A Joint Inversion Method and System Based on Cauchy Inequality and Contingency Structures

Abstract

This invention discloses a method and system for joint inversion of structural constraints based on Cauchy's inequality. It proposes a Cauchy inequality constraint applicable to structural constraints, achieving a linear correlation between the model's gradient vector set. Simultaneously, it calculates structural constraints separately according to different directions, constructing a structural constraint inversion. The directions can be freely combined as needed, including four directions: horizontal, vertical, 45° inclined, and 135°. The corresponding gradients and partial derivatives are obtained by discretizing the directions, with different weighting coefficients configured. Different directional combinations can better simulate the distribution characteristics of actual geological subsurface space. This method overcomes the limitation of previous structural constraint inversion techniques that lack consideration of the spatial differences of actual geological bodies. Furthermore, by explicitly expressing the gradients in different directions, it reduces the computational complexity of joint inversion using Cauchy's inequality constraints.

Description

Technical Field

[0001] This invention relates to the field of geophysical joint inversion technology, and in particular to a method and system for joint inversion based on directional structural constraints according to Cauchy inequality. Background Technology

[0002] Currently, mineral exploration technology is transitioning from shallow first-space exploration to deep second-space exploration. Undoubtedly, deep exploration will face more complex geological problems, highlighting the limitations of single geophysical methods and the ambiguity of inversion methods. The challenges in second-space exploration will inevitably be greater. Geophysical joint inversion, to some extent, overcomes the limitations of single-method solutions to geological problems and is gradually becoming a focus and challenge in the field of geophysical exploration. Geophysical joint inversion can, without increasing the amount of physical work, deeply explore the characteristics of different geophysical methods from different angles, thereby leveraging the advantages of different geophysical methods. This improves the utilization rate of geophysical data while enhancing the accuracy of geophysical interpretation. Developing new geophysical joint inversion methods also aligns with the practical needs of sustainable development. Simply put, joint inversion can be divided into structurally constrained joint inversion, property-constrained joint inversion, and generalized constraints that can, to some extent, take into account some characteristics of both. There is no clear superiority or inferiority among the three methods; the key lies in selecting an appropriate constraint strategy based on specific geological conditions and data characteristics. However, in reality, underground spaces often exhibit complex characteristics. Previous two-dimensional or three-dimensional structural constraint joint inversion methods have not adequately considered the constraint effects in specific directions, resulting in distortion or insufficient resolution in the inversion results in certain directions. Summary of the Invention

[0003] To address the technical problem of distortion or insufficient resolution in certain directions in current joint inversion results, this invention introduces Cauchy's inequality to construct multi-directional structural constraint terms. This fully utilizes the gradient coupling relationships of different physical fields in various spatial directions, effectively enhancing the spatial consistency representation of tectonic boundaries and key geological bodies. The directional structural constraint joint inversion method and system based on Cauchy's inequality provided by this invention exhibits stronger adaptability and stability in complex tectonic regions, providing higher-precision geophysical support for deep mineral resource exploration.

[0004] To achieve the above-mentioned technical objectives, the technical solution of the present invention is as follows:

[0005] On the one hand, this invention provides a method for joint inversion based on the constrained construction of directional parts using Cauchy's inequality, comprising the following steps:

[0006] Step 1: Based on the known underground space structure, construct a matching forward model; then calculate the forward response of the forward model to simulate various geophysical data collected by the observation system.

[0007] Step 2: Based on the actual geological prior information of the target area to be inverted, select suitable geophysical methods corresponding to the geophysical data from the results of Step 1 for joint inversion: First, construct a joint inversion objective function by combining different geophysical methods, and introduce a weighting strategy to balance the residual contributions of different geophysical data; then, introduce Cauchy inequality constraint terms into the joint inversion objective function, and use mathematical transformations to make the inversion model parameters satisfy the Cauchy inequality criterion, thereby realizing the coupling correlation between the inversion model parameters of different geophysical methods;

[0008] Step 3: Based on the spatial characteristics of the forward model constructed in Step 1, construct an initial inversion model that matches the forward spatial dimensions of the forward model, and set the initial physical property parameter distribution using a uniform half-space form.

[0009] Step 4: Based on the directional structural constraints, the gradients of the inversion model parameters are calculated from the horizontal, vertical, 45°, and 135° tilt directions, respectively, and the discrete approximation of the gradients is obtained through forward differencing. Then, the gradients of the multi-directional inversion model parameters are substituted into the Cauchy inequality to construct the directional constraint terms, and the explicit partial derivatives of the directional constraint terms with respect to the inversion model parameters are derived. Then, according to the geological structural characteristics, suitable direction combinations are selected from the horizontal, vertical, 45°, and 135° tilt directions, and directional weighted structural constraint terms are applied to the joint inversion objective function to enhance the ability to characterize the spatial distribution characteristics of geological bodies.

