong negative correlation, and equal to 0 indicates no correlation.

[0012] Preferably, the weighted filtering rule is as follows: Calculate the standard deviation of the two sets of physical property parameter datasets respectively, and compare the two sets of standard deviations with the preset thresholds respectively; When both sets of standard deviations are greater than the preset threshold, the current local subdomain is determined to be a valid subdomain, and a fixed valid weighting value is assigned to it and it participates in the constraint calculation. When any set of standard deviations is less than a preset threshold, the current local subdomain is determined to be an invalid subdomain, assigned a zero weight value, and excluded from the constraint calculation process.

[0013] Preferably, the preset threshold is adaptively configured based on the overall fluctuation range of the physical property parameters of the inverted region.

[0014] Preferably, the joint inversion objective function is composed of an airborne electromagnetic data fitting term, an airborne magnetic data fitting term, a model regularization term, and a weighted and corrected local structure constraint term.

[0015] Preferably, the joint inversion constraint method is applicable to the joint inversion constraint of any two types of geophysical property parameters among resistivity, density, magnetization, and wave velocity.

[0016] The beneficial effects of this invention include: This invention overcomes the limitation of traditional Pearson correlation techniques, which only apply to regular meshes. By defining local subdomains of unstructured mesh cells, it realizes correlation calculation within an unstructured mesh framework, filling a gap in this technical field. Furthermore, it introduces a weighting coefficient based on standard deviation and automatically determines whether a subdomain should be included in the constraint calculation by setting a threshold. This effectively avoids weak correlation constraints without objection in low-information regions, improving the pertinence and effectiveness of the constraints.

[0017] This invention allows for adaptive adjustment of the number of cells in a local subdomain based on grid density and geological features, enabling flexible adaptation to different exploration scenarios. Dense grids correspond to smaller subdomains, while sparse grids correspond to larger subdomains, achieving multi-scale constraint capabilities. Furthermore, compared to cross-gradient constraints, this invention does not involve gradients and derivatives in calculating the Pearson correlation coefficient, fundamentally avoiding the bottleneck of difficult gradient calculations on unstructured grids, and exhibiting better robustness to local model fluctuations.

[0018] The Pearson correlation coefficient calculation in this invention involves only basic statistical operations, without the need for gradient and derivative calculations. This significantly reduces the difficulty of implementing structural constraints on unstructured grids. Furthermore, the statistical method is insensitive to local model fluctuations, and the weighting mechanism avoids interference from meaningless constraints, making the joint inversion more stable and reliable. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram illustrating the local Pearson correlation coefficient constraint calculation provided in an embodiment of the present invention. Detailed Implementation

[0021] To make the technical problems, solutions, and beneficial effects of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0022] See Figure 1 As shown, this embodiment provides a geophysical joint inversion constraint method for unstructured grid Pearson coefficients, which is applicable to the joint inversion constraint of two types of geophysical property parameters, resistivity and magnetization.

[0023] In this embodiment, the specific technical solution of the present invention is described in detail using a joint inversion constraint based on a resistivity model and a magnetization model.

[0024] S1: In the resistivity model and the magnetization model, the joint inversion objective function is constructed as follows: (1) (2) (3) (4) (5) in, These are the physical property parameters obtained by airborne electromagnetic and airborne magnetic inversion methods, respectively. These represent the data fitting errors for airborne electromagnetic and airborne magnetic methods, respectively. This is the weighting factor for the fitting error term of the airborne magnetic data. These represent model constraints for airborne electromagnetic and airborne magnetic methods, respectively. These are the regularization parameters corresponding to the airborne electromagnetic and airborne magnetic constraint terms, respectively. For the regularization parameters of the joint constraint term, This is a joint constraint term for airborne electromagnetic and airborne magnetic methods. and These are measured data from airborne electromagnetic and airborne magnetic methods, respectively. and These are forward modeling data from airborne electromagnetic and airborne magnetic methods, respectively. and These are the covariances of the airborne electromagnetic data and the model terms, respectively. and They are and The reverse; and These are the covariances of the airborne magnetic data and the model terms, respectively. and They are and The reverse; and These are the covariances of the airborne magnetic data and the model terms, respectively. and They are and The reverse; and These are model datasets for airborne electrical and airborne magnetic methods, respectively. and These are the initial models for airborne electromagnetic and airborne magnetic methods, respectively.

