Method and apparatus for determining planetary lithospheric magnetic field model coefficient

Abstract

Provided in the present disclosure are a method and apparatus for determining a planetary lithospheric magnetic field model coefficient. The method comprises: acquiring at a magnetic-field observation point a vertical magnetic-field component which points to a planetary core and is represented by a spherical harmonic function; for the vertical magnetic-field component, obtaining a partial derivative in the geographical south direction, so as to determine a first linear representation corresponding to a spherical harmonic coefficient, and obtaining a partial derivative in the geographical east direction, so as to determine a second linear representation corresponding to the spherical harmonic coefficient; on the basis of the first linear representation and the second linear representation, determining the absolute value of a horizontal gradient corresponding to the vertical magnetic-field component to be a regular term; determining a third linear representation for the spherical harmonic coefficient corresponding to the regular term, and on the basis of the third linear representation, constructing a target function for solving a system of linear equations corresponding to a planetary lithospheric magnetic field model coefficient; and performing optimization processing on the target function, so as to determine a target model coefficient corresponding to the minimum value of the target function. The physical characteristics of a planetary lithospheric magnetic field model can be achieved while effectively solving the problem of model overfitting, and the accuracy of the calculation of a model coefficient is relatively high.

Description

Method and device for determining coefficients of a planetary lithospheric magnetic field model

[0001] Cross-reference to Related Applications

[0002] The present disclosure claims priority to the Chinese patent application No. 2024104244865, filed on April 10, 2024, and entitled "Method and device for determining coefficients of a planetary lithospheric magnetic field model", the entire content of which is incorporated herein by reference. TECHNICAL FIELD

[0003] The present disclosure relates to the technical field of planetary magnetic field detection, in particular to a method and device for determining coefficients of a planetary lithospheric magnetic field model. BACKGROUND

[0004] Currently, in the process of inverting the coefficients of a planetary lithospheric magnetic field model based on spherical harmonic function fitting, if the linear equation set is directly solved, the coefficients of high-order terms will have a serious overfitting phenomenon, which is manifested in that the power spectrum of the coefficients of high-order terms does not converge and is in a divergent state, which does not conform to the actual situation, and the model also models part of the noise, thus the overfitting phenomenon occurs.

[0005] In the process of model inversion, regularization needs to be performed, and a regularization term is added to the objective function to prevent the overfitting of the model after inversion. The regularization term in the inversion of the related planetary lithospheric magnetic field model is generally consistent with the regularization term in other optimization problems (such as machine learning), and the square sum of model coefficients or the square sum of its derivatives is selected. For example, the square sum of model parameters is used in the minimum model constraint; the square sum of model coefficient derivatives is used in the flattest model constraint; the square sum of second-order model coefficient derivatives is used in the smoothest model constraint, etc.

[0006] These regularization methods can effectively suppress the overfitting of the model, but if they are used as a universal regularization method for all model inversion problems, the physical characteristics of the planetary lithospheric magnetic field model are ignored, and the physical adaptability between the planetary lithospheric magnetic field model is poor.

[0007] SUMMARY

[0008] The embodiments of the present disclosure at least provide a method and device for determining coefficients of a planetary lithospheric magnetic field model, which can effectively solve the problem of model overfitting while meeting the physical characteristics of the planetary lithospheric magnetic field model, and the accuracy of the solution of the model coefficients is high.

[0009] The embodiments of the present disclosure provide a method for determining coefficients of a planetary lithospheric magnetic field model, which is applied to a planetary lithospheric magnetic field model based on spherical harmonic function fitting, and the method comprises:

[0010] a vertical magnetic field component represented by spherical harmonics is acquired, and a horizontal gradient absolute value of the vertical magnetic field component is determined according to the first linear expression and the second linear expression;

[0011] A first linear expression corresponding to spherical harmonics is determined by taking a partial derivative along a geographic south direction for the vertical magnetic field component, and a second linear expression corresponding to spherical harmonics is determined by taking a partial derivative along a geographic east direction for the vertical magnetic field component;

[0012] A horizontal gradient absolute value of the vertical magnetic field component is determined as a regular term according to the first linear expression and the second linear expression;

[0013] A third linear expression corresponding to the spherical harmonics is determined according to the regular term, and a target function for solving a linear equation set corresponding to planetary lithospheric magnetic field model coefficients is constructed according to the third linear expression;

[0014] Optimization processing is performed on the target function, and target model coefficients corresponding to a minimum value of the target function are determined.

[0015] In an optional implementation, the third linear expression corresponding to the spherical harmonics is determined according to the regular term, and specifically includes:

[0016] The regular term is subjected to Taylor expansion processing, and a corresponding Taylor expansion result is determined;

[0017] High-order small quantities corresponding to the Taylor expansion result are filtered;

[0018] A first-order term corresponding to the Taylor expansion result is determined as the third linear expression, where a coefficient corresponding to the first-order term is a linear coefficient corresponding to the third linear expression.

