CN112379413A

CN112379413A - Irregular seismic source characterization method and device based on energy spectrum equivalence

Info

Publication number: CN112379413A
Application number: CN202011173079.XA
Authority: CN
Inventors: 倪宇东; 闫智慧; 胡永贵; 蓝益军; 吴恒
Original assignee: China National Petroleum Corp; BGP Inc
Current assignee: China National Petroleum Corp; BGP Inc
Priority date: 2020-10-28
Filing date: 2020-10-28
Publication date: 2021-02-19
Anticipated expiration: 2040-10-28

Abstract

The invention provides an irregular seismic source characterization method and device based on energy spectrum equivalence, wherein the method comprises the following steps: establishing a regular gridding model, acquiring plane projection parameters of the seismic source, determining the most adjacent regular projection grid point index of the seismic source and the relative deviation between the actual seismic source plane position and the most adjacent grid projection direction, inputting the half-width parameter of the minimum approximate grid, determining the index range of the regular grid points of equivalent approximation of the seismic source and the weight function of the regular grid points of equivalent approximation of the seismic source, determining the two-dimensional space Fourier spectrum of the weight function of the regular grid points by combining the discretized wave number array, comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position, judging whether the energy error meets a preset energy error threshold value, and if the minimum approximate grid half-width parameter does not meet the preset energy error threshold, modifying the minimum approximate grid half-width parameter for iteration, and determining the grid node index and the corresponding node weight function value participating in the rule discretization representation. Spatial positioning errors can be reduced.

Description

Irregular seismic source characterization method and device based on energy spectrum equivalence

Technical Field

The invention relates to the technical field of seismic data processing, in particular to an irregular seismic source characterization method and device based on energy spectrum equivalence.

Background

This section is intended to provide a background or context to the embodiments of the invention that are recited in the claims. The description herein is not admitted to be prior art by inclusion in this section.

Conventional seismic data acquisition designs tend to use relatively regular temporal and spatial sampling for signal excitation and reception. Driven by the inherent requirements of the natural geographic conditions, safety and the like of the earth surface and the improvement of underground illumination, excitation points and receiving points in the actual data acquisition process are often distributed in a spatially irregular mode, the irregular characteristic of the excitation points is particularly obvious, and in seismic data processing, a regular and equidistant discretization grid is required to be used for data operation and storage, so that the purpose of improving the calculation efficiency is achieved. The irregular characteristic of the observation system may be further aggravated by the seismic data acquisition design scheme based on compressed sensing and sparse transformation which is gradually developed in recent years.

The seismic wave field simulation is a necessary core link of seismic imaging, illumination analysis and full waveform inversion. The higher the simulation precision of the seismic wave field is, the more beneficial the improvement of the seismic imaging, illumination analysis and full waveform inversion precision is. Common seismic wavefield simulation methods include two categories, ray approximation solution and wave equation direct numerical solution. The wave equation direct numerical solution simulation precision is high, wave field extrapolation and wave field snapshot storage are required to be performed by using a regular and equidistant discretization grid, and the purpose of improving the calculation efficiency is achieved. When the actual seismic source position distribution is in a spatial irregular characteristic, all seismic source points cannot be accurately projected to a preset regular grid point, and a large spatial positioning error may be caused when the actual regular grid point is sparse, so that adverse effects are brought to subsequent imaging, illumination analysis and full waveform inversion.

The current solutions to the above problems are mainly two: (1) regular grids are further encrypted by reducing the grid intervals, and the space error caused by positioning of a single grid is reduced, so that the requirements of grid density, storage and calculation amount are rapidly expanded, the calculation efficiency is low, and the practicability is difficult; (2) and carrying out spatial regularization interpolation and reconstruction processing on the irregular excitation and receiving data to ensure that the processed seismic data excitation and receiving points are consistent with the regular grid. For simple geological structures and lithologic stratums, the change of the seismic wave homomorphic axis is regular, and the method can obtain reasonable results. For the conditions of sparse seismic source distribution or complex structure and lithologic stratum wave fields, the physical stability and the geological rationality of the reconstruction method cannot be verified.

Therefore, how to provide a new solution, which can solve the above technical problems, is a technical problem to be solved in the art.

