Hilbert transform-based potential field downward continuation method for vertical guide number calculation

Abstract

The invention relates to a potential field downward continuation method based on vertical guide number calculation of Hilbert transform. The method comprises the following steps: acquiring actually measured potential field data at the height z0 of an observation surface; wherein the actually measured potential field data comprises gravitational field abnormal data or magnetic field abnormal data; performing finite difference calculation on the actually measured potential field data to obtain a horizontal derivative of the actually measured potential field data, and performing boundary effect elimination processing on the calculated horizontal derivative by using a moving average formula to obtain a processed horizontal derivative; according to the processed horizontal derivative, constructing a Hilbert transform-based vertical guide number recursion formula comprising a potential field function, and according to the Hilbert transform-based vertical guide number recursion formula, calculating six vertical guide numbers of the potential field function; and according to the Taylor series expansion of the downward continuation of the potential field and the six vertical guide numbers of the potential field function, potential field data of the downward continuation delta h height from the observation surface height z0 is calculated, so that the effects of noise suppression and relatively high calculation precision are achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of gravity and magnetic exploration, and particularly to a downward continuation method of potential field based on the calculation of vertical derivative by Hilbert transform. Background Art

[0002] Taylor series expansion is a method of representing the values of a function near a certain point as an infinite series. In the downward continuation of potential field, Taylor series expansion can be used to approximately represent the variation of potential field data with height. By calculating the derivatives of various orders of potential field data at a certain height and using the Taylor series formula for expansion, the values of potential field data at lower heights can be deduced. Moreover, the earliest downward continuation method of potential field is the Taylor series method, and the key to this method is to calculate the vertical derivatives of various orders in the series, including the first derivative, the second derivative, etc. Although the traditional Taylor series method can achieve the downward continuation of potential field to a certain extent, the continuation depth is limited, and the amplification effect on noise is relatively obvious. Subsequently, the Taylor series method was improved, and a new downward continuation method of potential field (ISVD) was proposed. The key to this method lies in using FFT for vertical integration, then calculating the horizontal second derivative, and then using the Laplace equation to obtain the vertical second derivative. Finally, through the characteristics of spatial domain difference and the fact that the derivatives of various orders satisfy the Laplace equation, the vertical even-order derivatives and the remaining odd-order derivatives are obtained. However, although this improved method improves the accuracy and depth of the downward continuation of potential field to a certain extent, it is still limited by the noise amplification effect. In recent years, some researchers have proposed a downward continuation method of potential field based on Taylor series iteration. This method realizes the accurate continuation of potential field data by introducing a recursive algorithm to accurately estimate extremely small function values. The Taylor series iteration method has extensive applications in the Internet field, such as website visual search, virtual disks, etc. However, in the field of downward continuation of potential field, its application is still in the exploratory stage. To sum up, the downward continuation method of potential field based on Taylor series expansion has made certain progress in research and application, but still faces many challenges.

[0003] After investigation of domestic and foreign literature, there is currently no relatively practical downward continuation method of potential field based on Taylor series expansion that does not require selecting too many parameters and can continue downward to a large depth. Therefore, there is an urgent need for a stable downward continuation method of potential field that can continue downward to a large depth. Summary of the Invention

[0004] (1) Technical Problems to be Solved

[0005] In view of the above-mentioned disadvantages and deficiencies of the prior art, the present invention provides a downward continuation method of potential field based on the calculation of vertical derivative by Hilbert transform, which solves the technical problem in the prior art that the traditional method is affected by the calculation accuracy and stability of high-order derivatives.

[0006] (2) Technical Solution

[0007] To achieve the above object, the main technical solutions adopted by the present invention include:

[0008] In a first aspect, an embodiment of the present invention provides a downward continuation method for potential fields based on Hilbert transform for vertical derivative calculation, including: obtaining measured potential field data at the observation surface height z 0 ; where the measured potential field data includes gravity field anomaly data or magnetic field anomaly data; performing finite difference calculation on the measured potential field data to obtain the horizontal derivative of the measured potential field data, and using a moving average formula to perform boundary effect elimination processing on the calculated horizontal derivative to obtain the processed horizontal derivative; constructing a vertical derivative recurrence formula based on Hilbert transform including the potential field function according to the processed horizontal derivative, and calculating six vertical derivatives of the potential field function according to the vertical derivative recurrence formula based on Hilbert transform; where the six vertical derivatives include the first-order vertical derivative of the potential field function, the second-order vertical derivative of the potential field function, the third-order vertical derivative of the potential field function, the fourth-order vertical derivative of the potential field function, the fifth-order vertical derivative of the potential field function, and the sixth-order vertical derivative of the potential field function; calculating the potential field data extended downward by a height of Δh from the observation surface height z 0 according to the Taylor series expansion of potential field downward continuation and the six vertical derivatives of the potential field function.

