Magnetization intensity vector sparse inversion method under strong residual magnetism condition

Abstract

The invention belongs to the technical field of geophysics, and particularly discloses a magnetization intensity vector sparse inversion method under a strong residual magnetism condition. The method comprises the following steps: firstly, subdividing an underground space, and simulating an underground magnetic anomalous body; obtaining a sensitivity matrix according to partial derivatives of observed magnetic anomaly values of the magnetic anomaly body in each unit magnetization direction, and constructing a total objective function of magnetization intensity vector inversion based on the sensitivity matrix; taking magnetization intensity amplitude as a parameter to introduce sparse constraint for the total objective function; converting the total target function into a standard L2 regularization form, and calculating a sensitivity matrix by using a singular value analysis method so as to obtain target parameters of the total target function; and finally, obtaining three components of the magnetization intensity vector from the target parameters, and further solving the magnetization intensity amplitude and the total magnetization direction. According to the scheme, the magnetization intensity inversion precision under the influence of strong residual magnetization is effectively improved.

Description

Technical Field

[0001] The present application belongs to the field of geophysical technology, and more specifically, relates to a sparse inversion method for magnetization intensity vector under strong remanent magnetization conditions. Background Art

[0002] Remanent magnetization is a kind of inherent physical property commonly found in underground rocks and minerals. It is generally caused by the magnetization generated by the rocks and minerals during their formation under the influence of the geomagnetic field at that time and has been preserved to this day. Usually, the magnetic anomalies we observe are caused by the combined effect of induced magnetization and residual magnetization. Magnetization vector inversion is an important means of processing data containing remanent magnetization, which is used to infer the magnetization vector distribution of underground rocks or ore bodies from the observed magnetic field data. The magnetization vector includes magnitude and direction, which can more comprehensively describe the characteristics of magnetic bodies.

[0003] At present, in the case of data containing strong residual magnetization, the magnetization intensity vector inversion method is affected by multiple solutions. The inversion results have blurred magnetization intensity boundaries and dispersed magnetization directions, which leads to low inversion accuracy. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a sparse inversion method of magnetization intensity vector under strong residual magnetization conditions, which aims to solve the technical problem of insufficient magnetization intensity inversion accuracy under the influence of strong residual magnetization.

[0005] To achieve the above objectives, in a first aspect, the present application provides a method for sparse inversion of magnetization intensity vector under strong remanent magnetization conditions, which specifically includes: Dissect the underground space and simulate the underground magnetic anomaly; A sensitivity matrix is ​​obtained by partial derivatives of the observed magnetic anomaly values ​​of the magnetic anomaly body in each unit magnetization direction, and a total objective function of the magnetization intensity vector inversion is constructed based on the sensitivity matrix; Introducing a sparse constraint for the overall objective function by taking the magnetization amplitude as a parameter; The total objective function is transformed into a standard L2 regularized form, and the sensitivity matrix is ​​calculated using the singular value analysis method to obtain the target parameters of the total objective function; The three components of the magnetization intensity vector are obtained from the target parameters, and the magnetization intensity amplitude and the total magnetization direction are further solved.

[0006] Preferably, the sensitivity matrix is ​​specifically:

[0007] in, , , represents the three components of the magnetization intensity vector in the Cartesian coordinate system; 、 and A sensitivity matrix representing the three components; Indicates the magnetic anomaly value observed for underground magnetic anomalies.

[0008] Preferably, the magnetic anomaly value of the underground magnetic anomaly body is observed , obtained by the forward modeling formula of the three-dimensional rectangular block magnetic field.

[0009] Preferably, the overall objective function is:

[0010] in, is the observed magnetic anomaly value of the magnetic anomaly body, is the sensitivity matrix of the target parameter, which is obtained by combining the sensitivity matrices of the three components. is the target parameter, is the data weighting matrix, is the regularization parameter, is the known target parameter, represents the L2 norm, is the model weight matrix, , is the hard constraint matrix, represents the depth weighted term.

[0011] Preferably, the magnetization amplitude is used as a parameter to introduce a sparse constraint into the overall objective function, specifically: The L1-norm-based regularized minimum support functional is introduced into the overall objective function:

[0012] in, , , represents the magnetization amplitude, is the known magnetization amplitude, is a preset constant, is the order of the norm.

