Density anomaly or magnetic anomaly vector solving method based on prior information optimization reconstruction

Abstract

The invention discloses a vector solving method for density anomaly or magnetic anomaly based on prior information optimization reconstruction. The method comprises the following steps: constructing an initial prior matrix # imgabs0 # by using prior information; solving the dual-objective function by using the initial prior matrix # imgabs1 # to obtain an optimized inverse prior vector; the optimized priori matrix is reconstructed; iteratively optimizing the prior matrix; and solving a density anomaly vector or a magnetic anomaly vector # imgabs3 # by using the optimized prior matrix # imgabs2 #. According to the method, various forms of prior constraints can be flexibly applied, and the prior information does not need to be converted into density anomaly or magnetic anomaly parameters, so that the constraint imaging process is greatly simplified, and the operation convenience is improved; iterative optimization is carried out on a priori matrix by adopting a dual-objective function, so that scientificity and reasonability of constraint information are ensured, and the risk of introducing error information in solving a density anomaly or magnetic anomaly vector is effectively avoided.

Description

Technical Field

[0001] The invention relates to the field of electrical digital data processing, and in particular to a method for obtaining a vector of density anomaly or magnetic anomaly based on prior information optimization and reconstruction. Background Art

[0002] In the process of using incomplete and noisy gravity and magnetic data to obtain underground density anomalies or magnetic anomaly vectors, effectively using prior information, such as wave velocity, reflection coefficient, resistivity, etc., to impose constraints on the process is a key way to improve the reliability of density anomalies 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 the prior information into a density anomaly or magnetic anomaly vector to form a reference vector, and find the density anomaly or magnetic anomaly vector closest to the reference vector through an optimization algorithm. The cross gradient constraint and 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. The dot product between the density anomaly or magnetic anomaly vector and the prior information gradient, and the inner product between the density anomaly or magnetic anomaly vector and the prior information are calculated, respectively, in order to obtain the 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 expressed as:

[0004] (1)

[0005] (2)

[0006] (3)

[0007] in, is the kernel matrix, is gravity or magnetic data, is the density anomaly or magnetic anomaly vector to be solved, represents the reference vector transformed by prior information, is the prior information vector, represents the 2-norm, and is the regularization factor, 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 relationship between their various physical parameters is far from being summarized by simple mathematical formulas, and even lacks a clear proportional or inverse relationship. For example, ultrabasic rocks often show the characteristics of high density, high magnetism and low wave velocity, while some ore bodies (such as fracture zones) may show the 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 derive the formula (1) This undoubtedly increases the difficulty of implementation based on reference constraints.

[0009] In addition, the cross-gradient constraint and Gramian constraint based on the structural similarity assumption also face severe challenges. Due to the diversity of underground rock (ore) physical properties and the complexity of underground structures, significant differences in wave velocity, reflection coefficient, and resistivity structure in a certain area do not necessarily mean that there are corresponding changes in density or magnetic anomaly structure. For example, the wave velocity of porous rocks or underground structures containing a large amount of fluid may be significantly reduced due to the presence of pore fluid, but the change in density anomaly or magnetic anomaly structure 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 effect on density anomaly or magnetic anomaly structure. In these cases, cross-gradient constraints and Gramian constraints will mistakenly directly associate the structural changes of prior information such as wave velocity, reflection coefficient or resistivity with the structural changes of density anomaly or magnetic anomaly through formula (2) or formula (3), thereby introducing misleading structural information into the final solved density anomaly or magnetic anomaly vector, and even mistakenly highlighting some non-existent density anomaly or magnetic anomaly bodies, thereby reducing the reliability of density anomaly or magnetic anomaly vectors.

[0010] Therefore, in the process of using incomplete and noisy gravity and magnetic data to obtain underground density anomalies or magnetic anomaly vectors, how to enhance the practicality and convenience of prior information constraints while effectively suppressing 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 density anomaly or magnetic anomaly vectors based on optimized reconstruction of prior information.

[0012] The objective of the present invention is achieved through the following technical solutions:

[0013] A first aspect of the present invention provides a method for obtaining a density anomaly or magnetic anomaly vector based on prior information optimization and reconstruction, comprising the following steps:

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

[0015] S0101: For the prior information, interpolation is used to obtain the original prior information values ​​of all units. ,in , 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 value of all units:

[0017]

[0018] in, For the The normalized prior information value of the unit cell, and Respectively represent the minimum and maximum values ​​of the original prior information values ​​of all units;

[0019] S0103: Construct the initial prior matrix:

[0020]

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

[0022] S02: Using the initial prior matrix obtained in step S01 , solve the dual objective function to obtain the optimized inverse prior vector:

[0023]

[0024] in, is the kernel matrix, is the gravity data vector or magnetic 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, Solve the vector for the first objective function, A vector for solving the second objective function and representing the optimized inverse prior vector;

