Method for obtaining density anomaly or magnetic anomaly vector by optimizing reconstruction based on prior information

Abstract

The present invention discloses a method for obtaining density anomaly or magnetic anomaly vectors based on optimizing reconstruction using prior information, including: constructing an initial prior matrix #imgabs0# using prior information; using the initial prior matrix #imgabs1# to solve a bi-objective function to obtain an optimized inverse prior vector; reconstructing the optimized prior matrix; iteratively optimizing the prior matrix; and solving the density anomaly vector or magnetic anomaly vector #imgabs3# using the optimized prior matrix #imgabs2#. The present invention can flexibly apply various forms of prior constraints without converting prior information into density anomaly or magnetic anomaly parameters, thus greatly simplifying the process of constrained imaging and improving the convenience of operation; the prior matrix is iteratively optimized using a bi-objective function, ensuring the scientificity and rationality of the constraint information and effectively avoiding the risk of introducing incorrect information in the obtained density anomaly or magnetic anomaly vectors.

Description

Technical Field

[0001] The present invention relates to the field of electrical digital data processing, and particularly to a method for obtaining vectors of density anomalies or magnetic anomalies based on optimizing reconstruction with prior information. Background Art

[0002] In the process of obtaining vectors of underground density anomalies or magnetic anomalies using incomplete and noisy gravity and magnetic data, effectively utilizing prior information, such as wave velocity, reflection coefficient, resistivity, etc., to impose constraints on the obtaining process is the key way to improve the reliability of density anomaly and magnetic anomaly vectors.

[0003] Traditional methods mainly rely on three strategies: reference constraint, cross-gradient constraint, or Gramian constraint. Among them, the reference constraint attempts to convert prior information into a density anomaly or magnetic anomaly vector to form a reference vector, and uses an optimization algorithm to find the density anomaly or magnetic anomaly vector that is closest to the reference vector. The cross-gradient constraint and the Gramian constraint are based on the assumption that there is a similar structure between the underground density anomaly or magnetic anomaly and the prior information. They respectively calculate the dot product between the density anomaly or magnetic anomaly vector and the gradient of the prior information, and the inner product between the density anomaly or magnetic anomaly vector and the prior information, in order to obtain a density anomaly or magnetic anomaly vector that best fits the spatial structure of the prior information. The objective functions corresponding to these three constraint strategies can be respectively expressed as:

[0004] (1)

[0005] (2)

[0006] (3)

[0007] Wherein, is the kernel matrix, is the gravity or magnetic measurement data, is the vector of density anomaly or magnetic anomaly to be solved, represents the reference vector converted from prior information, is the prior information vector, represents the 2-norm, and are regularization factors, is the depth weighting matrix, is the cross-gradient regularization term, is the Gramian regularization term.

[0008] However, the physical properties of underground rocks (ores) are extremely complex, and the relationships between their various physical parameters are far from being summarized by simple mathematical formulas, and even lack clear direct or inverse proportional relationships. For example, ultrabasic rocks often exhibit characteristics of high density, high magnetism, and low wave velocity, while some ore bodies (such as fracture zones) may show characteristics of medium density, high magnetism, and low wave velocity. In practical applications, even if a large amount of prior information is obtained, it may not be possible to accurately establish the mapping relationship between this prior information and density anomalies or magnetic anomalies, that is, it is difficult to effectively obtain in Equation (1). This undoubtedly increases the implementation difficulty based on reference constraints.

[0009] In addition, cross-gradient constraints and Gramian constraints based on the assumption of structural similarity also face severe challenges. Due to the diversity of the physical properties of underground rocks (ores) and the complexity of the underground structure, significant differences in wave velocity, reflection coefficient, and resistivity structures in a certain area do not necessarily mean corresponding changes in density or magnetic anomaly structures. For example, rocks rich in pores or underground structures containing a large amount of fluid may have significantly reduced wave velocity due to the presence of pore fluids, but the changes in density anomaly or magnetic anomaly structures may not be significant, or even remain unchanged; similarly, geological bodies with certain specific mineral combinations may cause significant changes in resistivity, while these mineral combinations have little impact on density anomaly or magnetic anomaly structures. In these cases, cross-gradient constraints and Gramian constraints will wrongly directly associate the structural changes of prior information such as wave velocity, reflection coefficient, or resistivity with the structural changes of density anomalies or magnetic anomalies through Equation (2) or Equation (3), thus introducing misleading structural information into the finally solved density anomaly or magnetic anomaly vector, or even wrongly highlighting some non-existent density anomaly or magnetic anomaly bodies, thereby reducing the reliability of the density anomaly or magnetic anomaly vector.

