Gravimetric field data downward continuation method and system based on high-order ABM prediction correction

Abstract

The application discloses a kind of based on high-order ABM prediction correction gravity and magnetic field data downward continuation method and system, comprising: the measured gravity and magnetic field data extension on observation surface;When measured gravity and magnetic field data contains gravity and magnetic field vertical first derivative, gravity and magnetic field vertical first derivative extension;When not containing, calculate gravity and magnetic field vertical first derivative on observation surface;Gravity and magnetic field vertical first derivative is upward continuation, and the gravity and magnetic field vertical first derivative on seven heights above observation surface is obtained;Based on gravity and magnetic field data, gravity and magnetic field vertical first derivative and the gravity and magnetic field vertical first derivative of seven heights, enter AB prediction format, downward continuation initial value;The vertical first derivative of gravity and magnetic field data downward continuation initial value is calculated;Gravity and magnetic field data, the vertical first derivative of downward continuation initial value and the gravity and magnetic field vertical first derivative of six heights are used, enter AM correction format, and the final value of gravity and magnetic field data downward continuation is obtained.The processing scheme of the present application can improve the result accuracy.

Description

Technical Field

[0001] This invention relates to the field of gravity and magnetic field measurement technology, and in particular to a method and system for downward extension of gravity and magnetic field data based on high-order ABM prediction correction. Background Technology

[0002] Downward continuation of gravity and magnetic field data, a common technique for data processing and interpretation, involves converting gravity and magnetic field data within the observation plane to a value below the observation plane. Its main functions include: compensating for insufficient data due to limitations in observation conditions, providing a three-dimensional database for auxiliary navigation systems such as missiles and submarines; for measurement problems in areas difficult to access (deserts, swamps, dense forests, high mountains, and other complex terrains), downward continuation of airborne gravity and magnetic field data above the ground can directly improve resolution; since it does not alter the physical properties of the original data, downward continuation is a crucial step in subsequent data processing and interpretation; and for addressing the equivalence and superposition effects of gravity and magnetic fields, downward continuation can highlight shallow and local source information and separate lateral superposition anomalies.

[0003] Although downward continuation of gravity and magnetic fields plays a vital role and holds significant importance, it remains a research hotspot and challenge due to its ill-posed nature. Downward continuation spatial domain interpolation methods are computationally complex and lack precision. Conventional downward continuation FFT methods not only suffer from high-frequency amplification effects in the downward continuation factor, but also experience high-frequency oscillations in the continuation results due to discretization and truncation errors in the Fourier transform. Improvements to conventional downward continuation FFT methods, such as regularization, generalized inverse methods, and matched filtering, while enhancing stability, limit the downward continuation depth (generally not exceeding 5 times the point spacing). Downward continuation integral iteration methods can achieve stable downward continuation with noise-free data and large point spacing, but the poor approximation effect of the initial iteration formula and the large number of iterations lead to reduced computational efficiency and noise accumulation. Downward continuation Adams-Bashforth and Milne methods are based on numerical solutions using the mean value theorem of differential equations, utilizing measured vertical first derivatives. A stable, accurate, computationally efficient, and noise-amplified downward continuation formula was established using numerical solutions to differential equations. However, the measured vertical first derivative of the gravity and magnetic field is not easily obtained, which poses a challenge to the application of the corresponding downward continuation method. To address the problem of insufficient measured vertical first derivative, Zhang Chong et al. proposed a downward continuation technique using a fourth-order explicit Milne scheme combined with a fourth-order implicit Simpson scheme in 2019. In this technique, the required vertical first derivative is calculated using the ISVD method with a second-order central difference. However, the accuracy of the fourth-order numerical solution method is not high. To obtain a higher-order method, Zhang Chong et al. proposed a downward continuation of aeromagnetic data in 2020 using an eighth-order Adams-Bashforth explicit scheme and an ISVD method with a second-order central difference.

[0004] The technique proposed by Zhang Chong et al. in 2020 is closest to this invention. This existing technique first uses the ISVD method with second-order central difference to obtain the vertical first derivative of the magnetic field on the same observation surface from the magnetic field data; then it uses the frequency domain upward continuation method to obtain the gravitational field and its vertical first derivative at different heights, and obtains the downward continuation result through the eighth-order Adams-Bashforth display format. This existing technique, while ensuring the stability, depth and high computational efficiency of downward continuation, solves the problem of the original Adams-Bashforth method (2017) which requires actual measurement of the vertical first derivative and thus lacks universality by calculating the vertical first derivative through the ISVD method.

[0005] To address the shortcomings of downward continuation, such as computational complexity, process instability, small continuation depth, lack of universality, and inaccurate results, this paper utilizes the existing technology of downward continuation proposed by Zhang Chong et al. in 2020, which uses the eighth-order Adams-Bashforth explicit scheme and the ISVD method containing second-order central difference, to achieve the characteristics of simple computation, stable process, large depth, and universality of downward continuation.

[0006] However, this existing technique has shortcomings. First, the Adams-Bashforth formula used for downward continuation in the existing technique is an eighth-order explicit scheme, with a truncation error of [missing information]. Where ω is an unknown constant on the interval (z0, z0+h), and h 9 This represents the step size h raised to the power of 9. This represents the ninth vertical derivative of the magnetic field u(x,y,ω).

[0007] Therefore, it is evident that the existing downward continuation methods described above still have inconveniences and shortcomings in use, and urgently need further improvement. How to create a new downward continuation method for gravity and magnetic field data has become a pressing goal for the industry. Summary of the Invention

[0008] In view of this, the present disclosure provides a method for downward extrapolation of gravity and magnetic field data based on high-order ABM prediction correction, which at least partially solves the problems existing in the prior art.

[0009] In a first aspect, embodiments of this disclosure provide a method for downward extrapolation of gravity and magnetic field data based on high-order ABM prediction correction, the method comprising the following steps:

[0010] The measured gravity and magnetic field data on the observation surface are expanded using the regional field method to obtain the expanded gravity and magnetic field data to be used on the observation surface.

[0011] Determine whether the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field; wherein, if the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field, expand the margin of the vertical first derivative of the gravity and magnetic field to obtain the expanded vertical first derivative of the gravity and magnetic field to be used on the observation surface; and,

[0012] When the measured gravity and magnetic field data on the observation surface do not include the vertical first derivative of the gravity and magnetic field, the vertical first derivative of the gravity and magnetic field to be used on the observation surface after the expansion is calculated using the ISVD method based on the gravity and magnetic field data to be used on the observation surface after the expansion.

[0013] The vertical first derivative of the gravity magnetic field to be used on the expanded observation surface is extended upward to obtain the vertical first derivative of the gravity magnetic field at seven different heights above the observation surface.

[0014] The gravity and magnetic field data to be used on the expanded observation surface, the first vertical derivative of the gravity and magnetic field to be used on the expanded observation surface, and the first vertical derivatives of the gravity and magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, and 7h) above the observation surface are used as input quantities. These are then substituted into the eighth-order AB prediction format in the downward extension of the eighth-order ABM prediction correction to obtain the initial value of the downward extension of the gravity and magnetic field data; where h is the preset extension height.

[0015] The vertical first derivative of the initial value of the downward extension of the gravity and magnetic field data was calculated using the ISVD method.

