High-precision point-to-point stable potential field downward continuation method and device

Abstract

The invention relates to a high-precision point-to-point stable potential field downward continuation method and a high-precision point-to-point stable potential field downward continuation device. The method comprises the following steps: acquiring first potential field data of a research area at an observation surface height z0; calculating a first-order horizontal derivative of the first potential field data according to a finite difference formula; according to the first-order horizontal derivative of the first potential field data, constructing a Hilbert transform-based vertical guide number recursion formula, and according to the vertical guide number recursion formula, calculating a second-order vertical guide number, a fourth-order vertical guide number and a sixth-order vertical guide number; substituting the first potential field data into a frequency domain potential field upward continuation formula, and calculating second potential field data which extend upwards from the observation surface height z0 to the height of delta h; and substituting the second-order vertical guide number, the fourth-order vertical guide number, the sixth-order vertical guide number and the second potential field data into a point-to-point potential field downward continuation analytical solution formula, and calculating third potential field data of a height deltah downward continuation from the observation surface height z0, so that the calculation precision can be improved.

Description

Technical Field

[0001] The present invention relates to the field of gravity and magnetic exploration technology, and in particular to a method and device for downward extension of a high-precision point-to-point stable potential field. Background Art

[0002] In the field of geophysical exploration, downward extension of potential field is an important and complex technical means. It aims to accurately extend the observed potential field data (such as gravity field, magnetic field, etc.) from a certain observation plane to a deeper underground or lower altitude in order to reveal the underground geological structure, mineral resource distribution or other geophysical characteristics. However, since the influence of high-frequency noise will be amplified during the downward extension process, the downward extension of potential field is extremely unstable.

[0003] At present, the main methods for potential field extension include integral equation method, Taylor series expansion method, extrapolation method, regularized filtering method, high-frequency truncation, Wiener filtering and iteration method. Although these improvement measures can effectively suppress the high-frequency amplification effect of the frequency domain potential field downward extension factor, it is difficult to select the filtering parameters, number of iterations and step size. In order to overcome the above technical difficulties and challenges, the point-to-point stable potential field downward extension method came into being.

[0004] Among them, the principle of the point-to-point downward extension method is to omit the high-order terms of the potential field anomaly expansion according to the Taylor series expansion method, and use the upward extension calculation results and the potential field value of the point to calculate the potential field distribution of a certain height downward extension. Since the upward extension is stable, the stability of this method is very good, but due to the omission of the high-order terms of the potential field anomaly expansion, the accuracy of this method is poor. The high-order terms of the potential field anomaly expansion include high-order derivative terms, and the calculation of the high-order derivatives of the potential field anomaly is unstable. If the high-order terms are retained, the calculation method will be unstable. Therefore, in the study of gravity and magnetic exploration methods, the high-precision stable potential field downward extension method needs to be further explored.

[0005] According to literature research at home and abroad, there is currently no practical, high-precision, stable potential field downward extension method that does not require the selection of too many parameters and can extend downward to a greater depth. Therefore, it is necessary to study and propose a stable potential field extension method that can extend downward to a greater depth. Summary of the invention

[0006] 1. Technical issues to be resolved

[0007] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a high-precision point-to-point stable potential field downward extension method and device, which solves the technical problem of low precision existing in the prior art.

[0008] (II) Technical solution

[0009] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0010] In the first aspect, an embodiment of the present invention provides a high-precision point-to-point stable potential field downward extension method, the method comprising: obtaining the first bit field data of the study area at the observation surface height z0; calculating the first-order horizontal derivative of the first bit field data according to the finite difference formula; constructing a vertical derivative recursion formula based on the Hilbert transform according to the first-order horizontal derivative of the first bit field data, and calculating the second-order vertical derivative, fourth-order vertical derivative and sixth-order vertical derivative according to the vertical derivative recursion formula; substituting the first bit field data into the frequency domain potential field upward extension formula, and calculating the second potential field data of Δh height extended upward from the observation surface height z0; substituting the second-order vertical derivative, fourth-order vertical derivative, sixth-order vertical derivative and the second potential field data into the analytical solution formula for the point-to-point potential field downward extension, and calculating the third potential field data of Δh height extended downward from the observation surface height z0.