Disclosure of Invention

The embodiment of the invention provides an irregular seismic source characterization method based on energy spectrum equivalence, which can better reduce larger space positioning errors and reduce adverse effects brought by subsequent imaging, illumination analysis and full waveform inversion, and comprises the following steps:

establishing a regular gridding model, and acquiring a seismic source plane projection parameter;

determining the nearest regular projection grid point index of the seismic source and the relative deviation of the actual seismic source plane position and the nearest grid projection direction according to the seismic source plane projection parameters;

inputting a minimum approximate grid half-width parameter, and determining a regular grid point index range of equivalent approximation of the seismic source and a regular grid point weight function of equivalent approximation of the seismic source according to the index of the nearest regular projection grid point of the seismic source and the relative deviation of the actual plane position of the seismic source and the nearest grid projection direction;

determining a two-dimensional space Fourier spectrum of the regular grid point weight function according to the discretization wave number array, the regular grid point index range of the seismic source equivalent approximation and the regular grid point weight function of the seismic source equivalent approximation;

comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum, and judging whether the energy error meets a preset energy error threshold value;

and when the energy error does not meet a preset energy error threshold, modifying the minimum approximate grid half-width parameter for iteration, and determining a grid node index and a corresponding node weight function value participating in the rule discretization representation until the energy error meets the preset energy error threshold.

The embodiment of the invention also provides an irregular seismic source characterization device based on energy spectrum equivalence, which comprises the following steps:

the seismic source plane projection parameter acquisition module is used for establishing a regular gridding model and acquiring seismic source plane projection parameters;

the seismic source nearest regular projection grid point index and the relative deviation between the actual seismic source plane position and the nearest grid projection direction are determined by the seismic source nearest regular projection grid point index and the relative deviation between the actual seismic source plane position and the nearest grid projection direction are determined according to the seismic source plane projection parameters;

the seismic source equivalent approximate regular grid point index range and the seismic source equivalent approximate regular grid point weight function determining module is used for inputting a minimum approximate grid half-width parameter, and determining the seismic source equivalent approximate regular grid point index range and the seismic source equivalent approximate regular grid point weight function according to the relative deviation of the seismic source nearest regular projection grid point index and the actual seismic source plane position and the nearest grid projection direction;

the regular grid point weight function two-dimensional space Fourier spectrum determining module is used for determining a regular grid point weight function two-dimensional space Fourier spectrum according to the discretization wave number array, the regular grid point index range of the seismic source equivalent approximation and the regular grid point weight function of the seismic source equivalent approximation;

the energy error judgment module is used for comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum and judging whether the energy error meets a preset energy error threshold value;

and the grid node index and corresponding node weight function value determination module is used for correcting the minimum approximate grid half-width parameter for iteration when the energy error does not meet the preset energy error threshold value, and determining the grid node index and corresponding node weight function value participating in the rule discretization representation until the energy error meets the preset energy error threshold value.

The embodiment of the invention also provides computer equipment which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the computer program to realize the irregular seismic source characterization method based on energy spectrum equivalence.

Embodiments of the present invention further provide a computer-readable storage medium storing a computer program for executing the irregular seismic source characterization method based on energy spectrum equivalence.

The embodiment of the invention provides a method and a device for representing an irregular seismic source based on energy spectrum equivalence.A regular gridding model is established to obtain a seismic source plane projection parameter; then, according to the plane projection parameters of the seismic source, determining the nearest regular projection grid point index of the seismic source and the relative deviation between the actual plane position of the seismic source and the nearest grid projection direction; then inputting a minimum approximate grid half-width parameter, and determining a regular grid point index range of equivalent approximation of the seismic source and a regular grid point weight function of equivalent approximation of the seismic source according to the index of the nearest regular projection grid point of the seismic source and the relative deviation of the actual plane position of the seismic source and the nearest grid projection direction; determining a two-dimensional space Fourier spectrum of the regular grid point weight function according to the discretization wave number array, the regular grid point index range of the seismic source equivalent approximation and the regular grid point weight function of the seismic source equivalent approximation; then comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum, and judging whether the energy error meets a preset energy error threshold value; and finally, when the energy error does not meet a preset energy error threshold, modifying the minimum approximate grid half-width parameter for iteration, and determining a grid node index and a corresponding node weight function value participating in the rule discretization representation until the energy error meets the preset energy error threshold. The embodiment of the invention establishes a regular discretization equivalent characterization method of an irregular excitation seismic source based on an energy spectrum equivalent principle, utilizes a method for characterizing the irregular seismic source by utilizing a regular discretization grid combined seismic source, finally generates a regular grid index and grid point weight which can be used for approximating the equivalent characterization, and can better reduce space positioning errors. For actual local sparse points, larger space positioning errors possibly caused are reduced, and adverse effects caused by subsequent imaging, illumination analysis and full waveform inversion are reduced. The method can calculate the weighting function of the seismic source combination in the corresponding rule discretization format under the condition of the given rule grid parameters and the plane coordinates of any seismic source, so that the error between the spectral energy of the corresponding equivalent seismic source combination and the actual seismic source spectral energy meets the given precision requirement.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts. In the drawings:

FIG. 1 is a schematic diagram of an irregular seismic source characterization method based on energy spectrum equivalence according to an embodiment of the present invention.