[0019] In an optional implementation, the target function is constructed based on the following steps:

[0020] The linear equation set is represented as a first expression for solving the planetary lithospheric magnetic field model coefficients;

[0021] The regular term is represented as a second expression for solving the planetary lithospheric magnetic field model coefficients;

[0022] A sum of the first expression and the second expression is determined as the target function.

[0023] In an optional implementation, the regular term is determined based on the following formula:

[0024] wherein, represents a horizontal gradient absolute value corresponding to the vertical magnetic field component, that is, the regular term; Z represents the vertical magnetic field component; θ represents a geographic south direction; and φ represents a geographic east direction.

[0025] In an alternative embodiment, the third linear representation is expressed based on the following formula:

[0026] wherein, represents the absolute value of the horizontal gradient corresponding to the vertical magnetic field component, i.e., the regularization term; Z represents the vertical magnetic field component; θ represents the geographic south direction; φ represents the geographic east direction; E represents the linear coefficient corresponding to the first linear representation; F represents the linear coefficient corresponding to the second linear representation; g represents the spherical harmonic coefficient; g0 represents the initial spherical harmonic coefficient corresponding to the planetary lithospheric magnetic field model without adding the regularization term.

[0027] In an alternative embodiment, the determination of the absolute value of the horizontal gradient corresponding to the vertical magnetic field component as the regularization term comprises:

[0028] An approximate integral of the absolute value of the horizontal gradient corresponding to the vertical magnetic field component is adopted as the regularization term.

[0029] In an alternative embodiment, the optimization processing on the target function to determine the target model coefficient corresponding to the minimum of the target function comprises:

[0030] A least square method algorithm is adopted to perform the optimization iteration processing on the target function to determine the model coefficient at the minimum of the target function as the target model coefficient.

[0031] The present disclosure also provides a planetary lithospheric magnetic field model coefficient determination device, which is applied to a planetary lithospheric magnetic field model based on spherical harmonic function fitting, and the device comprises:

[0032] A vertical magnetic field component acquisition module configured to acquire a vertical magnetic field component in a direction pointing to a planetary core of a magnetic field observation point expressed by a spherical harmonic function;

[0033] A linear representation module configured to, for the vertical magnetic field component, take a partial derivative along a geographic south direction to determine a first linear representation corresponding to a spherical harmonic coefficient, and take a partial derivative along a geographic east direction to determine a second linear representation corresponding to the spherical harmonic coefficient;

[0034] A regularization term determination module configured to determine, according to the first linear representation and the second linear representation, the absolute value of the horizontal gradient corresponding to the vertical magnetic field component as a regularization term;

[0035] A target function determination module configured to determine a third linear representation of the regularization term corresponding to the spherical harmonic coefficient, and construct a target function for solving a linear equation set corresponding to a planetary lithospheric magnetic field model coefficient according to the third linear representation;

[0036] A model coefficient determination module is configured to perform optimization processing on the target function to determine a target model coefficient corresponding to a minimum of the target function.

[0037] In an optional implementation, the target function determination module is specifically configured to:

[0038] perform Taylor expansion processing on the regular term to determine a corresponding Taylor expansion result;

[0039] filter a high-order small quantity corresponding to the Taylor expansion result;

[0040] determine a first-order term corresponding to the Taylor expansion result as the third linear representation, where a coefficient corresponding to the first-order term is a linear coefficient corresponding to the third linear representation.

[0041] In an optional implementation, the target function determination module is specifically configured to:

[0042] express the linear equation set as a first expression for solving the model coefficients of the planetary lithospheric magnetic field;

[0043] express the regular term as a second expression for solving the model coefficients of the planetary lithospheric magnetic field;

[0044] determine a sum of the first expression and the second expression as the target function.

[0045] In an optional implementation, the regular term determination module is specifically configured to use an approximate integral of an absolute value of a horizontal gradient of the vertical magnetic field component as the regular term.

[0046] In an optional implementation, the model coefficient determination module is specifically configured to perform optimization iteration processing on the target function by using a least square method algorithm to determine a model coefficient at which the target function is minimum as the target model coefficient.

[0047] The embodiments of the present disclosure further provide an electronic device, including a processor, a memory, and a bus, the memory stores machine readable instructions executable by the processor, when the electronic device is running, the processor and the memory communicate through the bus, and the machine readable instructions are executed by the processor to perform the method for determining the model coefficients of the planetary lithospheric magnetic field, or the steps in any possible implementation of the method for determining the model coefficients of the planetary lithospheric magnetic field.