[0010] Step 5: Using the conjugate gradient or quasi-Newton method, iteratively solve the joint inversion objective function by repeatedly executing steps 4 and 5, and update the inversion model parameters one by one until the convergence condition is met, thereby realizing the joint inversion with constraints constructed in different directions and obtaining the joint inversion result.

[0011] Preferably, in step 2, selecting suitable geophysical data from the results of step 1 involves filtering out geophysical data that matches the geological conditions and structural features of the target area to be inverted from a variety of geophysical data obtained from the simulation in step 1; and then using the corresponding geophysical methods to carry out joint inversion.

[0012] Preferably, in step 2, a joint inversion objective function is constructed by combining two different geophysical methods, and the joint inversion objective function is expressed as follows:

[0013] ;

[0014] In the formula, and These are the parameters of the inversion model to be solved using two different geophysical methods; For the inversion model functional; and Fit a functional to the data; and These are the weighting coefficients for two different geophysical methods; and To find the stable functional of the inversion model, and For two different geophysical methods, the regularization factor is used. For constraint factors; This is a horizontal constraint term. This represents the weighting factor of the horizontal constraint term. and These are the parameters of the inversion model to be solved in the horizontal direction for two different geophysical methods. Represents the gradient operator; This is a vertical constraint term. This represents the weighting factor for the vertical constraint term. and These are the parameters of the inversion model to be solved in the vertical direction for two different geophysical methods; The constraint term is for the 45° tilt direction. This represents the weighting factor for the 45° tilt direction constraint term. and The parameters of the inversion model to be solved by two different geophysical methods in the 45° tilt direction; The constraint term is for the 135° tilt direction. This represents the weighting factor for the 135° tilt direction constraint term. and These are the parameters of the inversion model to be solved using two different geophysical methods in the 135° tilt direction.

[0015] Preferably, in step 2, the Cauchy inequality constraint term is a joint inversion constraint based on the linear correlation of the inversion model vectors. From the Cauchy inequality, the constraint relationship of the inversion model parameters to be solved in the spatial orthogonal direction satisfies: the equality holds if and only if the inversion model parameters are linearly correlated, that is, the inversion model parameters have directional correlation characteristics in spatial distribution.

[0016] ;

[0017] C represents the Cauchy inequality function, and D represents the transformation operator.

[0018] Preferably, in step 4, when selecting a suitable combination of directions from horizontal, vertical, 45°, and 135° tilt directions, the direction constraints are determined based on the spatial structure of the inversion model: when the inversion model only has spatial structures in the horizontal and vertical directions, horizontal and vertical direction constraints are selected; when the inversion model has a 45° or 135° tilted interface spatial structure, the corresponding tilt direction constraint is selected; when the inversion model has both horizontal and vertical spatial structures and 45° or 135° tilted interface spatial structures, all the required direction constraints are selected; secondly, under the premise of conforming to the spatial structure of the inversion model, the direction combination is selected based on the spatial characteristics in the corresponding directions that need to be specifically revealed.

[0019] Preferably, in step 4, the direction-weighted construction constraint term is the gradient of the inversion model parameters calculated along the horizontal, vertical, 45° and 135° tilt directions respectively; directional weight factors are configured for different directions, and by adjusting the magnitude of the directional weights, the dominant constraint direction is aligned with the main structural direction of the geological body, so as to adapt to the spatial distribution characteristics of complex geological bodies and enhance the geological rationality and resolution of the inversion results.

[0020] Secondly, the present invention also provides a directional construction constraint joint inversion system based on Cauchy inequality, comprising:

[0021] The forward modeling module is used to construct a matching forward model based on known underground space structures; then, the forward modeling response of the forward model is calculated to simulate various geophysical data collected by the observation system.

[0022] The objective function construction module is used to select appropriate geophysical methods from the results of the forward modeling module to perform joint inversion based on the actual geological prior information of the target area to be inverted. First, a joint inversion objective function is constructed by combining different geophysical methods, and a weighting strategy is introduced to balance the residual contributions of different geophysical data. Then, Cauchy inequality constraint terms are introduced into the joint inversion objective function, and mathematical transformations are used to make the inversion model parameters satisfy the Cauchy inequality criterion, thereby realizing the coupling correlation between the inversion model parameters of different geophysical methods.

[0023] The initial inversion module is used to construct an initial inversion model that matches the forward spatial dimensions of the forward model based on the spatial characteristics of the forward model constructed by the forward model module, and sets the initial physical property parameter distribution in a uniform half-space form.