Fig. 2 is a graph showing a relationship between a regular grid model and an irregular seismic source planar projection of an irregular seismic source characterization method based on energy spectrum equivalence according to an embodiment of the present invention.

FIG. 3 is a graph of the index ranges of regular grid points of a seismic source equivalent approximation based on an irregular seismic source characterization method of energy spectrum equivalence according to an embodiment of the present invention.

FIG. 4 is a schematic diagram of values of a regular grid point weight function of a seismic source equivalent approximation based on an irregular seismic source characterization method of energy spectrum equivalence according to an embodiment of the present invention.

Fig. 5 is an energy error graph of a two-dimensional space fourier spectrum of a space unit impulse function and a two-dimensional space fourier spectrum of a weight function of a regular grid point corresponding to an actual seismic source position in an irregular seismic source characterization method based on energy spectrum equivalence according to an embodiment of the present invention.

FIG. 6 is a schematic diagram of a computer device running a method for irregular seismic source characterization based on energy spectrum equivalence implemented in the present invention.

FIG. 7 is a schematic diagram of an irregular seismic source characterization apparatus based on energy spectrum equivalence according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the embodiments of the present invention are further described in detail below with reference to the accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.

Fig. 1 is a schematic diagram of an irregular seismic source characterization method based on energy spectrum equivalence according to an embodiment of the present invention, and as shown in fig. 1, an irregular seismic source characterization method based on energy spectrum equivalence according to an embodiment of the present invention is provided, which can better reduce a large spatial positioning error and reduce adverse effects caused by subsequent imaging, illumination analysis, and full waveform inversion, and includes:

step 101: establishing a regular gridding model, and acquiring a seismic source plane projection parameter;

step 102: determining the nearest regular projection grid point index of the seismic source and the relative deviation of the actual seismic source plane position and the nearest grid projection direction according to the seismic source plane projection parameters;

step 103: inputting a minimum approximate grid half-width parameter, and determining a regular grid point index range of equivalent approximation of the seismic source and a regular grid point weight function of equivalent approximation of the seismic source according to the index of the nearest regular projection grid point of the seismic source and the relative deviation of the actual plane position of the seismic source and the nearest grid projection direction;

step 104: determining a two-dimensional space Fourier spectrum of the regular grid point weight function according to the discretization wave number array, the regular grid point index range of the seismic source equivalent approximation and the regular grid point weight function of the seismic source equivalent approximation;

step 105: comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum, and judging whether the energy error meets a preset energy error threshold value;

step 106: and when the energy error does not meet a preset energy error threshold, modifying the minimum approximate grid half-width parameter for iteration, and determining a grid node index and a corresponding node weight function value participating in the rule discretization representation until the energy error meets the preset energy error threshold.

The embodiment of the invention provides an irregular seismic source characterization method based on energy spectrum equivalence, which comprises the steps of firstly establishing a regular gridding model and obtaining a seismic source plane projection parameter; then, according to the plane projection parameters of the seismic source, determining the nearest regular projection grid point index of the seismic source and the relative deviation between the actual plane position of the seismic source and the nearest grid projection direction; then inputting a minimum approximate grid half-width parameter, and determining a regular grid point index range of equivalent approximation of the seismic source and a regular grid point weight function of equivalent approximation of the seismic source according to the index of the nearest regular projection grid point of the seismic source and the relative deviation of the actual plane position of the seismic source and the nearest grid projection direction; determining a two-dimensional space Fourier spectrum of the regular grid point weight function according to the discretization wave number array, the regular grid point index range of the seismic source equivalent approximation and the regular grid point weight function of the seismic source equivalent approximation; then comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum, and judging whether the energy error meets a preset energy error threshold value; and finally, when the energy error does not meet a preset energy error threshold, modifying the minimum approximate grid half-width parameter for iteration, and determining a grid node index and a corresponding node weight function value participating in the rule discretization representation until the energy error meets the preset energy error threshold. The embodiment of the invention establishes a regular discretization equivalent characterization method of an irregular excitation seismic source based on an energy spectrum equivalent principle, utilizes a method for characterizing the irregular seismic source by utilizing a regular discretization grid combined seismic source, finally generates a regular grid index and grid point weight which can be used for approximating the equivalent characterization, and can better reduce space positioning errors. For actual local sparse points, larger space positioning errors possibly caused are reduced, and adverse effects caused by subsequent imaging, illumination analysis and full waveform inversion are reduced. The method can calculate the weighting function of the seismic source combination in the corresponding rule discretization format under the condition of the given rule grid parameters and the plane coordinates of any seismic source, so that the error between the spectral energy of the corresponding equivalent seismic source combination and the actual seismic source spectral energy meets the given precision requirement.