[0011] In a possible embodiment, the calculation expression of the vertical derivative recursion formula is:

[0012]

[0013] Where, f represents the potential field function; represents the 2m-order vertical derivative of the potential field function; F and F -1 They are the forward and inverse transforms of Fourier transform respectively; represents the response of the two-dimensional Hilbert transform system in the wavenumber domain, u and v are the wave numbers in the x and y directions respectively, e x and e y are unit vectors in the x and y directions respectively; Represents the 2m-1th order vertical derivative of the potential field function; the values ​​of m are 1, 2 and 3.

[0014] In a possible embodiment, the calculation expression of the frequency domain potential field upward extension formula is:

[0015]

[0016] Wherein, Δf(x,y,z0-Δh) represents the second bit field data.

[0017] In a possible embodiment, the calculation expression of the analytical solution formula of the point-to-point potential field downward extension is:

[0018]

[0019] Among them, Δf(x,y,z0+Δh) represents the third field data; Δf(x,y,z0) represents the first field data.

[0020] In the second aspect, an embodiment of the present invention provides a high-precision point-to-point stable potential field downward extension device, including: an acquisition module, used to obtain the first bit field data of the study area at the observation surface height z0; a first calculation module, used to calculate the first-order horizontal derivative of the first bit field data according to the finite difference formula; a construction calculation module, used to construct a vertical derivative recursion formula based on the Hilbert transform according to the first-order horizontal derivative of the first bit field data, and calculate the second-order vertical derivative, fourth-order vertical derivative and sixth-order vertical derivative according to the vertical derivative recursion formula; a second calculation module, used to substitute the first bit field data into the frequency domain potential field upward extension formula, and calculate the second potential field data of Δh height extended upward from the observation surface height z0; a third calculation module, used to substitute the second-order vertical derivative, fourth-order vertical derivative, sixth-order vertical derivative and the second potential field data into the analytical solution formula of the point-to-point potential field downward extension, and calculate the third potential field data of Δh height extended downward from the observation surface height z0.

[0021] In a possible embodiment, the calculation expression of the vertical derivative recursion formula is:

[0022]

[0023] Where, f represents the potential field function; represents the 2m-order vertical derivative of the potential field function; F and F -1 They are the forward and inverse transforms of Fourier transform respectively; represents the response of the two-dimensional Hilbert transform system in the wavenumber domain, u and v are the wave numbers in the x and y directions respectively, e x and e y are unit vectors in the x and y directions respectively; Represents the 2m-1th order vertical derivative of the potential field function; the values ​​of m are 1, 2 and 3.

[0024] In a possible embodiment, the calculation expression of the frequency domain potential field upward extension formula is:

[0025]

[0026] Wherein, Δf(x,y,z0-Δh) represents the second bit field data.

[0027] In a possible embodiment, the calculation expression of the analytical solution formula of the point-to-point potential field downward extension is:

[0028]

[0029] Among them, Δf(x,y,z0+Δh) represents the third field data; Δf(x,y,z0) represents the first field data.

[0030] In a third aspect, an embodiment of the present application provides a storage medium having a computer program stored thereon, and the computer program is executed by a processor to execute the method described in the first aspect or any optional implementation of the first aspect.

[0031] In a fourth aspect, an embodiment of the present application provides an electronic device, comprising: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the method described in the first aspect or any optional implementation method of the first aspect is performed.

[0032] In a fifth aspect, the present application provides a computer program product, which, when running on a computer, enables the computer to execute the method in the first aspect or any possible implementation of the first aspect.

