Magnetic anomaly modulus reweighted inversion method and system under residual magnetism condition and storage medium

Abstract

The invention discloses a reweighted inversion method and system for a magnetic anomaly modulus under a residual magnetism condition and a storage medium, and belongs to the technical field of magnetic exploration, and the method comprises the following steps: converting the magnetic anomaly modulus to obtain the magnetic anomaly modulus; carrying out nonlinear forward modeling on the magnetic anomaly modulus; and linearizing a forward modeling formula of the magnetic anomaly modulus, constructing a reweighted minimum model objective function, solving the reweighted minimum model objective function, finally obtaining the magnetization intensity of an inversion space, and delineating a target geologic body. According to the scheme, the nonlinear forward modeling formula of the magnetic anomaly modulus is subjected to linear representation, and the sensitivity matrix serving as depth weighting is further updated by utilizing the magnetic anomaly modulus kernel function matrix updated along with iteration, so that the reweighting minimum model objective function is constructed, the precision of magnetic anomaly modulus inversion under the residual magnetism condition is improved, and the accuracy of the magnetic anomaly modulus inversion under the residual magnetism condition is improved. And a more reliable inversion result is provided for more accurate depiction of a deep magnetic structure, mineral resource exploration and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of magnetic exploration, and particularly relates to a method and system for reweighted inversion of magnetic anomaly modulus under remanent magnetization conditions. Background Art

[0002] As an important geophysical exploration method, magnetic exploration reveals magnetic structures, laws of mineral resources, etc. by observing and analyzing magnetic anomalies caused by magnetic differences of target bodies such as rocks and ores. Among them, the inversion of magnetization intensity is a key method for quantitative interpretation. Traditional magnetization intensity inversion is based on the assumption that the magnetization direction is consistent with the geomagnetic field direction, and the magnitude of magnetization intensity is inverted, which is applicable only in the case of only induced magnetization; however, when there is remanent magnetization, especially when the remanent magnetization is strong and the magnetization direction is quite different from the geomagnetic field direction, using traditional magnetization intensity inversion often results in a large deviation from the actual situation.

[0003] In the prior art, when there is remanent magnetization, the following methods are generally adopted: (1) The method of estimating the magnetization direction is used, such as the moment method of Helbig, the cross-correlation method, and the MAX-MIN method to estimate the total magnetization direction of the magnetic source, and then magnetic anomaly data is used for inversion, but these methods are more suitable for the inversion of isolated bodies; (2) Or data bodies less affected by the magnetization direction are used, such as the total gradient modulus (ASA), magnetic anomaly modulus (T a ) and normalized source strength (NSS) for inversion, and this kind of inversion is suitable for the inversion of complex magnetic anomaly bodies with multiple field sources; (3) It is also possible to directly perform magnetization intensity vector inversion. Since this kind of method is a direct inversion of the magnetization intensity vector, the inversion parameters are three times that of the magnetization intensity modulus inversion, so the problem of non-uniqueness is more serious, and the influence of the initial value on the inversion result is greater, and the introduced constraints are more and more complex than those in the magnetization intensity modulus inversion.

[0004] Therefore, when remanent magnetization cannot be ignored, data less affected by the magnetization direction is usually used for inversion, and its calculation is relatively simple and the result has a certain reliability. For the three converted data of ASA, T a , NSS, NSS is the least affected by the magnetization intensity method, but its calculation is complex. Next is T a with relatively simple calculation, while ASA is more affected by the magnetization intensity direction. Therefore, T a is often used for the inversion of magnetization intensity under remanent magnetization conditions. However, this kind of conversion quantity will eliminate the phase information contained in the original magnetic anomaly. Therefore, when using T a data for inversion, only the general position of the target body can be outlined, especially for the inversion of inclined target bodies, and it is difficult to determine the inclined shape of the inclined target body. This is because the magnetic anomaly modulus T a does not have a linear superposition relationship. Therefore, T aThe kernel function in data inversion is constructed based on the three components of the magnetic anomaly obtained by data transformation. The constructed kernel function plays an important role in the inversion result, making it impossible to determine the true occurrence of the target body in the inversion.