The invention relates to an irregular seismic source characterization method in seismic wave field forward modeling, in particular to a discretization equivalent seismic source characterization method under the condition that the plane projection position of a seismic source of an actual observation system is not coincident with regular grid nodes. The embodiment of the invention is based on an energy spectrum equivalence principle, a method for representing an irregular seismic source by utilizing a regular discretization grid combined seismic source is used for finally generating regular grid indexes and grid point weights which can be used for approximate equivalent representation, and when the irregular seismic source representing method based on energy spectrum equivalence provided by the embodiment of the invention is specifically implemented, the method can comprise the following steps:

establishing a regular gridding model, and acquiring a seismic source plane projection parameter; determining the nearest regular projection grid point index of the seismic source and the relative deviation of the actual seismic source plane position and the nearest grid projection direction according to the seismic source plane projection parameters; inputting a minimum approximate grid half-width parameter, and determining a regular grid point index range of equivalent approximation of the seismic source and a regular grid point weight function of equivalent approximation of the seismic source according to the index of the nearest regular projection grid point of the seismic source and the relative deviation of the actual plane position of the seismic source and the nearest grid projection direction; determining a two-dimensional space Fourier spectrum of the regular grid point weight function according to the discretization wave number array, the regular grid point index range of the seismic source equivalent approximation and the regular grid point weight function of the seismic source equivalent approximation; comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum, and judging whether the energy error meets a preset energy error threshold value; and when the energy error does not meet a preset energy error threshold, modifying the minimum approximate grid half-width parameter for iteration, and determining a grid node index and a corresponding node weight function value participating in the rule discretization representation until the energy error meets the preset energy error threshold.

In a specific implementation of the irregular seismic source characterization method based on energy spectrum equivalence provided by the embodiment of the present invention, in an embodiment, the establishing a regular grid model to obtain the seismic source planar projection parameters includes:

establishing a regular gridding model according to the geological task, the seismic resolution requirement and the model space range; wherein the model space range comprises all actual seismic source positions to be calculated and all discretized equivalent seismic source positions;

and acquiring the plane projection parameters of the seismic source according to the regular gridding model.

In an embodiment, a regular gridding model is first built that satisfies the geological mission, seismic resolution requirements, and model spatial range, which should be large enough to encompass all actual source locations to be computed and all discretized equivalent source locations.

Fig. 2 is a graph showing a relationship between a regular grid model and a planar projection of an irregular seismic source based on an energy spectrum equivalent irregular seismic source characterization method according to an embodiment of the present invention, as shown in fig. 2, the relationship between the regular grid model and the planar projection of the irregular seismic source is shown, a hollow circle represents a regular grid point position, and an asterisk represents an actual irregular seismic source position.

In a specific implementation of the irregular seismic source characterization method based on energy spectrum equivalence provided by the embodiment of the present invention, in an embodiment, the obtaining of the seismic source planar projection parameters according to the regular grid model includes:

determining a horizontal projection plane of the regular gridding model according to the regular gridding model;

and acquiring the reference origin coordinate, the plane grid distance, the grid number in the x and y directions, the projection sequence number and the seismic source plane projection coordinate of the horizontal projection plane according to the horizontal projection plane of the regular gridding model.

In an embodiment, according to the established regular grid model, the horizontal projection plane xoy of the regular grid model can be determined, and the reference origin coordinate (x) thereof is obtained₀,y₀) The plane grid spacing (Deltax, Deltay), the number of grids in the x and y directions are N_xAnd N_yThe projection sequence numbers are (1,2, …, N)_x) And (1,2, …, N)_y) Corresponding to the actual single shot forward acting source plane projection coordinates(s)_x,s_y)。

In an embodiment of the invention, when the method for characterizing an irregular seismic source based on energy spectrum equivalence provided by the embodiment of the present invention is implemented specifically, the determining, according to the seismic source plane projection parameters, an index of a nearest regular projection grid point of the seismic source and a relative deviation between an actual seismic source plane position and a nearest grid projection direction includes:

determining the nearest regular projection grid point index of the seismic source according to the plane projection coordinate of the seismic source, the reference origin coordinate and the plane grid spacing;

and determining the relative deviation of the actual plane position of the seismic source and the projection direction of the nearest grid according to the index of the nearest regular projection grid point of the seismic source, the plane projection coordinate of the seismic source, the reference origin coordinate and the plane grid spacing.