[0024] The multi-directional constraint module is used to calculate the gradients of the inversion model parameters from the horizontal, vertical, 45°, and 135° tilt directions based on the sub-directional structural constraints, and obtain discrete approximations of the gradients through forward differencing. Then, the gradients of the multi-directional inversion model parameters are substituted into Cauchy's inequality to construct the sub-directional constraint terms, and the explicit partial derivatives of the sub-directional constraint terms with respect to the inversion model parameters are derived. Then, according to the geological structural characteristics, suitable direction combinations are selected from the horizontal, vertical, 45°, and 135° tilt directions, and direction-weighted structural constraint terms are applied to the joint inversion objective function to enhance the ability to characterize the spatial distribution characteristics of geological bodies.

[0025] The inversion solution module is used to iteratively solve the joint inversion objective function using conjugate gradient or quasi-Newton method, and successively update the inversion model parameters until the convergence condition is met, thereby realizing the joint inversion with constraints constructed in different directions and obtaining the joint inversion result.

[0026] In three aspects, the present invention also provides an electronic device, comprising:

[0027] One or more processors;

[0028] Storage device for storing one or more programs;

[0029] When the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method.

[0030] Fourthly, the present invention also provides a computer-readable medium storing a computer program that, when executed by a processor, implements the aforementioned method.

[0031] The technical effects of this invention are as follows:

[0032] (1) This invention proposes a novel generalized constraint inversion method—Cauchy inequality constraint—and creatively introduces it into joint inversion technology to realize joint inversion of construction constraints. It also proposes a construction constraint scheme with different directions, configures weight factors for construction constraint terms in different directions, and derives the partial derivatives of the constraint terms for the solution parameters in different directions, thus realizing the effective characterization of the underground space of complex models.

[0033] (2) The directional construction constraint scheme proposed in this invention has horizontal and vertical gradient directions as well as 45° and 135° tilt directions. The weight factor of each direction can be adjusted according to the requirements to meet the inversion requirements of practical applications. Attached Figure Description

[0034] Figure 1 This is a basic flowchart of the directional construction constraint joint inversion method based on Cauchy inequality in this embodiment of the invention;

[0035] Figure 2 This is a schematic diagram of two-dimensional mesh partitioning in an embodiment of the present invention;

[0036] Figure 3 These are schematic diagrams illustrating four typical structural forms of a single-direction constraint term in embodiments of the present invention;

[0037] Figure 4 These are schematic diagrams illustrating six typical structural forms of two-directional combination constraint terms in embodiments of the present invention;

[0038] Figure 5 These are schematic diagrams illustrating four typical structural forms of composite three-directional constraint terms in embodiments of the present invention;

[0039] Figure 6 This is a schematic diagram of the inversion results of the dual-block model in an embodiment of the present invention; where (a) is the resistivity model; (b) is the resistivity regularized inversion result; (c) is the density model; (d) is the density regularized inversion result; (e-1)-(e-5) are the density joint inversion results of schemes 1-5;

[0040] Figure 7 This is a gradient coupling diagram of the two-block model in an embodiment of the present invention; where (a-1)-(a-5) are the physical property coupling diagrams of scheme 1-5; (b-1)-(b-5) are the horizontal gradient coupling diagrams of scheme 1-5; and (c-1)-(c-5) are the vertical gradient coupling diagrams of scheme 1-5.

[0041] Figure 8 This is a schematic diagram of the hardware connection of the electronic device in an embodiment of the present invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages 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 of the invention and are not intended to limit the invention. The technical features involved in the various embodiments of the invention described below can be combined with each other as long as they do not conflict with each other.

[0043] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0044] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0045] This invention explores the versatility of a novel generalized constraint inversion method—the Cauchy inequality constraint. Its mathematical essence lies in the linear correlation between two model vectors; hence, this constraint is called the linear correlation constraint. In joint inversion, by introducing the Cauchy inequality as a constraint term, the structural similarity between different physical property models can be effectively controlled, thereby enhancing the stability and resolution of the inversion results. This constraint term can flexibly combine multiple directional gradients according to actual needs, achieving accurate characterization of the boundaries and strikes of geological bodies. By adjusting the weighting factors of each direction, it adapts to complex tectonic scenarios, improving the coupling effect of joint inversion using multiple geophysical methods. In practical applications, this method further enhances the continuity and clarity of geological body edge information by constructing a multi-directional gradient weighted matrix. Utilizing a directional combination strategy, the optimal directional gradient coupling mode can be selected for different tectonic features.

[0046] The present invention will be described below with reference to specific embodiments.

[0047] Example 1.

[0048] See Figure 1 The directional construction constraint joint inversion method based on Cauchy inequality provided in this embodiment includes:

[0049] Step 1: Based on the actual underground space structure, quickly construct a forward model; calculate the forward response of the model using analytical or numerical integration methods, and use the forward response to simulate various geophysical data collected by the observation system, which are considered as processed observation data here.

[0050] In this embodiment, there are several ways to quickly build a forward model, including directly generating a forward model by reading any model data file, converting it, or generating it through a predefined internal spatial structure.