[0005] Aiming at the defects existing in the inversion of the magnetic anomaly modulus (T a ) under the remanence condition, it is urgent to develop a method that can update the kernel function with iteration and perform reweighted inversion based on the kernel function updated with iteration from the perspective of the kernel function, so as to improve the accuracy and reliability of the inversion of the magnetic anomaly modulus under the remanence condition. Summary of the Invention

[0006] In order to solve the problem that it is difficult to restore the true occurrence of the target body in the magnetization intensity inversion using the magnetic anomaly modulus in the prior art, the present invention proposes a method, system and storage medium for reweighted inversion of the magnetic anomaly modulus under the remanence condition. By linearly representing the non-linear forward formula of the magnetic anomaly modulus, using the magnetic anomaly modulus kernel function matrix updated with iteration to further update the sensitivity matrix as the depth weighting, a reweighted minimum model objective function is constructed to improve the accuracy and reliability of the inversion of the magnetic anomaly modulus under the remanence condition.

[0007] The present invention is implemented by the following technical solutions: A method for reweighted inversion of the magnetic anomaly modulus under the remanence condition includes the following steps:

[0008] Step S1, conversion of the magnetic anomaly modulus, to obtain the magnetic anomaly modulus of the input data for inversion;

[0009] Obtain the magnetic anomaly in the inversion target area, perform three-component conversion on the magnetic anomaly, calculate to obtain the magnetic anomaly modulus T a of the input data for inversion, and collect the elevation of the observation surface and the terrain elevation. The data are all input in the grid file (.grd) format;

[0010] Step S2, non-linear forward of the magnetic anomaly modulus: Determine the three-dimensional inversion space and perform upright hexahedron meshing. Forward the magnetic anomaly modulus caused by the meshing unit at the measurement point to obtain the non-linear forward expression of the magnetic anomaly modulus;

[0011] For the magnetic anomaly modulus obtained by processing in Step S1, determine the three-dimensional inversion space below the terrain and perform upright hexahedron meshing to obtain the meshing units of the inversion space. Among them, the horizontal coordinates of the center points of the meshing units correspond to the horizontal coordinates of the grid nodes of the observation network. Forward the magnetic anomaly modulus caused by the meshing unit at the measurement point, and compare the magnetic anomaly modulus T aij caused by the jth single meshing unit at the ith measurement point and the magnetic anomaly modulus T m caused by all N ai model units at the ith measurement point. There is That is, for the magnitude of magnetization, the magnetic anomaly modulus does not have a linear superposition relationship;

[0012] Step S3, linearized forward modeling: Linearize the forward modeling formula of the magnetic anomaly modulus, and construct the initial forward modeling kernel function matrix G (0) and the initial sensitivity matrix K (0) ;

[0013] Step S4, reweighted objective function: Update the forward modeling kernel function matrix G (k) and the sensitivity matrix K (k) with the number of iterations k of the solution, and construct the reweighted minimum model objective function;

[0014] Based on G (0) and K (0) obtained in step S3, update the forward modeling kernel function matrix G (k) and the sensitivity matrix K (k) used in the k-th iteration according to the iteration result of the (k - 1)-th time, so as to construct the reweighted minimum model objective function;

[0015] Step S5, solution of the reweighted objective function: For the reweighted objective function constructed in step S4, use the iteratively reweighted least squares algorithm to solve, and finally obtain the magnitude of magnetization in the inversion space to delineate the target geological body.

[0016] Furthermore, in step 2, the forward modeling formula of the magnetic anomaly modulus T aij caused by the j-th single subdivision unit at the i-th measuring point is:

[0017]

[0018] where H axij , H ayij and Z aij are the three components of the magnetic anomaly caused by the j-th single subdivision unit at the i-th measuring point respectively; m j represents the magnitude of magnetization of the j-th single subdivision unit; G xij , G yij and G zij are the kernel functions of the three components of the magnetic anomaly caused by the j-th single subdivision unit at the i-th measuring point respectively, which are only related to the distance between the j-th single subdivision unit and the i-th measuring point and have nothing to do with the magnitude of magnetization.

[0019] The forward modeling formula of the magnetic anomaly modulus T m caused by all N ai model units at the i-th measuring point is:

[0020]

[0021] This forward formula shows that, different from the magnetic anomaly and its three components, the magnetic anomaly modulus does not have a linear superposition relationship with the magnitude of magnetization, and

[0022] Furthermore, in the step 3, the forward kernel function matrix operator corresponding to the j-th single dissection unit at the i-th measurement point is calculated as follows:

[0023]

[0024] where T ai 、H axi 、H ayi and Z ai are the data of the i-th measurement point calculated after converting the known magnetic anomaly into three components; after determining the matrix operator , it is used as the element corresponding to the j-th row and the i-th column in the G (0) matrix, and then the initial forward kernel function matrix G (0) can be determined;

[0025] According to G (0) calculate the initial value of the sensitivity matrix K (0) as the depth weighting matrix; where the sensitivity matrix is a diagonal matrix of size N m ×N m , and the calculation formula of the sensitivity diagonal matrix operator corresponding to the j-th single dissection unit is:

[0026]

[0027] where N m is the number of measurement points. Similarly, after determining the element (0) corresponding to the j-th row and the j-th column in the initial sensitivity matrix K , the initial sensitivity matrix K (0) can be determined.