[0025] In the resistivity and magnetization models, a local subdomain is defined for each unstructured grid cell or its neighborhood, where the size of the subdomain is adaptively determined based on the geological characteristics and grid density of the inversion region; specifically: Let the total number of unstructured mesh elements be N. For the i-th element, define its local subdomain. The subdomain contains the unit and its K neighboring units; the value of K is adjusted according to the geological characteristics of the inversion area and the scale of the detection target, and can be between 10 and 30; when the geological structure is complex or the grid is dense, the value of K can be appropriately reduced, and when the geological structure is simple or the grid is sparse, the value of K can be appropriately increased.

[0026] S2: Extract local subdomains from the resistivity model and the magnetization model, respectively. resistivity value sequence within and magnetization value sequence Both sequences have a length of M, where M is a local subdomain of the subdomain. The total number of grid cells contained therein. i This is the index of a local subdomain within the global domain.

[0027] Specifically, in this embodiment, the entire detection area is discretized using an unstructured grid with a total of N cells. Each grid cell (usually a tetrahedral cell) corresponds to a set of physical property parameters. The resistivity parameter is used for electrical exploration, and the magnetization parameter is used for magnetic exploration, which respectively constitute a global resistivity model and a global magnetization model.

[0028] From the global resistivity model, traversing local subdomains All the grid cells contained therein are read sequentially according to a preset cell traversal order (such as cell number order or spatial position sorting), and the resistivity parameter value of each cell is read to form a resistivity value sequence of length M. Where M is a subfield The total number of grid cells contained within.

[0029] From the global magnetization model, using the same traversal order as described above, read the local subdomains sequentially. The magnetization parameter values ​​of all grid cells within the array form a sequence of magnetization values ​​of length M. .

[0030] S3: Calculate the Pearson correlation coefficient between the two sets of data: (6) In the formula, It is the Pearson correlation coefficient. and The definition is the same as above, because its vector can be used as an input term for the Pearson correlation coefficient, i.e., the model dataset for airborne electrical and magnetic methods. Represents resistivity. The value is related to the magnetization intensity; When the value approaches 1 or -1, it indicates a strong correlation between the two variables; when... When the condition is met, it indicates that there is no correlation between the two variables; usually when... When the correlation is strong, it can be considered that there is a strong correlation between the variables.

[0031] By replacing the covariance and root mean square in the above formula, we obtain the analytical expression for the Pearson correlation coefficient: (7) in, i For the first i Subdomains p i It is the first i Pearson correlation coefficients within local subdomains M For vectors and In subdomain i The number of elements in the sample (sample size).j Index number representing the tetrahedral element within a local subdomain , and Let be the electromagnetic and magnetic physical property parameters of the j-th element within subdomain i. and Let these represent the arithmetic mean of the resistivity and magnetization values ​​of all grid elements within the i-th local subdomain, respectively. , and Let these represent the electromagnetic and magnetic physical properties of all mesh elements within the i-th local subdomain, respectively. for transpose, No. j The deviation of the resistivity value of a cell from the mean resistivity of that subdomain (indicating the degree to which the resistivity at that point deviates from the local average level). No. j The deviation of the magnetization value of a unit from the mean magnetization value of that subdomain (indicating the degree to which the magnetization at that point deviates from the local average level). It represents the L2 norm in mathematical operations.

[0032] S4: Construct joint constraint terms based on local Pearson correlation coefficients When the correlation between resistivity and magnetization within a local subdomain is stronger, the contribution of the constraint term is smaller; when the correlation is weaker, the constraint term is weaker, and its contribution is larger. Therefore, the basic form of the constraint term is as follows: (8) In the formula: n is the number of subdomains, which is less than the number of grids within the unstructured subdomain. The stronger the correlation between subdomains, the better. The closer it gets to 1.