[0033] (III) Beneficial effects

[0034] The beneficial effects of the present invention are:

[0035] The present application provides a method and device for downward extension of a high-precision point-to-point stable potential field, which obtains the first-order horizontal derivative of the first-order field data at the observation surface height z0 of the study area, and constructs a vertical derivative recursion formula based on the Hilbert transform according to the first-order horizontal derivative of the first-order field data, and calculates the second-order vertical derivative, the fourth-order vertical derivative and the sixth-order vertical derivative according to the vertical derivative recursion formula, and substitutes the first-order field data into the frequency domain potential field upward extension formula to calculate The second potential field data of the height Δh extended upward from the observation surface height z0 is obtained, and the second-order vertical derivative, the fourth-order vertical derivative, the sixth-order vertical derivative and the second potential field data are substituted into the analytical solution formula of the point-to-point downward extension of the potential field, and the third potential field data of the height Δh extended downward from the observation surface height z0 is calculated. Compared with the prior art, the potential field downward extension method of the present application has the effect of suppressing high-frequency noise, and its downward extension depth and accuracy are better than the current mainstream methods, and can well serve the geological structure interpretation and mineral resource exploration and other aspects.

[0036] In order to make the above-mentioned objectives, features and advantages to be achieved by the embodiments of the present application more obvious and understandable, the following specifically cites preferred embodiments and describes them in detail with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 A flow chart of a method for downward extension of a high-precision point-to-point stable potential field provided by an embodiment of the present application is shown;

[0039] Figure 2 It is a comparison diagram of the theoretical gravity anomaly calculation result of the right hexahedron model, the calculation result of the potential field downward continuation by the ISVD method and the calculation result of the potential field downward continuation provided by the present invention, wherein (a), (d), (g), (j) are the theoretical gravity anomalies corresponding to the heights z=0m, 800m, 1600m, 2400m, and 3200m respectively; (b), (e), (h), (k) are the gravity anomalies corresponding to the downward continuation of 800m (4 times the point spacing), 1600m (8 times the point spacing), 2400m (12 times the point spacing), and 3200m (16 times the point spacing) according to the present invention respectively; (c), (f), (i), (l) are the gravity anomalies corresponding to the downward continuation of 800m (4 times the point spacing), 1600m (8 times the point spacing), 2400m (12 times the point spacing), and 3200m (16 times the point spacing) according to the ISVD method respectively;

[0040] Figure 3 After adding Gaussian white noise to the theoretical gravity anomaly of the right hexahedron model, the comparison diagram of the potential field downward continuation calculation results of the ISVD method and the potential field downward continuation calculation results provided by the present invention, wherein (a), (d), (g), (j) are the theoretical gravity anomalies corresponding to heights z=0m, 800m, 1600m, 2400m, and 3200m, respectively; (b), (e), (h), (k) are the gravity anomalies corresponding to the downward continuation of the present invention to 800m (4 times the point spacing), 1600m (8 times the point spacing), 2400m (12 times the point spacing), and 3200m (16 times the point spacing); (c), (f), (i), and (l) are the gravity anomalies corresponding to the downward continuation of the ISVD method to 800m (4 times the point spacing), 1600m (8 times the point spacing), 2400m (12 times the point spacing), and 3200m (16 times the point spacing);

[0041] Figure 4 A structural block diagram of a high-precision point-to-point stable potential field downward extension device provided in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0042] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation modes in conjunction with the accompanying drawings.

[0043] The present application provides a method and device for downward extension of a high-precision point-to-point stable potential field, which obtains the first-order horizontal derivative of the first-order field data at the observation surface height z0 of the study area, and constructs a vertical derivative recursion formula based on the Hilbert transform according to the first-order horizontal derivative of the first-order field data, and calculates the second-order vertical derivative, the fourth-order vertical derivative and the sixth-order vertical derivative according to the vertical derivative recursion formula, and substitutes the first-order field data into the frequency domain potential field upward extension formula to calculate The second potential field data of the height Δh extended upward from the observation surface height z0 is obtained, and the second-order vertical derivative, the fourth-order vertical derivative, the sixth-order vertical derivative and the second potential field data are substituted into the analytical solution formula of the point-to-point downward extension of the potential field, and the third potential field data of the height Δh extended downward from the observation surface height z0 is calculated. Compared with the prior art, the potential field downward extension method of the present application has the effect of suppressing high-frequency noise, and its downward extension depth and accuracy are better than the current mainstream methods, and can well serve the geological structure interpretation and mineral resource exploration and other aspects.