[0028] Furthermore, in the step 4, update the kernel function matrix G (k) at the k-th iteration; where the calculation formula of the kernel function matrix operator corresponding to the j-th single dissection unit at the i-th measurement point is:

[0029]

[0030] where, since the magnetic anomaly modulus and the magnitude of magnetization have a non-linear relationship, and are the values of the i-th measurement point calculated by forward calculation according to the results of the (k - 1)-th iteration;

[0031] Update the sensitivity matrix K at the k-th iteration (k) ; where the calculation formula for the sensitivity diagonal matrix operator corresponding to the j-th single dissection unit is:

[0032]

[0033] Construct the reweighted minimum model objective function; where the reweighted minimum model objective function at the k-th iteration can be expressed as:

[0034]

[0035] where is the data fitting objective function and the model constraint objective function at the k-th iteration, α is the regularization factor, and W d is the data fitting diagonal matrix, and T a represents the magnetic anomaly modulus vector, and m (k) represents the magnetization intensity magnitude vector to be solved at the k-th iteration.

[0036] Furthermore, in the step S5, the preconditioned conjugate gradient method is used to solve the reweighted minimum model objective function at the k-th iteration to obtain the result m at the k-th time (k) . Through this iterative process, until the given inversion accuracy is satisfied, the magnetization intensity magnitude in the inversion space is finally obtained to delineate the target geological body.

[0037] The present invention also provides a magnetic anomaly modulus reweighted inversion system under the remanence condition, including:

[0038] A magnetic anomaly modulus conversion module for obtaining the magnetic anomaly in the inversion target area, performing three-component conversion on the magnetic anomaly, and calculating the magnetic anomaly modulus T a to obtain the input data for inversion;

[0039] A magnetic anomaly modulus non-linear forward modeling module for determining the three-dimensional inversion space and performing upright hexahedron dissection, and forward modeling the magnetic anomaly modulus caused by the dissection unit at the measurement point to obtain a forward expression with a non-linear superposition relationship for the magnetization intensity magnitude;

[0040] A linearized forward modeling module for linearly expressing the non-linear forward expression to obtain the initial forward kernel function matrix G (0) , and calculating the initial value K of the sensitivity matrix as the depth-weighted diagonal matrix based on this (0) ;

[0041] A reweighted objective function construction module for constructing the reweighted minimum model objective function, where the forward kernel function matrix and the sensitivity matrix are updated to G with the number of iterations k of the solution (k)and K (k) ;

[0042] A reweighted objective function solving module, which is used to solve the objective function by using the iterative reweighted least squares algorithm, and finally obtain the magnitude of the magnetization in the inversion space to delineate the target geological body.

[0043] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned magnetic anomaly modulus reweighted inversion method under remanence conditions are realized.

[0044] The present invention also provides an intelligent terminal, including a memory, a processor, and a program stored on the memory and executable on the processor. When the program is loaded and executed by the processor, the magnetic anomaly modulus reweighted inversion method under remanence conditions as described above can be realized.

[0045] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0046] In this solution, the non-linear forward formula of the magnetic anomaly modulus is linearly represented, and the magnetic anomaly modulus kernel function matrix updated with iteration and the sensitivity matrix further updated as depth weighting are used to construct a reweighted minimum model objective function, so as to improve the inversion accuracy of the magnetic anomaly modulus under remanence conditions, and provide more reliable inversion results for more accurately depicting the deep magnetic structure and mineral resource exploration. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flowchart of the inversion method described in Embodiment 1 of the present invention;

[0048] Figure 2 is a schematic block diagram of the inversion system principle described in Embodiment 2 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] In order to more clearly understand the above objects, features and advantages of the present invention, the present invention will be further described below with reference to the accompanying drawings and embodiments. Many specific details are set forth in the following description in order to fully understand the present invention. However, the present invention may be implemented in other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below

[0050] Embodiment 1. In this embodiment, a magnetic anomaly modulus reweighted inversion method under remanence conditions is proposed, as Figure 1 shown, including the following steps:

[0051] Step S1, magnetic anomaly modulus conversion, to obtain the magnetic anomaly modulus T of the input data for inversion a ;

[0052] Obtain the magnetic anomaly in the inversion target area, perform three-component conversion on the magnetic anomaly, and calculate the magnetic anomaly modulus T of the input data for inversion. a Collect the elevation of the observation surface and the terrain elevation, and the data are all input in the format of grid files (.grd).

