CN112800657B - Gravity field numerical simulation method and device based on complex terrain and computer equipment - Google Patents
Gravity field numerical simulation method and device based on complex terrain and computer equipment Download PDFInfo
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Abstract
The application relates to a gravity field numerical simulation method and device based on complex terrain, computer equipment and a storage medium. The method comprises the following steps: constructing a three-dimensional cuboid model containing complex terrain and an exploration target, carrying out grid subdivision to obtain a plurality of small cuboids, and setting the spatial domain density values of the small cuboids; obtaining an offset wave number according to grid parameters of grid subdivision and preset Gaussian parameters, dividing a three-dimensional cuboid model into a lower part model and an upper part model according to topographic information, calculating frequency domain gravity abnormal fields of a plurality of observation surfaces in a blocking and overlapping mode, performing two-dimensional Gaussian Fourier inversion to obtain space domain gravity abnormal fields of the plurality of observation surfaces, and obtaining the space domain gravity abnormal fields of complex topographic relief surfaces through a spline interpolation algorithm. The method has the advantages that the vertical direction is reserved in a spatial domain, the grid subdivision is flexible, the method is suitable for simulating complex terrains and complex geologic bodies, the multiple offset wave numbers are convenient for parallel calculation, and the calculation efficiency of the gravity anomaly is improved.
Description
Technical Field
The present invention relates to the field of computer numerical simulation technologies, and in particular, to a gravity field numerical simulation method and apparatus based on a complex terrain, a computer device, and a storage medium.
Background
At the present stage, due to the increase of gravity observation data, the memory and calculation required by the forward performance of the gravity field are increased rapidly, and the problem that the realization of a common computer is difficult and the problem becomes a difficult problem of three-dimensional density rapid imaging.
At present, the spatial domain method still dominates the accuracy, but with the application of the standard FFT edge extension method and the NUFFT in the gravity anomaly forward numerical simulation, the frequency domain method becomes the preferred method for dealing with the large-scale forward with the simplicity, accuracy and high correction. In the literature (Chai Y, Hinze W J. Gravity inversion of an interface above while the noise contrast with depth. Geophysics, 1988, 53(6):837 and 845.) the offset sampling method is adopted to effectively improve the precision of Fourier transform, so that the frequency domain method is gradually applied to the forward modeling of a complex model. The literature (Tontini, F.C., L. Cocchi, C. Carmicroscopical No. Rapid 3-D forward model of potential fields with application to the Linear magnetic analysis (southern Tyrrhean Sea, Italy) Journal of geographic Research, 2009.114.) gives an expression for the frequency domain of gravity anomaly in the case of arbitrary density distributions.
In the prior art, large-scale and large-scale aviation gravity measurement is already started, but the terrain in actual aviation measurement is not a plane but a complex undulating terrain, the traditional space domain method and frequency domain method are difficult to meet the requirement of fine and rapid inversion of massive high-resolution data, and the problem of poor adaptability exists, so that the research of the three-dimensional gravity anomaly high-efficiency high-precision numerical simulation method based on the complex terrain has practical significance.
Disclosure of Invention
In view of the foregoing, it is desirable to provide a gravity field numerical simulation method and apparatus based on complex terrain, a computer device, and a storage medium, which are applicable to the gravity field numerical simulation of complex terrain.
A gravity field numerical simulation method based on complex terrain, the method comprising:
according to terrain information of a complex terrain and target information of an exploration target, constructing a three-dimensional cuboid model containing the complex terrain and the exploration target, carrying out grid subdivision on the three-dimensional cuboid model in the x-axis direction, the y-axis direction and the z-axis direction to obtain a plurality of small cuboids, wherein the sizes of the small cuboids in the x-axis direction and the y-axis direction are the same, and setting the spatial domain density value of the small cuboids according to the terrain information and the target information;
obtaining an offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters;
obtaining a space domain gravity potential integral expression of the three-dimensional rectangular solid model according to the space domain density value and the grid parameters, and performing two-dimensional Gaussian Fourier transform on the space domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional rectangular solid model;
dividing the three-dimensional rectangular solid model into a lower part model and an upper part model according to the topographic information, and respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number; the lower part model is a cuboid model of a part below the lowest point of the complex terrain, and the upper part model is a cuboid model of a part above the lowest point;
obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, preset relationship information among frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral, and calculating frequency domain gravity anomaly fields of a plurality of observation surfaces according to the frequency domain gravity anomaly expression;
performing two-dimensional Gaussian Fourier inversion on the frequency domain gravity abnormal field along the horizontal direction to obtain space domain gravity abnormal fields of a plurality of observation surfaces; the observation surface is a horizontal surface corresponding to a fixed value in the z-axis direction;
and obtaining a numerical simulation result of the space domain gravity abnormal field of the undulating surface of the complex terrain by a spline interpolation algorithm according to the space domain gravity abnormal fields of the plurality of observation surfaces.
In one embodiment, the method further comprises the following steps: setting the spatial domain density value of the small cuboid according to the terrain information and the target information; the density of the small cuboid is a constant value, the density values of different small cuboids are different, and the density of the small cuboid in the air part is set to be zero.