[0010] Therefore, in the process of using incomplete and noisy gravity and magnetic data to obtain the density anomaly or magnetic anomaly vector underground, how to enhance the practicality and convenience of prior information constraints and effectively suppress the generation of false structures is an urgent problem to be solved in this field. Summary of the Invention

[0011] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for obtaining a density anomaly or magnetic anomaly vector based on optimized reconstruction of prior information.

[0012] The purpose of the present invention is achieved by the following technical solutions:

[0013] In the first aspect of the present invention, a method for obtaining a density anomaly or magnetic anomaly vector based on optimized reconstruction of prior information is provided, including the following steps:

[0014] S01: Construct an initial prior matrix using prior information , including the following sub-steps:

[0015] S0101: For the prior information, use interpolation to obtain the original prior information values of all cells , where , M represents the number of elements of the density anomaly vector or magnetic anomaly vector to be solved;

[0016] S0102: Calculate the normalized prior information values of all cells:

[0017]

[0018] where, is the normalized prior information value of the th cell, and represent the minimum and maximum values among the original prior information values of all cells respectively;

[0019] S0103: Construct the initial prior matrix:

[0020]

[0021] where, is the initial prior matrix, represents the diagonal matrix;

[0022] S02: Use the initial prior matrix obtained in step S01 to solve the bi-objective function to obtain the optimized inverse prior vector:

[0023]

[0024] where, is the kernel matrix, is the gravity data vector or magnetic survey data vector, is the density anomaly vector or magnetic anomaly vector to be solved, represents the 2-norm, is the regularization factor, is the depth weighting matrix, is the solution vector of the first objective function, is the solution vector of the second objective function and at the same time represents the optimized inverse prior vector;

[0025] S03: Reconstruct the optimized prior matrix, including the following sub-steps:

[0026] S0301: Use the optimized inverse prior vector obtained in step S02 to calculate the normalized optimized prior information values of all cells:

[0027]

[0028] Among them, is the normalized optimized prior information value of the th unit cell, and respectively represent the minimum and maximum values of the inverse prior vectors after optimization for all unit cells;

[0029] S0302: Reconstruct the optimized prior matrix:

[0030]

[0031] Among them, is the optimized prior matrix;

[0032] S04: Iteratively optimize the prior matrix: Use to replace , and repeat steps S02 and S03 until is less than or equal to the set threshold;

[0033] S05: Substitute the optimized prior matrix into the following formula to solve the density anomaly vector or magnetic anomaly vector :

[0034] .

[0035] Furthermore, the prior information includes reflection coefficient, wave velocity or resistivity.

[0036] Furthermore, the threshold in step S04 is set to .

[0037] The beneficial effects of the present invention are:

[0038] In an exemplary embodiment of the present invention, various forms of prior constraints can be flexibly applied without converting the prior information into density anomaly or magnetic anomaly parameters, thus greatly simplifying the process of constrained imaging and improving the convenience of operation. Compared with cross-gradient constraint and Gramian constraint, this method uses a dual-objective function to iteratively optimize the prior matrix, ensuring the scientificity and rationality of the constraint information and effectively avoiding the risk of introducing incorrect information in solving the density anomaly or magnetic anomaly vector. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of a method for obtaining a density anomaly or magnetic anomaly vector optimized and reconstructed based on prior information provided in an exemplary embodiment of the present invention;

[0040] Figure 2Schematic diagram of the gravity data curve of the density vector calculation test results provided in an exemplary embodiment of the present invention;

[0041] Figure 3 Seismic wave velocity map of the density vector calculation test results provided in an exemplary embodiment of the present invention;

[0042] Figure 4 True density anomaly vector map of the density vector calculation test results provided in an exemplary embodiment of the present invention;

[0043] Figure 5 Density anomaly vector map obtained from the density vector calculation test results provided in an exemplary embodiment of the present invention. Detailed implementation manners

[0044] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0045] In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0046] In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal connection of two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0047] In addition, the technical features involved in different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0048] See Figure 1 , Figure 1The flowchart of the method for obtaining the density anomaly or magnetic anomaly vector optimized and reconstructed based on prior information provided in an exemplary embodiment of the present invention is shown, including the following steps:

[0049] S01: Construct an initial prior matrix using prior information . To improve the convenience of constrained imaging and enable it to flexibly apply various forms of prior information for constraint, this exemplary embodiment adopts a new strategy to construct an initial prior matrix and weight the density anomaly or magnetic anomaly vector to be solved. Since the prior information is not directly converted into a reference density or reference magnetic anomaly vector, there is no need to struggle with the difficult problem of constructing a complex mapping relationship between the prior information and the density anomaly or magnetic anomaly. Specifically, this step includes the following sub-steps:

[0050] S0101: For the prior information (in a preferred exemplary embodiment, the prior information is, for example, parameters such as reflection coefficient, wave velocity, or resistivity), interpolation processing is performed to obtain the original prior information values of all unit cells , where , M represents the number of elements of the density anomaly vector or magnetic anomaly vector to be solved;

[0051] S0102: To unify the dimension and ensure the comparability of data, calculate the normalized prior information values of all unit cells:

[0052]

[0053] where, is the normalized prior information value of the th unit cell, and represent the minimum and maximum values of the original prior information values of all unit cells respectively;

[0054] S0103: Construct the initial prior matrix:

[0055]

[0056] where, is the initial prior matrix, represents a diagonal matrix.