[0009] In a possible embodiment, the calculation expression of the horizontal derivative of the measured potential field data is as follows:

[0010]

[0011] In the formula, represents the first-order derivative in the x direction of the grid node where the i-th row grid node and the j-th column grid node intersect; f i,j+1 represents the field value in the x direction of the grid node where the i-th row grid node and the (j + 1)-th column grid node intersect; f i,j-1 represents the field value in the x direction of the grid node where the i-th row grid node and the (j - 1)-th column grid node intersect; Δx represents the point spacing in the x direction; represents the first-order derivative in the y direction of the grid node where the i-th row grid node and the j-th column grid node intersect; f i+1,j represents the field value in the y direction of the grid node where the (i + 1)-th row grid node and the j-th column grid node intersect; f i-1,j represents the field value in the y direction of the grid node where the (i - 1)-th row grid node and the j-th column grid node intersect; Δy represents the point spacing in the y direction.

[0012] In a possible embodiment, the calculation expression of the moving average formula is as follows:

[0013]

[0014] In the formula, represents the first-order derivative in the x direction of the grid node where the grid nodes in the i-th row and the j-th column intersect; k represents the size of the sliding window, and k is an odd number greater than 3. For example, k is equal to 7, etc.; represents the first-order derivative in the x direction of the grid node where the grid nodes in the l-th row and the m-th column intersect; represents the first-order derivative in the y direction of the grid node where the grid nodes in the i-th row and the j-th column intersect; represents the first-order derivative in the y direction of the grid node where the grid nodes in the l-th row and the m-th column intersect.

[0015] In a possible embodiment, the calculation expression of the potential field data extended downward by a height of Δh from the observation surface height z 0 is as follows:

[0016]

[0017] In the formula, Δf(x, y, z 0 +Δh) represents the potential field data extended downward by a height of Δh from the observation surface height z 0 ; Δf(x, y, z 0 ) represents the measured potential field data at the observation surface height z 0 ; n takes values from 1 to 6; Δh represents the downward extension height; z represents the height of the extension surface and is located below the observation surface.

[0018] In a second aspect, an embodiment of the present invention provides a potential field downward continuation system based on Hilbert transform for vertical derivative calculation, including:

[0019] An acquisition module, configured to acquire the measured potential field data at the observation surface height z 0 ; wherein, the measured potential field data includes gravity field anomaly data or magnetic field anomaly data;

[0020] A first calculation module, configured to perform finite difference calculation on the measured potential field data to obtain the horizontal derivative of the measured potential field data, and perform boundary effect elimination processing on the calculated horizontal derivative by using a moving average formula to obtain the processed horizontal derivative;

[0021] A construction calculation module is used to construct a recurrence formula of the vertical derivative based on the Hilbert transform including the potential field function according to the processed horizontal derivative, and calculate six vertical derivatives of the potential field function according to the recurrence formula of the vertical derivative based on the Hilbert transform; among them, the six vertical derivatives include the first-order vertical derivative of the potential field function, the second-order vertical derivative of the potential field function, the third-order vertical derivative of the potential field function, the fourth-order vertical derivative of the potential field function, the fifth-order vertical derivative of the potential field function, and the sixth-order vertical derivative of the potential field function;

[0022] A second calculation module is used to calculate the potential field data extended downward by Δh height from the observation surface height z according to the Taylor series expansion of the potential field downward continuation and the six vertical derivatives of the potential field function. 0 The potential field data extended downward by Δh height.

[0023] In a possible embodiment, the calculation expression of the horizontal derivative of the measured potential field data is as follows:

[0024]

[0025] In the formula, represents the first-order derivative in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; f i,j+1 represents the field value in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the (j + 1)-th column grid node is located; f i,j-1 represents the field value in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the (j - 1)-th column grid node is located; Δx represents the point distance in the x direction; represents the first-order derivative in the y direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; f i+1,j represents the field value in the y direction of the grid node where the grid node at the intersection of the (i + 1)-th row grid node and the j-th column grid node is located; f i-1,j represents the field value in the y direction of the grid node where the grid node at the intersection of the (i - 1)-th row grid node and the j-th column grid node is located; Δy represents the point distance in the y direction.