[0053] Step S2: Nonlinear forward modeling of the magnetic anomaly modulus.

[0054] For the magnetic anomaly modulus obtained in Step S1, determine the three-dimensional inversion space and perform upright hexahedron meshing. Forward model the magnetic anomaly modulus caused by the meshing elements at the measuring points to obtain the nonlinear forward expression of the magnetic anomaly modulus.

[0055] Step S3: Linear forward modeling: Linearize the nonlinear forward expression of the magnetic anomaly modulus, and construct the initial forward kernel function matrix G (0) and the initial sensitivity matrix K (0) ;

[0056] Step S4: Construct a reweighted objective function: Update the forward kernel function matrix G (k) and the sensitivity matrix K (k) with the iteration number k of the solution, and construct a reweighted minimum model objective function.

[0057] Step S5: Solve the reweighted objective function: For the reweighted objective function constructed in Step S4, use the iteratively reweighted least squares algorithm to solve, and finally obtain the magnitude of the magnetization in the inversion space to delineate the target geological body.

[0058] To understand the solution of the present invention more clearly, the following will introduce this embodiment in detail in combination with specific steps:

[0059] In Step S2, for the magnetic anomaly modulus obtained in Step S1, determine the three-dimensional inversion space below the terrain and perform upright hexahedron meshing to obtain the meshing elements of the inversion space. Among them, the horizontal coordinates of the center points of the meshing elements correspond to the horizontal coordinates of the grid nodes of the observation network. Forward model the magnetic anomaly modulus caused by the meshing elements at the measuring points, and compare the magnetic anomaly modulus T aij caused by the j-th single meshing element at the i-th measuring point with the magnetic anomaly modulus T m caused by all N ai model elements at the i-th measuring point. There is That is, for the magnitude of magnetization, the magnetic anomaly modulus does not have a linear superposition relationship.

[0060] Among them, the forward formula for the magnetic anomaly modulus T aij caused by the j-th single meshing element at the i-th measuring point is:

[0061]

[0062] Among them, H axij , H ayij and Z aij are the three components of the magnetic anomaly caused by the j-th single subdivision unit at the i-th measuring point, respectively; m j represents the magnitude of the magnetization intensity of the j-th single subdivision unit; G xij , G yij and G zij are the kernel functions of the three components of the magnetic anomaly caused by the j-th single subdivision unit at the i-th measuring point, respectively, which are only related to the distance between the j-th single subdivision unit and the i-th measuring point and have nothing to do with the magnitude of the magnetization intensity.

[0063] The forward formula for the modulus T m of the magnetic anomaly caused by all N ai model units at the i-th measuring point is:

[0064]

[0065] This forward formula indicates that, different from the magnetic anomaly and its three components, the modulus of the magnetic anomaly does not have a linear superposition relationship with the magnitude of the magnetization intensity, and Therefore, it is necessary to linearize this non-linear forward formula and, based on this, convert a non-linear inversion problem into a linear inversion problem, so as to solve it by numerical methods.

[0066] In step S3, the non-linear forward formula of T ai is linearized to obtain the initial forward kernel function matrix G (0) ; among them, the calculation formula for the forward kernel function matrix operator corresponding to the j-th single subdivision unit at the i-th measuring point is:

[0067]

[0068] Among them, T ai , H axi , H ayi and Z ai are the data of the i-th measuring point calculated after the three-component conversion of the known magnetic anomaly; after determining the matrix operator , it is used as the element corresponding to the j-th row and the i-th column in the G (0) matrix, and then the initial forward kernel function matrix G (0) can be determined.

[0069] Calculate the initial sensitivity matrix K (0) from G (0) as the depth weighting matrix; among them, the initial sensitivity matrix is N m ×N mThe diagonal matrix of size, and the sensitivity diagonal matrix operator corresponding to the j-th single subdivision unit The calculation formula is as follows:

[0070]

[0071] where N m is the number of measurement points. Similarly, after determining the element corresponding to the j-th row and j-th column in the initial sensitivity matrix K (0) , the initial sensitivity matrix K can be determined. (0) .

[0072] The constructed kernel function plays an important role in the inversion result. For the inversion of conventional T a data, the obtained initial forward kernel function matrix G (0) will not be updated with the number of inversion iterations. The initial sensitivity matrix K (0) used as the depth weighting matrix will also not be iteratively updated, resulting in the inability to correct the deviation between the initial forward kernel function matrix G (0) and the actual forward kernel function matrix. In this embodiment, starting from the perspective of the kernel function, the kernel function is iteratively updated to ensure that the inversion can more accurately determine the true occurrence of the target body.