In an embodiment, the source plane projection coordinates(s) are acquired according to the foregoing_x,s_y) Reference origin coordinate (x)₀,y₀) And plane grid spacing (Δ x, Δ y), calculating the index (i) of the nearest regular projection grid point of the seismic source in the two coordinate axis directions of the projection plane_x0,i_y0)。

In a specific implementation of the irregular seismic source characterization method based on energy spectrum equivalence provided by the embodiment of the present invention, in an embodiment, the nearest neighbor regular projection grid point index of the seismic source is determined as follows:

i_x0＝NINT[(s_x-x₀)/Δx)]+1 ①

i_y0＝NINT[(s_y-y₀)/Δy)]+1 ②

wherein (i)_x0,i_y0) Projecting a grid point index for the nearest rule of the seismic source; (s)_x,s_y) Projecting coordinates for the seismic source plane; (x)₀,y₀) As reference origin coordinates; (Δ x, Δ y) is the planar grid spacing; NINT is rounded according to rounding.

The foregoing expressions for determining the index of the nearest regular projected grid points of the seismic source are given as examples, and it will be understood by those skilled in the art that the above equations may be modified in some form and other parameters or data may be added as needed, or other specific equations may be provided, and such modifications are intended to fall within the scope of the present invention.

Obtaining the nearest regular projection grid point index (i) of the seismic source in the calculation_x0,i_y0) Then, combining the plane projection coordinates of the seismic source, the coordinates of the reference origin and the plane grid spacing, calculating the relative deviation (e) between the actual plane position of the seismic source and the projection direction of the nearest grid_x，e_y)。

In an embodiment of the invention, when the irregular seismic source characterization method based on energy spectrum equivalence is implemented, the relative deviation between the actual seismic source plane position and the projection direction of the nearest grid is determined as follows:

wherein (e)_x，e_y) Relative deviation between the actual seismic source plane position and the projection direction of the nearest grid is obtained; (i)_x0,i_y0) Projecting a grid point index for the nearest rule of the seismic source; (s)_x,s_y) Projecting coordinates for the seismic source plane; (x)₀,y₀) As reference origin coordinates; (Δ x, Δ y) is the planar grid spacing.

While the foregoing expressions for determining the relative deviation of the actual source plane position from the projection direction of the nearest neighbor grid are provided as examples, those skilled in the art will appreciate that the above equations may be modified in some manner and other parameters or data may be added as needed, or other specific equations may be provided, and such modifications are intended to fall within the scope of the present invention.

In a specific implementation of the method for characterizing an irregular seismic source based on energy spectrum equivalence provided by the embodiment of the present invention, in an embodiment, the determining a range of indexes of regular grid points of equivalent approximation of the seismic source and a weight function of the regular grid points of equivalent approximation of the seismic source according to a maximum half-width parameter of a minimum approximate grid and a relative deviation between an actual plane position of the seismic source and a projection direction of a maximum approximate grid includes:

inputting a minimum approximate grid half-width parameter, and determining a regular grid point index range of equivalent approximation of the seismic source according to the nearest regular projection grid point index of the seismic source;

determining the unidirectional grid weight of the regular grid points of the seismic source equivalent approximation according to the relative deviation of the actual seismic source plane position and the projection direction of the nearest grid, the index range of the regular grid points of the seismic source equivalent approximation, the index of the nearest regular projection grid points of the seismic source and the half-width parameter of the minimum approximation grid;

and combining the unidirectional grid weights of the regular grid points of the equivalent approximation of the seismic source to determine a weight function of the regular grid points of the equivalent approximation of the seismic source.

In an embodiment, the minimum approximate grid half-width parameter d for the input_wRespectively calculating the index ranges (i) of all regular grid points participating in the equivalent approximation of the seismic source in the x direction and the y direction according to the index of the nearest regular projection grid point of the seismic source_x,i_y) (ii) a In an embodiment of the invention, when the irregular seismic source characterization method based on energy spectrum equivalence is implemented, the regular grid point index range of the equivalent approximation of the seismic source is determined as followsEnclosing:

i_x0-d_w≤i_x≤i_x0+d _w ⑤

i_y0-d_w≤i_y≤i_y0+d_w ⑥

wherein (i)_x,i_y) Index ranges in x-and y-directions for regular grid points, i, which are equivalent approximations of the seismic source_xAnd i_yIs a positive integer; d_wIs a minimum approximate grid half-width parameter; (i)_x0,i_y0) The grid point index is projected for the nearest neighbor rule of the seismic source.