[0016] Using the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data for downward extension, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface, the input quantities of the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction are constructed. Based on the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction, the final value of the downward extension of the gravity and magnetic field data is obtained.

[0017] According to a specific implementation of this disclosure, the input quantities for the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction are constructed using the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data extended downward, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface. This is achieved through the following formula:

[0018]

[0019] Where x and y are the coordinates on the X-axis and Y-axis, which are perpendicular to each other in the horizontal east-west and north-south directions, respectively; z is the coordinate on the Z-axis, which is perpendicular to the horizontal plane, with upward Z-axis being positive; z0 is the coordinate on the Z-axis, which is the vertical coordinate of the observation surface, with upward Z-axis being positive; h is a positive number representing the extension height, -h for downward extension and +h for upward extension; u(x,y,z0-h) is the final value of the downward extension of the gravity and magnetic field data calculated by the eighth-order AM correction scheme; u(x,y,z0) is the gravity and magnetic field data at height z0, i.e., the gravity and magnetic field data on the observation surface; u z ′(x,y,z0-h) represents the vertical first derivative of the initial values ​​of the downward extension of the gravity and magnetic field data; u z (x,y,z0) represents the first vertical derivative of the gravity and magnetic field on the observation surface; u z (x,y,z0+h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height h above the observation surface; u z (x,y,z0+2h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 2h from the observation surface; u z (x,y,z0+3h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 3h from the observation surface; u z (x,y,z0+4h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 4h above the observation surface; u z (x,y,z0+5h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 5h from the observation surface; u z (x,y,z0+6h) is the vertical first derivative of the magnetic field extending upwards by 6h above the observation surface.

[0020] According to a specific implementation of this disclosure, the process of expanding the measured gravity and magnetic field data on the observation surface using the regional field method is achieved through the following formula:

[0021] (1)

[0022] ZK(i,j)=ZY(i,1)+(1-j)·g(i),(1≤i≤m,1-n'≤j≤0)

[0023] (2)

[0024] ZK(i,j)=ZY(i,n)+(jn)·g(i),(1≤i≤m,n+1≤j≤n+n')

[0025] (3)

[0026] ZK(i,j)=ZY(1,j)+(1-i)·g(j),(1-m'≤i≤0,1-n'≤j≤n+n')

[0027] (4)

[0028] ZK(i,j)=ZY(m,j)+(im)·g(j),(m+1≤i≤m+m',1-n'≤j≤n+n')

[0029] Where ZY(i,k) represents the gravity and magnetic field data of the i-th row and k-th column on the observation surface before edge expansion; ZY(i,k+1) represents the gravity and magnetic field data of the i-th row and k+1-th column on the observation surface before edge expansion; ZY(i,n-k+1) represents the gravity and magnetic field data of the i-th row and n-k+1-th column on the observation surface before edge expansion; ZY(i,nk) represents the gravity and magnetic field data of the i-th row and nk-th column on the observation surface before edge expansion; ZY(i,n) represents the gravity and magnetic field data of the i-th row and n-th column on the observation surface before edge expansion; ZY(k,j) represents the gravity and magnetic field data of the k-th row and j-th column on the observation surface before edge expansion; ZY(k+1,j) represents the gravity and magnetic field data of the k+1-th row and j-th column on the observation surface before edge expansion; ZY(1,j) represents the gravity and magnetic field data of the i ... ZY(m-k+1,j) represents the gravity and magnetic field data in the first row and j column of the observation surface before edge expansion; ZY(m-k+1,j) represents the gravity and magnetic field data in the (m-k+1)th row and j column of the observation surface before edge expansion; ZY(mk,j) represents the gravity and magnetic field data in the (mk)th row and j column of the observation surface before edge expansion; ZK(i,j) represents the gravity and magnetic field data in the first row and j column of the observation surface after edge expansion; m and n represent the number of points and lines in the horizontal direction of the spatial domain (x) and the horizontal direction of the spatial domain (y) perpendicular to x; m' and n' are the lengths of the edge expansion in the x and y directions; satisfying ZK(i,j)=ZY(i,j), (1≤i≤m,1≤j≤n); g(i) and g(j) are intermediate variables for convenient edge expansion calculation.

[0030] According to a specific implementation of this disclosure, the step of calculating the vertical first derivative of the gravity and magnetic field on the expanded observation surface using the ISVD method based on the gravity and magnetic field data to be used on the expanded observation surface includes the following steps:

[0031] The gravity and magnetic potential data v(x,y,z0) corresponding to the measured gravity and magnetic field data u(x,y,z0) on the observation surface are calculated using the wavenumber domain conversion method, and are achieved through the following formula:

[0032]

[0033] Where v(x,y,z0) represents the gravity and magnetic potential data at height z0 on the observation surface; u(x,y,z0) represents the gravity and magnetic field data at height z0 on the observation surface; x,y are the spatial domain plane coordinates; k x ,k y Represents the wavenumber domain coordinates corresponding to the spatial domain coordinates x, y; Indicates the positive Fourier transform; Show the inverse Fourier transform; Represents the wavenumber domain vertical integral operator;

[0034] The horizontal second derivative of the gravity and magnetic potential data v(x,y,z0) was calculated using the fourth-order central difference method:

[0035]

[0036] Among them, v xx v represents the second derivative of the gravity and magnetic potential data at height z0 on the observation surface along the X-axis; yy Δx and Δy represent the second derivative of the gravity and magnetic potential data at height z0 on the observation surface in the Y-axis direction; Δx and Δy represent the sampling interval in the horizontal direction.

[0037] The vertical second derivative of the gravity and magnetic potential data v(x,y,z0) is calculated using the Laplace equation:

[0038] u z (x,y,z0)=v zz (x,y,z0)

[0039] =-[v xx (x,y,z0)+v yy (x,y,z0)].

[0040] Among them, u z (x,y,z0) is the vertical second derivative of the gravity and magnetic potential data v(x,y,z0); v zz (x,y,z0) represents the second derivative of the gravity and magnetic potential data at height z0 on the observation surface in the Z-axis direction.

[0041] According to a specific implementation of this disclosure, the step of extending the vertical first derivative of the gravity magnetic field to be used on the expanded observation surface upward to obtain seven vertical first derivatives of the gravity magnetic field at different heights above the observation surface includes:

[0042] The conversion formula for gravity and magnetic field data at different altitudes is as follows:

[0043]

[0044] Where u(x,y,z0+h) is the final value of the upward extension of the gravity and magnetic field data; ξ,η are another representation of the coordinates x,y; h is a positive number representing the extension height;

[0045] The upward continuation method in the wavenumber domain obtained by performing a Fourier transform on the data conversion relationships at different altitudes is as follows:

[0046]

[0047] Among them, U(k) x ,k x ,z0) is the wavenumber domain representation of u(x,y,z0); For wavenumber domain upward extension operators;

[0048] The vertical first derivatives of the gravity magnetic fields at the seven different heights are, for extensions of h, 2h, 3h, 4h, 5h, 6h, and 7h, respectively:

[0049]

[0050] According to a specific implementation of this disclosure, the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, and 7h) above the observation surface are used as input quantities. These are then substituted into the eighth-order AB prediction format in the downward continuation of the eighth-order ABM prediction correction to obtain the initial value for the downward continuation of the gravity and magnetic field data. This is achieved through the following formula:

[0051]

[0052] Where u′(x,y,z0-h) is the initial value for downward extension of the gravity and magnetic field data calculated by the eighth-order AB prediction scheme; u(x,y,z0) is the gravity and magnetic field data at height z0, i.e., the gravity and magnetic field data on the observation surface; h is a positive number representing the extension height; u z (x,y,z0) represents the first vertical derivative of the gravity and magnetic field on the observation surface; u z (x,y,z0+h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height h above the observation surface; u z (x,y,z0+2h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 2h from the observation surface; u z (x,y,z0+3h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 3h from the observation surface; u z (x,y,z0+4h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 4h above the observation surface; u z (x,y,z0+5h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 5h from the observation surface; u z (x,y,z0+6h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 6h above the observation surface; u z (x,y,z0+7h) is the vertical first derivative of the magnetic field extending upwards at a height of 7h above the observation surface.