[0044] In order to better understand the above technical solution, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a clearer and more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0045] See also Figure 1 , Figure 1 A flow chart of a method for downward extension of a high-precision point-to-point stable potential field provided by an embodiment of the present application is shown. It should be understood that the method for downward extension of a high-precision point-to-point stable potential field can be performed by a high-precision point-to-point stable potential field downward extension device, and the specific device of the high-precision point-to-point stable potential field downward extension device can be set according to actual needs, and the embodiment of the present application is not limited to this. For example, the high-precision point-to-point stable potential field downward extension device can be a computer, or a server, etc. Specifically, the method for downward extension of a high-precision point-to-point stable potential field includes:

[0046] Step S110, obtaining the first bit field data of the study area at the observation surface height z0.

[0047] It should be understood that the first bit field data may include first gravity anomaly data or first magnetic anomaly data.

[0048] Correspondingly, the second bit field data and the third bit field data are similar to the first bit field data. For example, the second bit field data may include second gravity anomaly data or second magnetic anomaly data; for another example, the third bit field data may include third gravity anomaly data or third magnetic anomaly data.

[0049] Specifically, the relevant data of step S110 is input data, and the first field data may include Bouguer gravity anomaly or polarization magnetic anomaly, which can be collected through a public website to obtain free space gravity anomaly and magnetic anomaly data, and Bouguer gravity anomaly obtained through generalized terrain correction technology, and polarization magnetic anomaly obtained through full-angle polarization technology. In addition, all data are input in grid file (.grd) format.

[0050] Step S120, calculating the first-order horizontal derivative of the first bit field data according to the finite difference formula.

[0051] Specifically, for the first bit field data of step S110, the first-order horizontal derivative of the first bit field data can be calculated using a finite difference formula, and the calculation expression of the finite difference formula is as follows:

[0052]

[0053] 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-2 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-2-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; 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+2 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+2-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-2,j represents the field value in the y direction of the grid node where the grid node in the i-2th row intersects the grid node in the jth column; 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 intersects the grid node in the jth column; 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+2,j It represents the field value in the y direction of the grid node where the grid node in the i+2th row intersects with the grid node in the jth column; Δy represents the point distance in the y direction.

[0054] Step S130, constructing a vertical derivative recursion formula based on Hilbert transform according to the first-order horizontal derivative of the first bit field data, and calculating the second-order vertical derivative, the fourth-order vertical derivative and the sixth-order vertical derivative according to the vertical derivative recursion formula.

[0055] Specifically, according to the calculation result of the first-order horizontal derivative of the first field data, the first-order vertical derivative is calculated using the potential field vertical derivative recursion formula based on Hilbert transform, and the calculation expression of the vertical derivative recursion formula is as follows:

[0056]

[0057] Where, f represents the potential field function; represents the 2m-order vertical derivative of the potential field function; F and F -1 They are the forward and inverse transforms of Fourier transform respectively; represents the response of the two-dimensional Hilbert transform system in the wavenumber domain, u and v are the wave numbers in the x and y directions respectively, e x and e y are unit vectors in the x and y directions respectively; Represents the 2m-1th order vertical derivative of the potential field function; the values ​​of m are 1, 2 and 3.

[0058] On the basis of the above vertical derivative recursion formula, using the potential field vertical derivative recursion formula based on Hilbert transform, the above steps S120 and S130 are continuously repeated to obtain the second-order vertical derivative, the fourth-order vertical derivative and the sixth-order vertical derivative.