In one embodiment, the method further comprises the following steps: obtaining an offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters:
wherein the content of the first and second substances,
、
representing the offset wavenumbers in the x and y directions respectively,
which represents the coordinates of a gaussian point or points,
indicates the number of the adopted Gaussian points,
，
the number of base waves in the x and y directions, respectively, can be expressed as:
，
；p andqrespectively represent a sequence of integers whenp Andqwhen the number is even:
when in usep Andqwhen the number is odd:
In one embodiment, the method further comprises the following steps: obtaining a space domain gravitational potential integral expression of the three-dimensional rectangular solid model according to the space domain density value and the grid parameters, wherein the space domain gravitational potential integral expression comprises the following expression:
wherein the content of the first and second substances,Urepresenting the spatial domain gravitational potential;Gis a constant of attraction;m、n、lfor convolution countingAn amount;
is indicated by the reference number
The spatial domain density value of the small cuboid;
，
in order to observe the coordinates of the points,
representing source point coordinates;
and performing two-dimensional Fourier transform on the spatial domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional rectangular solid model, wherein the frequency domain gravity potential integral expression comprises the following components:
wherein the content of the first and second substances,
which represents the potential of gravity in the frequency domain,
and
are respectivelyxAndythe number of directional spatial waves is such that,
is the wave number;irepresenting an imaginary number;erepresents a natural constant;
as an integral coefficient, it can be expressed as:
Ione-dimensional integrals representing different offset wavenumbers:
in one embodiment, the method further comprises the following steps: dividing the three-dimensional rectangular solid model into a lower part model and an upper part model according to the terrain information, and respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number as follows:
wherein the content of the first and second substances,
representing the first vertical one-dimensional integral;
representing the second vertical one-dimensional integral;
representing the mesh division number in the z-axis direction of the part below the lowest point of the complex terrain;
and the mesh division number in the z-axis direction of the part above the lowest point is shown.
In one embodiment, the method further comprises the following steps: obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, preset relationship information among frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral:
wherein the content of the first and second substances,
representing a frequency domain gravity anomaly;
respectively representing the components of the frequency domain gravity anomaly in the x direction, the y direction and the z direction;
the density value of the frequency domain is shown,
。
in one embodiment, the method further comprises the following steps: corresponding the different offset wavenumbers to the integral coefficients
Component values in the first vertical one-dimensional integral
And component values of said second vertical one-dimensional integral
、
Storing;
and directly calling the stored values when calculating the frequency domain gravity anomaly fields of the plurality of observation surfaces.
A gravity field numerical simulation apparatus based on complex terrain, the apparatus comprising:
the model establishing module is used for establishing a three-dimensional cuboid model containing the complex terrain and an exploration target according to terrain information of the complex terrain and target information of the exploration target, carrying out grid subdivision on the three-dimensional cuboid model in the x-axis direction, the y-axis direction and the z-axis direction to obtain a plurality of small cuboids, wherein the sizes of each small cuboid in the x-axis direction and the y-axis direction are the same, and setting the spatial domain density value of each small cuboid according to the terrain information and the target information;
the offset wave number calculation module is used for obtaining an offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters;
the frequency domain gravity potential integral expression acquisition module is used for acquiring a space domain gravity potential integral expression of the three-dimensional rectangular solid model according to the space domain density value and the grid parameters, and performing two-dimensional Fourier transform on the space domain gravity potential integral expression along the horizontal direction to acquire the frequency domain gravity potential integral expression of the three-dimensional rectangular solid model;
a vertical one-dimensional integral obtaining module, configured to divide the three-dimensional rectangular solid model into a lower part model and an upper part model according to the terrain information, and calculate a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number; the lower part model is a cuboid model of a part below the lowest point of the complex terrain, and the upper part model is a cuboid model of a part above the lowest point;
the frequency domain gravity abnormal field acquisition module is used for obtaining a frequency domain gravity abnormal expression according to the frequency domain gravity potential integral expression, preset relationship information among frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral, and calculating the frequency domain gravity abnormal fields of a plurality of observation surfaces according to the frequency domain gravity abnormal expression;
the spatial domain gravity abnormal field acquisition module is used for performing two-dimensional Fourier inverse transformation on the frequency domain gravity abnormal field along the horizontal direction to obtain spatial domain gravity abnormal fields of a plurality of observation surfaces; the observation surface is a horizontal surface corresponding to a specific value in the z-axis direction; and obtaining the space domain gravity abnormal field of the undulating surface of the complex terrain by a spline interpolation algorithm according to the space domain gravity abnormal fields of the plurality of observation surfaces.
A computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the following steps when executing the computer program:
according to terrain information of a complex terrain and target information of an exploration target, constructing a three-dimensional cuboid model containing the complex terrain and the exploration target, carrying out grid subdivision on the three-dimensional cuboid model in the x-axis direction, the y-axis direction and the z-axis direction to obtain a plurality of small cuboids, wherein the sizes of the small cuboids in the x-axis direction and the y-axis direction are the same, and setting the spatial domain density value of the small cuboids according to the terrain information and the target information;
obtaining an offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters;
obtaining a space domain gravity potential integral expression of the three-dimensional rectangular solid model according to the space domain density value and the grid parameters, and performing two-dimensional Gaussian Fourier transform on the space domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional rectangular solid model;
dividing the three-dimensional rectangular solid model into a lower part model and an upper part model according to the topographic information, and respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number; the lower part model is a cuboid model of a part below the lowest point of the complex terrain, and the upper part model is a cuboid model of a part above the lowest point;
obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, preset relationship information among frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral, and calculating frequency domain gravity anomaly fields of a plurality of observation surfaces according to the frequency domain gravity anomaly expression;
performing two-dimensional Gaussian Fourier inversion on the frequency domain gravity abnormal field along the horizontal direction to obtain space domain gravity abnormal fields of a plurality of observation surfaces; the observation surface is a horizontal surface corresponding to a fixed value in the z-axis direction;
and obtaining a numerical simulation result of the space domain gravity abnormal field of the undulating surface of the complex terrain by a spline interpolation algorithm according to the space domain gravity abnormal fields of the plurality of observation surfaces.