[0053] Secondly, embodiments of this disclosure provide a gravity and magnetic field data downward continuation system based on high-order ABM prediction correction, the system comprising:

[0054] The margin expansion module is configured to expand the measured gravity and magnetic field data on the observation surface using the region field method, obtaining the expanded gravity and magnetic field data to be used on the observation surface; and,

[0055] Determine whether the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field; wherein, if the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field, expand the margin of the vertical first derivative of the gravity and magnetic field to obtain the expanded vertical first derivative of the gravity and magnetic field to be used on the observation surface; and,

[0056] When the measured gravity and magnetic field data on the observation surface do not include the vertical first derivative of the gravity and magnetic field, the vertical first derivative of the gravity and magnetic field to be used on the observation surface after the expansion is calculated using the ISVD method based on the gravity and magnetic field data to be used on the observation surface after the expansion.

[0057] The extension module is configured to extend the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface upwards, obtaining the vertical first derivatives of the gravity and magnetic field at seven different heights above the observation surface; and,

[0058] The gravity and magnetic field data to be used on the expanded observation surface, the first vertical derivative of the gravity and magnetic field to be used on the expanded observation surface, and the first vertical derivatives of the gravity and magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, and 7h) above the observation surface are used as input quantities. These are then substituted into the eighth-order AB prediction format in the downward continuation of the eighth-order ABM prediction correction to obtain the initial values ​​for the downward continuation of the gravity and magnetic field data; where h is the preset continuation height; and...

[0059] The vertical first derivative of the initial values ​​of the downward extension of the gravity and magnetic field data was calculated using the ISVD method; and,

[0060] Using the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data for downward extension, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface, the input quantities of the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction are constructed. Based on the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction, the final value of the downward extension of the gravity and magnetic field data is obtained.

[0061] Thirdly, embodiments of this disclosure also provide an electronic device, the electronic device comprising:

[0062] At least one processor; and,

[0063] A memory communicatively connected to the at least one processor; wherein,

[0064] The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, cause the at least one processor to perform the gravity magnetic field data downward extension method based on high-order ABM prediction correction as described in any of the aforementioned first aspects or any implementation thereof.

[0065] Fourthly, embodiments of this disclosure also provide a non-transitory computer-readable storage medium storing computer instructions that, when executed by at least one processor, cause the at least one processor to perform the gravity and magnetic field data downward extrapolation method based on higher-order ABM prediction correction in the first aspect or any implementation thereof.

[0066] Fifthly, embodiments of this disclosure also provide a computer program product, the computer program product including a computing program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, which, when executed by a computer, cause the computer to execute the gravity magnetic field data downward continuation method based on high-order ABM prediction correction in the first aspect or any implementation thereof.

[0067] The gravity and magnetic field data downward extension method based on high-order ABM prediction correction in this embodiment realizes the reduction process (downward extension) of gravity and magnetic field data from aerial observations to the ground and even the passive space below the ground. Under the premise of ensuring computational efficiency, downward extension to a large depth (greater than 10 times the point spacing) and stability, it improves the accuracy of downward extension and has an enhanced effect on satellite and airborne gravity and magnetic field data, thereby realizing a refined improvement in the interpretation of satellite and airborne gravity and magnetic field data. Attached Figure Description

[0068] The above is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0069] Figure 1 A schematic flowchart of a method for downward continuation of gravity and magnetic field data based on high-order ABM prediction correction provided in this embodiment of the present disclosure;

[0070] Figure 2 This is a schematic diagram illustrating the distribution of a synthetic cuboid model of an underground geological body that generates gravity field data, provided in an embodiment of this disclosure.

[0071] Figure 3This embodiment of the present disclosure provides a schematic diagram of the gravity field data of the ground surface when the downward continuation depth is 8 meters. (a) represents the theoretical gravity field data when the observation surface is the ground surface; (b) represents the theoretical gravity field data when the observation surface is 8 meters below the ground surface; (c) represents the downward continuation using the FFT method; (d) represents the downward continuation using the integral iteration method; (e) represents the downward continuation using the Milne method; (f) represents the downward continuation using the Milne-Simpson prediction correction method; (g) represents the downward continuation using the Adams-Bashforth method; and (h) represents the downward continuation using the Adams-Bashforth-Moulton prediction correction method.

[0072] Figure 4 A schematic diagram of a downward continuation structure for gravity and magnetic field data based on high-order ABM prediction correction provided in this disclosure embodiment; and

[0073] Figure 5 A schematic diagram of an electronic device provided in an embodiment of this disclosure. Detailed Implementation

[0074] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0075] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0076] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0077] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0078] Compared to this application, existing technologies have larger computational errors. Currently, the truncation error of the eighth-order explicit Adams-Bashforth (AB) method is greater than that of the equivalent-order implicit Moulton method. Therefore, using the Adams-Bashforth-Moulton (ABM) prediction and correction method, which consists of explicit and implicit methods, for downward continuation will improve the accuracy of the downward continuation results. Secondly, the finite difference method used in the ISVD method for calculating derivatives in this existing technology is a second-order central difference, but the fourth-order central difference has higher accuracy. Finally, although the numerical solution method in this existing technology has no obvious boundary effects, since it involves upward continuation calculations at multiple heights, without edge expansion processing, it will cause significant inaccuracies in the results. However, the region field edge expansion method can solve this problem to some extent.

[0079] To address the shortcomings of existing technologies, a downward extension method for gravity and magnetic field data is proposed, based on the eighth-order Adams-Bashforth-Moulton prediction correction and the fourth-order central difference ISVD derivative solution.

[0080] Terminology Explanation:

[0081] Gravity and magnetic field data: a collective term for gravity field data and geomagnetic field data.

[0082] Downward extension: The process of determining the gravity and magnetic field values ​​on a lower surface based on the measured values ​​of the gravity and magnetic field on a plane or curved surface.

[0083] Adams-Bashforth-Moulton (ABM) prediction correction: In this invention, it refers to the Adams-Bashforth-Moulton scheme in the numerical solution of ordinary differential equations.

[0084] Vertical gradient: also known as vertical derivative, in this invention it refers to the vertical first derivative of the potential field.

[0085] Integrated second vertical derivative (ISVD) method: In this invention, ISVD refers to the method for calculating the vertical derivatives of the gravity and magnetic fields.