The foregoing expressions for determining the range of indices of regular grid points of equivalent approximation of a seismic source are merely exemplary, and it will be understood by those skilled in the art that the above equations may be modified in some manner and other parameters or data may be added as needed, or other specific equations may be provided, and such modifications are intended to fall within the scope of the present invention.

FIG. 3 is an index range diagram of regular grid points of equivalent approximation of a seismic source based on an irregular seismic source characterization method of energy spectrum equivalence according to an embodiment of the present invention, as shown in FIG. 3, nearest regular grid points calculated according to the half-width of the minimum approximation grid are represented by black dots; and then the relative deviation (e) from the nearest grid projection direction according to the actual source plane position_x，e_y) Regular grid point index range (i) of equivalent approximation to seismic source_x,i_y) Source nearest regular projection grid point index (i)_x0,i_y0) And a minimum approximate grid half-width parameter d_wRespectively calculating all the unidirectional grid weights C of the regular grid points participating in equivalent approximation of the seismic source_x(i_x) And C_y(i_y) (ii) a Regular grid points participating in equivalent approximation in the model are represented by black dots; in a specific implementation of the irregular seismic source characterization method based on energy spectrum equivalence provided by the embodiment of the present invention, in an embodiment, the unidirectional grid weights of the regular grid points of the equivalent approximation of the seismic source are determined as follows:

wherein, C_x(i_x) And C_y(i_y) A one-way grid weight of a regular grid point which is equivalent and approximate to the seismic source; (i)_x,i_y) Index ranges in x-and y-directions for regular grid points, i, which are equivalent approximations of the seismic source_xAnd i_yIs a positive integer; d_wIs a minimum approximate grid half-width parameter; (i)_x0,i_y0) Projecting a grid point index for the nearest rule of the seismic source; (e)_x，e_y) Relative deviation between the actual seismic source plane position and the projection direction of the nearest grid is obtained; sinc is a sine function notation; cos is the cosine function notation.

The foregoing expressions for determining the unidirectional grid weights of regular grid points of an equivalent approximation of a seismic source are merely exemplary, and it will be understood by those skilled in the art that the above equations may be modified in some manner and other parameters or data may be added as needed, or other specific equations may be provided, and such modifications are intended to fall within the scope of the present invention.

After the unidirectional grid weights of the regular grid points of the equivalent approximation of the seismic source are obtained, combining the unidirectional grid weights to obtain all the weight functions of the regular grid points participating in the equivalent approximation of the seismic source;

FIG. 4 is a schematic diagram showing values of regular grid point weight functions of seismic source equivalent approximation based on an irregular seismic source characterization method of energy spectrum equivalence, and a weight function C of all regular grid points participating in equivalent approximation is calculated_xy(i_x,i_y) In particular, when the irregular seismic source characterization method based on energy spectrum equivalence provided by the embodiment of the present invention is implemented, in an embodiment, a regular grid point weight function of seismic source equivalent approximation is determined as follows:

C_xy(i_x,i_y)＝C_x(i_x)C_y(i_y) ⑨

wherein, C_xy(i_x,i_y) A regular grid point weight function that is an equivalent approximation of the seismic source; c_x(i_x) And C_y(i_y) Unidirectional grid weights for regular grid points that are equivalent approximations of the seismic source.

The foregoing expressions of the weighting function for regular grid points for determining an equivalent approximation of a seismic source are merely exemplary, and it will be understood by those skilled in the art that the above equations may be modified in some manner and other parameters or data may be added or other specific equations may be provided as desired, and such modifications are intended to fall within the scope of the present invention.

According to the input discretization wave number arrays (kx, ky) in the x-axis direction and the y-axis direction, the dimensions are p and q respectively, and the subscripts of corresponding array elements are represented by l and m respectively. Computing a regular grid point weight function C_xy(i_x,i_y) At each pair (k)_xl,k_ym) Two-dimensional Fourier spectrum F (kx) of (A)_l,ky_m)；

In a specific implementation of the irregular seismic source characterization method based on energy spectrum equivalence provided by the embodiment of the present invention, in an embodiment, a two-dimensional spatial fourier spectrum of a weight function of a regular grid point is determined as follows:

wherein, F (kx)_l,ky_m) Two-dimensional spatial Fourier spectrum of a weight function of a regular grid point; c_xy(i_x,i_y) A regular grid point weight function that is an equivalent approximation of the seismic source; (i)_x,i_y) Index ranges in x-and y-directions for regular grid points, i, which are equivalent approximations of the seismic source_xAnd i_yIs a positive integer; (i)_x0,i_y0) Projecting a grid point index for the nearest rule of the seismic source; (e)_x，e_y) For the actual source plane position and the nearest grid projection directionRelative deviation; (kx, ky) is a discretization wave number array in the x-axis direction and the y-axis direction, the dimensions are p and q respectively, and subscripts of corresponding array elements are represented by l and m respectively; j is a unit imaginary number; exp is an exponential function.