[0026] In a possible embodiment, the calculation expression of the moving average formula is as follows:

[0027]

[0028] In the formula, represents the first-order derivative in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; k represents the moving window size, and k is an odd number greater than 3. For example, k is equal to 7, etc.; represents the first-order derivative in the x direction of the grid node where the grid node at the intersection of the l-th row grid node and the m-th column grid node is located; represents the first-order derivative in the y direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; Denote the first-order derivative in the y direction of the grid node where the l-th row grid node intersects the m-th column grid node.

[0029] In a possible embodiment, from the observation surface height z 0 The calculation expression for downward continuation of potential field data by a height of Δh is as follows:

[0030]

[0031] In the formula, Δf(x, y, z 0 +Δh) represents the potential field data after downward continuation by a height of Δh from the observation surface height z 0 Δf(x, y, z 0 ) represents the measured potential field data at the observation surface height z 0 n takes values from 1 to 6; Δh represents the downward continuation height; z represents the height of the continuation surface and is below the observation surface.

[0032] In a third aspect, an embodiment of the present application provides a storage medium, on which a computer program is stored, and when the computer program is run by a processor, it executes the method described in the first aspect or any optional implementation manner of the first aspect.

[0033] In a fourth aspect, an embodiment of the present application provides 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 runs, the processor communicates with the memory through the bus, and when the machine-readable instructions are executed by the processor, they execute the method described in the first aspect or any optional implementation manner of the first aspect.

[0034] In a fifth aspect, the present application provides a computer program product, and when the computer program product runs on a computer, it causes the computer to execute the method in the first aspect or any possible implementation manner of the first aspect.

[0035] (III) Advantageous Effects

[0036] The beneficial effects of the present invention are:

[0037] An embodiment of the present application provides a method for downward continuation of potential field based on Hilbert transform for vertical derivative calculation. By obtaining the potential field data at the observation surface height z 0The measured potential field data at [the specific location]; among them, the measured potential field data includes gravity field anomaly data or magnetic field anomaly data, and performs finite difference calculation on the measured potential field data to obtain the horizontal derivative of the measured potential field data, and uses the moving average formula to eliminate the boundary effect of the calculated horizontal derivative to obtain the processed horizontal derivative, and constructs a vertical derivative recurrence formula based on the Hilbert transform including the potential field function according to the processed horizontal derivative, and calculates six vertical derivatives of the potential field function according to the vertical derivative recurrence formula based on the Hilbert transform, where the six vertical derivatives include the first-order vertical derivative of the potential field function, the second-order vertical derivative of the potential field function, the third-order vertical derivative of the potential field function, the fourth-order vertical derivative of the potential field function, the fifth-order vertical derivative of the potential field function, and the sixth-order vertical derivative of the potential field function, and calculates the potential field data extended downward by Δh height from the observation surface height z according to the Taylor series expansion of the potential field downward continuation and the six vertical derivatives of the potential field function. 0 The potential field data extended downward by Δh height. Compared with the prior art, the present application has the technical effects of suppressing noise and higher calculation accuracy.

[0038] In order to make the above-mentioned objects, features, and advantages to be achieved by the embodiments of the present application more obvious and understandable, the following specifically enumerates preferred embodiments and, in conjunction with the accompanying drawings, makes a detailed description as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings required to be used in the embodiments of the present application. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings.

[0040] Figure 1 Shows a flowchart of a potential field downward continuation method based on Hilbert transform for vertical derivative calculation provided by an embodiment of the present application;

[0041] Figure 2 Shows a structural block diagram of a potential field downward continuation system based on Hilbert transform for vertical derivative calculation provided by an embodiment of the present application.