[0013] Preferably, the total objective function is converted into a standard L2 regularization form, and the sensitivity matrix is ​​calculated using a singular value analysis method to obtain the target parameters of the total objective function, specifically: The overall objective function is transformed into the standard L2 regularization form:

[0014] in, is the intermediate variable, , , is the regularization parameter, represents the L2 norm; is the data weighting matrix of the overall objective function, is the model weighting matrix of the overall objective function, represents the observed magnetic anomaly data, is the sensitivity matrix of the target parameter, which is obtained by combining the sensitivity matrices of the three components. is a known target parameter; Further deduction:

[0015] in, Represents matrix transpose; is the identity matrix; Perform singular value decomposition and get:

[0016] in, is the target parameter The order of It is The singular values ​​of the column, and is the singular value matrix and Through the singular value decomposition algorithm The obtained Column orthogonal singular vectors; The regularization parameter Substituting into the above formula, we get ,Will Substitute the following formula:

[0017] Get target parameters .

[0018] Preferably, the regularization parameter Solve by minimizing the following: .

[0019] Preferably, the three components of the magnetization intensity vector are obtained from the target parameters , and ; The magnetization amplitude is further solved as:

[0020] The total magnetization direction is further solved as:

[0021] in, is the magnetization amplitude, is the total magnetization inclination, is the total magnetization deflection.

[0022] In a second aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0023] In a third aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0024] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art: (1) This application introduces a regularized minimum support functional based on the L1 norm into the overall objective function of the magnetization vector inversion to make the solution sparse, thereby achieving magnetic modeling with clear boundaries and accurately recovering the magnetization vector from data affected by strong remanence.

[0025] (2) This application uses the singular value analysis method to avoid the computational consumption of large matrices and improve the computational efficiency. At the same time, the singular values ​​of the target matrix are used to accurately estimate the regularization parameters and improve the inversion accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a flow chart of the magnetization intensity inversion method provided in the embodiment of the present application.

[0027] Figure 2 It is the observed magnetic anomaly under the experimental model and theoretical conditions provided in the embodiments of the present application.

[0028] Figure 3 The embodiments of the present application provide methods for obtaining magnetization amplitude, vector three-dimensional modeling and total magnetization direction distribution diagram based on magnetic anomaly inversion.

[0029] Figure 4 It is a magnetic cross-section diagram drawn according to the magnetization intensity vector obtained by inversion provided in an embodiment of the present application.

[0030] Figure 5 It is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0032] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0033] like Figure 1 As shown, the embodiment of the present application includes the following steps: Step 1: Divide the underground space, assign magnetization intensity to some underground areas, simulate underground anomalies, and use analytical forward modeling to simulate observations to obtain magnetic anomaly values. Figure 2 , Figure 2 Part (a) is a three-dimensional schematic diagram of the underground magnetic body model. Figure 2 Part (b) is the magnetic anomaly response of the magnetic body model, which is calculated using the three-dimensional rectangular block magnetic field forward modeling formula.

[0034] In the test of the present embodiment, the survey lines are set to 41, and there are 41 survey points on each survey line, and the line distance and point distance are both set to 50m. The magnetization intensity of the magnetic body model is set to 2A / m, the total magnetization inclination angle and the magnetization declination angle are set to 56° and 24°, and the geomagnetic inclination angle and the geomagnetic declination angle are 90° and 90°, which means that the magnetic body model has the influence of significant remanent magnetism. The inversion area is set to the east-west distance of 1000m, the north distance of 1000m, and the depth of 500m. The underground grid in the x, y, and z directions is divided into 40, 40, and 20. The side length of each cube grid is 25m.

[0035] Step 2: Based on the underground space divided in the previous step, construct the sensitivity matrix of the three components of the magnetization intensity vector inversion. The geophysical meaning is the superposition of magnetic anomalies generated by the unit magnetization intensity at each grid point underground at the observation point:

[0036] in, represents the east-west component of the magnetization vector, represents the north-south component of the magnetization intensity vector, represents the perpendicular component of the magnetization vector; 、 and It represents the sensitivity matrix of the three components of the magnetization intensity vector with M×n dimensions (M is the number of observation data, and n is the number of grid cells); Indicates the magnetic anomaly value observed for underground magnetic anomalies.