[0073] In step S4, when constructing the reweighted objective function, the following specific method is adopted

[0074] Based on G (0) and K (0) obtained in step S3, the first inversion result m (0) is obtained by inversion. After that, the kernel function matrix G (k) for the k-th iteration is updated according to the (k - 1)-th iteration result; among them, the kernel function matrix operator corresponding to the j-th single subdivision unit at the i-th measurement point has the following calculation formula:

[0075]

[0076] where, since the magnetic anomaly modulus and the magnetization intensity are non-linear relationships, and are the values at the i-th measurement point obtained by forward calculation according to the (k - 1)-th iteration result, and the calculation formula is:

[0077]

[0078] Thus, based on the (k - 1)-th iteration result m (k-1) the kernel function matrix G (k) for the k-th iteration is updated to correct the deviation from the true kernel function matrix.

[0079] Update the sensitivity matrix K at the k-th iteration (k) ; where, the sensitivity diagonal matrix operator corresponding to the j-th single subdivision unit The calculation formula is:

[0080]

[0081] Construct the reweighted minimum model objective function; where, the reweighted minimum model objective function at the k-th iteration can be expressed as:

[0082]

[0083] where, is the data fitting item objective function and the model constraint item objective function at the k-th iteration, α is the regularization factor, W d is the data fitting diagonal matrix, m (k) represents the magnetization intensity magnitude vector to be solved at the k-th iteration.

[0084] Use the preconditioned conjugate gradient method to solve the reweighted minimum model objective function at the k-th iteration to obtain the result m at the k-th time (k) . Through this iterative process, until the given inversion accuracy is met, finally obtain the magnetization intensity magnitude in the inversion space and delineate the target geological body.

[0085] In this embodiment, by linearly representing the non-linear forward formula of the magnetic anomaly modulus, using the magnetic anomaly modulus kernel function matrix updated with iteration, and further updating the sensitivity matrix as depth weighting, the reweighted minimum model objective function is constructed, improving the accuracy of the magnetic anomaly modulus inversion under the remanence condition, and providing more reliable inversion results for more accurately depicting the deep magnetic structure, mineral resource exploration, etc.

[0086] Embodiment 2. This embodiment provides a reweighted inversion system for magnetic anomaly modulus under the remanence condition, as Figure 2 shown, including:

[0087] Magnetic anomaly modulus conversion module, used to obtain the magnetic anomaly in the inversion target area, perform three-component conversion on the magnetic anomaly, and calculate the magnetic anomaly modulus T a , so as to obtain the input data for inversion;

[0088] Magnetic anomaly modulus non-linear forward module, used to determine the three-dimensional inversion space and perform upright hexahedron subdivision, and perform forward calculation on the magnetic anomaly modulus caused by the subdivision unit at the measuring point to obtain a forward expression with a non-linear superposition relationship for the magnetization intensity magnitude; including:

[0089] Single subdivision unit for forward modeling of a single measurement point, used to construct the forward magnetic anomaly modulus T for a vertical hexahedron subdivision unit a ; among them, the forward formula for the magnetic anomaly modulus T caused by the j-th single subdivision unit at the i-th measurement point aij is:

[0090]

[0091] where H axij , H ayij and Z aij are respectively the three components of the magnetic anomaly caused by the j-th single subdivision unit at the i-th measurement point; m j represents the magnitude of the magnetization intensity of the j-th single subdivision unit; G xij , G yij and G zij are respectively the kernel functions of the three components of the magnetic anomaly caused by the j-th single subdivision unit at the i-th measurement point, which are only related to the distance between the j-th single subdivision unit and the i-th measurement point and have nothing to do with the magnitude of the magnetization intensity.

[0092] Forward modeling unit for multiple subdivision units with respect to a single measurement point, used to calculate the magnetic anomaly modulus T m caused by all N ai model units at the i-th measurement point; among them, the forward formula for T ai is:

[0093]

[0094] This forward formula indicates that, different from the magnetic anomaly and its three components, the magnetic anomaly modulus T ai does not have a linear superposition relationship with the magnitude of the magnetization intensity, and therefore, it is necessary to linearly express this non-linear forward formula and, based on this, convert a non-linear inversion problem into a linear inversion problem, so as to solve it using numerical methods.