[0051] The forward model that can be constructed quickly should have complex features such as undulating or abrupt stratigraphic boundaries or significant differences in structures at different scales, which also determines the applicability of directional structural constraints.

[0052] It should be noted that for simple, regularly shaped underground spaces, inversion can be achieved through joint inversion using basic horizontal and vertical structural constraints. However, to better apply to geologically complex underground spaces, it is necessary to consider that the target geological body exhibits significant irregularities or that the target area has uneven interfaces. In such cases, this invention can more accurately reflect the spatial distribution of physical properties, effectively improving the ability to simultaneously characterize deep structural morphology and shallow interface details. Furthermore, the smoothness of possible stratigraphic boundaries in rapidly generated forward models with complex underground spaces is limited by the fineness of the forward modeling mesh.

[0053] Step 2: Considering the differences in resolution of subsurface medium parameters among different methods, and combining the prior geological information of the target area, select suitable geophysical data for joint inversion. That is, from the various geophysical data obtained in Step 1, select geophysical data that are compatible with the geological conditions and structural features of the target area to be inverted, and use the corresponding geophysical methods to carry out joint inversion. In this way, combine multiple geophysical methods such as gravity, magnetic and electromagnetic methods to construct a joint inversion objective function, and introduce a weighting strategy to balance the residual contributions of different geophysical data.

[0054] Different geophysical methods have their own advantages and disadvantages. This embodiment takes the joint inversion of two different geophysical methods as an example. The objective function of the joint inversion is expressed as:

[0055] ;

[0056] In the formula, and These are the parameters of the inversion model to be solved using two different geophysical methods; For the inversion model functional; and Fit a functional to the data; and These are the weighting coefficients for two different geophysical methods; and To find the stable functional of the inversion model, and For two different geophysical methods, the regularization factor is used. For constraint factors; This is a horizontal constraint term. This represents the weighting factor of the horizontal constraint term. and These are the parameters of the inversion model to be solved in the horizontal direction for two different geophysical methods. Represents the gradient operator; This is a vertical constraint term. This represents the weighting factor for the vertical constraint term. and These are the parameters of the inversion model to be solved in the vertical direction for two different geophysical methods; The constraint term is for the 45° tilt direction. This represents the weighting factor for the 45° tilt direction constraint term. and The parameters of the inversion model to be solved by two different geophysical methods in the 45° tilt direction; Cauchy constraint in a 135° tilt direction. This represents the weighting factor for the 135° tilt direction constraint term. and These are the parameters of the inversion model to be solved using two different geophysical methods in the 135° tilt direction.

[0057] Step 3: Based on the spatial characteristics of the forward model, construct an initial inversion model that matches the forward spatial dimensions of the forward model, and set the corresponding physical property parameter distribution. Generally, a uniform half-space is used as the initial inversion model.

[0058] In this embodiment, the construction of the initial inversion model mainly considers that the size of the inversion grid space and the size of the forward grid space should match. Therefore, a uniform half-space is generally used as the initial inversion model.

[0059] Step 4: Based on the directional structural constraint technique, calculate the gradients of the inversion model parameters from the horizontal, vertical, and 45° and 135° tilt directions respectively, and obtain the partial derivatives through explicit expressions; according to the possible structural features of the model space, an appropriate combination of directions can be selected to construct gradient constraint terms that include the horizontal, vertical, or 45° and 135° tilt directions, and apply the directional weighted structural constraint terms to the joint inversion objective function to enhance the ability to characterize the spatial distribution features of geological bodies.

[0060] The constraint method proposed in this embodiment, applicable to rock physical properties and structural constraints, is based on a novel joint inversion constraint method using linear correlation of inversion model vectors. This method starts from Cauchy's inequality, from which the constraint relationship of the inversion model parameters in the horizontal and vertical (orthogonal) directions can be obtained, if and only if... and The equality holds when there is a linear correlation, meaning that the parameters of the inversion model have a directional correlation in their spatial distribution.

[0061] ;

[0062] Where C represents the Cauchy inequality function and D represents the space transformation operator.

[0063] Specifically: Let V be the inner product space over the number field P, then for any vector ,have:

[0064] ;

[0065] The above equation is a Cauchy inequality if and only if the vectors... For linear correlation, the equality sign holds; rearranging the terms, we have:

[0066] ;

[0067] From the above equation, we can see that the condition for the equality of the two equations to hold is that the vectors are linearly dependent.

[0068] If we let the vectors of the physical properties of the two rocks be... , ,in This represents the value of the first type of rock property vector in the m-th dimension. Let m represent the value of the second type of rock property vector in the m-th dimension, and and If there is a linear dependence, then Cauchy's inequality equals zero:

[0069] .

[0070] Where M is the dimension of the vector, and the subscript i denotes the i-th dimension of the vector. If the above formula is incorporated into the joint inversion objective function, it can be foreseen that this formula can play a role in promoting the vector in the joint inversion process. and The effect of linear dependence constraints. The above equations are the inner product form and discrete form of the new constraint method. Because the mathematical essence of this constraint method is that the two model vectors are linearly dependent, this constraint method is called linear dependence constraint.