[0037] According to the sensitivity matrix and magnetic anomaly values, the target parameters are assumed to be , using the reweighted least squares method to iteratively solve, the total objective function is constructed as:

[0038] in, is the sensitivity matrix of the target parameter, which consists of the three components of the sensitivity matrix 、 and Combined to get, is the data weighting matrix, is the regularization parameter, is the known target parameter, represents the L2 norm, Weight the model matrix:

[0039] in, It is a hard constraint matrix, which is used to adjust the weight of prior information when solving equations. If there is prior information, it is generally set to a large value, otherwise it is set to a unit matrix; represents the depth weighting term, which can prevent the distribution of the model from being too close to the surface. Specifically:

[0040] in, represents the underground grid depth, obtained in step 1, It represents the magnetic field attenuation constant, and its value is related to the attenuation rate of the magnetic field.

[0041] Step 3: Use the L1 norm as the minimum support functional. In the Cartesian coordinate system, if the three magnetization intensity vectors are solved independently, the weak correlation between the three components will be ignored, and the inversion result will have a large error. Therefore, in the inversion process, the square root of the sum of the squares of the three vectors, that is, the magnetization intensity amplitude, is used as a variable in the sparse matrix for solution. The constraints based on the L1 norm are as follows:

[0042]

[0043] in, is the known magnetization amplitude, is a very small constant, which is used to prevent the denominator from being 0. is the order of the norm, represents the target magnetization amplitude, where the three magnetization vector components , , In the underground j The magnetization intensity generated by a grid can be expressed as:

[0044] Model weight matrix of the overall objective function Expands to:

[0045] Step 4: The total objective function Converted to standard L2 regularization form:

[0046] in, is the intermediate variable, , , is the regularization parameter, represents the L2 norm; is the data weighting matrix of the overall objective function, is the model weighting matrix of the overall objective function, represents the observed magnetic anomaly data, is a known target parameter. In order to solve the above intermediate variables The total objective function is minimized, the partial derivative of the total objective function is calculated and set to 0, and the following expression is obtained:

[0047] in, Represents matrix transpose; is the unit matrix; according to the above derivation, the intermediate variable With the required parameters The relationship can be expressed as:

[0048] In summary, we only need to obtain the intermediate variables And prior information , we can get the target parameters According to the above formula, we can get Find ,right Performing singular value decomposition, we can get:

[0049] in, is the target parameter The order of It is The singular values ​​of the column, and is the singular value matrix and Through the singular value decomposition algorithm The obtained Column orthogonal singular vectors; The unbiased risk estimation (UPER) method is used to calculate the target value by minimizing the following objective function: .

[0050] Step 5: From the target parameters Get the three components of the magnetization vector from , , , extracting information from it can be used for geophysical quantitative analysis and solving the amplitude of magnetization intensity :

[0051] like Figure 3 As shown in part (a), the target magnetic body can be spatially located and its boundary estimated. Further, based on the angle between the three components of the magnetization intensity, the total magnetization direction can be equivalently calculated:

[0052] in, is the total magnetization inclination, is the total magnetization deflection. The vector modeling of the three-dimensional space is calculated as follows Figure 3 As shown in part (b), the total magnetization direction distribution is as follows Figure 3 Part (c) and Figure 3 As shown in part (d), the total magnetization direction can provide a basis for locating the lithogenesis and mineralization eras by comparing the tectonic movement period. Figure 4 In two-dimensional slices, the magnetic intensity vector information of the abnormal body in a specific orientation can be obtained to understand the magnetic structure of the abnormal internal space.

[0053] At this point, the sparse inversion of the magnetization intensity vector applied to the remanence data is completed.

[0054] It can be seen that the solution disclosed in the embodiment of the present application can provide a focused accurate solution when processing magnetic survey data containing significant residual magnetization intensity, and has the ability to restore the total magnetization direction information, which can provide richer magnetic information for subsequent geological research.