[0095] Linearization forward module, used to linearly express the non-linear forward expression to obtain the initial forward kernel function matrix G (0) , and calculate the initial value K (0) of the sensitivity matrix as a depth-weighted diagonal matrix accordingly;

[0096] Kernel function matrix linearization unit, used to linearly express the non-linear forward expression to obtain the initial forward kernel function matrix G (0) ; among them, the calculation formula for the forward kernel function matrix operator corresponding to the j-th single subdivision unit at the i-th measurement point is:

[0097]

[0098] Among them, T ai , H axi , H ayi and Z ai are the data of the i-th measurement point calculated after performing three-component conversion on the known magnetic anomaly; furthermore, the initial forward kernel function matrix G (0) can be determined.

[0099] Sensitivity matrix linearization unit, used to calculate the initial value K (0) of the sensitivity matrix as the depth weighting matrix according to G (0) ; among them, the sensitivity matrix is a diagonal matrix of size N m ×N m , and the sensitivity diagonal matrix operator corresponding to the j-th single subdivision unit is calculated as follows:

[0100]

[0101] Among them, N m is the number of measurement points. Similarly, after determining the element (0) corresponding to the j-th row and j-th column in the initial sensitivity matrix K , the initial sensitivity matrix K (0) can be determined.

[0102] Reweighted objective function construction module, used to construct the reweighted minimum model objective function, where the forward kernel function matrix and the sensitivity matrix are updated to G (k) and K (k) with the number of iterations k of the solution; including:

[0103] Kernel function matrix update unit, used to update the kernel function matrix G (k) at the k-th iteration; among them, the kernel function matrix operator corresponding to the j-th single subdivision unit at the i-th measurement point is calculated as follows:

[0104]

[0105] Among them, since the magnetic anomaly modulus and the magnetization intensity have a non-linear relationship, and are the values of the i-th measurement point calculated by forward calculation based on the results of the (k - 1)-th iteration, and the calculation formula is:

[0106]

[0107] Thus, based on the iteration result m (k-1) of the (k - 1)-th time, the kernel function matrix G (k) at the k-th time is updated to correct the deviation from the true kernel function matrix.

[0108] A sensitivity matrix updating unit for updating the sensitivity matrix K at the k-th iteration (k) ; where the sensitivity diagonal matrix operator corresponding to the j-th single subdivision unit The calculation formula is:

[0109]

[0110] A reweighted objective function constructing unit for constructing a reweighted minimum model objective function. Where the reweighted minimum model objective function at the k-th iteration Can be expressed as:

[0111]

[0112] Where Is the data fitting item objective function and the model constraint item objective function at the k-th iteration, α is the regularization factor, and W d Is the data fitting diagonal matrix, and T a Represents the magnetic anomaly modulus vector, and m (k) Represents the magnetization intensity magnitude vector to be solved at the k-th iteration.

[0113] A reweighted objective function solving module for using the preconditioned conjugate gradient method to solve the reweighted minimum model objective function at the k-th iteration To obtain the result m of the k-th time (k) . Through this iterative process, until the given inversion accuracy is met, the magnetization intensity magnitude in the inversion space is finally obtained to delineate the target geological body.

[0114] Example 3. This example provides a computer-readable storage medium, on which a computer program is stored. The computer program, when executed by a processor, implements the steps in the method for reweighted inversion of magnetic anomaly modulus under remanent magnetization conditions described in Example 1.

[0115] Example 4. This example provides an intelligent terminal, including a memory, a processor, and a program stored on the memory and executable on the processor. When the program is loaded and executed by the processor, it can implement the method for reweighted inversion of magnetic anomaly modulus under remanent magnetization conditions as described in Example 1.

[0116] Those skilled in the art can clearly understand that for the convenience and simplicity of description, only the above division of each functional module is used for illustration. In actual applications, the above functions can be allocated to different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. The specific working processes of the systems, devices, and units described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated here.

[0117] In several embodiments provided in the present application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the division of the modules or units is only a logical function division, and there may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections to each other can be indirect couplings or communication connections through some interfaces, devices, or units, and can be in electrical, mechanical, or other forms. In addition, in each embodiment of the present application, the functional units can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above-mentioned integrated units can be implemented in the form of hardware or in the form of software functional units.

[0118] If the above-mentioned integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute all or part of the steps of the methods described in various embodiments of the present application. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories, random access memories, magnetic disks, or optical discs that can store program codes.