[0071] The transformation operator T in the novel constraint method has a rich variety of expressions. When D is the unit operator, constraint construction can be carried out:

[0072] ;

[0073] The above equation represents the mathematical constraint between two rock property vectors. Compared to traditional rock property constraints, the new constraint method does not require prior knowledge of any explicit or implicit correlation characteristics between the rock property parameters, facilitating joint inversion. When D is a gradient operator, constructive constraints can be implemented:

[0074] ;

[0075] in Describes the gradient operator, if , Since the two vectors are not zero, rearranging the terms in the above equation and taking the square root, we get:

[0076] ;

[0077] The left side of the above equation is and The cosine of the angle between two vectors, where the angle is 0° or 180°. Therefore, when the D operator is a gradient operator, it is mathematically consistent with the novel constraint method proposed in this invention and the gradient cross product (cross gradient) and gradient dot product. It is also easy to see that when , Even when one of the vectors is zero, Cauchy's inequality still holds. Therefore, similar to cross gradients and gradient dot products, this new constraint method is applicable to coupled underground spatial structures.

[0078] See Figure 2 In this embodiment, taking the two-dimensional mesh partitioning condition as an example, a Cauchy inequality constraint term is constructed in each direction, and the constraint effect in a specific direction is highlighted by configuring the weight factor of each direction.

[0079] ;

[0080] Where x represents the horizontal direction and z represents the vertical direction; This represents the weighting factor of the horizontal constraint term. This represents the weighting factor for the vertical constraint term; This indicates the horizontal constraint term. This indicates a vertical constraint term.

[0081] In a two-dimensional grid of size M×N, M and N represent the length and width of the grid, respectively; x represents the horizontal direction; z represents the vertical direction; i represents the i-th cell in the horizontal direction; and j represents the j-th cell in the vertical direction. For a given cell in a two-dimensional uniform grid... For example, its horizontal and vertical gradients can be approximated using the forward difference form:

[0082] .

[0083] .

[0084] in This represents the distance between the centers of two adjacent cells in the x-direction. This represents the distance between the centers of two adjacent cells in the z-direction.

[0085] Similarly The directional gradient is:

[0086] .

[0087] .

[0088] Under two-dimensional mesh partitioning conditions, with horizontal constraint terms For example, the specific derivation process is as follows:

[0089] From the formula We can obtain:

[0090] ;

[0091] Introducing intermediate variables and ,make ,Right now:

[0092] ;

[0093] ;

[0094] At this point:

[0095] ;

[0096] That is, horizontal constraint terms It can be expressed as follows:

[0097] ;

[0098] At this time, the horizontal constraint term About and The partial derivatives are:

[0099] ;

[0100] ;

[0101] Similarly, we can obtain the vertical constraint term. The expression and its relation and Partial derivative form:

[0102] ;

[0103] ;

[0104] .

[0105] This embodiment allows for the selection of applicable direction combinations. Specific direction construction combinations can be categorized into three types: the first type contains only a single-direction constraint term, the form of which is shown below. Figure 3 , Figure 3The first type uses red to indicate the single direction selected for the constraint. The second type consists of constraints composed of any two of the following: horizontal, vertical, and 45° and 135° inclined directions. The form is shown in the image. Figure 4 , Figure 4 The two-direction combination selected for the constraint is highlighted in red. The third type considers composite constraint terms that combine any three of the following directions: horizontal, vertical, and 45° and 135° tilt directions. Figure 5 As shown, Figure 5 The three-directional combinations of the selected constraints are highlighted in red. It should be noted that the choice of which to use depends on the accuracy requirements and computational resource limitations of the actual application scenario. If high detail features are required, it is recommended to use the third type of composite constraint to enhance the model's expressive power; conversely, in scenarios with high real-time requirements, the first or second type of constraint can be used to improve computational efficiency. Regarding the method of using all directions simultaneously (not listed), verification shows that the selection of constraint factors significantly affects the overall optimization process; improper factor settings can easily lead to numerical instability or convergence difficulties.

[0106] Step 5: Iteratively solve the problem using conjugate gradient or quasi-Newton algorithm, update the model parameters until the convergence condition is met, thereby achieving joint inversion of constraints constructed in different directions and obtaining joint inversion results.

[0107] This embodiment uses the mature and efficient conjugate gradient method to minimize the objective function. The basic process is as follows:

[0108] ;

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] In the formula, This represents the current iteration number; The data is fitted with residuals; and These are calculated data and observed data, respectively. The model to be solved; For prior models; Weighting matrix for the model; As a regularization factor; The gradient direction; This is the sensitivity matrix; For coefficients; These are the conjugate gradient directions; This is the iteration step size; This is the initial gradient; For the initial conjugate gradient, These are the weighting coefficients. This represents the model after the (n+1)th iteration update. The gradient of the previous iteration. express The transpose of the sensitivity matrix.