[0048] The embodiment of the present disclosure further provides a computer readable storage medium, and the computer readable storage medium stores a computer program. When the computer program is executed by a processor, the steps of the method for determining a planetary lithospheric magnetic field model coefficient or the steps of any possible implementation of the method for determining a planetary lithospheric magnetic field model coefficient are performed.

[0049] The embodiment of the present disclosure further provides a computer program product, which comprises computer programs / instructions. When the computer programs / instructions are executed by a processor, the steps of the method for determining a planetary lithospheric magnetic field model coefficient or the steps of any possible implementation of the method for determining a planetary lithospheric magnetic field model coefficient are implemented.

[0050] The embodiment of the present disclosure provides a method and device for determining a planetary lithospheric magnetic field model coefficient. The vertical magnetic field component is represented by a spherical harmonic function by obtaining a magnetic field observation point pointing to the core direction of a planet. For the vertical magnetic field component, the partial derivative is taken along the geographic south direction to determine a first linear representation of the corresponding spherical harmonic coefficient, and the partial derivative is taken along the geographic east direction to determine a second linear representation of the corresponding spherical harmonic coefficient. The absolute value of the horizontal gradient of the vertical magnetic field component is determined as a positive term according to the first linear representation and the second linear representation. A third linear representation of the spherical harmonic coefficient corresponding to the positive term is determined, and a target function for solving a linear equation group of the planetary lithospheric magnetic field model coefficient is constructed according to the third linear representation. The target function is optimized to determine the target model coefficient corresponding to the minimum of the target function. The model overfitting problem can be effectively solved, the physical characteristics of the planetary lithospheric magnetic field model are met, and the solution accuracy of the model coefficient is high.

[0051] In order to make the above-mentioned purpose, features and advantages of the present disclosure more obvious and easy to understand, the following preferred embodiments are specifically described below, and the accompanying drawings are described in detail as follows. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the following will briefly introduce the drawings needed to be used in the embodiments. The drawings are incorporated into the specification and form a part of the specification. The drawings show the embodiments consistent with the present disclosure, and are used to illustrate the technical solutions of the present disclosure together with the specification. It should be understood that the following drawings only show some embodiments of the present disclosure, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor.

[0053] FIG. 1 shows a flowchart of a method for determining a planetary lithospheric magnetic field model coefficient according to an embodiment of the present disclosure;

[0054] FIG. 2 shows a flow chart of determining a third linear representation of spherical harmonic coefficients corresponding to a regularization term according to an embodiment of the present disclosure;

[0055] FIG. 3 shows a schematic diagram of a device for determining a planetary lithospheric magnetic field model coefficient according to an embodiment of the present disclosure;

[0056] FIG. 4 shows a schematic diagram of an electronic device according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0057] In order to make the objects, technical solutions and advantages of the embodiments of the present disclosure clearer, the following will be combined with the accompanying drawings for the embodiments of the present disclosure to make a clear and complete description of the technical solutions in the embodiments of the present disclosure. Obviously, the described embodiments are only a part of the embodiments of the present disclosure and not all the embodiments. The components of the embodiments of the present disclosure described and shown in the accompanying drawings can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present disclosure provided in the accompanying drawings is not intended to limit the scope of the claimed present disclosure, but only represents selected embodiments of the present disclosure. Based on the embodiments of the present disclosure, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present disclosure.

[0058] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0059] The term "and / or" herein only describes an association relationship and means that there can be three relationships, for example, A and / or B can mean that A exists alone, A and B exist together, and B exists alone. In addition, the term "at least one" herein means any one of a plurality or any combination of at least two of a plurality, for example, including at least one of A, B and C can mean including any one or more elements selected from the set consisting of A, B and C.

[0060] It is found through research that the regularization term in the related planetary lithospheric magnetic field model inversion is generally consistent with the regularization term in other optimization problems (such as machine learning), and the square sum of model coefficients or the square sum of its derivative is selected. For example, the square sum of model parameters is used in the minimum model constraint; the square sum of model coefficient derivatives is used in the flattest model constraint; the square sum of second-order model coefficient derivatives is used in the smoothest model constraint. These regularization methods can effectively suppress the overfitting of the model, but if they are used as a universal regularization method for all model inversion problems, the physical characteristics of the planetary lithospheric magnetic field model are ignored, and the physical adaptability between the planetary lithospheric magnetic field model is poor.