[0042] Figure 3Comparison diagram of the theoretical gravity anomaly calculation results of a vertical hexahedron model, the downward continuation calculation results of the potential field by the ISVD method, and the downward continuation calculation results of the potential field provided by the present invention. Among them, (a), (d), (g), and (j) are the theoretical gravity anomalies corresponding to heights z = 0m, 1000m, 2000m, 3000m, and 4000m respectively; (b), (e), (h), and (k) are the gravity anomalies corresponding to the downward continuation of the present invention by 1000m (5 times the point spacing), 2000m (10 times the point spacing), 3000m (15 times the point spacing), and 4000m (20 times the point spacing) respectively; (c), (f), (i), and (l) are the gravity anomalies corresponding to the downward continuation of the ISVD method by 1000m (5 times the point spacing), 2000m (10 times the point spacing), 3000m (15 times the point spacing), and 4000m (20 times the point spacing) respectively.

[0043] Figure 4 Comparison diagram of the downward continuation calculation results of the potential field by the ISVD method and the downward continuation calculation results of the potential field provided by the present invention after adding Gaussian white noise to the theoretical gravity anomaly of the vertical hexahedron model. Among them, (a), (d), (g), and (j) are the theoretical gravity anomalies corresponding to heights z = 0m, 1000m, 2000m, 3000m, and 4000m respectively; (b), (e), (h), and (k) are the gravity anomalies corresponding to the downward continuation of the present invention by 1000m (5 times the point spacing), 2000m (10 times the point spacing), 3000m (15 times the point spacing), and 4000m (20 times the point spacing) respectively; (c), (f), (i), and (l) are the gravity anomalies corresponding to the downward continuation of the ISVD method by 1000m (5 times the point spacing), 2000m (10 times the point spacing), 3000m (15 times the point spacing), and 4000m (20 times the point spacing) respectively. Detailed implementation manners

[0044] In order to better explain the present invention for easy understanding, the present invention will be described in detail below with reference to the accompanying drawings through specific implementation manners.

[0045] In order to solve the technical problem in the prior art that the traditional method is affected by the calculation accuracy and stability of the high-order derivative, the embodiment of the present application provides a downward continuation method of the potential field based on the calculation of the vertical derivative by the Hilbert transform, by obtaining at the observation surface height z 0The measured potential field data at [z]; among them, the measured potential field data includes gravity field anomaly data or magnetic field anomaly data, and performs finite difference calculation on the measured potential field data to obtain the horizontal derivative of the measured potential field data, and constructs a vertical derivative recurrence formula based on Hilbert transform including the potential field function according to the horizontal derivative of the measured potential field data, and calculates six vertical derivatives of the potential field function according to the vertical derivative recurrence formula based on Hilbert transform, where the six vertical derivatives include the first-order vertical derivative of the potential field function, the second-order vertical derivative of the potential field function, the third-order vertical derivative of the potential field function, the fourth-order vertical derivative of the potential field function, the fifth-order vertical derivative of the potential field function, and the sixth-order vertical derivative of the potential field function, and calculates the potential field data extended downward by Δh height from the observation surface height z according to the Taylor series expansion of the potential field downward continuation and the six vertical derivatives of the potential field function. 0 Compared with the prior art, the present application has the technical effects of suppressing noise and higher calculation accuracy.

[0046] To better understand the above technical solutions, the exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more clear and thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0047] Please refer to Figure 1 , Figure 1 shows a flowchart of a potential field downward continuation method based on Hilbert transform vertical derivative calculation provided by an embodiment of the present application. It should be understood that this potential field downward continuation method can be executed by a potential field downward continuation system based on Hilbert transform vertical derivative calculation, and the specific system of this potential field downward continuation system can be set according to actual needs, and the embodiments of the present application are not limited thereto. Specifically, this potential field downward continuation method includes:

[0048] Step S110, obtain the measured potential field data at the observation surface height z 0 . Among them, the measured potential field data includes gravity field anomaly data or magnetic field anomaly data.

[0049] It should be understood that the gravity field anomaly data can be Bouguer gravity anomaly data, and the magnetic field anomaly data can be reduced-to-pole magnetic anomaly data.

[0050] Step S120, perform finite difference calculation on the measured potential field data to obtain the horizontal derivative of the measured potential field data, and use the moving average formula to perform boundary effect elimination processing on the calculated horizontal derivative to obtain the processed horizontal derivative.

[0051] It should be understood that the calculation formula of the horizontal derivative of the measured potential field data can be set according to actual needs, and the embodiments of the present application are not limited thereto.