[0114] In this embodiment, the following is designed: Figure 6 (a) and Figure 6 The bi-block model is shown in (c). In the model test, the background values ​​were 100 Ω·m and 0 g / cm³. 3 , Figure 6 In the resistivity model of (a), the physical property values ​​of the anomalous body are all 10 Ω·m; Figure 6 In the density model of (c), the physical property value of the anomalous body is 0.1 g / cm³. 3 . Figure 6 (b) and Figure 6 (d) shows the resistivity and density regularization inversion results, respectively. This embodiment sets five schemes with different horizontal and vertical weighting factors. Figure 6 (e-1) to Figure 6 Table (e-5) shows the joint inversion results of density and magnetic susceptibility for five schemes under five different horizontal and vertical weights. The corresponding weight factor coefficient schemes for the five schemes are shown in Table 1 below.

[0115] Table 1 Weighting factor coefficients for different schemes

[0116]

[0117] Figure 6 The resistivity regularization inversion result in (b) reproduces the spatial structure of the anomalous body quite well. Figure 6 The density regularization inversion results in (d) are relatively focused, but compared with the real model outlined by the red dashed line, the spatial morphology restoration did not meet expectations, the lateral restoration was insufficient, and the bottom tail was slightly too large. Comparative Analysis Figure 6 (e-1)- Figure 6 The density joint inversion results shown in (e-5) reveal a significant change in the inversion results. Figure 6 (e-1) to Figure 6In (e-5), compared to the real model, the horizontal width of the reconstructed anomaly shows a trend of increasing, while the vertical width shows a trend of decreasing. This reflects the gradual decrease in the weight of the horizontal constraint term and the gradual increase in the weight of the vertical constraint term. When the weight factors of the horizontal and vertical constraint terms are equal, the shape of the inversion result is a compromise.

[0118] Figure 7 (a-1)- Figure 7 Figure (a-5) shows the coupling of density and resistivity parameters in the joint inversion results under five different scenarios. Figure 7 (b-1)- Figure 7 Figure (b-5) shows the coupling of the horizontal density and resistivity parameter gradients in the joint inversion results under five different scenarios. Figure 7 (c-1)- Figure 7 Figure (c-5) shows the gradient coupling of density and resistivity parameters in the vertical direction of the joint inversion results under five different schemes. It can be seen that... Figure 7 (a-1)- Figure 7 Compared to (a-5), Figure 7 (b-1)- Figure 7 (b-5) and Figure 7 (c-1)- Figure 7 The linear correlation characteristics of (c-5) are more obvious, which is a manifestation of the role of the directional construction constraints. In addition, as the weight factor of the horizontal or vertical constraint term increases, the linear characteristics of the gradient of the physical property parameters in the horizontal or vertical direction become more obvious.

[0119] Example 2.

[0120] This invention also provides a directional construction constraint joint inversion system based on Cauchy inequality, comprising:

[0121] The forward modeling module is used to construct a matching forward model based on known underground spatial structures; then, the forward modeling response of the forward model is calculated to simulate various geophysical data collected by the observation system.

[0122] The objective function construction module is used to select appropriate geophysical methods from the results of the forward modeling module to perform joint inversion based on the actual geological prior information of the target area to be inverted. First, a joint inversion objective function is constructed by combining different geophysical methods, and a weighting strategy is introduced to balance the residual contributions of different geophysical data. Then, Cauchy inequality constraint terms are introduced into the joint inversion objective function, and mathematical transformations are used to make the inversion model parameters satisfy the Cauchy inequality criterion, thereby realizing the coupling correlation between the inversion model parameters of different geophysical methods.

[0123] The initial inversion module is used to construct an initial inversion model that matches the forward spatial dimensions of the forward model based on the spatial characteristics of the forward model constructed by the forward model module, and sets the initial physical property parameter distribution in a uniform half-space form.

[0124] The multi-directional constraint module is used to calculate the gradients of the inversion model parameters from the horizontal, vertical, 45°, and 135° tilt directions based on the sub-directional structural constraints, and obtain discrete approximations of the gradients through forward differencing. Then, the gradients of the multi-directional inversion model parameters are substituted into Cauchy's inequality to construct the sub-directional constraint terms, and the explicit partial derivatives of the constraint terms with respect to the inversion model parameters are derived. Then, according to the geological structural characteristics, suitable direction combinations are selected from the horizontal, vertical, 45°, and 135° tilt directions, and direction-weighted structural constraint terms are applied to the joint inversion objective function to enhance the ability to characterize the spatial distribution characteristics of geological bodies.