A computer-readable storage medium, on which a computer program is stored which, when executed by a processor, carries out the steps of:
according to terrain information of a complex terrain and target information of an exploration target, constructing a three-dimensional cuboid model containing the complex terrain and the exploration target, carrying out grid subdivision on the three-dimensional cuboid model in the x-axis direction, the y-axis direction and the z-axis direction to obtain a plurality of small cuboids, wherein the sizes of the small cuboids in the x-axis direction and the y-axis direction are the same, and setting the spatial domain density value of the small cuboids according to the terrain information and the target information;
obtaining an offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters;
obtaining a space domain gravity potential integral expression of the three-dimensional rectangular solid model according to the space domain density value and the grid parameters, and performing two-dimensional Gaussian Fourier transform on the space domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional rectangular solid model;
dividing the three-dimensional rectangular solid model into a lower part model and an upper part model according to the topographic information, and respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number; the lower part model is a cuboid model of a part below the lowest point of the complex terrain, and the upper part model is a cuboid model of a part above the lowest point;
obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, preset relationship information among frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral, and calculating frequency domain gravity anomaly fields of a plurality of observation surfaces according to the frequency domain gravity anomaly expression;
performing two-dimensional Gaussian Fourier inversion on the frequency domain gravity abnormal field along the horizontal direction to obtain space domain gravity abnormal fields of a plurality of observation surfaces; the observation surface is a horizontal surface corresponding to a fixed value in the z-axis direction;
and obtaining a numerical simulation result of the space domain gravity abnormal field of the undulating surface of the complex terrain by a spline interpolation algorithm according to the space domain gravity abnormal fields of the plurality of observation surfaces.
According to the gravity field numerical simulation method and device based on the complex terrain, the computer equipment and the storage medium, the three-dimensional cuboid model containing the complex terrain and the exploration target is constructed, the three-dimensional cuboid model is subjected to grid subdivision in the directions of the x axis, the y axis and the z axis to obtain a plurality of small cuboids, and the spatial domain density value of each small cuboid is set according to terrain information and target information; obtaining an offset wave number according to a grid parameter of the grid subdivision of the three-dimensional cuboid model and a preset Gaussian parameter; obtaining a space domain gravity potential integral expression of the three-dimensional cuboid model according to the space domain density value and the grid parameters, and performing two-dimensional Fourier transform on the space domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional cuboid model; dividing the three-dimensional cuboid model into a lower part model and an upper part model according to topographic information, respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number to obtain a frequency domain gravity anomaly expression, and calculating frequency domain gravity anomaly fields of a plurality of observation surfaces according to the frequency domain gravity anomaly expression; and performing two-dimensional Gaussian Fourier inversion on the frequency domain gravity abnormal field along the horizontal direction to obtain space domain gravity abnormal fields of a plurality of observation surfaces, and obtaining the space domain gravity abnormal field of the undulating surface of the complex terrain through a spline interpolation algorithm. The method divides a research area into a plurality of small cuboids, and describes a complex terrain according to the density change of each small cuboid; the method is reserved in a space domain in the vertical direction, is flexible in mesh generation and is suitable for simulating complex terrains and complex geologic bodies; the plurality of offset wave numbers are mutually independent, so that parallel calculation is facilitated, the calculation efficiency of gravity anomaly is greatly improved, and the memory required by calculation is reduced; and calculating the gravity anomaly on any complex terrain by adopting a spline interpolation method according to the gravity anomaly on a plurality of observation planes, thereby realizing the rapid forward modeling of the gravity anomaly based on the complex terrain.
Drawings
FIG. 1 is a schematic flow chart of a gravity field numerical simulation method based on complex terrain according to an embodiment;
FIG. 2 is a schematic flow chart of a gravity field numerical simulation method based on complex terrain according to another embodiment;
FIG. 3 is a diagram of a complex terrain model in one embodiment;
FIG. 4 is a diagram illustrating an embodiment of a spatial domain gravity anomaly field
Three-component analytic solution, numerical solution and relative error contour map; wherein a is
Component analysis solution contour map, b is obtained by the method of the invention
Numerical solution contour map of the components, c being
An analytical solution of the components and a relative error contour plot of the numerical solution; d is
Analytic solution contour map of the components, e is obtained by the method of the invention
The values of the components are solved by contour map, f is
An analytical solution of the components and a relative error contour plot of the numerical solution; g is
The analytic solution contour map of the component, h is obtained by the method of the invention
The numerical solution of the components is a contour map, i is
An analytical solution of the components and a relative error contour plot of the numerical solution;
FIG. 5 is a graph illustrating the trend of the time of the algorithm calculation with the number of observation surfaces of a complex terrain according to the method of the present invention and the algorithm calculation with the conventional accumulation method in one embodiment;
FIG. 6 is a block diagram of a gravity field numerical simulation apparatus based on complex terrain according to an embodiment;
FIG. 7 is a diagram illustrating an internal structure of a computer device according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The gravity field numerical simulation method based on the complex terrain can be applied to the following application environments. The gravity field numerical simulation method based on the complex terrain is executed through the terminal. Giving a research area, three-dimensional geologic body density distribution and complex terrain model data; according to the research area, the density distribution of the three-dimensional geologic body and a three-dimensional frequency domain gravity anomaly forward modeling method, calculating the gravity anomaly generated by the three-dimensional geologic body on the surface of the complex terrain; when the gravity anomaly calculated by the method is the same as the gravity anomaly generated by the three-dimensional geologic body measured by the gravimeter, the method is used for exploring the density distribution anomaly body. The terminal may be, but is not limited to, various personal computers, notebook computers, tablet computers, and portable devices.