[0061] Based on the above research, the present disclosure provides a method and device for determining the coefficients of a planetary lithospheric magnetic field model. The vertical magnetic field component is expressed by a spherical harmonic function by obtaining the direction of the magnetic field observation point pointing to the core of the planet. For the vertical magnetic field component, the partial derivative is taken along the geographic south direction to determine the first linear representation of the corresponding spherical harmonic coefficient, and the partial derivative is taken along the geographic east direction to determine the second linear representation of the corresponding spherical harmonic coefficient. According to the first linear representation and the second linear representation, the positive term of the absolute value of the horizontal gradient of the vertical magnetic field component is determined. The third linear representation of the spherical harmonic coefficient corresponding to the positive term is determined, and the objective function for solving the linear equation set of the coefficients of the planetary lithospheric magnetic field model is constructed according to the third linear representation. The optimal processing is performed on the objective function to determine the target model coefficient corresponding to the minimum of the objective function. The model overfitting problem can be effectively solved, the physical characteristics of the planetary lithospheric magnetic field model are met, and the accuracy of the solution of the model coefficient is high.

[0062] To facilitate the understanding of the present embodiment, first, a method for determining the coefficients of a planetary lithospheric magnetic field model is described in detail. The execution subject of the method for determining the coefficients of a planetary lithospheric magnetic field model provided by the present embodiment is generally a computer device with certain computing power, which may, for example, include a terminal device or a server or other processing device. The terminal device may be a user equipment (User Equipment, UE), a mobile device, a user terminal, a terminal, a cellular phone, a cordless phone, a personal digital assistant (Personal Digital Assistant, PDA), a handheld device, a computing device, a vehicle-mounted device, a wearable device, etc. In some possible implementation manners, the method for determining the coefficients of a planetary lithospheric magnetic field model can be realized by a processor calling computer readable instructions stored in a memory.

[0063] Referring to FIG. 1, a flowchart of a method for determining the coefficients of a planetary lithospheric magnetic field model provided by the present embodiment is shown. The method includes steps S101-S105.

[0064] S101, obtaining the vertical magnetic field component expressed by a spherical harmonic function by obtaining the direction of the magnetic field observation point pointing to the core of the planet.

[0065] In a specific implementation, the lithospheric magnetic field of a target planet is observed at a selected magnetic field observation point, and the magnetic field component in the vertical downward direction, i.e., the vertical magnetic field component pointing to the core of the planet, is obtained in the spherical coordinate system of the planet magnetic field observation point.

[0066] Here, the vertical magnetic field component is expressed by a spherical harmonic function, which can be realized by the following formula:

[0067] wherein Z represents a vertical magnetic field component; represents a magnetic field along a unit vector e r direction component; e r represents a direction of a magnetic field observation point outward from a planetary core; r represents a distance from the observation point to the planetary core; φ represents a geographic longitude of the observation point; θ represents a geographic co-latitude of the observation point; respectively represent spherical harmonic coefficients; n represents a spherical harmonic function order, and takes a value range of 1, 2, … N; N represents a highest order; m represents a spherical harmonic function time, and takes a value range of 0, 1, … n; a represents a planetary radius; represents a Schmidt quasi-normalized form of associated Legendre function of n order and m time.

[0068] S102, for the vertical magnetic field component, partial derivation is taken along the geographic south direction to determine a first linear representation of corresponding spherical harmonic coefficients, and partial derivation is taken along the geographic east direction to determine a second linear representation of corresponding spherical harmonic coefficients.

[0069] In a specific implementation, the vertical magnetic field component expressed in the spherical harmonic function is taken partial derivation along the geographic south direction, and the vertical magnetic field component after the partial derivation is converted into a linear representation for the spherical harmonic coefficients, that is, the first linear representation; at the same time, the vertical magnetic field component expressed in the spherical harmonic function is taken partial derivation along the geographic east direction, and the vertical magnetic field component after the partial derivation is converted into a linear representation for the spherical harmonic coefficients, that is, the second linear representation.

[0070] Here, the first linear representation can be determined by the following formula:

[0071] wherein, represents the partial derivation of the vertical magnetic field component along the geographic south direction, that is, the first linear representation; Z represents the vertical magnetic field component; r represents the distance from the observation point to the planetary core; φ represents the geographic longitude of the observation point; θ represents the geographic co-latitude of the observation point; respectively represent spherical harmonic coefficients; g represents the spherical harmonic coefficients arranged in a column; E represents a linear coefficient matrix corresponding to the first linear representation. Alternatively, the second linear representation can be determined by the following formula:

[0072] wherein,

[0073] represents the partial derivation of the vertical magnetic field component along the geographic east direction, that is, the second linear representation; Z represents the vertical magnetic field component; r represents the distance from the observation point to the planetary core; φ represents the geographic longitude of the observation point; θ represents the geographic co-latitude of the observation point; respectively represent spherical harmonic coefficients; g represents the spherical harmonic coefficients arranged in a column; E represents a linear coefficient matrix corresponding to the first linear representation. ​The spherical harmonic coefficients arranged in a column; F represents a linear coefficient matrix corresponding to the second linear representation.

[0074] S103, determining, according to the first linear representation and the second linear representation, a horizontal gradient absolute value corresponding to the vertical magnetic field component as a positive term.