[0052] Specifically, the calculation expression of the horizontal derivative of the measured potential field data is as follows:

[0053]

[0054] In the formula, represents the first-order derivative in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; f i,j+1 represents the field value in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the (j + 1)-th column grid node is located; f i,j-1 represents the field value in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the (j - 1)-th column grid node is located; Δx represents the point distance in the x direction; represents the first-order derivative in the y direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; f i+1,j represents the field value in the y direction of the grid node where the grid node at the intersection of the (i + 1)-th row grid node and the j-th column grid node is located; f i-1,j represents the field value in the y direction of the grid node where the grid node at the intersection of the (i - 1)-th row grid node and the j-th column grid node is located; Δy represents the point distance in the y direction.

[0055] It should also be understood that the specific formula of the moving average formula can also be set according to actual needs, and the embodiments of the present application are not limited thereto.

[0056] Specifically, the calculation expression of the moving average formula is as follows:

[0057]

[0058] In the formula, represents the first-order derivative in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; k represents the moving window size, and k is an odd number greater than 3. For example, k is equal to 7, etc.; represents the first-order derivative in the x direction of the grid node where the grid node at the intersection of the l-th row grid node and the m-th column grid node is located; represents the first-order derivative in the y direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; represents the first-order derivative in the y direction of the grid node where the grid node at the intersection of the l-th row grid node and the m-th column grid node is located.

[0059] Step S130: Based on the processed horizontal derivative, construct a recurrence formula for the vertical derivative based on the Hilbert transform that includes the potential field function, and calculate six vertical derivatives of the potential field function according to the recurrence formula for the vertical derivative based on the Hilbert transform. Among them, the six vertical derivatives include the first-order vertical derivative of the potential field function, the second-order vertical derivative of the potential field function, the third-order vertical derivative of the potential field function, the fourth-order vertical derivative of the potential field function, the fifth-order vertical derivative of the potential field function, and the sixth-order vertical derivative of the potential field function.

[0060] It should be understood that the specific formula of the recurrence formula for the vertical derivative based on the Hilbert transform can be set according to actual needs, and the embodiments of the present application are not limited thereto.

[0061] For example, the recurrence formula for the vertical derivative based on the Hilbert transform can be the recurrence formula for the vertical derivative involved in a method for obtaining the vertical derivative of a potential field, an inversion method, a system, a device, and a medium disclosed in Patent Application No. 202410141490.0. Different from it, the value of the truncation order n in this recurrence formula for the vertical derivative is from 1 to 6, so that the first-order vertical derivative of the potential field function, the second-order vertical derivative of the potential field function, the third-order vertical derivative of the potential field function, the fourth-order vertical derivative of the potential field function, the fifth-order vertical derivative of the potential field function, and the sixth-order vertical derivative of the potential field function can be obtained.

[0062] Step S140: Calculate the potential field data extended downward by Δh height from the observation surface height z according to the Taylor series expansion of the potential field downward continuation and the six vertical derivatives of the potential field function. 0 The potential field data extended downward by Δh height.

[0063] It should be understood that the specific formula of the Taylor series expansion of the potential field downward continuation can be set according to actual needs, and the embodiments of the present application are not limited thereto.

[0064] For example, the calculation expression of the Taylor series expansion of the potential field downward continuation is as follows:

[0065]

[0066] In the formula, Δf(x, y, z 0 +Δh) represents the potential field data extended downward by Δh height from the observation surface height z 0 ; Δf(x, y, z 0 ) represents the measured potential field data at the observation surface height z 0 ; the value of n is from 1 to 6; Δh represents the downward extension height; z represents the height of the extension surface and is located below the observation surface.

[0067] In addition, as shown in Table 1 below, Table 1 shows the root mean square error between the present invention and the ISVD downward continuation calculation method of the potential field and the calculated result of the theoretical gravity anomaly of the upright hexahedron. Moreover, the error results in Table 1 indicate that the calculation accuracy of the present invention patent is higher and the error is smaller.

[0068] Table 1

[0069]

[0070] In addition, as shown in Table 2 below, Table 2 shows the root mean square error between the present invention and the ISVD downward continuation calculation method of the potential field and the theoretical anomaly of the height surface where the theoretical gravity anomaly of the upright hexahedron is added with Gaussian white noise. Moreover, the error results in Table 2 indicate that the calculation accuracy of the present invention patent is higher and the stability is stronger.

[0071] Table 2

[0072]

[0073] Therefore, compared with the prior art, the potential field downward continuation method of the present application has the technical effects of suppressing noise and high calculation accuracy, and can serve well in aspects such as geological structure interpretation and mineral resource exploration.