[0086] Wavenumber domain: In this invention, it refers to the space in which the result obtained by Fourier transforming spatial domain data resides.

[0087] Central difference: This is a method of finite difference. The finite difference method is a numerical method for finding the boundary value problems of partial differential (or ordinary differential) equations and systems of equations.

[0088] Figure 1 This is a schematic diagram of the process of a downward extrapolation method for gravity and magnetic field data based on high-order ABM prediction correction provided in an embodiment of this disclosure.

[0089] like Figure 1 As shown, in step S110, the measured gravity and magnetic field data on the observation surface are expanded using the regional field method to obtain the expanded gravity and magnetic field data to be used on the observation surface.

[0090] More specifically, the measured gravity and magnetic field data on the observation surface are expanded using the region field method. The expanded gravity and magnetic field data u(x,y,z0) to be used on the observation surface are obtained, where x,y,z0 represent the coordinates of the horizontal X-axis, Y-axis and vertical Z-axis, respectively, and z0 is a specific value of the vertical coordinate z, which represents the height (depth) of the observation surface. The vertical coordinate Z-axis is positive when it is vertically upward.

[0091] In this embodiment of the invention, the process of expanding the measured gravity and magnetic field data on the observation surface using the regional field method is achieved through the following formula:

[0092] (1)

[0093] ZK(i,j)=ZY(i,1)+(1-j)·g(i),(1≤i≤m,1-n'≤j≤0)

[0094] (2)

[0095] ZK(i,j)=ZY(i,n)+(jn)·g(i),(1≤i≤m,n+1≤j≤n+n')

[0096] (3)

[0097] ZK(i,j)=ZY(1,j)+(1-i)·g(j),(1-m'≤i≤0,1-n'≤j≤n+n')

[0098] (4)

[0099] ZK(i,j)=ZY(m,j)+(im)·g(j),(m+1≤i≤m+m,1-n≤j≤n+n')

[0100] Where ZY(i,k) represents the gravity and magnetic field data of the i-th row and k-th column on the observation surface before edge expansion; ZY(i,k+1) represents the gravity and magnetic field data of the i-th row and k+1-th column on the observation surface before edge expansion; ZY(i,n-k+1) represents the gravity and magnetic field data of the i-th row and n-k+1-th column on the observation surface before edge expansion; ZY(i,nk) represents the gravity and magnetic field data of the i-th row and nk-th column on the observation surface before edge expansion; ZY(i,n) represents the gravity and magnetic field data of the i-th row and n-th column on the observation surface before edge expansion; ZY(k,j) represents the gravity and magnetic field data of the k-th row and j-th column on the observation surface before edge expansion; ZY(k+1,j) represents the gravity and magnetic field data of the k+1-th row and j-th column on the observation surface before edge expansion; ZY(1,j) represents the gravity and magnetic field data of the i ... ZY(m-k+1,j) represents the gravity and magnetic field data in the first row and j column of the observation surface before edge expansion; ZY(m-k+1,j) represents the gravity and magnetic field data in the (m-k+1)th row and j column of the observation surface before edge expansion; ZY(mk,j) represents the gravity and magnetic field data in the (mk)th row and j column of the observation surface before edge expansion; ZK(i,j) represents the gravity and magnetic field data in the first row and j column of the observation surface after edge expansion; m and n represent the number of points and lines in the horizontal direction of the spatial domain (x) and the horizontal direction of the spatial domain (y) perpendicular to x; m' and n' are the lengths of the edge expansion in the x and y directions; satisfying ZK(i,j)=ZY(i,j), (1≤i≤m,1≤j≤n); g(i) and g(j) are intermediate variables for convenient edge expansion calculation.

[0101] More specifically, we now proceed to step S120.

[0102] In step S120, it is determined whether the measured gravity magnetic field data on the observation surface contains the first vertical derivative of the gravity magnetic field; wherein, when the measured gravity magnetic field data on the observation surface contains the first vertical derivative of the gravity magnetic field, the first vertical derivative of the gravity magnetic field is expanded to obtain the first vertical derivative of the gravity magnetic field to be used on the observation surface after expansion.

[0103] More specifically, it is determined whether the vertical first derivative data of the gravity magnetic field has been measured on the observation surface. If measured vertical first derivative data of the gravity magnetic field exists, the edge expansion process is performed as in step S110, and the vertical first derivative of the gravity magnetic field to be used on the observation surface after edge expansion is obtained as the measured value u. z (x,y,z0).

[0104] Next, proceed to step S130.

[0105] In step S130, when the measured gravity magnetic field data on the observation surface does not include the vertical first derivative of the gravity magnetic field, the vertical first derivative of the gravity magnetic field to be used on the expanded observation surface is calculated using the ISVD method based on the gravity magnetic field data to be used on the expanded observation surface.

[0106] More specifically, if there are no measured values ​​of the vertical first derivative of the gravity and magnetic field on the observation surface, the vertical first derivative value u of the gravity and magnetic field to be used on the observation surface after expansion is calculated using the Integrated Second Vertical Derivative (ISVD) method, which is based on the fourth-order central difference. z (x,y,z0).

[0107] In this embodiment of the invention, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface is calculated using the ISVD method based on the gravity and magnetic field data to be used on the expanded observation surface, including the following steps:

[0108] The gravity and magnetic potential data v(x,y,z0) corresponding to the measured gravity and magnetic field data u(x,y,z0) on the observation surface are calculated using the wavenumber domain conversion method, and are achieved through the following formula:

[0109]

[0110] Where v(x,y,z00) represents the gravity and magnetic potential data at height z0 on the observation surface; u(x,y,z0) represents the gravity and magnetic field data at height z0 on the observation surface; x,y are the spatial domain plane coordinates; k x ,k y Represents the wavenumber domain coordinates corresponding to the spatial domain coordinates x, y; Indicates the positive Fourier transform; Show the inverse Fourier transform; Represents the wavenumber domain vertical integral operator;

[0111] Secondly, the horizontal second derivative of the gravity and magnetic potential data v(x,y,z0) is calculated using the fourth-order central difference method:

[0112]

[0113] Among them, v xx v represents the second derivative of the gravity and magnetic potential data at height z0 on the observation surface along the X-axis; yy Δx and Δy represent the second derivative of the gravity and magnetic potential data at height z0 on the observation surface in the Y-axis direction; Δx and Δy represent the sampling interval in the horizontal direction.

[0114] The vertical second derivative of the gravity and magnetic potential data v(x,y,z0) is calculated using the Laplace equation:

[0115]

[0116] Among them, u z (x,y,z0) is the vertical second derivative of the gravity and magnetic potential data v(x,y,z0); v zz(x,y,z0) represents the second derivative of the gravity and magnetic potential data at height z0 on the observation surface in the Z-axis direction.

[0117] Next, proceed to step S140.

[0118] In step S140, the vertical first derivative of the gravity magnetic field to be used on the expanded observation surface is extended upward to obtain seven vertical first derivatives of the gravity magnetic field at different heights above the observation surface.

[0119] More specifically, the vertical first derivative data (obtained by measurement or calculation) of the gravity and magnetic field at the observation surface. z Extending (x, y, z0) upwards, we obtain the vertical first derivatives u of the gravity and magnetic fields at seven different heights above the observation surface. z (x,y,z0+h),u z (x,y,z0+2h),u z (x,y,z0+3h),u z (x,y,z0+4h),u z (x,y,z0+5h),u z (x,y,z0+6h),u z (x,y,z0+7h) data.