[0033] S5: To avoid meaningless weak correlation constraints due to excessively small standard deviations, which would affect the effectiveness of the inversion constraints, the joint inversion constraint terms will be... Introducing weighting coefficients The expression for the weighting coefficient is: (9) In the formula: This represents the standard deviation of the two sets of data; and This is a pre-set threshold for the standard deviation of the judgment. When the standard deviations of both the resistivity sequence and the magnetization sequence are greater than the preset threshold, [the following condition is met]. A value of 1 indicates that the subdomain participates in the constraint calculation; otherwise... Setting it to 0 indicates that the subdomain does not participate in the constraint calculation.

[0034] The above threshold The core function is to exclude local subdomains with excessively gradual changes in physical properties and lacking statistical significance when calculating local Pearson correlation coefficients, thus avoiding outliers or meaningless strong correlations caused by standard deviations approaching zero. To achieve adaptive configuration, this invention first statistically analyzes the standard deviation distribution characteristics of the current resistivity model and magnetization model across the entire domain in each inversion iteration. Specifically, this includes calculating the mean of the absolute values ​​of the first-order differences of the resistivity values ​​of all grid cells. and the mean of the absolute values ​​of the first-order differences of the magnetization intensity values These two statistics reflect the overall fluctuation range of the two physical property parameters throughout the entire inversion region. Based on this, the threshold is... Set as Multiply by an empirical coefficient α (usually 0.1~0.2), the threshold Set as Multiply by the same empirical coefficient α. Thus, when the overall physical properties of the stratum change drastically, the threshold is automatically raised, allowing only local subdomains with sufficiently large fluctuations to participate in Pearson constraints; when the overall physical properties of the stratum change gradually, the threshold is automatically lowered, allowing more subdomains to participate in the constraints, but subdomains with extremely small fluctuations are still excluded. Furthermore, to prevent individual extreme outliers from causing the threshold to be too large or too small, the absolute deviation of the median can be used instead of the standard deviation, or the statistic can be clamped with upper and lower limits (e.g., limiting ε to 10). -6 Up to 10 -2 (between). Through the above method, the threshold can dynamically adapt to the changes in the model as the inversion process progresses. That is, as the inversion iteration proceeds, the model gradually tends to converge, the amplitude of material property fluctuations may gradually decrease, and the threshold will also adaptively decrease accordingly. This allows for more refined local structures to participate in constraints in the later stages of the inversion, realizing automatic adjustment of constraint granularity.

[0035] After introducing weighting coefficients, the improved joint inversion constraint term for local Pearson correlation coefficients can be expressed in the following form: (10) Where: index number of the local subdomain , where n is the number of effective local subdomains.

[0036] S6: By solving the problem using an optimization algorithm, the objective function can be minimized, thereby achieving the maximum correlation constraint between the resistivity model and the magnetization model on the local structure.

[0037] Substituting formula (9) into formula (1), we obtain the objective function for the joint inversion: (11) Equation (11) can be converted into objective functions for different properties of aero-electromagnetism and aero-magnetism as follows: (12) (13) Gradient calculation of the objective function for the two physical properties yields: (14) (15) In the formula, and These are the gradients of the objective functions for airborne electromagnetic and airborne magnetic methods, respectively. and These are the FAR-Jacobi matrices (sensitivity matrices) for aerospace electromagnetics and aerospace magnetics, respectively. and They are respectively and transpose; It is the symbol for partial differential in mathematics.

[0038] By setting formulas (14) and (15) to 0, the equations for aerospace electromagnetics and aerospace magnetics can be obtained. By iterating different models each time, a model that meets the predetermined conditions can be obtained, and the objective function can be minimized in the end.