In one embodiment, as shown in fig. 1, there is provided a gravity field numerical simulation method based on complex terrain, comprising the steps of:
102, constructing a three-dimensional cuboid model containing the complex terrain and the exploration target according to terrain information of the complex terrain and target information of the exploration target, carrying out grid subdivision on the three-dimensional cuboid model in the x-axis direction, the y-axis direction and the z-axis direction to obtain a plurality of small cuboids, wherein the sizes of each small cuboid in the x-axis direction and the y-axis direction are the same, and setting the spatial domain density value of each small cuboid according to the terrain information and the target information.
Constructing a three-dimensional cuboid model comprising an exploration target and a complex terrain according to the shape, size and density distribution of the exploration target and the complex terrain; the three-dimensional cuboid model is subjected to mesh subdivision, x, y, zthe number of the cuboids which are divided in the direction is respectively
,
, 
The length, width and height of each small cuboid are respectively
,
, 
Each small rectangular parallelepiped
,
Of cuboids of different layers which must be identical
It is possible to make the difference,
the size of the model is set according to the change condition of the magnetic susceptibility, so that the model is more flexibly established, and the calculation efficiency can be improved.
And 104, obtaining the offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters.
Given a gaussian parameter comprising gaussian points and corresponding coefficients, any number of gaussian points may be used in calculating the offset wavenumber using the gaussian parameter. In practical application, when the algorithm precision is not enough, the precision can be improved by increasing the number of Gaussian points, and the method has strong applicability, and is particularly suitable for complex medium models with any density distribution and any section shape distribution.
And 106, obtaining a space domain gravity potential integral expression of the three-dimensional cuboid model according to the space domain density value and the grid parameters, and performing two-dimensional Gaussian Fourier transform on the space domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional cuboid model.
The Gaussian Fourier transform method reduces the problem of boundary truncation effect and can improve the calculation precision.
The lower part model is a cuboid model of the part below the lowest point of the complex terrain, when the gravity on different heights between the lowest point and the highest point of the undulating terrain is abnormal, the integral of the part of the cuboid model of the part below the lowest point of the complex terrain needs to be continuously and repeatedly calculated to cause the superposition of calculation time, the part below the undulating terrain is calculated and stored firstly and is directly called when needed, and the calculation cost and the memory space are saved; the upper part is a cuboid model of the part above the lowest point, the cuboid model is divided into two parts above and below the observation point, calculation and storage are sequentially carried out, and the calculation of the lowest point and the calculation of the highest point are directly called when the highest point is abnormal, so that the calculation efficiency is improved.
And 110, obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, preset relation information among frequency domain potential fields, a first vertical one-dimensional integral and a second vertical one-dimensional integral, and calculating the frequency domain gravity anomaly fields of the multiple observation surfaces according to the frequency domain gravity anomaly expression.
The observation surface is a horizontal plane corresponding to a fixed value in the z-axis direction, a plurality of z values are set to calculate the frequency domain gravity anomaly fields of the observation surfaces, and the change of the gravity anomaly fields in the z-axis direction is equivalently observed so as to be used for calculating the gravity anomaly of the complex terrain undulating surface later.
And 112, performing two-dimensional Gaussian Fourier inversion on the frequency domain gravity abnormal field along the horizontal direction to obtain spatial domain gravity abnormal fields of a plurality of observation surfaces.
And step 114, obtaining a numerical simulation result of the space domain gravity abnormal field of the undulating surface of the complex terrain through a spline interpolation algorithm according to the space domain gravity abnormal fields of the plurality of observation surfaces.
The cubic spline interpolation function is:
in the above formula, z represents the z-axis coordinate value of the observation plane, coefficient
Can be obtained by interpolation calculation based on fixed edge conditions.
In the gravity field numerical simulation method based on the complex terrain, a three-dimensional cuboid model containing the complex terrain and an exploration target is constructed, the three-dimensional cuboid model is subjected to grid subdivision in the directions of x, y and z axes to obtain a plurality of small cuboids, and the spatial domain density value of each small cuboid is set according to terrain information and target information; obtaining an offset wave number according to a grid parameter of the grid subdivision of the three-dimensional cuboid model and a preset Gaussian parameter; obtaining a space domain gravity potential integral expression of the three-dimensional cuboid model according to the space domain density value and the grid parameters, and performing two-dimensional Fourier transform on the space domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional cuboid model; dividing the three-dimensional cuboid model into a lower part model and an upper part model according to topographic information, respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number to obtain a frequency domain gravity anomaly expression, and calculating frequency domain gravity anomaly fields of a plurality of observation surfaces according to the frequency domain gravity anomaly expression; and performing two-dimensional Fourier inverse transformation on the frequency domain gravity abnormal field along the horizontal direction to obtain space domain gravity abnormal fields of a plurality of observation surfaces, and obtaining the space domain gravity abnormal field of the undulating surface of the complex terrain through a spline interpolation algorithm. The method divides a research area into a plurality of small cuboids, and describes a complex terrain according to the density change of each small cuboid; the method is reserved in a space domain in the vertical direction, is flexible in mesh generation and is suitable for simulating complex terrains and complex geologic bodies; the plurality of offset wave numbers are mutually independent, so that parallel calculation is facilitated, the calculation efficiency of gravity anomaly is greatly improved, and the memory required by calculation is reduced; and calculating the gravity anomaly on any complex terrain by adopting a spline interpolation method according to the gravity anomaly on a plurality of observation planes, thereby realizing the rapid forward modeling of the gravity anomaly based on the complex terrain.