[0125] The inversion solution module is used to iteratively solve the joint inversion objective function using the conjugate gradient or quasi-Newton method, and successively update the inversion model parameters until the convergence condition is met, thereby realizing the joint inversion of structural constraints in different directions and obtaining joint inversion results with both high resolution and high fit to actual geology.

[0126] It should also be understood that the specific implementation process of each module is described in the above method. This invention will not repeat it here. The division of the above functional modules is only for illustrative purposes. In some embodiments, some functional modules can be merged and some functional modules can be split. Each functional module can be implemented in software, hardware, or a combination of software and hardware. The software and hardware devices include, but are not limited to, general electronic terminals, programmable gate arrays, digital signal processors, microprocessors and their corresponding programming or burning software.

[0127] Example 3.

[0128] This embodiment provides an electronic device, including: one or more processors; and a memory storing one or more computer programs; wherein the processor calls the computer programs to implement the steps of a joint inversion method based on Cauchy inequality with directional construction constraints. For the specific implementation process of each step, please refer to the description of the aforementioned embodiment of the joint inversion method based on Cauchy inequality with directional construction constraints.

[0129] In some embodiments, such as Figure 8 As shown, the electronic components of the electronic device include:

[0130] The processor 1600 can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. The processor 1600 is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present invention.

[0131] The memory 1700 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 1700 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 1700, and the processor 1600 calls and executes the algorithm program of the constrained joint inversion method based on Cauchy inequality in the embodiments of this invention.

[0132] The input / output interface 1800 is used to implement information input and output.

[0133] The communication interface 1900 is used to enable communication and interaction between this device and other devices. Communication can be achieved via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0134] Bus 2000 transmits information between various components of the device, such as processor 1600, memory 1700, input / output interface 1800, and communication interface 1900.

[0135] The processor 1600, memory 1700, input / output interface 1800 and communication interface 1900 are connected to each other within the device via bus 2000.

[0136] Example 4.

[0137] This invention also provides a computer-readable storage medium storing a computer program that is invoked by a processor to implement the steps of a constrained joint inversion method based on Cauchy inequality.

[0138] The present invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the core ideas of the invention. It should be noted that those skilled in the art can make various improvements and modifications to the invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for joint inversion based on directional construction constraints using Cauchy's inequality, characterized in that, Includes the following steps: Step 1: Based on the known underground space structure, construct a matching forward model; then calculate the forward response of the forward model to simulate various geophysical data collected by the observation system. Step 2: Based on the actual geological prior information of the target area to be inverted, select suitable geophysical methods corresponding to the geophysical data from the results of Step 1 for joint inversion: First, construct a joint inversion objective function by combining different geophysical methods, and introduce a weighting strategy to balance the residual contributions of different geophysical data; then, introduce Cauchy inequality constraint terms into the joint inversion objective function, and use mathematical transformations to make the inversion model parameters satisfy the Cauchy inequality criterion, thereby realizing the coupling correlation between the inversion model parameters of different geophysical methods; Step 3: Based on the spatial characteristics of the forward model constructed in Step 1, construct an initial inversion model that matches the forward spatial dimensions of the forward model, and set the initial physical property parameter distribution using a uniform half-space form. Step 4: Based on the directional structural constraints, the gradients of the inversion model parameters are calculated from the horizontal, vertical, 45°, and 135° tilt directions, respectively, and the discrete approximation of the gradients is obtained through forward differencing. Then, the gradients of the multi-directional inversion model parameters are substituted into the Cauchy inequality to construct the directional constraint terms, and the explicit partial derivatives of the directional constraint terms with respect to the inversion model parameters are derived. Then, according to the geological structural characteristics, suitable direction combinations are selected from the horizontal, vertical, 45°, and 135° tilt directions, and directional weighted structural constraint terms are applied to the joint inversion objective function to enhance the ability to characterize the spatial distribution characteristics of geological bodies. Step 5: Using the conjugate gradient or quasi-Newton method, steps 4 and 5 are executed iteratively to solve the joint inversion objective function, and the inversion model parameters are updated one after another until the convergence condition is met, thereby realizing the joint inversion with constraints constructed in different directions and obtaining the joint inversion result. In step 2, the Cauchy inequality constraint term is a joint inversion constraint based on the linear correlation of the inversion model vectors. From the Cauchy inequality, the constraint relationship of the inversion model parameters to be solved in the spatial orthogonal direction is satisfied: the equality holds if and only if the inversion model parameters are linearly correlated, that is, the inversion model parameters have directional correlation characteristics in spatial distribution. ； C represents the Cauchy inequality function, and D represents the transformation operator. and These are the parameters of the inversion model to be solved using two different geophysical methods.

2. The method according to claim 1, characterized in that, In step 2, suitable geophysical data is selected from the results of step 1. This involves filtering out geophysical data that matches the geological conditions and structural features of the target area to be inverted from the various geophysical data obtained from the simulation in step 1. Then, the corresponding geophysical methods are used to carry out joint inversion.