[0057] It should be noted that the formula in step S0103 ensures that the initial weighting values of all unit cells are strictly limited within the range of -1 to 1. When the weighting value approaches 0, it means that the density anomaly or magnetic susceptibility anomaly of the corresponding unit cell is almost zero; while when the weighting value approaches 1 or -1, it indicates that the unit cell has a relatively high density anomaly or magnetic anomaly, and the unit cell has a relatively low density anomaly or magnetic anomaly respectively.

[0058] It should be noted that the initial prior matrix may have insufficient fineness or may contain some non-real structures. Therefore, in the preferred case, it is necessary to optimize it to ensure its quality and applicability.

[0059] S02: Using the initial prior matrix obtained in step S01 , solve the bi-objective function to obtain the optimized inverse prior vector:

[0060]

[0061] wherein, is the kernel matrix, is the gravity data vector or the magnetic survey data vector, is the density anomaly vector or the magnetic anomaly vector to be solved, represents the 2-norm, is the regularization factor, is the depth weighting matrix, is the solution vector of the first objective function, is the solution vector of the second objective function and at the same time represents the optimized inverse prior vector.

[0062] It should be noted that step S02 optimizes to prevent false structures in the prior information from being mixed into the finally solved density anomaly vector or magnetic anomaly vector. In view of the fact that has no direct and clear mapping relationship with the gravity or magnetic survey data, there is currently no feasible way to optimize it. For this reason, in this exemplary embodiment, a bi-objective function optimization strategy is proposed to optimize .

[0063] Observing the formula in step S02, it can be found that for any element in the vector there is:

[0064]

[0065] wherein, represents the element in the diagonal matrix at the th row and the th column. Therefore, by solving the bi-objective function of the formula in step S02, the obtained

[0066] S03: After obtaining After that, the normalized optimized prior information values of all unit cells can be obtained. Specifically, the reconstructed and optimized prior matrix includes the following sub-steps:

[0067] S0301: Using the optimized inverse prior vector obtained in step S02, calculate the normalized optimized prior information values of all unit cells:

[0068]

[0069] where, is the normalized optimized prior information value of the th unit cell, and represent the minimum and maximum values of the optimized inverse prior vectors of all unit cells respectively;

[0070] S0302: Correspondingly, reconstruct the optimized prior matrix:

[0071]

[0072] where, is the optimized prior matrix;

[0073] S04: Iteratively optimize the prior matrix: Use to replace , and repeat steps S02 and S03 until is less than or equal to the set threshold; preferably, in a specific exemplary embodiment, according to the test results, the threshold can be set to ;

[0074] S05: Substitute the optimized prior matrix into the following formula to solve for the density anomaly vector or magnetic anomaly vector :

[0075] .

[0076] By solving the regularization objective function in step S05, a density anomaly vector or magnetic anomaly vector with significantly improved reliability and accuracy can be obtained.

[0077] In summary, the patent of this exemplary embodiment innovatively proposes a method for obtaining density anomaly or magnetic anomaly vectors based on optimizing and reconstructing prior information. Compared with traditional reference constraints, this method can flexibly apply various forms of prior constraints without converting prior information into density anomaly or magnetic anomaly parameters, thus greatly simplifying the process of constrained imaging and improving the convenience of operation. Compared with cross-gradient constraints and Gramian constraints, this method uses a dual-objective function to iteratively optimize the prior matrix, ensuring the scientificity and rationality of the constraint information and effectively avoiding the risk of introducing incorrect information in the obtained density anomaly or magnetic anomaly vectors.

[0078] It should be additionally noted that:

[0079] (1) Traditional reference constraints, cross-gradient constraints, and Gramian constraints usually assume that prior information is reliable and has a strong correlation with density anomalies or magnetic anomalies. However, if this assumption does not hold, misleading information will be introduced into the solution results. In contrast, in this exemplary embodiment, before obtaining density anomaly vectors and magnetic anomaly vectors, any given prior matrix that may have errors is optimized and reconstructed to ensure its quality and applicability. Finally, the optimized and reconstructed prior matrix is used for constraint to obtain density anomaly or magnetic anomaly vectors. This method is convenient to implement, can be compatible with various types of prior information, effectively reduces the risk of introducing false structures, and significantly improves the reliability of the obtained density or magnetic anomaly vectors.