In one embodiment, the method further comprises the following steps: setting a spatial domain density value of the small cuboid according to the terrain information and the target information; the density of the small cuboid is a constant value, the density values of different small cuboids are different, and the density of the small cuboid in the air part is set to be zero.
In one embodiment, the method further comprises the following steps: obtaining the offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters:
wherein the content of the first and second substances,
、
representing the offset wavenumbers in the x and y directions respectively,
which represents the coordinates of a gaussian point or points,
indicates the number of the adopted Gaussian points,
，
the number of base waves in the x and y directions, respectively, can be expressed as:
，
；p andqrespectively represent a sequence of integers whenp Andqwhen the number is even:
when in usep Andqwhen the number is odd:
In one embodiment, the method further comprises the following steps: obtaining a space domain gravity potential integral expression of the three-dimensional cuboid model according to the space domain density value and the grid parameters as follows:
wherein the content of the first and second substances,Urepresenting the spatial domain gravitational potential;Gis a constant of attraction;m、n、lcounting variables for convolution;
is indicated by the reference number
The spatial domain density value of the small cuboid;
，
in order to observe the coordinates of the points,
representing source point coordinates;
the frequency domain gravity potential integral expression of the three-dimensional cuboid model obtained by performing two-dimensional Fourier transform on the spatial domain gravity potential integral expression along the horizontal direction is as follows:
wherein the content of the first and second substances,
which represents the potential of gravity in the frequency domain,
and
are respectivelyxAndythe number of directional spatial waves is such that,
is the wave number;irepresenting an imaginary number;erepresents a natural constant;
as an integral coefficient, it can be expressed as:
Ione-dimensional integrals representing different offset wavenumbers:
in one embodiment, the method further comprises the following steps: according to the topographic information, dividing the three-dimensional cuboid model into a lower part model and an upper part model, and respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number as follows:
wherein the content of the first and second substances,
representing a first vertical one-dimensional integral;
representing a second vertical one-dimensional integral;
representing the mesh division number in the z-axis direction of the part below the lowest point of the complex terrain;
and the mesh division number in the z-axis direction of the part above the lowest point is shown.
In one embodiment, the method further comprises the following steps: obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, preset relationship information between frequency domain potential fields, a first vertical one-dimensional integral and a second vertical one-dimensional integral:
wherein the content of the first and second substances,
representing a frequency domain gravity anomaly;
respectively representing the components of the frequency domain gravity anomaly in the x direction, the y direction and the z direction;
the density value of the frequency domain is shown,
。
in one embodiment, the method further comprises the following steps: integrating coefficients corresponding to different offset wavenumbers
The component values in the first vertical one-dimensional integral
And the component values of the second vertical one-dimensional integral
、
Storing; and directly calling the stored values when calculating the frequency domain gravity anomaly fields of the plurality of observation surfaces.
According to the calculation formula of the first vertical one-dimensional integral of the lower part model and the second vertical one-dimensional integral of the upper part model, the common part is divided into two parts
、
、
And integral coefficient
The value of (A) is stored in the computer in advance, so that the passing formula is not needed when the gravity abnormal field is calculated
The vertical one-dimensional integral is calculated, and only the corresponding value stored in the computer needs to be called, so that repeated accumulation is reduced, and the algorithm efficiency can be improved.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
In one embodiment, as shown in fig. 2, a gravity field numerical simulation method based on complex terrain is provided, a cuboid model containing an exploration target is constructed according to the size and density distribution of the exploration target, the large cuboid model is divided into a plurality of small cuboid models and given model parameters, density assignment is carried out on each small cuboid, the number of Gaussian points and corresponding Gaussian points and Gaussian coefficients are given, a two-dimensional Gaussian Fourier transform offset wave number is calculated according to the model parameters and the Gaussian points, two-dimensional Gaussian Fourier transform is carried out on a spatial domain gravity potential three-dimensional convolution formula along the horizontal direction, frequency domain density is calculated by adopting the two-dimensional Gaussian Fourier transform, a frequency domain gravity abnormal field formula is directly obtained according to the derivation characteristic of the frequency domain, gravity abnormal fields on a plurality of horizontal observation planes of the complex terrain are calculated according to block superposition, and performing two-dimensional Gaussian Fourier inverse transformation on the frequency domain gravity anomaly along the horizontal direction, and calculating a gravity anomaly field on the undulating terrain by adopting a spline interpolation algorithm on the gravity anomaly on the plurality of observation surfaces.