[0075] In a specific implementation, the absolute value of the horizontal gradient corresponding to the vertical magnetic field component is determined according to the partial derivative of the vertical magnetic field component along the geographic south direction, that is, the first linear representation, and the partial derivative of the vertical magnetic field component along the geographic east direction, that is, the second linear representation, and the absolute value of the horizontal gradient corresponding to the vertical magnetic field component is determined as a positive term for preventing model overfitting of the result after inversion.

[0076] Here, the positive term is determined based on the following formula:

[0077] Wherein, The absolute value of the horizontal gradient corresponding to the vertical magnetic field component, that is, the positive term; Z represents the vertical magnetic field component; θ represents the geographic south direction; and φ represents the geographic east direction.

[0078] Here, since the interplanetary magnetic field is mostly transverse near the planet, the radial component is very small, and therefore the magnetic field component corresponding to the direction of the planet's lithospheric magnetic field pointing to the core is least affected by the solar wind. In the embodiments of the present application, the absolute value of the horizontal gradient corresponding to the vertical magnetic field component is used as an approximation integral of the smoothness of the model, that is, the positive term.

[0079] Optionally, the result of the positive term constraint is to make the horizontal gradient of the magnetic field value of the vertical magnetic field component of the obtained model small, that is, the horizontal spatial variation of the vertical magnetic field component is relatively smooth, which is consistent with the true physical situation.

[0080] Here, since the lithospheric magnetic body has a certain spatial scale, the magnetic field generated thereby changes relatively smoothly in the horizontal direction and does not appear to be stepwise.

[0081] In this way, the regularization method proposed in the embodiments conforms to the real observation situation and has physical meaning, and is suitable for modeling the planet's lithospheric magnetic field.

[0082] S104, determining a third linear representation of the positive term corresponding to the spherical harmonic coefficients, and constructing a target function for solving a linear equation set of the planet's lithospheric magnetic field model coefficient according to the third linear representation.

[0083] In a specific implementation, since the absolute value of the horizontal gradient corresponding to the vertical magnetic field component is a nonlinear form of the spherical harmonic coefficient, it is necessary to convert the regularization term into a third linear representation, and construct a target function for solving the linear equation set corresponding to the planetary lithospheric magnetic field model coefficient by the inversion method through the linear representation.

[0084] Here, referring to FIG. 2, a flowchart for determining a third linear representation of a regularization term corresponding to a spherical harmonic coefficient provided by an embodiment of the present disclosure is shown, and the method comprises steps S201-S203, wherein:

[0085] S201, performing Taylor expansion processing on the regularization term to determine the corresponding Taylor expansion result.

[0086] S202, filtering the high-order small amount corresponding to the Taylor expansion result.

[0087] S203, determining the first-order term corresponding to the Taylor expansion result as the third linear representation, wherein the coefficient corresponding to the first-order term is the linear coefficient corresponding to the third linear representation.

[0088] In a specific implementation, the third linear representation of the regularization term corresponding to the spherical harmonic coefficient can be:

[0089] wherein, the absolute value of the horizontal gradient corresponding to the vertical magnetic field component, i.e. the regularization term; Z represents the vertical magnetic field component; θ represents the geographic south direction; φ represents the geographic east direction; E represents the linear coefficient matrix corresponding to the first linear representation; F represents the linear coefficient matrix corresponding to the second linear representation; R represents the linear coefficient matrix corresponding to the third linear representation; g represents the spherical harmonic coefficient; g0 represents the spherical harmonic coefficient solution without using the regularization term.

[0090] Optionally, the linear equation set for solving the planetary lithospheric magnetic field model coefficient is represented as a first expression for solving the planetary lithospheric magnetic field model coefficient; the regularization term is represented as a second expression for solving the planetary lithospheric magnetic field model coefficient; and the sum of the first expression and the second expression is determined as the target function.

[0091] Here, the target function can be represented by the following formula:

[0092] wherein, φ represents the target function; φ D represents the first expression for solving the planetary lithospheric magnetic field model coefficient; φ Rd represents the magnetic field observation value; g represents the spherical harmonic coefficient; R represents the linear coefficient matrix corresponding to the third linear representation; D represents the linear coefficient matrix corresponding to the planetary lithospheric magnetic field model linear equation set; W D d represents the magnetic field observation value; g represents the spherical harmonic coefficient; R represents the linear coefficient matrix corresponding to the third linear representation; D represents the linear coefficient matrix corresponding to the planetary lithospheric magnetic field model linear equation set; W R d represents the magnetic field observation value; g represents the spherical harmonic coefficient; R represents the linear coefficient matrix corresponding to the third linear representation; D represents the linear coefficient matrix corresponding to the planetary lithospheric magnetic field model linear equation set; W

[0093] S105, optimizing the target function to determine the target model coefficient corresponding to the minimum of the target function.