[0074] It should be understood that the above potential field downward continuation method based on the calculation of the vertical derivative by Hilbert transform is only exemplary, and those skilled in the art can make various deformations according to the above method, and the deformed solutions also fall within the protection scope of the present application.

[0075] Please refer to Figure 2 , Figure 2 which shows a structural block diagram of a potential field downward continuation system 200 provided by an embodiment of the present application based on the calculation of the vertical derivative by Hilbert transform. It should be understood that the potential field downward continuation system 200 can execute each step in the above method embodiment, and the specific functions of the potential field downward continuation system 200 can be referred to the description above. To avoid repetition, the detailed description is appropriately omitted here. The potential field downward continuation system 200 includes at least one software function module that can be stored in the memory in the form of software or firmware or solidified in the operating system (OS) of the potential field downward continuation system 200. Specifically, the potential field downward continuation system 200 includes:

[0076] An acquisition module 210, configured to acquire the measured potential field data at the observation surface height z 0 ; wherein, the measured potential field data includes gravity field anomaly data or magnetic field anomaly data;

[0077] The first calculation module 220 is configured to perform finite difference calculation on the measured potential field data to obtain the horizontal derivative of the measured potential field data, and use the moving average formula to eliminate the boundary effect of the calculated horizontal derivative, so as to obtain the processed horizontal derivative;

[0078] The construction calculation module 230 is configured to construct a vertical derivative recurrence formula based on the Hilbert transform including the potential field function according to the processed horizontal derivative, and calculate six vertical derivatives of the potential field function according to the vertical derivative recurrence formula based on the Hilbert transform; wherein, the six vertical derivatives include the first-order vertical derivative of the potential field function, the second-order vertical derivative of the potential field function, the third-order vertical derivative of the potential field function, the fourth-order vertical derivative of the potential field function, the fifth-order vertical derivative of the potential field function, and the sixth-order vertical derivative of the potential field function;

[0079] The second calculation module 240 is configured to calculate the potential field data extended downward by Δh height from the observation surface height z according to the Taylor series expansion of the potential field downward continuation and the six vertical derivatives of the potential field function. 0 Downward extended Δh height of the potential field data.

[0080] In a possible embodiment, the calculation expression of the horizontal derivative of the measured potential field data is as follows:

[0081]

[0082] In the formula, represents the first-order derivative in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; f i,j+1 represents the field value in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the (j + 1)-th column grid node is located; f i,j-1 represents the field value in the x direction of the grid node where the grid node at the intersection of the i-th row grid node and the (j - 1)-th column grid node is located; Δx represents the point distance in the x direction; represents the first-order derivative in the y direction of the grid node where the grid node at the intersection of the i-th row grid node and the j-th column grid node is located; f i+1,j represents the field value in the y direction of the grid node where the grid node at the intersection of the (i + 1)-th row grid node and the j-th column grid node is located; f i-1,j represents the field value in the y direction of the grid node where the grid node at the intersection of the (i - 1)-th row grid node and the j-th column grid node is located; Δy represents the point distance in the y direction.

[0083] In a possible embodiment, the calculation expression of the moving average formula is as follows:

[0084]

[0085] In the formula, represents the first-order derivative in the x direction of the grid node where the grid nodes in the i-th row and the j-th column intersect; k represents the sliding window size, and k is an odd number greater than 3. For example, k is equal to 7, etc.; represents the first-order derivative in the x direction of the grid node where the grid nodes in the l-th row and the m-th column intersect; represents the first-order derivative in the y direction of the grid node where the grid nodes in the i-th row and the j-th column intersect; represents the first-order derivative in the y direction of the grid node where the grid nodes in the l-th row and the m-th column intersect.

[0086] In a possible embodiment, the calculation expression for the potential field data extended downward by a height of Δh from the observation surface height z 0 is as follows:

[0087]

[0088] In the formula, Δf(x, y, z 0 +Δh) represents the potential field data extended downward by a height of Δh from the observation surface height z 0 Δf(x, y, z 0 ) represents the measured potential field data at the observation surface height z 0 n takes values from 1 to 6; Δh represents the downward extension height; z represents the height of the extension surface and is below the observation surface.

[0089] Since the system described in the above embodiments of the present invention is the system adopted for implementing the method in the above embodiments of the present invention, based on the method described in the above embodiments of the present invention, those skilled in the art can understand the specific structure and variations of the system, so it will not be elaborated here. Any system adopted for the method in the above embodiments of the present invention falls within the scope of protection of the present invention.