The aforementioned expression for determining the two-dimensional spatial fourier spectrum of the regular grid point weight function is an example, and those skilled in the art will understand that, in implementation, the above formula may be modified in some form and other parameters or data may be added as needed, or other specific formulas may be provided, and these modifications are all within the scope of the present invention.

Fig. 5 is an energy error diagram of a two-dimensional fourier spectrum of a space unit pulse function and a two-dimensional fourier spectrum of a weight function of a regular grid point corresponding to an actual seismic source position of an irregular seismic source characterization method based on energy spectrum equivalence, as shown in fig. 5, next, an energy error between a two-dimensional fourier spectrum energy of the weight function and an impulse spectrum is calculated, and the two-dimensional spatial fourier spectrum error of the equivalent seismic source spectrum is compared with the energy error between the impulse seismic source spectrum, which specifically includes: comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum; in a specific implementation of the irregular seismic source characterization method based on energy spectrum equivalence provided by the embodiment of the present invention, in an embodiment, the energy error of the two-dimensional fourier spectrum of the spatial unit impulse function corresponding to the actual seismic source position and the two-dimensional spatial fourier spectrum of the regular grid point weight function is compared as follows:

wherein, F (kx)_l,ky_m) Two-dimensional spatial Fourier spectrum of a weight function of a regular grid point; e (kx)_l,ky_m) A two-dimensional fourier spectrum of the unit impulse function in space corresponding to the actual source location.

The aforementioned expression comparing the energy error of the two-dimensional space fourier spectrum of the pulse function in space unit corresponding to the actual source position with the two-dimensional space fourier spectrum of the weighting function of the regular grid points is an example, and it can be understood by those skilled in the art that, in implementation, the above formula may be modified in some form and other parameters or data may be added as needed, or other specific formulas may be provided, and these modifications all fall within the protection scope of the present invention.

After the energy error of the space unit impulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position and the regular grid point weight function two-dimensional space Fourier spectrum is obtained,

judging whether all the discretization Fourier spectrum energy errors meet a preset energy error threshold value or not;

and when the energy error meets a preset energy error threshold, finishing the estimation of the equivalent approximate weight function, and directly outputting the grid node index participating in the rule discretization representation and the corresponding node weight function value.

When the energy error does not meet the preset energy error threshold, modifying the minimum approximate grid half-width parameter for iterative repetition until the energy error meets the preset energy error threshold, and determining a grid node index (i) participating in the rule discretization characterization_x,i_y) And corresponding node weight function value C_xy(i_x,i_y)。

The embodiment of the invention also provides an implementation step of the irregular seismic source characterization method based on energy spectrum equivalence, which mainly comprises the following steps:

(1) establishing a regular grid model, and acquiring seismic source plane projection parameters;

(2) determining the nearest regular grid point index of the seismic source and the relative deviation of the actual coordinates, mainly comprising the following steps: determining the nearest regular projection grid point index of the seismic source and the relative deviation of the actual seismic source plane position and the nearest grid projection direction according to the seismic source plane projection parameters;

(3) determining a regular grid point index range and a grid weight function for equivalent approximation, mainly comprising: inputting a minimum approximate grid half-width parameter, and determining a regular grid point index range of equivalent approximation of the seismic source and a regular grid point weight function of equivalent approximation of the seismic source according to the index of the nearest regular projection grid point of the seismic source and the relative deviation of the actual plane position of the seismic source and the nearest grid projection direction;

(4) calculating a two-dimensional spatial Fourier spectrum of a weight function, which mainly comprises the following steps: determining a two-dimensional space Fourier spectrum of the regular grid point weight function according to the discretization wave number array, the regular grid point index range of the seismic source equivalent approximation and the regular grid point weight function of the seismic source equivalent approximation;

(5) comparing the equivalent seismic source spectrum two-dimensional space Fourier spectrum with the pulse seismic source spectrum error, mainly comprising: comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum;

(6) judging whether all the discretization Fourier spectrum energies meet the precision requirement or not according to a preset energy error threshold, and finishing the estimation of the equivalent approximate weight function if the discretization Fourier spectrum energies meet the precision requirement; and when the energy error does not meet the preset energy error threshold, modifying the minimum approximate grid half-width parameter for iteration, and performing the processing from (3) to (5) again until the discretization Fourier spectrum energy error meets the preset energy error threshold requirement.