[0059] Step S140, substitute the first bit field data into the frequency domain bit field upward extension formula to calculate the second bit field data extending upward from the observation surface height z0 by Δh. The specific height of Δh can be set according to actual needs, and the embodiment of the present application is not limited thereto.

[0060] Specifically, according to the frequency domain potential field upward extension formula, the first potential field data is used to calculate the second potential field data extending upward from the observation surface height z0 to a height of Δh, and the calculation expression of the second potential field data is as follows:

[0061]

[0062] In the formula, z0 represents the height of the observation surface; the z-axis direction is positive downward; Δh=z-z0 represents the downward extension height; x and y represent the horizontal coordinates respectively; Δf(x, y, z0-Δh) represents the second bit field data at the Δh height extended upward from the z0 height.

[0063] Step S150, substitute the second-order vertical derivative, the fourth-order vertical derivative, the sixth-order vertical derivative and the second potential field data into the analytical solution formula of the point-to-point potential field downward extension, and calculate the third potential field data extending downward from the observation surface height z0 to a height of Δh.

[0064] Specifically, according to the analytical solution formula of the downward extension of the potential field from point to point, the second-order vertical derivative, the fourth-order vertical derivative, the sixth-order vertical derivative and the second potential field data of the potential field are used to calculate the downward extension abnormal field of the potential field, and the analytical solution formula of the downward extension of the potential field from point to point is:

[0065]

[0066] In the formula, Δf(x, y, z0) represents the first bit field data; Δf(x, y, z0+Δh) represents the third bit field data; Δh=z-z0 represents the downward extension height, and takes half of the truncation order: m=3.

[0067] In addition, according to the above process, the comparison of the theoretical gravity anomaly calculation results of the right hexahedron model, the downward extension calculation results of the potential field of the ISVD method and the downward extension calculation results of the potential field provided by the present invention is shown in the figure below: Figure 2 shown.

[0068] In a specific embodiment, Table 1 shows the root mean square error of the calculation results of the gravity anomaly of the present invention and the ISVD potential field downward extension calculation method and the right hexahedron theory, and as shown in Table 1, the error results show that the calculation accuracy of the patent of the present invention is higher and the error is smaller.

[0069] Table 1

[0070]

[0071] In addition, according to the above process, after adding Gaussian white noise to the theoretical gravity anomaly of the right hexahedron model, the comparison diagram of the potential field downward continuation calculation results of the ISVD method and the potential field downward continuation calculation results provided by the present invention is shown in the figure below: Figure 3 shown.

[0072] In a specific embodiment, Table 2 shows the root mean square error of the present invention and the ISVD potential field downward extension calculation method and the theoretical anomaly of the height surface after Gaussian white noise is added to the theoretical gravity anomaly of the right hexahedron. As shown in Table 2, the error results show that the calculation accuracy of the patent of the present invention is higher and the stability is stronger.

[0073] Table 2

[0074]

[0075] From the above description, it can be seen that the present application achieves the following technical effects: the first is strong noise resistance, because in the process of calculating each order of vertical derivatives, the noise will be suppressed once, so when the calculation of the potential field is abnormally extended downward, the noise suppression effect will be enhanced; the second is that the calculation result has high precision. In the point-to-point stable potential field downward extension method based on high-precision vertical derivatives proposed in the present invention, the semi-truncation order of the Taylor series is m=3, while the traditional method is affected by the calculation accuracy and stability of high-order derivatives, and the semi-truncation order m is usually 1 or 2. Therefore, the calculation result of the present invention has high calculation accuracy.

[0076] It should be understood that the above-mentioned high-precision point-to-point stable potential field downward extension method is only exemplary, and those skilled in the art can make various modifications based on the above-mentioned method, and the modified scheme also belongs to the protection scope of this application.