[0090] This application provides a storage medium, on which a computer program is stored, and when the computer program is run by a processor, it executes the method described in the embodiment.

[0091] This application also provides a computer program product, when the computer program product runs on a computer, it causes the computer to execute the method described in the method embodiment.

[0092] Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process of the system described above can refer to the corresponding process in the foregoing method, and will not be elaborated here too much.

[0093] It should be noted that the various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For device embodiments, since they are basically similar to method embodiments, they are described relatively simply. For the relevant parts, reference can be made to the descriptions in the method embodiments.

[0094] It should be understood that in various embodiments of the present application, the order numbers of the above processes do not indicate the order of execution. The execution order of each process should be determined according to its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present application.

[0095] In several embodiments provided by the present application, it should be understood that the disclosed devices and methods can also be implemented in other ways. The device embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the drawings show the possible architectures, functions, and operations of devices, methods, and computer program products according to multiple embodiments of the present application. In this regard, each block in the flowchart or block diagram can represent a module, a program segment, or a part of code, and the module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than marked in the drawings. For example, two consecutive blocks can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0096] In addition, in each embodiment of the present application, the functional modules can be integrated together to form an independent part, or each module can exist separately, or two or more modules can be integrated to form an independent part.

[0097] When the above-mentioned functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of this application. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes. It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including", or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements not only includes those elements, but also includes other elements not explicitly listed, or further includes elements inherent to such process, method, article, or device. Without more limitations, an element defined by the statement "comprising one..." does not exclude the existence of additional identical elements in the process, method, article, or device comprising the said element.

[0098] The above are only the preferred embodiments of this application and are not used to limit this application. For those skilled in the art, this application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of this application shall be included within the protection scope of this application. 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.

[0099] The above is only the specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any person skilled in the art within the technical scope disclosed by this application can easily think of changes or replacements, which should all be covered within the protection scope of this application. Therefore, the protection scope of this application should be subject to the protection scope of the claims.

Claims

1. A method for downward extension of potential field based on vertical derivative calculation of Hilbert transform, characterized in that: include: Acquire measured potential field data at the observation surface height z0; wherein the measured potential field data includes gravity field anomaly data or magnetic field anomaly data; Performing finite difference calculation on the measured potential field data to obtain horizontal derivatives of the measured potential field data, and performing boundary effect elimination processing on the calculated horizontal derivatives using a sliding average formula to obtain processed horizontal derivatives; According to the processed horizontal derivatives, a recursive formula of vertical derivatives based on Hilbert transform including the potential field function is constructed, and according to the recursive formula of vertical derivatives based on Hilbert transform, six vertical derivatives of the potential field function are calculated; wherein the six vertical derivatives include a first-order vertical derivative of the potential field function, a second-order vertical derivative of the potential field function, a third-order vertical derivative of the potential field function, a fourth-order vertical derivative of the potential field function, a fifth-order vertical derivative of the potential field function and a sixth-order vertical derivative of the potential field function; The potential field data extending downward from the observation surface height z0 to the height Δh are calculated based on the Taylor series expansion of the potential field downward and the six vertical derivatives of the potential field function.

2. The potential field downward extension method according to claim 1, characterized in that: The calculation expression of the horizontal derivative of the measured potential field data is as follows: In the formula, represents the first-order derivative of the grid node in the x direction where the grid node in the i-th row and the grid node in the j-th column intersect; f i,j+1 represents the field value in the x direction of the grid node where the grid node in the i-th row intersects the grid node in the j+1-th column; f i,j-1 represents the field value in the x direction of the grid node where the grid node in the i-th row intersects the grid node in the j-1-th column; Δx represents the point distance in the x direction; represents the first-order derivative of the grid node in the y direction where the grid node in the i-th row and the grid node in the j-th column intersect; f i+1,j represents the field value in the y direction of the grid node where the grid node in the i+1th row and the grid node in the jth column intersect; f i-1,j It represents the field value in the y direction of the grid node where the grid node in the i-1th row intersects the grid node in the jth column; Δy represents the point distance in the y direction.