In one embodiment, the complex terrain model shown in FIG. 3 is designed as follows:
the simulation area range is as follows:xandythe directions are from-10 km to 10km, the z direction is from-1 km to 0.8km, and the height of the complex terrain is from 0.077km to 0.798 km. The size of the large cuboid is 20 km multiplied by 1.8 km, and the large cuboid is divided into small cuboids of 200 multiplied by 90. An abnormal body with a buried depth of 0.4km and a size of 4km multiplied by 0.4km is arranged underground, and the residual density of the abnormal body is 1000kg/m3. The gravity abnormal field on the complex terrain is calculated by adopting the algorithm.
The three-dimensional gravity anomaly calculation method in the embodiment is realized by using Fortran language programming, and a personal notebook computer used for running a program is configured as follows: CPU-Intercore i7-8700 with a dominant frequency of 3.2GHz and runningThe memory is 8.00 GB. FIG. 4 is a three-component analytic solution, a numerical solution and a relative error contour map of a gravity anomaly field on a complex terrain calculated by the method of the invention, and the maximum relative error can be seen from the relative error map of FIG. 4
The analytic solution of the three components is well matched with the numerical solution, and the numerical simulation precision of the method is high. Fig. 5 shows that the number of the multiple horizontal observation surfaces between the complex terrain calculated by the method of the present invention and the complex terrain calculated by the conventional accumulation increases with time, and it can be seen that the calculation time of the algorithm increases with the increase of the number of the horizontal observation surfaces of the complex terrain, but the time of the conventional algorithm increases more rapidly, when the number of the observation surfaces of the complex terrain is 32, the calculation efficiency of the algorithm of the present invention is improved by 5 times compared with the conventional accumulation algorithm of the frequency domain, and it can be seen that the advantages of the algorithm are more obvious with the increase of the number of the observation surfaces of the complex terrain and the size of the.
In one embodiment, as shown in fig. 6, there is provided a gravity field numerical simulation apparatus based on complex terrain, including: the method comprises a model establishing module 602, an offset wave number calculating module 604, a frequency domain gravity potential integral expression obtaining module 606, a vertical one-dimensional integral obtaining module 608, a frequency domain gravity abnormal field obtaining module 610 and a space domain gravity abnormal field obtaining module 612, wherein:
the model establishing module 602 is configured to establish a three-dimensional cuboid model including a complex terrain and an exploration target according to terrain information of the complex terrain and target information of the exploration target, perform mesh subdivision on the three-dimensional cuboid model in an x-axis direction, a y-axis direction and a z-axis direction to obtain a plurality of small cuboids, wherein the sizes of each small cuboid in the x-axis direction and the y-axis direction are the same, and set a spatial domain density value of each small cuboid according to the terrain information and the target information;
the offset wave number calculation module 604 is configured to obtain an offset wave number according to a mesh parameter of mesh generation of the three-dimensional cuboid model and a preset gaussian parameter;
a frequency domain gravity potential integral expression obtaining module 606, configured to obtain a space domain gravity potential integral expression of the three-dimensional rectangular solid model according to the space domain density value and the grid parameters, and perform two-dimensional fourier transform on the space domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional rectangular solid model;
a vertical one-dimensional integral obtaining module 608, configured to divide the three-dimensional rectangular solid model into a lower part model and an upper part model according to the terrain information, and calculate a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number; the lower part model is a cuboid model of the part below the lowest point of the complex terrain, and the upper part model is a cuboid model of the part above the lowest point;
the frequency domain gravity abnormal field acquisition module 610 is configured to obtain a frequency domain gravity abnormal expression according to the frequency domain gravity potential integral expression, preset relationship information between frequency domain potential fields, a first vertical one-dimensional integral and a second vertical one-dimensional integral, and calculate frequency domain gravity abnormal fields of a plurality of observation surfaces according to the frequency domain gravity abnormal expression;
a spatial domain gravity anomaly field acquisition module 612, configured to perform two-dimensional inverse fourier transform on the frequency domain gravity anomaly field along the horizontal direction to obtain spatial domain gravity anomaly fields of multiple observation surfaces; the observation surface is a horizontal surface corresponding to the specific value in the z-axis direction; and obtaining the space domain gravity abnormal field of the undulating surface of the complex terrain by a spline interpolation algorithm according to the space domain gravity abnormal fields of the plurality of observation surfaces.
The offset wave number calculating module 604 is further configured to obtain an offset wave number according to the mesh parameters of the mesh generation of the three-dimensional rectangular solid model and preset gaussian parameters, where:
wherein the content of the first and second substances,
、
representing the offset wavenumbers in the x and y directions respectively,
which represents the coordinates of a gaussian point or points,
indicates the number of the adopted Gaussian points,
，
the number of base waves in the x and y directions, respectively, can be expressed as:
，
；p andqrespectively represent a sequence of integers whenp Andqwhen the number is even:
when in usep Andqwhen the number is odd:
The frequency domain gravity potential integral expression obtaining module 606 is further configured to obtain a space domain gravity potential integral expression of the three-dimensional rectangular parallelepiped model according to the space domain density value and the grid parameter, where the space domain gravity potential integral expression is:
wherein the content of the first and second substances,Urepresenting the spatial domain gravitational potential;Gis a constant of attraction;m、n、lis a convolution ofCounting variables;
is indicated by the reference number
The spatial domain density value of the small cuboid;
，
in order to observe the coordinates of the points,
representing source point coordinates;
the frequency domain gravity potential integral expression of the three-dimensional cuboid model obtained by performing two-dimensional Fourier transform on the spatial domain gravity potential integral expression along the horizontal direction is as follows:
wherein the content of the first and second substances,
which represents the potential of gravity in the frequency domain,
and
are respectivelyxAndythe number of directional spatial waves is such that,
is the wave number;irepresenting an imaginary number;erepresents a natural constant;
as an integral coefficient, it can be expressed as:
Ione-dimensional integrals representing different offset wavenumbers:
the vertical one-dimensional integral obtaining module 608 is further configured to divide the three-dimensional rectangular solid model into a lower portion model and an upper portion model according to the terrain information, and calculate a first vertical one-dimensional integral of the lower portion model and a second vertical one-dimensional integral of the upper portion model according to the offset wave number as:
wherein the content of the first and second substances,
representing a first vertical one-dimensional integral;
representing a second vertical one-dimensional integral;
representing the mesh division number in the z-axis direction of the part below the lowest point of the complex terrain;
and the mesh division number in the z-axis direction of the part above the lowest point is shown.