[0077] See also Figure 4 , Figure 4 A structural block diagram of a high-precision point-to-point stable potential field downward extension device 400 provided in an embodiment of the present application is shown. It should be understood that the high-precision point-to-point stable potential field downward extension device 400 is capable of executing each step in the above method embodiment. The specific functions of the high-precision point-to-point stable potential field downward extension device 400 can be found in the description above. To avoid repetition, the detailed description is appropriately omitted here. The high-precision point-to-point stable potential field downward extension device 400 includes at least one software function module that can be stored in a memory in the form of software or firmware or solidified in the operating system (OS) of the high-precision point-to-point stable potential field downward extension device 400. Specifically, the high-precision point-to-point stable potential field downward extension device 400 includes:

[0078] An acquisition module 410 is used to acquire the first bit field data of the study area at the observation surface height z0;

[0079] A first calculation module 420, used for calculating the first-order horizontal derivative of the first bit field data according to a finite difference formula;

[0080] A calculation module 430 is constructed to construct a vertical derivative recursion formula based on Hilbert transform according to the first-order horizontal derivative of the first bit field data, and calculate the second-order vertical derivative, the fourth-order vertical derivative and the sixth-order vertical derivative according to the vertical derivative recursion formula;

[0081] The second calculation module 440 is used to substitute the first potential field data into the frequency domain potential field upward extension formula to calculate the second potential field data extending upward from the observation surface height z0 to a height of Δh;

[0082] The third calculation module 450 is used to substitute the second-order vertical derivative, the fourth-order vertical derivative, the sixth-order vertical derivative and the second potential field data into the analytical solution formula of the point-to-point potential field downward extension, and calculate the third potential field data extending downward from the observation surface height z0 to a height of Δh.

[0083] In a possible embodiment, the calculation expression of the vertical derivative recursion formula is:

[0084]

[0085] Where, f represents the potential field function; represents the 2m-order vertical derivative of the potential field function; F and F -1 They are the forward and inverse transforms of Fourier transform respectively; represents the response of the two-dimensional Hilbert transform system in the wavenumber domain, u and v are the wave numbers in the x and y directions respectively, e x and e y are unit vectors in the x and y directions respectively; Represents the 2m-1th order vertical derivative of the potential field function; the values ​​of m are 1, 2 and 3.

[0086] In a possible embodiment, the calculation expression of the frequency domain potential field upward extension formula is:

[0087]

[0088] Wherein, Δf(x,y,z0-Δh) represents the second bit field data.

[0089] In a possible embodiment, the calculation expression of the analytical solution formula of the point-to-point potential field downward extension is:

[0090]

[0091] Among them, Δf(x,y,z0+Δh) represents the third field data; Δf(x,y,z0) represents the first field data.

[0092] Since the device described in the above embodiment of the present invention is a device used to implement the method of the above embodiment of the present invention, based on the method described in the above embodiment of the present invention, a person skilled in the art can understand the specific structure and deformation of the device, so it is not described here. All devices used in the method of the above embodiment of the present invention belong to the scope of protection of the present invention.

[0093] The present application provides a storage medium having a computer program stored thereon. The computer program is executed by a processor to execute the method described in the embodiment.

[0094] The present application also provides a computer program product, which, when executed on a computer, enables the computer to execute the method described in the method embodiment.

[0095] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0096] The present invention is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present invention. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions.

[0097] It should be noted that in the claims, any reference numerals placed between brackets shall not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention may be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In the claims enumerating several means, several of these means may be embodied by the same hardware. The use of the words first, second, third, etc., is for convenience of expression only and does not indicate any order. These words may be understood as part of the component name.

[0098] In addition, it should be noted that, in the description of this specification, the description of the terms "one embodiment", "some embodiments", "embodiment", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

[0099] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments after knowing the basic creative concept. Therefore, the claims should be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0100] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include these modifications and variations.