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

[0026] S0301: Using the optimized inverse prior vector obtained in step S02, calculate the normalized optimized prior information value of all unit cells:

[0027]

[0028] in, For the The normalized optimized prior information value of each unit cell, and Respectively represent the minimum and maximum values ​​of the inverse prior vectors after optimization of all unit cells;

[0029] S0302: Reconstruct the optimized prior matrix:

[0030]

[0031] in, is the optimized prior matrix;

[0032] S04: Iterative optimization of the prior matrix: using replace , and repeat steps S02 and S03 until Less than or equal to the set threshold;

[0033] S05: The optimized prior matrix Substitute 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, and there is no need to convert prior information into density anomaly or magnetic anomaly parameters, thereby 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 erroneous information in the solved density anomaly or magnetic anomaly vector. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flow chart of a method for obtaining a density anomaly or magnetic anomaly vector based on prior information optimization and reconstruction provided in an exemplary embodiment of the present invention;

[0040] Figure 2A schematic diagram of a gravity data curve for obtaining a test result of a density vector provided in an exemplary embodiment of the present invention;

[0041] Figure 3 A seismic velocity diagram of a density vector obtained from a test result provided in an exemplary embodiment of the present invention;

[0042] Figure 4 A true density anomaly vector diagram of a density vector acquisition test result provided in an exemplary embodiment of the present invention;

[0043] Figure 5 A density anomaly vector diagram of a density vector acquisition test result provided in an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0044] The technical solution of the present invention is described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] In the description of the present invention, it should be noted that the directions or positional relationships indicated by "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside", etc. are directions or positional relationships based on the drawings, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, "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 specified and limited, "installation", "connection" and "connection" 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 a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0047] In addition, the technical features involved in the 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 also Figure 1 , Figure 1A flow chart of a method for obtaining a density anomaly or magnetic anomaly vector based on prior information optimization and reconstruction provided in an exemplary embodiment of the present invention is shown, comprising the following steps:

[0049] S01: Constructing the initial prior matrix using prior information In order to improve the convenience of constrained imaging and enable it to flexibly apply various forms of prior information for constraints, this exemplary embodiment adopts a new strategy to construct an initial prior matrix to 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 worry about 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 parameters such as reflection coefficient, wave velocity or resistivity), the original prior information values ​​of all unit cells are obtained by interpolation processing ,in , M represents the number of elements of the density anomaly vector or magnetic anomaly vector to be solved;

[0051] S0102: To unify the dimensions and ensure data comparability, calculate the normalized prior information values ​​of all units:

[0052]

[0053] in, For the The normalized prior information value of the unit cell, and Respectively represent the minimum and maximum values ​​of the original prior information values ​​of all units;

[0054] S0103: Construct the initial prior matrix:

[0055]

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

[0057] It should be noted that the formula of step S0103 ensures that the initial weighted values ​​of all unit cells are strictly limited to the range of -1 to 1. When the weighted value approaches 0, it means that the density anomaly or magnetic susceptibility anomaly of the corresponding unit cell is close to zero; and when the weighted value is close to 1 or -1, it indicates that the unit cell has a higher density anomaly or magnetic anomaly, and the unit cell has a lower density anomaly or magnetic anomaly, respectively.

[0058] It is worth noting that the initial prior matrix There may be insufficient refinement or may contain some unreal 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 dual objective function to obtain the optimized inverse prior vector:

[0060]

[0061] in, is the kernel matrix, is the gravity data vector or magnetic 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, Solve the vector for the first objective function, Solve the vector for the second objective function and represent the optimized inverse prior vector.

[0062] It should be noted that step S02 The optimization is performed to prevent false structures in the prior information from being mixed into the final solved density anomaly vector or magnetic anomaly vector. There is a lack of direct and clear mapping relationship between gravity or magnetic data, and there is currently no feasible way to optimize it. To this end, in this exemplary embodiment, a dual objective function optimization strategy is proposed to optimize .

[0063] Observing the formula in step S02, we can find that the vector Any element in have:

[0064]

[0065] in, Represents a diagonal matrix No. Row, No. Therefore, by solving the dual objective function of the formula in step S02, the obtained In fact, it represents the optimized inverse prior vector. And the fitting and regularization constraints of the observed data are involved in the solution process, which can ensure that the solved inverse prior vector is more consistent with the actual density or magnetic anomaly, and at the same time play a role in eliminating false structures in the prior information.

[0066] S03: After the conclusion After that, the normalized optimized prior information values ​​of all unit cells can be obtained. Specifically, reconstructing the 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 value of all unit cells:

[0068]

[0069] in, For the The normalized optimized prior information value of each unit cell, and Respectively represent the minimum and maximum values ​​of the inverse prior vectors after optimization of all unit cells;

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

[0071]

[0072] in, is the optimized prior matrix;

[0073] S04: Iterative optimization of the prior matrix: using replace , and repeat steps S02 and S03 until Less than or equal to a set threshold; preferably, in a specific exemplary embodiment, according to the test results, the threshold can be set to ;

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

[0075] .