The frequency domain gravity abnormal field obtaining module 610 is further configured to obtain a frequency domain gravity abnormal expression according to the frequency domain gravity potential integral expression, the preset relationship information between the frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral:
wherein the content of the first and second substances,
representing a frequency domain gravity anomaly;
respectively representing the components of the frequency domain gravity anomaly in the x direction, the y direction and the z direction;
the density value of the frequency domain is shown,
。
the spatial domain gravity anomaly field obtaining module 612 is further configured to calculate integral coefficients corresponding to different offset wave numbers before calculating the frequency domain gravity anomaly fields of the multiple observation surfaces according to the frequency domain gravity anomaly expression
The component values in the first vertical one-dimensional integral
And the component values of the second vertical one-dimensional integral
、
Storing; and directly calling the stored values when calculating the frequency domain gravity anomaly fields of the plurality of observation surfaces.
For specific limitations of the gravity field numerical simulation device based on the complex terrain, reference may be made to the above limitations of the gravity field numerical simulation method based on the complex terrain, and details thereof are not repeated here. The modules in the gravity field numerical simulation device based on complex terrain can be wholly or partially realized by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as shown in fig. 7. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a method for the numerical simulation of gravitational fields based on complex terrain. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on the shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.
Those skilled in the art will appreciate that the architecture shown in fig. 7 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In an embodiment, a computer device is provided, comprising a memory storing a computer program and a processor implementing the steps of the above method embodiments when executing the computer program.
In an embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which computer program, when being executed by a processor, carries out the steps of the above-mentioned method embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (7)
1. A gravity field numerical simulation method based on complex terrain is characterized by comprising the following steps:
according to terrain information of a complex terrain and target information of an exploration target, constructing a three-dimensional cuboid model containing the complex terrain and the exploration target, carrying out grid subdivision on the three-dimensional cuboid model in the x-axis direction, the y-axis direction and the z-axis direction to obtain a plurality of small cuboids, wherein the sizes of the small cuboids in the x-axis direction and the y-axis direction are the same, and setting the spatial domain density value of the small cuboids according to the terrain information and the target information; the density of the small cuboids is a constant value, the density values of different small cuboids are different, and the density of the small cuboids in the air part is set to be zero;
obtaining an offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters:
wherein the content of the first and second substances,
、
representing the offset wavenumbers in the x and y directions respectively,
which represents the coordinates of a gaussian point or points,
indicates the number of the adopted Gaussian points,
，
the number of base waves in the x and y directions, respectively, can be expressed as:
，
；p andqrespectively represent a sequence of integers whenp Andqwhen the number is even:
when in usep Andqwhen the number is odd:
obtaining a space domain gravitational potential integral expression of the three-dimensional rectangular solid model according to the space domain density value and the grid parameters, wherein the space domain gravitational potential integral expression comprises the following expression:
wherein the content of the first and second substances,Urepresenting the spatial domain gravitational potential;Gis a constant of attraction;m、n、lcounting variables for convolution;
is indicated by the reference number
The spatial domain density value of the small cuboid;
，
in order to observe the coordinates of the points,
representing source point coordinates;
and performing two-dimensional Fourier transform on the spatial domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional rectangular solid model, wherein the frequency domain gravity potential integral expression comprises the following components:
wherein the content of the first and second substances,
which represents the potential of gravity in the frequency domain,
and
are respectivelyxAndythe number of directional spatial waves is such that,
is the wave number;irepresenting an imaginary number;erepresents a natural constant;
as an integral coefficient, it can be expressed as:
Ione-dimensional integrals representing different offset wavenumbers:
dividing the three-dimensional rectangular solid model into a lower part model and an upper part model according to the topographic information, and respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number; the lower part model is a cuboid model of a part below the lowest point of the complex terrain, and the upper part model is a cuboid model of a part above the lowest point;
obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, preset relationship information among frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral, and calculating frequency domain gravity anomaly fields of a plurality of observation surfaces according to the frequency domain gravity anomaly expression; the observation surface is a horizontal surface corresponding to a fixed value in the z-axis direction;
performing two-dimensional Gaussian Fourier inversion on the frequency domain gravity abnormal field along the horizontal direction to obtain space domain gravity abnormal fields of a plurality of observation surfaces;
and obtaining a numerical simulation result of the space domain gravity abnormal field of the undulating surface of the complex terrain by a spline interpolation algorithm according to the space domain gravity abnormal fields of the plurality of observation surfaces.