[0055] Based on the method in the above embodiment, the embodiment of the present application provides an electronic device, such as Figure 5 The system shown includes: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus. The processor can call the logic instructions in the memory to execute the method in the above embodiment.

[0056] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0057] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0058] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0059] It is understandable that the processor in the embodiment of the present application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, transistor logic devices, hardware components or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0060] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0061] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions may be transmitted from a website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)), etc.

[0062] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0063] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A sparse inversion method for magnetization intensity vector under strong remanent magnetization conditions, characterized in that: Specifically include: Dissect the underground space and simulate the underground magnetic anomaly; A sensitivity matrix is ​​obtained by partial derivatives of the observed magnetic anomaly values ​​of the magnetic anomaly body in each unit magnetization direction, and a total objective function of the magnetization intensity vector inversion is constructed based on the sensitivity matrix; Introducing a sparse constraint for the overall objective function by taking the magnetization amplitude as a parameter; The total objective function is transformed into a standard L2 regularized form, and the sensitivity matrix is ​​calculated using the singular value analysis method to obtain the target parameters of the total objective function; The three components of the magnetization intensity vector are obtained from the target parameters, and the magnetization intensity amplitude and the total magnetization direction are further solved.

2. The method for sparse inversion of magnetization intensity vector according to claim 1, characterized in that: The sensitivity matrix is ​​specifically: in, , , represents the three components of the magnetization intensity vector in the Cartesian coordinate system; 、 and A sensitivity matrix representing the three components; Indicates the magnetic anomaly value observed for underground magnetic anomalies.

3. The method for sparse inversion of magnetization intensity vector according to claim 1 or 2, characterized in that: The magnetic anomaly value observed by the underground magnetic anomaly , obtained by the forward modeling formula of the three-dimensional rectangular block magnetic field.

4. The method for sparse inversion of magnetization intensity vector according to claim 1, characterized in that: The overall objective function is: in, is the observed magnetic anomaly value of the magnetic anomaly body, is the sensitivity matrix of the target parameter, which is obtained by combining the sensitivity matrices of the three components. is the target parameter, is the data weighting matrix, is the regularization parameter, is the known target parameter, represents the L2 norm, is the model weight matrix, , is the hard constraint matrix, represents the depth weighted term.

5. The method for sparse inversion of magnetization intensity vector according to claim 1, characterized in that: The magnetization amplitude is used as a parameter to introduce a sparse constraint into the overall objective function, specifically: The L1-norm-based regularized minimum support functional is introduced into the overall objective function: in, , , represents the magnetization amplitude, is the known magnetization amplitude, is a preset constant, is the order of the norm.

6. The method for sparse inversion of magnetization intensity vector according to claim 1, characterized in that: The total objective function is transformed into a standard L2 regularization form, and the sensitivity matrix is ​​calculated using the singular value analysis method to obtain the target parameters of the total objective function, which are: The overall objective function is transformed into the standard L2 regularization form: in, is the intermediate variable, , , is the regularization parameter, represents the L2 norm; is the data weighting matrix of the overall objective function, is the model weighting matrix of the overall objective function, represents the observed magnetic anomaly data, is the sensitivity matrix of the target parameter, which is obtained by combining the sensitivity matrices of the three components. is a known target parameter; Further deduction: in, Represents matrix transpose; is the identity matrix; Perform singular value decomposition and get: in, is the target parameter The order of It is The singular values ​​of the columns, and is the singular value matrix and Through the singular value decomposition algorithm The obtained Column orthogonal singular vectors; The regularization parameter Substituting into the above formula, we get ,Will Substitute the following formula: Get target parameters .

7. The method for sparse inversion of magnetization intensity vector according to claim 6, characterized in that: The regularization parameter Solve by minimizing the following: 。 8. The method for sparse inversion of magnetization intensity vector according to claim 1, characterized in that: The three components of the magnetization vector are obtained from the target parameters. , and ; The magnetization amplitude is further solved as: The total magnetization direction is further solved as: in, is the magnetization amplitude, is the total magnetization inclination, is the total magnetization deflection.

9. An electronic device, characterized in that: include: at least one memory for storing a computer program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method according to any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program runs on a processor, the processor is caused to execute the method according to any one of claims 1 to 8.

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