[0039] The above are merely preferred embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A geophysical joint inversion constraint method for unstructured grid Pearson coefficients, characterized in that, Includes the following steps: Construct an unstructured network model corresponding to the geophysical joint inversion. For each grid cell in the unstructured network model, match the corresponding local subdomain. Adaptively determine the coverage of each local subdomain based on the geological characteristics of the exploration area and the grid density. Based on the determined local subdomains, two sets of physical property parameter datasets corresponding to each local subdomain are extracted in batches from the two types of geophysical property models to be inverted. The amount of data in each dataset is consistent with the number of grid cells in the corresponding local subdomain. For each local subdomain, two sets of physical property parameter datasets are used to analyze the discrete characteristics and overall trend characteristics of the data sets. Based on the statistical results, the corresponding local Pearson correlation coefficient is calculated to quantify the linear correlation between the two sets of physical property parameters. Based on the local Pearson correlation coefficients of each local subdomain, a joint inversion local structure constraint term is constructed. The constraint weights of the constraint term are inversely corresponding to the strength of the local correlation of the physical property parameters, thereby realizing the model structure similarity constraint. Based on the dispersion values ​​of two sets of physical property parameter datasets, a weighted filtering rule is set. By setting a threshold, effective constraint subdomains and invalid constraint subdomains are identified. The local structural constraint terms are then weighted and corrected to eliminate interference from undisputed constraints. The weighted and corrected local structural constraint terms are introduced into the joint inversion objective function along with the preset constraint weights. The minimum value of the objective function is then solved iteratively using an optimization algorithm to complete the stable joint inversion of multiple physical property parameters under unstructured grids.

2. The unstructured grid Pearson coefficient geophysical joint inversion constraint method according to claim 1, characterized in that, The local subdomain corresponding to any grid cell is composed of that grid cell and its multiple neighboring grid cells. The number of neighboring grid cells is adjusted according to the geological structure and grid density. The more complex the geological structure or the denser the grid, the smaller the number of neighboring cells. The simpler the geological structure or the sparser the grid, the larger the number of neighboring cells.

3. The unstructured grid Pearson coefficient geophysical joint inversion constraint method according to claim 1, characterized in that, The two types of geophysical property models to be inverted are resistivity models and magnetization models, and the corresponding two sets of property parameter datasets are resistivity parameter datasets and magnetization parameter datasets, respectively.

4. The unstructured grid Pearson coefficient geophysical joint inversion constraint method according to claim 1, characterized in that, The quantification of the linear correlation between the two sets of physical property parameters is based on the following rules: A local Pearson correlation coefficient approaching 1 indicates a strong positive correlation, approaching -1 indicates a strong negative correlation, and equal to 0 indicates no correlation.

5. The unstructured grid Pearson coefficient geophysical joint inversion constraint method according to claim 1, characterized in that, The weighted filtering rule is as follows: Calculate the standard deviation of the two sets of physical property parameter datasets respectively, and compare the two sets of standard deviations with the preset thresholds respectively; When both sets of standard deviations are greater than the preset threshold, the current local subdomain is determined to be a valid subdomain, and a fixed valid weighting value is assigned to it and it participates in the constraint calculation. When any set of standard deviations is less than a preset threshold, the current local subdomain is determined to be an invalid subdomain, assigned a zero weight value, and excluded from the constraint calculation process.

6. The unstructured grid Pearson coefficient geophysical joint inversion constraint method according to claim 5, characterized in that, The preset threshold is adaptively configured based on the overall fluctuation range of the physical property parameters of the inverted region.

7. The unstructured grid Pearson coefficient geophysical joint inversion constraint method according to claim 1, characterized in that, The joint inversion objective function is composed of airborne electromagnetic data fitting terms, aeromagnetic data fitting terms, model regularization terms, and weighted modified local structure constraint terms.

8. The unstructured grid Pearson coefficient geophysical joint inversion constraint method according to claim 1, characterized in that, The joint inversion constraint method is applicable to the joint inversion constraint of any two geophysical property parameters among resistivity, density, magnetization, and wave velocity.

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