[0120] In this embodiment of the invention, the vertical first derivative of the gravity magnetic field to be used on the expanded observation surface is extended upward to obtain seven vertical first derivatives of the gravity magnetic field at different heights above the observation surface, including:

[0121] The conversion formula for gravity and magnetic field data at different altitudes is as follows:

[0122]

[0123] Where u(x,y,z0+h) is the final value of the upward extension of the gravity and magnetic field data; ξ,η are another representation of the coordinates x,y; h is a positive number, representing the extension height; the z-axis is positive upwards, so the upward extension is +h;

[0124] To facilitate integral calculations, a Fourier transform is performed on the data conversion relationships at different heights in Formula 4 to obtain the upward extension method in the wavenumber domain:

[0125]

[0126] Among them, U(k) x ,k x ,z0) is the wavenumber domain representation of u(x,y,z0); For wavenumber domain upward extension operators;

[0127] The vertical first derivatives of the gravity magnetic fields at the seven different heights are, for extensions of h, 2h, 3h, 4h, 5h, 6h, and 7h, respectively:

[0128]

[0129] Next, proceed to step S150.

[0130] In step S150, the gravity magnetic field data to be used on the expanded observation surface, the vertical first derivative of the gravity magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, 7h) above the observation surface are used as input quantities. These are substituted into the eighth-order AB prediction format in the downward extension of the eighth-order ABM prediction correction to obtain the initial value of the downward extension of the gravity magnetic field data; where h is the preset extension height.

[0131] More specifically, using the gravity and magnetic field data u(x,y,z0) on the observation surface and the vertical first derivative data u of the gravity and magnetic field... z (x,y,z0) and its data extended upwards to seven heights constitute the eighth-order Adams-Bashforth prediction scheme in the downward extension of the eighth-order Adams-Bashforth-Moulton prediction correction, and obtain the initial value of the downward extension of the gravity and magnetic field data, i.e., u′(x,y,z0-h).

[0132] In this embodiment of the invention, the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, and 7h) above the observation surface are used as input quantities. These are substituted into the eighth-order AB prediction format in the downward extension of the eighth-order ABM prediction correction to obtain the initial value of the downward extension of the gravity and magnetic field data, which is achieved through the following formula:

[0133]

[0134] Where u′(x,y,z0-h) is the initial value for downward extension of the gravity and magnetic field data calculated by the eighth-order AB prediction scheme; u(x,y,z0) is the gravity and magnetic field data at height z0, i.e., the gravity and magnetic field data on the observation surface; h is a positive number representing the extension height; u z (x,y,z0) represents the first vertical derivative of the gravity and magnetic field on the observation surface; u z (x,y,z0+h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height h above the observation surface; u z (x,y,z0+2h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 2h from the observation surface; u z(x,y,z0+3h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 3h from the observation surface; u z (x,y,z0+4h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 4h above the observation surface; u z (x,y,z0+5h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 5h from the observation surface; u z (x,y,z0+6h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 6h above the observation surface; u z (x,y,z0+7h) is the vertical first derivative of the magnetic field extending upwards at a height of 7h above the observation surface.

[0135] Next, proceed to step S160.

[0136] In step S160, the vertical first derivative of the initial value of the downward extension of the gravity and magnetic field data is calculated using the ISVD method.

[0137] More specifically, using the Integrated Second Vertical Derivative Method (ISVD method) based on the fourth-order central difference improved in step S130, the vertical first derivative value u of the initial value of the gravity and magnetic field data obtained from the eighth-order Adams-Bashforth prediction scheme in step S150 is calculated. z ′(x,y,z0-h).

[0138] Next, proceed to step S170.

[0139] In step S170, the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data for downward extension, the vertical first derivative of the gravity and magnetic field data to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface are used to construct the input of the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction. Based on the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction, the final value of the downward extension of the gravity and magnetic field data is obtained.

[0140] More specifically, using the measured gravity and magnetic field data u(x,y,z0) on the observation surface, and the vertical first derivative of the initial value of the gravity and magnetic field extending downward to a depth h, u z ′(x,y,z0-h), the vertical first derivative data of the gravity and magnetic field to be used on the observation surface after expansion u zThe data (x, y, z0) and the data from six upward extensions above the observation surface constitute the eighth-order Adams-Moulton correction scheme in the downward extension of the eighth-order Adams-Bashforth-Moulton prediction correction, yielding the final value of the downward extension of the gravity and magnetic field data, i.e., u(x, y, z0-h). The final improved result of the downward extension of the gravity and magnetic field data based on the eighth-order Adams-Bashforth-Moulton prediction correction method and the fourth-order central difference improved ISVD differentiation method is obtained.

[0141] In this embodiment of the invention, the input quantities for the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction are constructed using the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data extended downward, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface. This is achieved through the following formula:

[0142]

[0143] Where x and y are the coordinates on the X-axis and Y-axis, which are perpendicular to each other in the horizontal east-west and north-south directions, respectively; z0 is the coordinate on the Z-axis, which is perpendicular to the horizontal plane, with upward Z-axis being positive; u(x,y,z0-h) is the final value of the downward extension of the gravity and magnetic field data calculated by the eighth-order AM correction scheme; u(x,y,z0) is the gravity and magnetic field data at height z0, i.e., the gravity and magnetic field data on the observation surface; h is a positive number representing the extension height; u z ′(x,y,z0-h) represents the vertical first derivative of the initial values ​​of the downward extension of the gravity and magnetic field data; u z (x,y,z0) represents the first vertical derivative of the gravity and magnetic field on the observation surface; u z (x,y,z0+h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height h above the observation surface; u z (x,y,z0+2h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 2h from the observation surface; u z (x,y,z0+3h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 3h from the observation surface; u z (x,y,z0+4h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 4h above the observation surface; u z (x,y,z0+5h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 5h from the observation surface; u z (x,y,z0+6h) is the vertical first derivative of the magnetic field extending upwards by 6h above the observation surface.

[0144] The key point of this invention is the method for downward continuation of gravity and magnetic field data based on high-order ABM prediction correction. This method innovates and improves upon existing techniques within the framework of downward continuation of gravity and magnetic field data. Specifically:

[0145] 1. Calculate the final value u(x,y,z0-h) of the downward continuation of the gravity and magnetic field data using the eighth-order Adams-Bashforth-Moulton predictor correction scheme;

[0146] 2. The obtained eighth-order Adams-Bashforth prediction format gravity and magnetic field data are extended downwards with initial values ​​u′(x,y,z0-h)0. The vertical first derivative u of the downward extension initial values ​​of the gravity and magnetic field is calculated using the Integrated Second Vertical Derivative Method (ISVD method) based on the fourth-order central difference. z Then, substituting ′(x,y,z0-h) into the eighth-order Adams-Moulton correction scheme, we obtain the final result u(x,y,z0-h) by downward extension of the gravity and magnetic field data.

[0147] 3. None of the downward continuation methods using numerical solutions of the mean value theorem of differential equations have used edge expansion processing, including the third-order Adams-Bashforth method, the fourth-order downward continuation Milne method, the downward continuation of the fourth-order explicit Milne scheme combined with the fourth-order implicit Simpson scheme, and the eighth-order Adams-Bashforth method. This invention introduces edge expansion processing for the region field.