3. The method according to claim 1, characterized in that: In step 2, a joint inversion objective function is constructed by combining two different geophysical methods. The joint inversion objective function is expressed as follows: ； In the formula, For the inversion model functional; and Fit a functional to the data; and These are the weighting coefficients for two different geophysical methods; and To find the stable functional of the inversion model, and For two different geophysical methods, the regularization factor is used. For constraint factors; This is a horizontal constraint term. This represents the weighting factor of the horizontal constraint term. and These are the parameters of the inversion model to be solved in the horizontal direction for two different geophysical methods. Represents the gradient operator; This is a vertical constraint term. This represents the weighting factor for the vertical constraint term. and These are the parameters of the inversion model to be solved in the vertical direction for two different geophysical methods; The constraint term is for the 45° tilt direction. This represents the weighting factor for the 45° tilt direction constraint term. and The parameters of the inversion model to be solved by two different geophysical methods in the 45° tilt direction; The constraint term is for the 135° tilt direction. This represents the weighting factor for the 135° tilt direction constraint term. and These are the parameters of the inversion model to be solved using two different geophysical methods in the 135° tilt direction.

4. The method according to claim 1, characterized in that: In step 4, when selecting a suitable combination of directions from horizontal, vertical, 45°, and 135° tilt directions, the direction constraints are determined based on the spatial structure of the inversion model: when the inversion model only has spatial structures in the horizontal and vertical directions, horizontal and vertical direction constraints are selected; when the inversion model has a 45° or 135° tilted interface spatial structure, the corresponding tilt direction constraint is selected; when the inversion model has both horizontal and vertical spatial structures and 45° or 135° tilted interface spatial structures, all the required direction constraints are selected; secondly, under the premise of conforming to the spatial structure of the inversion model, the direction combination is selected based on the spatial characteristics in the corresponding directions that need to be specifically revealed.

5. The method according to claim 3, characterized in that: In step 4, the direction-weighted structural constraint term is the gradient of the inversion model parameters calculated along the horizontal, vertical, 45° and 135° tilt directions respectively; the direction weight factor is configured for different directions, and by adjusting the magnitude of the direction weight, the dominant constraint direction is aligned with the main structural direction of the geological body.

6. A directional construction constraint joint inversion system based on Cauchy's inequality, characterized in that, include: The forward modeling module is used to construct a matching forward model based on known underground space structures; then, the forward modeling response of the forward model is calculated to simulate various geophysical data collected by the observation system. The objective function construction module is used to select appropriate geophysical methods from the results of the forward modeling module to perform joint inversion based on the actual geological prior information of the target area to be inverted. First, a joint inversion objective function is constructed by combining different geophysical methods, and a weighting strategy is introduced to balance the residual contributions of different geophysical data. Then, Cauchy inequality constraint terms are introduced into the joint inversion objective function, and mathematical transformations are used to make the inversion model parameters satisfy the Cauchy inequality criterion, thereby realizing the coupling correlation between the inversion model parameters of different geophysical methods. The initial inversion module is used to construct an initial inversion model that matches the forward spatial dimensions of the forward model based on the spatial characteristics of the forward model constructed by the forward model module, and sets the initial physical property parameter distribution in a uniform half-space form. The multi-directional constraint module is used to calculate the gradients of the inversion model parameters from the horizontal, vertical, 45°, and 135° tilt directions based on the sub-directional structural constraints, and obtain discrete approximations of the gradients through forward differencing. Then, the gradients of the multi-directional inversion model parameters are substituted into Cauchy's inequality to construct the sub-directional constraint terms, and the explicit partial derivatives of the sub-directional constraint terms with respect to the inversion model parameters are derived. Then, according to the geological structural characteristics, suitable direction combinations are selected from the horizontal, vertical, 45°, and 135° tilt directions, and direction-weighted structural constraint terms are applied to the joint inversion objective function to enhance the ability to characterize the spatial distribution characteristics of geological bodies. The inversion solution module is used to iteratively solve the joint inversion objective function using conjugate gradient or quasi-Newton method, and update the inversion model parameters one by one until the convergence condition is met, thereby realizing the joint inversion with constraints constructed in different directions and obtaining the joint inversion result. In the objective function construction module, the Cauchy inequality constraint term is a joint inversion constraint based on the linear correlation of the inversion model vectors. From the Cauchy inequality, the constraint relationship of the inversion model parameters to be solved in the spatial orthogonal direction satisfies: the equality holds if and only if the inversion model parameters are linearly correlated, that is, the inversion model parameters have directional correlation characteristics in spatial distribution. ； C represents the Cauchy inequality function, and D represents the transformation operator. and These are the parameters of the inversion model to be solved using two different geophysical methods.

7. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-6.

8. A computer-readable medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-6.

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