[0080] (2) The advantage of using a dual-objective function in this exemplary embodiment is that there is no direct and clear mapping relationship between the prior matrix and gravity or magnetic measurement data, and theoretically it cannot be optimized. Therefore, this exemplary embodiment proposes a dual-objective function to cleverly solve the inverse prior vector and then reconstruct it to obtain an optimized prior matrix. In short, with the help of the dual-objective function, a prior matrix that has no direct and clear mapping relationship with the observed data can be optimized to ensure that it is more consistent with the actual density or magnetic anomaly and eliminate false structures in the prior information.

[0081] Figures 2 to 5 Shows the simulation test results of obtaining density anomaly vectors based on optimizing and reconstructing the prior matrix of seismic wave velocity. Among them:

[0082] Appendix Figure 2 is the gravity data curve, representing the variation of observed data and fitting data; Appendix Figure 3 is the seismic wave velocity image, which reveals the actual distribution characteristics of the wave velocity of underground media; Appendix Figure 4 is the true density anomaly vector image, reflecting the actual distribution of underground density anomalies. It should be noted that Appendix Figure 3 and Appendix Figure 4There are many significant differences, which are mainly reflected in: there is no clear direct mapping relationship between wave velocity and density anomaly, and they are neither simply directly proportional nor inversely proportional; in addition, in some regions, although the seismic wave velocity does not show obvious anomalies, the density has significant anomalies. Faced with such complex situations, traditional reference constraints, cross-gradient constraints, and even Gramian constraint methods are often difficult to implement effectively.

[0083] However, the method for obtaining the density anomaly vector or magnetic anomaly vector based on prior matrix optimization and reconstruction proposed in this exemplary embodiment can easily handle it. The image corresponding to the density anomaly vector obtained by using this exemplary embodiment is shown in the appendix Figure 5 . By comparing the appendix Figure 4 and the appendix Figure 5 It can be seen that the method of this exemplary embodiment successfully restores the anomaly amplitude and anomaly structure in the true density anomaly image: the anomaly morphologies of the two are basically the same; combined with the color scale, it can be seen that the anomaly amplitudes of the two are very similar. This shows that the method of this exemplary embodiment significantly improves the reliability of solving the density anomaly vector and greatly weakens the misleading structure existing in the prior information.

[0084] Therefore, the experiment shows that this method greatly improves the accuracy and reliability of solving the density or magnetic anomaly vector.

[0085] Obviously, the above embodiments are only examples clearly described and not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of this invention.

Claims

1. A method for obtaining density anomaly or magnetic anomaly vectors by optimizing reconstruction based on prior information, which is used to obtain underground density anomaly or magnetic anomaly vectors by using incomplete and noisy gravity and magnetic data in view of the diversity of underground rock physical properties and the complexity of underground structures, and is characterized in that: It includes the following steps: S01: Construct an initial prior matrix using prior information , where the prior information includes reflection coefficient, wave velocity or resistivity; It includes the following sub-steps: S0101: For the prior information, interpolation processing is used to obtain the original prior information values of all elements , where , M represents the number of elements of the density anomaly vector or magnetic anomaly vector to be solved; S0102: Calculate the normalized prior information values of all unit cells: ； Among them, is the normalized prior information value of the th unit body, and represent the minimum and maximum values among the original prior information values of all unit bodies respectively; S0103: Construct the initial prior matrix: ； Among them, is the initial prior matrix, representing a diagonal matrix; S02: Using the initial prior matrix obtained in step S01 , solve the bi-objective function to obtain the optimized inverse prior vector: ； Among them, is the kernel matrix, is the gravity data vector or the magnetic survey data vector, is the density anomaly vector or the magnetic anomaly vector to be solved, represents the 2-norm, is the regularization factor, is the depth weighting matrix, is the solution vector of the first objective function, is the solution vector of the second objective function and at the same time represents the optimized inverse prior vector; S03: Reconstruct the optimized prior matrix, including the following sub-steps: S0301: Use the optimized inverse prior vector obtained in step S02 to calculate the normalized optimized prior information values of all unit cells: ； Among them, is the normalized optimized prior information value of the th unit cell, and represent the minimum and maximum values of the inverse prior vectors after optimization of all unit cells, respectively; S0302: Reconstruct the optimized prior matrix: ； Among them, is the optimized prior matrix; S04: Iteratively optimize the prior matrix: Use to replace , and repeat steps S02 and S03 until is less than or equal to the set threshold; S05: Substitute the optimized prior matrix into the following formula to solve the density anomaly vector or magnetic anomaly vector : 。 2. The method for obtaining density anomaly or magnetic anomaly vectors by optimizing reconstruction based on prior information according to claim 1, wherein: The threshold value in step S04 is set to .

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