3. The potential field downward extension method according to claim 1, characterized in that: The calculation expression of the sliding average formula is as follows: In the formula, represents the first-order derivative of the grid node in the x direction where the grid node in the i-th row and the grid node in the j-th column intersect; k represents the sliding window size; Represents the first-order derivative of the grid node in the x direction where the grid node in the lth row and the grid node in the mth column intersect; represents the first-order derivative in the y direction of the grid node where the grid node in the i-th row and the grid node in the j-th column intersect; Represents the first-order derivative in the y direction of the grid node where the l-th row grid node and the m-th column grid node intersect.

4. The potential field downward extension method according to claim 1, characterized in that: The calculation expression of the potential field data extending downward from the observation surface height z0 to the height Δh is as follows: In the formula, Δf(x,y,z0+Δh) represents the potential field data of the height Δh extended downward from the observation surface height z0; Δf(x,y,z0) represents the measured potential field data at the observation surface height z0; the value of n is 1 to 6; Δh represents the downward extension height; z represents the height of the extension surface and is located below the observation surface.

5. A potential field downward extension system based on Hilbert transform vertical derivative calculation, characterized in that: include: An acquisition module, used to acquire measured potential field data at the observation surface height z0; wherein the measured potential field data includes gravity field anomaly data or magnetic field anomaly data; A first calculation module is used to perform finite difference calculation on the measured potential field data to obtain the horizontal derivative of the measured potential field data, and to perform boundary effect elimination processing on the calculated horizontal derivative using a sliding average formula to obtain a processed horizontal derivative; Constructing a calculation module, used for constructing a vertical derivative recursion formula based on Hilbert transform including the potential field function according to the processed horizontal derivative, and calculating six vertical derivatives of the potential field function according to the vertical derivative recursion formula based on Hilbert transform; wherein the six vertical derivatives include the first-order vertical derivative of the potential field function, the second-order vertical derivative of the potential field function, the third-order vertical derivative of the potential field function, the fourth-order vertical derivative of the potential field function, the fifth-order vertical derivative of the potential field function and the sixth-order vertical derivative of the potential field function; The second calculation module is used to calculate the potential field data extending downward from the observation surface height z0 to the height Δh according to the Taylor series expansion of the potential field downward extension and the six vertical derivatives of the potential field function.

6. The potential field downward extension system according to claim 5, characterized in that: The calculation expression of the horizontal derivative of the measured potential field data is as follows: In the formula, represents the first-order derivative of the grid node in the x direction where the grid node in the i-th row and the grid node in the j-th column intersect; f i,j+1 represents the field value in the x direction of the grid node where the grid node in the i-th row intersects the grid node in the j+1-th column; f i,j-1 represents the field value in the x direction of the grid node where the grid node in the i-th row intersects the grid node in the j-1-th column; Δx represents the point distance in the x direction; represents the first-order derivative of the grid node in the y direction where the grid node in the i-th row and the grid node in the j-th column intersect; f i+1,j represents the field value in the y direction of the grid node where the grid node in the i+1th row and the grid node in the jth column intersect; f i-1,j It represents the field value in the y direction of the grid node where the grid node in the i-1th row intersects the grid node in the jth column; Δy represents the point distance in the y direction.

7. The potential field downward extension system according to claim 5, characterized in that: The calculation expression of the sliding average formula is as follows: In the formula, represents the first-order derivative of the grid node in the x direction where the grid node in the i-th row and the grid node in the j-th column intersect; k represents the sliding window size; Represents the first-order derivative of the grid node in the x direction where the grid node in the lth row and the grid node in the mth column intersect; represents the first-order derivative in the y direction of the grid node where the grid node in the i-th row and the grid node in the j-th column intersect; Represents the first-order derivative in the y direction of the grid node where the l-th row grid node and the m-th column grid node intersect.

8. The potential field downward extension system according to claim 5, characterized in that: The calculation expression of the potential field data extending downward from the observation surface height z0 to the height Δh is as follows: In the formula, Δf(x,y,z0+Δh) represents the potential field data of the height Δh extended downward from the observation surface height z0; Δf(x,y,z0) represents the measured potential field data at the observation surface height z0; the value of n is 1 to 6; Δh represents the downward extension height; z represents the height of the extension surface and is located below the observation surface.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for downward extension of the potential field based on vertical derivative calculation based on Hilbert transform as claimed in any one of claims 1 to 4 is executed.

10. An electronic device comprising a processor, a memory and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the potential field downward extension method for vertical derivative calculation based on Hilbert transform as described in any one of claims 1 to 4.

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