[0094] In specific implementation, the least square method or other algorithm is used to process the target function for optimal iterative processing, and the model coefficient corresponding to the minimum of the target function is determined as the target model coefficient.

[0095] The method for determining the planetary lithospheric magnetic field model coefficient provided by the embodiments of the present disclosure comprises the following steps: obtaining the vertical magnetic field component represented by the spherical harmonic function by pointing to the direction of the planet core at the magnetic field observation point; taking the partial derivative along the geographic south direction for the vertical magnetic field component to determine the first linear representation corresponding to the spherical harmonic coefficient, and taking the partial derivative along the geographic east direction to determine the second linear representation corresponding to the spherical harmonic coefficient; determining the horizontal gradient absolute value corresponding to the vertical magnetic field component as a regular term according to the first linear representation and the second linear representation; determining the third linear representation of the spherical harmonic coefficient corresponding to the regular term, constructing a target function for solving the linear equation set of the planetary lithospheric magnetic field model coefficient according to the third linear representation; and optimizing the target function to determine the target model coefficient corresponding to the minimum of the target function. The method can effectively solve the problem of model overfitting, meet the physical characteristics of the planetary lithospheric magnetic field model, and has high accuracy in solving the model coefficient.

[0096] Those skilled in the art can understand that the writing order of each step in the above method of the specific implementation manner does not mean a strict execution order and does not constitute any limitation on the implementation process, and the specific execution order of each step should be determined by its function and possible internal logic.

[0097] Based on the same inventive concept, the determination device of the planetary lithospheric magnetic field model coefficient corresponding to the determination method of the planetary lithospheric magnetic field model coefficient is also provided in the embodiments of the present disclosure. Since the principle of solving problems of the device in the embodiments of the present disclosure is similar to the above-mentioned determination method of the planetary lithospheric magnetic field model coefficient of the present disclosure, the implementation of the device can be referred to the implementation of the method, and the repeated parts will not be described here.

[0098] Please refer to Figure 3, which is a schematic diagram of a device for determining coefficients of a planetary lithospheric magnetic field model according to an embodiment of the present disclosure. As shown in Figure 3, the device 300 for determining coefficients of a planetary lithospheric magnetic field model according to an embodiment of the present disclosure comprises:

[0099] A vertical magnetic field component acquisition module 310 configured to acquire a vertical magnetic field component of a magnetic field observation point pointing towards a planetary core direction expressed in a spherical harmonic function.

[0100] A linear expression module 320 configured to, for the vertical magnetic field component, determine a first linear expression of corresponding spherical harmonic coefficients by taking a partial derivative along a geographic south direction, and determine a second linear expression of corresponding spherical harmonic coefficients by taking a partial derivative along a geographic east direction.

[0101] A regularization term determination module 330 configured to determine, according to the first linear expression and the second linear expression, a horizontal gradient absolute value corresponding to the vertical magnetic field component as a regularization term.

[0102] An objective function determination module 340 configured to determine a third linear expression of the spherical harmonic coefficients corresponding to the regularization term, and construct an objective function for solving a linear equation set corresponding to coefficients of a planetary lithospheric magnetic field model according to the third linear expression.

[0103] A model coefficient determination module 350 configured to perform optimization processing on the objective function to determine target model coefficients corresponding to a minimum of the objective function.

[0104] The processing flow of each module in the device and the interaction flow between the modules can be referred to the related description in the above method embodiments, which will not be described in detail here.

[0105] The device for determining coefficients of a planetary lithospheric magnetic field model according to an embodiment of the present disclosure acquires a vertical magnetic field component of a magnetic field observation point pointing towards a planetary core direction expressed in a spherical harmonic function, determines a first linear expression of corresponding spherical harmonic coefficients by taking a partial derivative along a geographic south direction for the vertical magnetic field component, and determines a second linear expression of corresponding spherical harmonic coefficients by taking a partial derivative along a geographic east direction, determines a horizontal gradient absolute value corresponding to the vertical magnetic field component as a regularization term according to the first linear expression and the second linear expression, determines a third linear expression of the spherical harmonic coefficients corresponding to the regularization term, and constructs an objective function for solving a linear equation set corresponding to coefficients of a planetary lithospheric magnetic field model according to the third linear expression, and performs optimization processing on the objective function to determine target model coefficients corresponding to a minimum of the objective function. The model overfitting problem can be effectively solved, the physical characteristics of the planetary lithospheric magnetic field model are met, and the accuracy of the solution of the model coefficients is high.