[0076] By solving the regularized 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, this exemplary embodiment patent innovatively proposes a method for obtaining density anomaly or magnetic anomaly vectors based on prior information optimization and reconstruction. Compared with traditional reference constraints, this method can flexibly apply various forms of prior constraints, and there is no need to convert prior information into density anomaly or magnetic anomaly parameters, thereby 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 erroneous information in the solved density anomaly or magnetic anomaly vector.

[0078] Additional explanation is needed:

[0079] (1) Traditional reference constraints, cross-gradient constraints, and Gramian constraints usually assume that the prior information is reliable and strongly correlated with density anomalies or magnetic anomalies. However, if this assumption is not true, misleading information will be introduced into the solution. In contrast, before obtaining the density anomaly vector and the magnetic anomaly vector, this exemplary embodiment optimizes and reconstructs any given prior matrix that may have errors to ensure its quality and applicability, and finally uses the optimized and reconstructed prior matrix for constraint to obtain the density anomaly or magnetic anomaly vector. This method is easy to implement and can be compatible with multiple types of prior information. It effectively reduces the risk of introducing false structures and significantly improves the reliability of the density or magnetic anomaly vector obtained.

[0080] (2) This exemplary embodiment adopts a dual objective function, which has the advantage that there is no direct and clear mapping relationship between the prior matrix and the gravity or magnetic survey data, and it is theoretically impossible to optimize it. To this end, this exemplary embodiment proposes a dual objective function, cleverly solves the inverse prior vector, and then reconstructs it to obtain the optimized prior matrix. In summary, with the help of the dual objective function, the 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, while eliminating false structures in the prior information.

[0081] Figure 2~Figure 5 The results of a simulation test for obtaining a density anomaly vector based on the optimization and reconstruction of the seismic velocity prior matrix are shown.

[0082] Attached Figure 2 is the gravity data curve, which represents the changes of observed data and fitted data; Figure 3 It is a seismic wave velocity image, which reveals the actual distribution characteristics of the wave velocity of the underground medium; Figure 4 is a real density anomaly vector image, reflecting the actual distribution of underground density anomalies. Figure 3 With attached Figure 4There are many significant differences between them, which are mainly reflected in: there is no clear direct mapping relationship between velocity and density anomaly, and they are neither simply proportional nor inversely proportional; in addition, in some areas, although the seismic 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 constraints are often difficult to implement effectively.

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

[0084] Therefore, the experiments show that this method greatly improves the accuracy and reliability of the solved density or magnetic anomaly vector.

[0085] Obviously, the above embodiments are merely examples for clear explanation, and are not intended to limit the implementation methods. For ordinary technicians in the relevant field, 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 methods here. The obvious changes or modifications derived from them are still within the protection scope of the invention.

Claims

1. A method for obtaining density anomaly or magnetic anomaly vector based on prior information optimization and reconstruction, characterized in that: The following steps are involved: S01: Constructing the initial prior matrix using prior information , including the following sub-steps: S0101: For the prior information, interpolation is used to obtain the original prior information values ​​of all units. ,in , M represents the number of elements of the density anomaly vector or magnetic anomaly vector to be solved; S0102: Calculate the normalized prior information value of all units: ； in, For the The normalized prior information value of the unit cell, and Respectively represent the minimum and maximum values ​​of the original prior information values ​​of all units; S0103: Construct the initial prior matrix: ； in, is the initial prior matrix, represents a diagonal matrix; S02: Using the initial prior matrix obtained in step S01 , solve the dual objective function to obtain the optimized inverse prior vector: ； in, is the kernel matrix, is the gravity data vector or magnetic 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, Solve the vector for the first objective function, A vector for solving the second objective function and representing the optimized inverse prior vector; S03: Reconstruct the optimized prior matrix, including the following sub-steps: S0301: Using the optimized inverse prior vector obtained in step S02, calculate the normalized optimized prior information value of all unit cells: ； in, For the The normalized optimized prior information value of each unit cell, and Respectively represent the minimum and maximum values ​​of the inverse prior vectors after optimization of all unit cells; S0302: Reconstruct the optimized prior matrix: ； in, is the optimized prior matrix; S04: Iterative optimization of the prior matrix: using replace , and repeat steps S02 and S03 until Less than or equal to the set threshold; S05: The optimized prior matrix Substitute the following formula to solve the density anomaly vector or magnetic anomaly vector : 。 2. The method for obtaining density anomaly or magnetic anomaly vector based on prior information optimization and reconstruction according to claim 1 is characterized in that: The prior information includes reflection coefficient, wave velocity or resistivity.

3. The method for obtaining density anomaly or magnetic anomaly vector based on prior information optimization and reconstruction according to claim 1 is characterized in that: The threshold value in step S04 is set to .

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