[0148] The purpose of this invention is to further improve the accuracy of the downward continuation method while ensuring that the calculation is simple, the process is stable, the depth is large, and the applicability is universal.

[0149] Figure 4 The present invention illustrates a gravity and magnetic field data downward extension system 400 based on high-order ABM prediction correction, including an extension module 410 and an extension module 420.

[0150] The margin expansion module 410 is used to expand the measured gravity and magnetic field data on the observation surface according to the regional field method, so as to obtain the expanded gravity and magnetic field data to be used on the observation surface; and,

[0151] Determine whether the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field; wherein, if the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field, expand the margin of the vertical first derivative of the gravity and magnetic field to obtain the expanded vertical first derivative of the gravity and magnetic field to be used on the observation surface; and,

[0152] When the measured gravity and magnetic field data on the observation surface do not include the vertical first derivative of the gravity and magnetic field, the vertical first derivative of the gravity and magnetic field to be used on the observation surface after the expansion is calculated using the ISVD method based on the gravity and magnetic field data to be used on the observation surface after the expansion.

[0153] The extension module 420 is used to extend the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface upwards, obtaining the vertical first derivatives of the gravity and magnetic field at seven different heights above the observation surface; and,

[0154] The gravity and magnetic field data to be used on the expanded observation surface, the first vertical derivative of the gravity and magnetic field to be used on the expanded observation surface, and the first vertical derivatives of the gravity and magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, and 7h) above the observation surface are used as input quantities. These are then substituted into the eighth-order AB prediction format in the downward continuation of the eighth-order ABM prediction correction to obtain the initial values ​​for the downward continuation of the gravity and magnetic field data; where h is the preset continuation height; and...

[0155] The vertical first derivative of the initial values ​​of the downward extension of the gravity and magnetic field data was calculated using the ISVD method; and,

[0156] Using the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data for downward extension, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface, the input quantities of the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction are constructed. Based on the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction, the final value of the downward extension of the gravity and magnetic field data is obtained.

[0157] To verify the feasibility of the method proposed in this invention, this invention utilizes a synthesis model of the gravitational field in a gravity magnetic field ( Figure 2The synthetic model consists of three cuboids of different sizes, with different top interface depths and different densities compared to the surrounding rock. The Z-axis is positive upwards throughout the model. Cuboid 1 has side lengths of 40m, 10m, and 20m along the X, Y, and Z axes, respectively, with its center point at (75, 65, -25)m. Its top interface is located 15m below the observation surface (representing the ground), its Z-axis is horizontally 0m, and its density contrast with the surrounding rock is 0.6kg / m³. Cuboid 2 has side lengths of 10m, 20m, and 20m along the X, Y, and Z axes, respectively, with its center point at (65, 90, -22)m. Its top interface is located 12m below the ground, and its density contrast is 0.5kg / m³. The cuboid 3 has side lengths of 10m, 12m, and 20m along its X, Y, and Z axes, respectively. The coordinates of its center point are (85, 90, -21)m. The burial depth of its top interface is 11m, and its density contrast is 0.4mg / m³. This invention assumes measurements are taken on the ground, i.e., the ground is the observation surface. There are 150 measurement lines, each with 150 points, and a grid spacing of 1 meter.

[0158] The downward extension depth was set to 8 meters, or eight times the point spacing. Simultaneously, the gravity field data on the ground observation surface was extended downwards using the FFT method, integral iteration method, Milne method, Milne-Simpson method, Adams-Bashforth method, and the Adams-Bashforth-Moulton prediction correction method of this invention. For the method of this invention, the vertical first derivative, even the first derivative of the gravity field, is not always measured when measuring gravity field data. In this case, the first vertical derivative on the ground must be calculated before upward extension. This invention uses the ISVD method to calculate the first vertical derivative of the ground gravity field data, and then uses the upward extension method to extend the calculated vertical first derivative and the theoretical gravity field data from ground height to different heights above the ground. Finally, the downward extension result is obtained by substituting the eighth-order Adams-Bashforth-Moulton prediction correction formula of this invention. Figure 3 As shown.

[0159] and Figure 3 (b) Comparison with the reference value, the downward extension result of the present invention Figure 3 (h) has the highest accuracy. This demonstrates the effectiveness and significance of this invention in further improving the accuracy of the gravity magnetic field downward continuation method while ensuring computational simplicity, process stability, large depth, and universality.

[0160] The closest existing technology to this invention is the eighth-order Adams-Bashforth downward continuation method, which has an accuracy of eighth order and a truncation error of [missing information]. ω is a constant defined between (z0-h, z0+8h). This invention uses the eighth-order Adams-Bashforth-Moulton predictor correction formula, which has higher accuracy and a truncation error of [missing value]. The truncation error of this invention is much smaller than that of the latest existing technology, thus improving the accuracy of the downward continuation results.

[0161] Compared to this invention, the latest existing ISVD method for calculating the vertical first derivative uses finite difference as a second-order central difference, while this invention improves the ISVD method for calculating the vertical first derivative by using a fourth-order central difference with higher accuracy. Since this invention calculates not only the vertical first derivative of the gravity and magnetic field on the observation surface but also the vertical first derivative of the downward extension estimate (initial value), the calculation of the vertical first derivative is crucial. Therefore, this invention uses a more precise differentiation method to improve the overall accuracy of the calculation.

[0162] Compared with the present invention, although the numerical solution method in the latest existing technology has no obvious boundary effect, it involves upward extension calculations at multiple heights. If the edge expansion process is not performed, it will cause the inaccuracy of the downward extension results to a large extent. The present invention can solve this problem to a certain extent by using the region field edge expansion method.

[0163] In summary, the advantage of this invention is that it further improves the accuracy of the gravity magnetic field downward continuation method while ensuring simple calculation, stable process, large depth, and universality.

[0164] See Figure 5 This disclosure also provides an electronic device 50, which includes:

[0165] At least one processor; and,

[0166] The memory is communicatively connected to the at least one processor; wherein,

[0167] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the gravity and magnetic field data downward extrapolation method based on high-order ABM prediction correction in the foregoing method embodiments.

[0168] This disclosure also provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the gravity and magnetic field data downward extrapolation method based on high-order ABM prediction correction in the foregoing method embodiments.

[0169] This disclosure also provides a computer program product, which includes a computing program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions that, when executed by a computer, cause the computer to perform the gravity magnetic field data downward continuation method based on high-order ABM prediction correction in the foregoing method embodiments.

[0170] The following is for reference. Figure 5 The diagram illustrates a structural schematic of an electronic device 50 suitable for implementing embodiments of the present disclosure. The electronic devices in the embodiments of the present disclosure may include, but are not limited to, mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 5 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0171] like Figure 5 As shown, the electronic device 50 may include a processing unit (e.g., a central processing unit, a graphics processing unit, etc.) 501, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 502 or a program loaded from a storage device 508 into a random access memory (RAM) 503. The RAM 503 also stores various programs and data required for the operation of the electronic device 50. The processing unit 501, ROM 502, and RAM 503 are interconnected via a bus 504. An input / output (I / O) interface 505 is also connected to the bus 504.