[0106] Corresponding to the determination method of the planetary lithospheric magnetic field model coefficient in FIG. 1, the embodiment of the disclosure also provides an electronic device 400, as shown in FIG. 4, which is a structural schematic diagram of the electronic device 600 provided by the embodiment of the disclosure, comprising:

[0107] The processor 41, the memory 42, and the bus 43; the memory 42 is configured to store execution instructions, including the internal memory 421 and the external memory 422; the internal memory 421 here is also called the internal memory, which is configured to temporarily store operation data in the processor 41 and exchange data with the external memory 422 such as a hard disk, and the processor 41 exchanges data with the external memory 422 through the internal memory 421; when the electronic device 400 is running, the processor 41 and the memory 42 communicate through the bus 43, so that the processor 41 executes the steps of the determination method of the planetary lithospheric magnetic field model coefficient in FIG. 1.

[0108] The embodiment of the disclosure also provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to perform the steps of the determination method of the planetary lithospheric magnetic field model coefficient described in the above method embodiment. Wherein, the storage medium can be a volatile or non-volatile computer readable storage medium.

[0109] The embodiment of the disclosure also provides a computer program product, which includes computer instructions, and the computer instructions are executed by a processor to perform the steps of the determination method of the planetary lithospheric magnetic field model coefficient described in the above method embodiment. For details, please refer to the above method embodiment, which will not be repeated here.

[0110] Among them, the above-mentioned computer program product can be realized by hardware, software or combination thereof. In one optional embodiment, the computer program product is specifically embodied as a computer storage medium, and in another optional embodiment, the computer program product is specifically embodied as a software product, such as software development kit (Software Development Kit, SDK) and the like.

[0111] Those skilled in the art can clearly understand that, for the convenience and brevity of the description, the specific working process of the apparatus described above can refer to the corresponding process in the foregoing method embodiment, and will not be repeated here. In several embodiments provided in the present disclosure, it should be understood that the disclosed apparatus and method can be implemented in other ways. The apparatus embodiments described above are only schematic. For example, the division of the units is only a logical function division, and another division can be made in actual implementation. For example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some communication interface, and can be electrical, mechanical or other forms.

[0112] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e. can be located in one place or distributed on a plurality of network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiment.

[0113] In addition, the functional units in each embodiment of the present disclosure can be integrated in one processing unit, or each unit can be physically present separately, or two or more units can be integrated in one unit.

[0114] If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a non-volatile computer readable storage medium executable by a processor. Based on this understanding, the technical solutions of the present disclosure or the part that contributes to the related art or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing 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 the various embodiments of the present disclosure. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various program code storage media.

[0115] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present disclosure, which are used to illustrate the technical solutions of the present disclosure, rather than limit the same. The protection scope of the present disclosure is not limited thereto. Although the present disclosure has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that any person skilled in the art can make modifications or easily think of changes to the technical solutions described in the foregoing embodiments, or make equivalent replacements to some of the technical features within the technical scope disclosed by the present disclosure. The modifications, changes or replacements do not cause the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present disclosure, and should be covered within the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be subject to the protection scope of the claims. Industrial applicability

[0116] With the above scheme, the model overfitting problem can be effectively solved, the physical characteristics of the planetary lithospheric magnetic field model are met, and the accuracy of the solution of the model coefficients is high.

Claims

1. A method for determining the coefficients of a planetary lithosphere magnetic field model, characterized in that: Applied to a planetary lithosphere magnetic field model based on spherical harmonic function fitting, the method comprises: Obtain the vertical magnetic field component expressed as a spherical harmonic function when the magnetic field observation point points to the planet's core; For the vertical magnetic field component, taking a partial derivative along the geographic south direction to determine a first linear representation of the corresponding spherical harmonic coefficient, and taking a partial derivative along the geographic east direction to determine a second linear representation of the corresponding spherical harmonic coefficient; determining, based on the first linear representation and the second linear representation, an absolute value of a horizontal gradient corresponding to the vertical magnetic field component as a regularization term; Determining a third linear representation of the spherical harmonic coefficients corresponding to the regularization term, and constructing an objective function for solving a system of linear equations corresponding to the coefficients of the planetary lithosphere magnetic field model based on the third linear representation; Optimizing the objective function to determine the target model coefficient corresponding to the minimum objective function.

2. The method for determining the coefficients of the planetary lithosphere magnetic field model according to claim 1, characterized in that: Determining a third linear representation of the spherical harmonic coefficients corresponding to the regularization term specifically includes: Performing Taylor expansion processing on the regularization term to determine a corresponding Taylor expansion result; Filtering the high-order small quantities corresponding to the Taylor expansion results; Determine that the first-order term corresponding to the Taylor expansion result is the third linear representation, wherein the coefficient corresponding to the first-order term is the linear coefficient corresponding to the third linear representation.

3. The method for determining the coefficients of the planetary lithosphere magnetic field model according to claim 1, wherein: Construct the objective function based on the following steps: Representing the linear equations as a first expression for solving the coefficients of the planetary lithosphere magnetic field model; Representing the regularization term as a second expression for solving the coefficients of the planetary lithosphere magnetic field model; The sum of the first expression and the second expression is determined as the objective function.