[0119] As mentioned above, the above are only the preferred embodiments of the present invention, and the present invention is not limited in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes and apply them to other fields. However, as long as it does not depart from the technical solution content of the present invention, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A reweighted inversion method for magnetic anomaly modulus under remanent magnetization conditions, characterized in that: The following steps are involved: Step S1, magnetic anomaly modulus conversion: obtaining the magnetic anomaly in the inversion target area, performing three-component conversion on the magnetic anomaly, and calculating the magnetic anomaly modulus; Step S2, nonlinear forward modeling of magnetic anomaly modulus: for the magnetic anomaly modulus obtained in step S1, determine the three-dimensional inversion space below the terrain and perform right hexahedron partitioning to obtain the partitioning unit of the inversion space, forward model the magnetic anomaly modulus caused by the partitioning unit at the measuring point, and obtain the nonlinear forward expression of the magnetic anomaly modulus; Step S3, linearized forward modeling: linearize the nonlinear forward modeling expression and construct the initial forward kernel function matrix G based on it (0) and the initial sensitivity matrix K (0) ; Step S4, construct a reweighted objective function; based on step S3, update the forward kernel function matrix G with the number of iterations k solved (k) And the sensitivity matrix K (k) , construct the reweighted minimum model objective function; Step S5: Analyze and solve the reweighted objective function to obtain the magnetization intensity of the inversion space and delineate the target geological body.

2. The magnetic anomaly modulus reweighted inversion method under residual magnetization conditions according to claim 1 is characterized in that: In the step S2, when performing nonlinear forward modeling, the horizontal coordinates of the center point of the subdivision unit correspond to the horizontal coordinates of the observation network grid nodes, and the magnetic anomaly modulus caused by the subdivision unit at the measuring point is forward modeled to obtain all N m The magnetic anomaly modulus T caused by the model unit to the i-th measuring point ai The forward expression of is as follows: Among them, H axi , H ayi and Z ai are the three components of magnetic anomaly caused by the i-th measuring point; m j represents the magnetization intensity of the jth single segmentation unit; G xij , G yij and G zij are the kernel functions of the three components of the magnetic anomaly caused by the jth single subdivision unit at the ith measuring point; and then the magnetic anomaly modulus T is determined. ai There is no linear superposition relationship for the magnitude of magnetization.

3. The magnetic anomaly modulus reweighted inversion method under residual magnetization conditions according to claim 1 is characterized in that: In step 3, the linearized forward modeling process is as follows: The initial forward kernel function matrix G (0) and the initial sensitivity matrix K (0) It is expressed as follows: (1) Construct the initial forward kernel function matrix G (0) ; The forward kernel function matrix operator corresponding to the jth single mesh element at the ith measurement point is It is expressed as: Among them, T ai , H axi , H ayi and Z ai is the data of the i-th measuring point calculated after three-component conversion of the known magnetic anomaly; determine the matrix operator After that, it is used as G (0) The element corresponding to the jth row and the ith column in the matrix is ​​used to determine the initial forward kernel function matrix G. (0) ; (2) According to the initial forward kernel function moment G (0) Construct the initial sensitivity matrix K (0) , as the depth weighting matrix; Among them, the sensitivity matrix is ​​N m ×N m The diagonal matrix of size, the sensitivity matrix operator corresponding to the j-th single subdivision unit It is expressed as: Among them, N m is the number of measuring points; determine the initial sensitivity matrix K (0) The element corresponding to the jth row and jth column in Then, the initial sensitivity matrix K is determined (0) .

4. The magnetic anomaly modulus reweighted inversion method under residual magnetization conditions according to claim 3 is characterized in that: In step S4, the specific process of constructing the reweighted objective function is as follows: (1) Update the kernel function matrix G at the kth iteration (k) , where the kernel function matrix operator corresponding to the jth single subdivision unit at the i-th measurement point is It is expressed as: Among them, since the magnetic anomaly modulus and the magnetization intensity are nonlinear, and is the value calculated based on the result of the k-1th iteration; (2) Update the sensitivity matrix K at the kth iteration (k) ; Among them, the sensitivity diagonal matrix operator corresponding to the j-th single subdivision unit is It is expressed as: (3) The reweighted objective function is constructed as follows: The reweighted minimum model objective function at the kth iteration It is expressed as: in, is the target function of the data fitting project and the target function of the model constraint project at k iterations, α is the regularization factor, W d is the data fitting diagonal matrix, m (k) Represents the magnetization intensity vector that needs to be solved for the kth iteration.