[0172] Typically, the following devices can be connected to I / O interface 505: input devices 506 including, for example, touchscreens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 507 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 508 including, for example, magnetic tapes, hard disks, etc.; and communication devices 509. Communication device 509 allows electronic device 50 to communicate wirelessly or wiredly with other devices to exchange data. Although an electronic device 50 with various devices is shown in the figure, it should be understood that it is not required to implement or possess all the devices shown. More or fewer devices may be implemented or possessed alternatively.

[0173] In particular, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 509, or installed from a storage device 508, or installed from a ROM 502. When the computer program is executed by the processing device 501, it performs the functions defined in the methods of embodiments of this disclosure.

[0174] It should be noted that the computer-readable medium described in this disclosure can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this disclosure, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this disclosure, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0175] The aforementioned computer-readable medium may be included in the aforementioned electronic device; or it may exist independently and not assembled into the electronic device.

[0176] The aforementioned computer-readable medium carries one or more programs that, when executed by the electronic device, cause the electronic device to: acquire at least two Internet Protocol (IP) addresses; send a node evaluation request including the at least two IP addresses to a node evaluation device, wherein the node evaluation device selects an IP address from the at least two IP addresses and returns it; and receive the IP address returned by the node evaluation device; wherein the acquired IP address indicates an edge node in a content delivery network.

[0177] Alternatively, the aforementioned computer-readable medium carries one or more programs that, when executed by the electronic device, cause the electronic device to: receive a node evaluation request including at least two Internet Protocol (IP) addresses; select an IP address from the at least two IP addresses; and return the selected IP address; wherein the received IP address indicates an edge node in the content delivery network.

[0178] Computer program code for performing the operations of this disclosure can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0179] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0180] The units described in the embodiments of this disclosure can be implemented in software or in hardware. The name of a unit does not necessarily limit the unit itself; for example, the first acquisition unit can also be described as "a unit that acquires at least two Internet Protocol addresses".

[0181] It should be understood that the various parts of this disclosure can be implemented in hardware, software, firmware, or a combination thereof.

[0182] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A method for downward extrapolation of gravity and magnetic field data based on high-order ABM prediction correction, characterized in that, The method includes the following steps: The measured gravity and magnetic field data on the observation surface are expanded using the regional field method to obtain the expanded gravity and magnetic field data to be used on the observation surface. Determine whether the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field; wherein, if the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field, expand the margin of the vertical first derivative of the gravity and magnetic field to obtain the expanded vertical first derivative of the gravity and magnetic field to be used on the observation surface; and, When the measured gravity and magnetic field data on the observation surface do not include the vertical first derivative of the gravity and magnetic field, the vertical first derivative of the gravity and magnetic field to be used on the observation surface after the expansion is calculated using the ISVD method based on the gravity and magnetic field data to be used on the observation surface after the expansion. The vertical first derivative of the gravity magnetic field to be used on the expanded observation surface is extended upward to obtain the vertical first derivative of the gravity magnetic field at seven different heights above the observation surface. The gravity and magnetic field data to be used on the expanded observation surface, the first vertical derivative of the gravity and magnetic field to be used on the expanded observation surface, and the first vertical derivatives of the gravity and magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, and 7h) above the observation surface are used as input quantities. These are then substituted into the eighth-order AB prediction format in the downward extension of the eighth-order ABM prediction correction to obtain the initial value of the downward extension of the gravity and magnetic field data; where h is the preset extension height. The vertical first derivative of the initial value of the downward extension of the gravity and magnetic field data was calculated using the ISVD method. Using the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data for downward extension, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface, the input quantities of the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction are constructed. Based on the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction, the final value of the downward extension of the gravity and magnetic field data is obtained.

2. The method for downward extrapolation of gravity and magnetic field data based on high-order ABM prediction correction according to claim 1, characterized in that, The input quantities for the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction are constructed using the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data extended downward, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface. This is achieved through the following formula: Where x and y are the coordinates on the X-axis and Y-axis, which are perpendicular to each other in the horizontal east-west and north-south directions, respectively; z is the coordinate on the Z-axis, which is perpendicular to the horizontal plane, with upward Z-axis being positive; z0 is the coordinate on the Z-axis, which is the vertical coordinate of the observation surface, with upward Z-axis being positive; h is a positive number representing the extension height, -h for downward extension and +h for upward extension; u(x,y,z0-h) is the final value of the downward extension of the gravity and magnetic field data calculated by the eighth-order AM correction scheme; u(x,y,z0) is the gravity and magnetic field data at height z0, i.e., the gravity and magnetic field data on the observation surface; u z ′(x,y,z0-h) represents the vertical first derivative of the initial values ​​of the downward extension of the gravity and magnetic field data; u z (x,y,z0) represents the first vertical derivative of the gravity and magnetic field on the observation surface; u z (x,y,z0+h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height h above the observation surface; u z (x,y,z0+2h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 2h from the observation surface; u z (x,y,z0+3h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 3h from the observation surface; u z (x,y,z0+4h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 4h above the observation surface; u z (x,y,z0+5h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 5h from the observation surface; u z (x,y,z0+6h) is the vertical first derivative of the magnetic field extending upwards by 6h above the observation surface.

3. The method for downward extrapolation of gravity and magnetic field data based on high-order ABM prediction correction according to claim 1, characterized in that, The measured gravity and magnetic field data on the observation surface are expanded using the regional field method, which is achieved through the following formula: (1) ZK(i,j)=ZY(i,1)+(1-j)·g(i),(1≤i≤m,1-n'≤j≤0) (2) ZK(i,j)=ZY(i,n)+(jn)·g(i),(1≤i≤m,n+1≤j≤n+n') (3) ZK(i,j)=ZY(1,j)+(1-i)·g(j),(1-m'≤i≤0,1-n'≤j≤n+n') (4) ZK(i,j)=ZY(m,j)+(im)·g(j),(m+1≤i≤m+m′,1-n′≤j≤n+n’) Where ZY(i,k) represents the gravity and magnetic field data of the i-th row and k-th column on the observation surface before edge expansion; ZY(i,k+1) represents the gravity and magnetic field data of the i-th row and k+1-th column on the observation surface before edge expansion; ZY(i,n-k+1) represents the gravity and magnetic field data of the i-th row and n-k+1-th column on the observation surface before edge expansion; ZY(i,nk) represents the gravity and magnetic field data of the i-th row and nk-th column on the observation surface before edge expansion; ZY(i,n) represents the gravity and magnetic field data of the i-th row and n-th column on the observation surface before edge expansion; ZY(k,j) represents the gravity and magnetic field data of the k-th row and j-th column on the observation surface before edge expansion; ZY(k+1,j) represents the gravity and magnetic field data of the k+1-th row and j-th column on the observation surface before edge expansion; ZY(1,j) represents the gravity and magnetic field data of the i ... ZY(m-k+1,j) represents the gravity and magnetic field data in the first row and j column of the observation surface before edge expansion; ZY(m-k+1,j) represents the gravity and magnetic field data in the (m-k+1)th row and j column of the observation surface before edge expansion; ZY(mk,j) represents the gravity and magnetic field data in the (mk)th row and j column of the observation surface before edge expansion; ZK(i,j) represents the gravity and magnetic field data in the first row and j column of the observation surface after edge expansion; m and n represent the number of points and lines in the horizontal direction of the spatial domain (x) and the horizontal direction of the spatial domain (y) perpendicular to x; m' and n' are the lengths of the edge expansion in the x and y directions; satisfying ZK(i,j)=ZY(i,j), (1≤i≤m,1≤j≤n); g(i) and g(j) are intermediate variables for convenient edge expansion calculation.