Claims

1. A high-precision point-to-point stable potential field downward continuation method, characterized in that: include: Obtain the first bit field data of the study area at the observation surface height z0; Calculate the first-order horizontal derivative of the first potential field data according to a finite difference formula; According to the first-order horizontal derivative of the first potential field data, a vertical derivative recursion formula based on Hilbert transform is constructed, and according to the vertical derivative recursion formula, a second-order vertical derivative, a fourth-order vertical derivative and a sixth-order vertical derivative are calculated; Substituting the first potential field data into the frequency domain potential field upward extension formula, calculating the second potential field data extending upward from the observation surface height z0 to a height of Δh; Substitute the second-order vertical derivative, the fourth-order vertical derivative, the sixth-order vertical derivative and the second potential field data into the analytical solution formula of the point-to-point potential field downward extension to calculate the third potential field data extending downward from the observation surface height z0 by the height Δh.

2. The high-precision point-to-point stable potential field downward continuation method according to claim 1 is characterized in that: The calculation expression of the vertical derivative recursion formula is: Where, f represents the potential field function; represents the 2m-order vertical derivative of the potential field function; F and F -1 They are the forward and inverse transforms of Fourier transform respectively; represents the response of the two-dimensional Hilbert transform system in the wavenumber domain, u and v are the wave numbers in the x and y directions respectively, e x and e y are unit vectors in the x direction and the y direction respectively; represents the 2m-1 order vertical derivative of the potential field function; the value of m is 1, 2 and 3.

3. The high-precision point-to-point stable potential field downward continuation method according to claim 2 is characterized in that: The calculation expression of the upward extension formula of the frequency domain potential field is: Wherein, Δf(x, y, z0-Δh) represents the second bit field data.

4. The high-precision point-to-point stable potential field downward continuation method according to claim 3 is characterized in that: The calculation expression of the analytical solution formula for the downward extension of the point-to-point potential field is: Among them, Δf(x, y, z0+Δh) represents the third bit field data; Δf(x, y, z0) represents the first bit field data.

5. A high-precision point-to-point stable potential field downward extension device, characterized in that: include: An acquisition module is used to acquire the first bit field data of the study area at the observation surface height z0; A first calculation module, used for calculating the first-order horizontal derivative of the first potential field data according to a finite difference formula; Constructing a calculation module, for constructing a vertical derivative recursion formula based on Hilbert transform according to the first-order horizontal derivative of the first potential field data, and calculating the second-order vertical derivative, the fourth-order vertical derivative and the sixth-order vertical derivative according to the vertical derivative recursion formula; A second calculation module is used to substitute the first potential field data into the frequency domain potential field upward extension formula to calculate the second potential field data extending upward from the observation surface height z0 to a height of Δh; The third calculation module is used to substitute the second-order vertical derivative, the fourth-order vertical derivative, the sixth-order vertical derivative and the second potential field data into the analytical solution formula of the point-to-point potential field downward extension, and calculate the third potential field data extending downward from the observation surface height z0 to the height Δh.

6. The high-precision point-to-point stable potential field downward extension device according to claim 5, characterized in that: The calculation expression of the vertical derivative recursion formula is: Where, f represents the potential field function; represents the 2m-order vertical derivative of the potential field function; F and F -1 They are the forward and inverse transforms of Fourier transform respectively; represents the response of the two-dimensional Hilbert transform system in the wavenumber domain, u and v are the wave numbers in the x and y directions respectively, e x and e y are unit vectors in the x direction and the y direction respectively; represents the 2m-1 order vertical derivative of the potential field function; the value of m is 1, 2 and 3.

7. The high-precision point-to-point stable potential field downward extension device according to claim 6, characterized in that: The calculation expression of the upward extension formula of the frequency domain potential field is: Wherein, Δf(x, y, z0-Δh) represents the second bit field data.

8. The high-precision point-to-point stable potential field downward extension device according to claim 7, characterized in that: The calculation expression of the analytical solution formula for the downward extension of the point-to-point potential field is: Among them, Δf(x, y, z0+Δh) represents the third bit field data; Δf(x, y, z0) represents the first bit field data.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the high-precision point-to-point stable potential field downward extension method as described in any one of claims 1-4 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 high-precision point-to-point stable potential field downward extension method as described in any one of claims 1-4.

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