5. A magnetic anomaly modulus reweighted inversion system under remanent magnetism conditions, characterized in that: include: The magnetic anomaly modulus conversion module is used to obtain the magnetic anomaly in the inversion target area, perform three-component conversion on the magnetic anomaly, and calculate the magnetic anomaly modulus; The nonlinear forward modeling module of magnetic anomaly modulus is used to determine the three-dimensional inversion space and perform right hexahedron partitioning, and to perform forward modeling on the magnetic anomaly modulus caused by the partitioned unit at the measuring point, and obtain a forward modeling expression with a nonlinear superposition relationship on the magnetization intensity; A linearized forward modeling module is used to linearize the nonlinear forward modeling expression, obtain the initial forward kernel function matrix, and calculate the initial value of the sensitivity matrix as the depth-weighted diagonal matrix based on it; The reweighted objective function construction module uses the magnetic anomaly modulus kernel function matrix updated with iterations to further update the sensitivity matrix as depth weighting, thereby constructing the reweighted objective function. The reweighted objective function solving module is used to solve the reweighted objective function, obtain the magnetization intensity in the inversion space, and delineate the target geological body.

6. The magnetic anomaly modulus reweighted inversion system under residual magnetization conditions according to claim 5, characterized in that: The magnetic anomaly modulus nonlinear forward modeling module includes: The forward modeling unit of a single subdivision unit to a single measuring point is used to construct the forward modeling magnetic anomaly modulus of the right hexahedron subdivision unit, where the magnetic anomaly modulus T caused by the jth single subdivision unit at the i-th measuring point is aij The forward formula is: Among them, H axij , H ayij and Z aij are the three components of magnetic anomaly caused by the jth single segmentation unit at the i-th measuring point; m j represents the magnetization intensity of the jth single segmentation unit; G xij , G yij and G zij are the kernel functions of the three components of magnetic anomaly caused by the j-th single subdivision unit at the i-th measuring point; Multi-division unit forward modeling unit for a single measuring point is used to calculate all N m The magnetic anomaly modulus T caused by the model unit to the i-th measuring point ai ; Among them, T ai The forward modeling formula is: It can be known that the magnetic anomaly modulus T ai There is no linear superposition relationship for the magnitude of magnetization.

7. The magnetic anomaly modulus reweighted inversion system under residual magnetization conditions according to claim 5, characterized in that: The linearized forward modeling module comprises: The kernel function matrix linearization unit is used to linearize the nonlinear forward expression and obtain the initial forward kernel function matrix G. (0) ; Among them, the kernel function matrix operator corresponding to the j-th single subdivision unit at the i-th measurement point is The calculation formula is: Among them, T ai , H axi , H ayi and Z ai is the data of the i-th measuring point calculated after three-component conversion of the known magnetic anomaly; determine the matrix operator After that, it is used as G (0) The element corresponding to the jth row and the ith column in the matrix can then determine the initial forward kernel function matrix G (0) ; Sensitivity matrix linearization unit, used to calculate the sensitivity matrix linearization unit according to G (0) Calculate the initial value K of the sensitivity matrix (0) As the depth weighting matrix; where the sensitivity matrix is ​​N m ×N m The diagonal matrix of size, the sensitivity matrix operator corresponding to the j-th single subdivision unit The calculation formula is: Among them, N m is the number of measurement points, determine the initial sensitivity matrix K (0) The element corresponding to the jth row and jth column in Then, the initial sensitivity matrix K is obtained. (0) .

8. The magnetic anomaly modulus reweighted inversion system under residual magnetization conditions according to claim 5, characterized in that: The reweighted objective function building module includes: Kernel function matrix update unit, used to update the kernel function matrix G at the kth iteration (k) ; Among them, the kernel function matrix operator corresponding to the j-th single subdivision unit at the i-th measurement point is The calculation formula is: Among them, since the magnetic anomaly modulus and the magnetization intensity are nonlinear, and is the value of the i-th measuring point obtained by forward calculation based on the k-1-th iteration result; Sensitivity matrix update unit, used to update the sensitivity matrix K at the kth iteration (k) ; Among them, the calculation formula of the sensitivity diagonal matrix operator corresponding to the j-th single subdivision unit is: Reweighted objective function construction unit, used to construct the reweighted minimum model objective function Among them, the reweighted minimum model objective function at the kth iteration is It is expressed as: in, is the target function of the data fitting project and the target function of the model constraint project at k iterations, α is the regularization factor, W d is the data fitting diagonal matrix, T a represents the magnetic anomaly modulus vector, m (k) Represents the magnetization intensity vector that needs to be solved for the kth iteration.

9. A computer-readable storage medium, characterized in that: The invention stores a program which can be loaded and executed by a processor to implement the magnetic anomaly modulus reweighted inversion method under the residual magnetization condition as described in any one of claims 1 to 4.

10. An intelligent terminal, characterized in that: The invention comprises a memory, a processor and a program stored in the memory and capable of running on the processor, wherein the program can be loaded and executed by the processor to implement the magnetic anomaly modulus reweighted inversion method under the residual magnetization condition as described in any one of claims 1 to 4.

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