4. The method for downward extrapolation of gravity and magnetic field data based on high-order ABM prediction correction according to claim 1, characterized in that, The method of using ISVD to calculate the vertical first derivative of the gravity and magnetic field on the expanded observation surface based on the gravity and magnetic field data includes the following steps: The gravity and magnetic potential data v(x,y,z0) corresponding to the measured gravity and magnetic field data u(x,y,z0) on the observation surface are calculated using the wavenumber domain conversion method, and are achieved through the following formula: Where v(x,y,z0) represents the gravity and magnetic potential data at height z0 on the observation surface; u(x,y,z0) represents the gravity and magnetic field data at height z0 on the observation surface; x,y are the spatial domain plane coordinates; k x ,k y Represents the wavenumber domain coordinates corresponding to the spatial domain coordinates x, y; Indicates the positive Fourier transform; Show the inverse Fourier transform; Represents the wavenumber domain vertical integration operator; The horizontal second derivative of the gravity and magnetic potential data v(x,y,z0) was calculated using the fourth-order central difference method: Among them, v xx v represents the second derivative of the gravity and magnetic potential data at height z0 on the observation surface along the X-axis; yy Δx and Δy represent the second derivative of the gravity and magnetic potential data at height z0 on the observation surface in the Y-axis direction; Δx and Δy represent the sampling interval in the horizontal direction. The vertical second derivative of the gravity and magnetic potential data v(x,y,z0) is calculated using the Laplace equation: u z (x,y,z0)=v zz (x,y,z0) =-[v] xx (x,y,z0)+v yy (x,y,z0)]. Among them, u z (x,y,z0) is the vertical second derivative of the gravity and magnetic potential data v(x,y,z0); v zz (x,y,z0) represents the second derivative of the gravity and magnetic potential data at height z0 on the observation surface in the Z-axis direction.

5. The method for downward extrapolation of gravity and magnetic field data based on high-order ABM prediction correction according to claim 1, characterized in that, The vertical first derivative of the gravity magnetic field to be used on the expanded observation surface is extended upward to obtain seven vertical first derivatives of the gravity magnetic field at different heights above the observation surface, including: The conversion formula for gravity and magnetic field data at different altitudes is as follows: Where u(x,y,z0+h) is the final value of the upward extension of the gravity and magnetic field data; ξ,η are another representation of the coordinates x,y; h is a positive number representing the extension height; The upward continuation method in the wavenumber domain obtained by performing a Fourier transform on the data conversion relationships at different altitudes is as follows: Among them, U(k) x ,k x ,z0) is the wavenumber domain representation of u(x,y,z0); For wavenumber domain upward extension operators; The vertical first derivatives of the gravity magnetic fields at the seven different heights are, for extensions of h, 2h, 3h, 4h, 5h, 6h, and 7h, respectively:

6. The method for downward continuation of gravity and magnetic field data based on high-order ABM prediction correction according to claim 1, characterized in that, The input consists of the gravity and magnetic field data to be used on the expanded observation surface, the first vertical derivative of the gravity and magnetic field to be used on the expanded observation surface, and the first vertical derivatives of the gravity and magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, and 7h) above the observation surface. These are then substituted into the eighth-order AB prediction scheme in the downward continuation of the eighth-order ABM prediction correction to obtain the initial values ​​for the downward continuation of the gravity and magnetic field data. This is achieved through the following formula: Where u′(x,y,z0-h) is the initial value for downward extension of the gravity and magnetic field data calculated by the eighth-order AB prediction scheme; u(x,y,z0) is the gravity and magnetic field data at height z0, i.e., the gravity and magnetic field data on the observation surface; h is a positive number representing the extension height; u z (x,y,z0) represents the first vertical derivative of the gravity and magnetic field on the observation surface; u z (x,y,z0+h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height h above the observation surface; u z (x,y,z0+2h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 2h from the observation surface; u z (x,y,z0+3h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 3h from the observation surface; u z (x,y,z0+4h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 4h above the observation surface; u z (x,y,z0+5h) represents the vertical first derivative of the gravity and magnetic field extending upwards by 5h from the observation surface; u z (x,y,z0+6h) represents the vertical first derivative of the gravity and magnetic field extending upwards at a height of 6h above the observation surface; u z (x,y,z0+7h) is the vertical first derivative of the magnetic field extending upwards at a height of 7h above the observation surface.

7. A gravity and magnetic field data downward continuation system based on high-order ABM prediction correction, characterized in that, The system includes: The margin expansion module is configured to expand the measured gravity and magnetic field data on the observation surface using the region field method, obtaining the expanded gravity and magnetic field data to be used on the observation surface; and, Determine whether the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field; wherein, if the measured gravity and magnetic field data on the observation surface contains the vertical first derivative of the gravity and magnetic field, expand the margin of the vertical first derivative of the gravity and magnetic field to obtain the expanded vertical first derivative of the gravity and magnetic field to be used on the observation surface; and, When the measured gravity and magnetic field data on the observation surface do not include the vertical first derivative of the gravity and magnetic field, the vertical first derivative of the gravity and magnetic field to be used on the observation surface after the expansion is calculated using the ISVD method based on the gravity and magnetic field data to be used on the observation surface after the expansion. The extension module is configured to extend the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface upwards, obtaining the vertical first derivatives of the gravity and magnetic field at seven different heights above the observation surface; and, The gravity and magnetic field data to be used on the expanded observation surface, the first vertical derivative of the gravity and magnetic field to be used on the expanded observation surface, and the first vertical derivatives of the gravity and magnetic field at seven different heights (h, 2h, 3h, 4h, 5h, 6h, and 7h) above the observation surface are used as input quantities. These are then substituted into the eighth-order AB prediction format in the downward continuation of the eighth-order ABM prediction correction to obtain the initial values ​​for the downward continuation of the gravity and magnetic field data; where h is the preset continuation height; and... The vertical first derivative of the initial values ​​of the downward extension of the gravity and magnetic field data was calculated using the ISVD method; and, Using the gravity and magnetic field data to be used on the expanded observation surface, the vertical first derivative of the initial value of the gravity and magnetic field data for downward extension, the vertical first derivative of the gravity and magnetic field to be used on the expanded observation surface, and the vertical first derivatives of the gravity and magnetic field at six different heights (h, 2h, 3h, 4h, 5h, and 6h) above the observation surface, the input quantities of the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction are constructed. Based on the eighth-order AM correction scheme in the downward extension of the eighth-order ABM prediction correction, the final value of the downward extension of the gravity and magnetic field data is obtained.

8. An electronic device, characterized in that, The electronic device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, cause the at least one processor to perform the gravity magnetic field data downward continuation method based on higher-order ABM prediction correction as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that, when executed by at least one processor, cause the at least one processor to perform the gravity and magnetic field data downward extrapolation method based on higher-order ABM prediction correction as described in any one of claims 1 to 6.

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