4. The method for determining the coefficients of the planetary lithosphere magnetic field model according to claim 1, wherein: The regularization term is determined based on the following formula: in, represents the absolute value of the horizontal gradient corresponding to the vertical magnetic field component, that is, the regularization term; Z represents the vertical magnetic field component; θ represents the geographic south direction; Represents the geographical east direction.

5. The method for determining the coefficients of the planetary lithosphere magnetic field model according to claim 1, wherein: The third linear representation is expressed based on the following formula: in, represents the absolute value of the horizontal gradient corresponding to the vertical magnetic field component, that is, the regularization term; Z represents the vertical magnetic field component; θ represents the geographic south direction; Represents the geographic easting; E represents the linear coefficient corresponding to the first linear representation; F represents the linear coefficient corresponding to the second linear representation; g represents the spherical harmonic coefficient; g0 represents the initial spherical harmonic coefficient corresponding to the planetary lithosphere magnetic field model when the regularization term is not added.

6. The method for determining the coefficients of the planetary lithosphere magnetic field model according to claim 1, wherein: The determining the absolute value of the horizontal gradient corresponding to the vertical magnetic field component as a regularization term includes: The approximate integral of the absolute value of the horizontal gradient corresponding to the vertical magnetic field component is used as the regularization term.

7. The method for determining the coefficients of the planetary lithosphere magnetic field model according to claim 1, wherein: The optimizing process for the objective function to determine the target model coefficient corresponding to the minimum objective function includes: The objective function is optimized iteratively using a least squares algorithm, and the model coefficient when the objective function is minimized is determined as the target model coefficient.

8. A device for determining the coefficients of a planetary lithosphere magnetic field model, characterized in that: Applied to a planetary lithosphere magnetic field model based on spherical harmonic function fitting, the device comprises: a vertical magnetic field component acquisition module configured to acquire a vertical magnetic field component represented by a spherical harmonic function when the magnetic field observation point points to the direction of the planetary core; a linear representation module configured to take a partial derivative of the vertical magnetic field component along the geographic south direction to determine a first linear representation of the corresponding spherical harmonic coefficients, and take a partial derivative along the geographic east direction to determine a second linear representation of the corresponding spherical harmonic coefficients; a regularization term determination module configured to determine, based on the first linear representation and the second linear representation, an absolute value of a horizontal gradient corresponding to the vertical magnetic field component as a regularization term; an objective function determination module configured to determine a third linear representation of the regularization term corresponding to the spherical harmonic coefficients, and construct an objective function for solving a system of linear equations corresponding to the coefficients of the planetary lithosphere magnetic field model based on the third linear representation; The model coefficient determination module is configured to perform optimization processing on the objective function and determine the target model coefficient corresponding to the minimum of the objective function.

9. The device for determining the coefficients of the planetary lithosphere magnetic field model according to claim 8, characterized in that: The objective function determination module is specifically configured to: Performing Taylor expansion processing on the regularization term to determine a corresponding Taylor expansion result; Filtering the high-order small quantities corresponding to the Taylor expansion results; Determine that the first-order term corresponding to the Taylor expansion result is the third linear representation, wherein the coefficient corresponding to the first-order term is the linear coefficient corresponding to the third linear representation.

10. The device for determining the coefficients of the planetary lithosphere magnetic field model according to claim 8, characterized in that: The objective function determination module is specifically configured to: Representing the linear equations as a first expression for solving the coefficients of the planetary lithosphere magnetic field model; Representing the regularization term as a second expression for solving the coefficients of the planetary lithosphere magnetic field model; The sum of the first expression and the second expression is determined as the objective function.

11. The device for determining the coefficients of the planetary lithosphere magnetic field model according to claim 8, characterized in that: The regularization term determination module is specifically configured to use the approximate integral of the absolute value of the horizontal gradient corresponding to the vertical magnetic field component as the regularization term.

12. The device for determining the coefficients of the planetary lithosphere magnetic field model according to claim 8, characterized in that: The model coefficient determination module is specifically configured to use a least squares algorithm to perform iterative optimization processing on the objective function, and determine the model coefficient when the objective function is minimized as the target model coefficient.

13. An electronic device, characterized in that: include: A processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the steps of the method for determining the coefficients of the planetary lithosphere magnetic field model as described in any one of claims 1 to 7 are performed.

14. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of the method for determining the coefficients of the planetary lithosphere magnetic field model according to any one of claims 1 to 7.

15. A computer program product, characterized in that The method comprises a computer program or an instruction, which, when executed by a processor, implements the steps of the method for determining the coefficients of the planetary lithosphere magnetic field model as described in any one of claims 1 to 7.

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