2. The method according to claim 1, wherein the dividing of the three-dimensional rectangular solid model into a lower partial model and an upper partial model based on the topographic information, the calculating of a first vertical one-dimensional integral of the lower partial model and a second vertical one-dimensional integral of the upper partial model based on the offset wavenumber, respectively, comprises:
dividing the three-dimensional rectangular solid model into a lower part model and an upper part model according to the terrain information, and respectively calculating a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number as follows:
wherein the content of the first and second substances,
representing the first vertical one-dimensional integral;
representing the second vertical one-dimensional integral;
representing the mesh division number in the z-axis direction of the part below the lowest point of the complex terrain;
and the mesh division number in the z-axis direction of the part above the lowest point is shown.
3. The method of claim 2, wherein obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, relationship information between preset frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral comprises:
obtaining a frequency domain gravity anomaly expression according to the frequency domain gravity potential integral expression, preset relationship information among frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral:
wherein the content of the first and second substances,
representing a frequency domain gravity anomaly;
respectively representing the components of the frequency domain gravity anomaly in the x direction, the y direction and the z direction;
the density value of the frequency domain is shown,
。
4. the method of claim 3, wherein before computing the frequency domain gravity anomaly field for the plurality of observation surfaces according to the frequency domain gravity anomaly expression, comprising:
corresponding the different offset wavenumbers to the integral coefficients
Component values in the first vertical one-dimensional integral
And component values of said second vertical one-dimensional integral
、
Storing;
and directly calling the stored values when calculating the frequency domain gravity anomaly fields of the plurality of observation surfaces.
5. The method of any of claims 1 to 4, wherein the number of offset wavenumbers is adjustable according to algorithmic accuracy requirements.
6. A gravity field numerical simulation apparatus based on complex terrain, the apparatus comprising:
the model establishing module is used for establishing a three-dimensional cuboid model containing the complex terrain and an exploration target according to terrain information of the complex terrain and target information of the exploration target, carrying out grid subdivision on the three-dimensional cuboid model in the x-axis direction, the y-axis direction and the z-axis direction to obtain a plurality of small cuboids, wherein the sizes of each small cuboid in the x-axis direction and the y-axis direction are the same, and setting the spatial domain density value of each small cuboid according to the terrain information and the target information; the density of the small cuboids is a constant value, the density values of different small cuboids are different, and the density of the small cuboids in the air part is set to be zero;
the offset wave number calculation module is used for obtaining the offset wave number according to the grid parameters of the grid subdivision of the three-dimensional cuboid model and preset Gaussian parameters;
wherein the content of the first and second substances,
、
representing the offset wavenumbers in the x and y directions respectively,
which represents the coordinates of a gaussian point or points,
indicates the number of the adopted Gaussian points,
，
the number of base waves in the x and y directions, respectively, can be expressed as:
，
；p andqrespectively represent a sequence of integers whenp Andqwhen the number is even:
when in usep Andqwhen the number is odd:
a frequency domain gravity potential integral expression obtaining module, configured to obtain a space domain gravity potential integral expression of the three-dimensional rectangular solid model according to the space domain density value and the grid parameters, where the space domain gravity potential integral expression is:
wherein the content of the first and second substances,Urepresenting the spatial domain gravitational potential;Gis a constant of attraction;m、n、lcounting variables for convolution;
is indicated by the reference number
The spatial domain density value of the small cuboid;
，
in order to observe the coordinates of the points,
representing source point coordinates;
and performing two-dimensional Fourier transform on the spatial domain gravity potential integral expression along the horizontal direction to obtain a frequency domain gravity potential integral expression of the three-dimensional rectangular solid model, wherein the frequency domain gravity potential integral expression comprises the following components:
wherein the content of the first and second substances,
which represents the potential of gravity in the frequency domain,
and
are respectivelyxAndythe number of directional spatial waves is such that,
is the wave number;irepresenting an imaginary number;erepresents a natural constant;
as an integral coefficient, it can be expressed as:
Ione-dimensional integrals representing different offset wavenumbers:
a vertical one-dimensional integral obtaining module, configured to divide the three-dimensional rectangular solid model into a lower part model and an upper part model according to the terrain information, and calculate a first vertical one-dimensional integral of the lower part model and a second vertical one-dimensional integral of the upper part model according to the offset wave number; the lower part model is a cuboid model of a part below the lowest point of the complex terrain, and the upper part model is a cuboid model of a part above the lowest point;
the frequency domain gravity abnormal field acquisition module is used for obtaining a frequency domain gravity abnormal expression according to the frequency domain gravity potential integral expression, preset relationship information among frequency domain potential fields, the first vertical one-dimensional integral and the second vertical one-dimensional integral, and calculating the frequency domain gravity abnormal fields of a plurality of observation surfaces according to the frequency domain gravity abnormal expression;
the spatial domain gravity abnormal field acquisition module is used for performing two-dimensional Fourier inverse transformation on the frequency domain gravity abnormal field along the horizontal direction to obtain spatial domain gravity abnormal fields of a plurality of observation surfaces; the observation surface is a horizontal surface corresponding to a specific value in the z-axis direction; and obtaining the space domain gravity abnormal field of the undulating surface of the complex terrain by a spline interpolation algorithm according to the space domain gravity abnormal fields of the plurality of observation surfaces.
7. A computer device comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the steps of the method of any one of claims 1 to 5 when executing the computer program.
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