(7) Outputting the grid node index (i) meeting the precision requirement and participating in the rule discretization characterization_x,i_y) And corresponding node weight function value C_xy(i_x,i_y)。

Table 1 shows the grid node index and the corresponding node weight function of the rule discretization representation that the output meets the requirements.

TABLE 1

The embodiment of the invention establishes a regular discretization equivalent characterization method of an irregular excitation seismic source based on an energy spectrum equivalent principle, utilizes a method for characterizing the irregular seismic source by utilizing a regular discretization grid combined seismic source, finally generates a regular grid index and grid point weight which can be used for approximating the equivalent characterization, and can better reduce space positioning errors. For actual local sparse points, larger space positioning errors possibly caused are reduced, and adverse effects caused by subsequent imaging, illumination analysis and full waveform inversion are reduced. The method can calculate the weighting function of the seismic source combination in the corresponding rule discretization format under the condition of the given rule grid parameters and the plane coordinates of any seismic source, so that the error between the spectral energy of the corresponding equivalent seismic source combination and the actual seismic source spectral energy meets the given precision requirement. The method has wide application prospect because the regularization method is an important basic step in the current data processing in the seismic data processing. The feasibility of the method is proved through theoretical data simulation verification.

Fig. 6 is a schematic diagram of a computer device for executing an irregular seismic source characterization method based on energy spectrum equivalence implemented by the present invention, and as shown in fig. 6, an embodiment of the present invention further provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the irregular seismic source characterization method based on energy spectrum equivalence when executing the computer program.

Embodiments of the present invention further provide a computer-readable storage medium storing a computer program for implementing the irregular seismic source characterization method based on energy spectrum equivalence.

The embodiment of the invention also provides an irregular seismic source characterization device based on energy spectrum equivalence, and the irregular seismic source characterization device is described in the following embodiments. Because the principle of solving the problems of the device is similar to the irregular seismic source characterization method based on energy spectrum equivalence, the implementation of the device can refer to the implementation of the irregular seismic source characterization method based on energy spectrum equivalence, and repeated details are omitted.

Fig. 7 is a schematic diagram of an irregular seismic source characterization device based on energy spectrum equivalence according to an embodiment of the present invention, and as shown in fig. 7, an irregular seismic source characterization device based on energy spectrum equivalence is further provided in an embodiment of the present invention, and may include:

the seismic source plane projection parameter acquisition module 701 is used for establishing a regular gridding model and acquiring seismic source plane projection parameters;

a seismic source nearest regular projection grid point index and actual seismic source plane position relative deviation from nearest grid projection direction determination module 702, configured to determine, according to the seismic source plane projection parameters, a seismic source nearest regular projection grid point index and actual seismic source plane position relative deviation from nearest grid projection direction;

a seismic source equivalent approximate regular grid point index range and seismic source equivalent approximate regular grid point weight function determination module 703, configured to input a minimum approximate grid half-width parameter, and determine a seismic source equivalent approximate regular grid point index range and a seismic source equivalent approximate regular grid point weight function according to a relative deviation between a seismic source nearest regular projection grid point index and an actual seismic source plane position and a nearest grid projection direction;

a regular grid point weight function two-dimensional space fourier spectrum determination module 704, configured to determine a regular grid point weight function two-dimensional space fourier spectrum according to the discretized wave number array, the regular grid point index range of the seismic source equivalent approximation, and the regular grid point weight function of the seismic source equivalent approximation;

the energy error judgment module 705 is configured to compare an energy error of a two-dimensional space fourier spectrum of a spatial unit pulse function corresponding to an actual seismic source position with a two-dimensional space fourier spectrum of a regular grid point weight function, and judge whether the energy error meets a preset energy error threshold;

and a grid node index and corresponding node weight function value determining module 706, configured to modify the minimum approximate grid half-width parameter for iteration when the energy error does not meet the preset energy error threshold, and determine the grid node index and corresponding node weight function value participating in the rule discretization characterization until the energy error meets the preset energy error threshold.

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence is implemented specifically, the seismic source planar projection parameter obtaining module is specifically configured to:

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence is implemented specifically, the seismic source planar projection parameter obtaining module is further configured to:

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence provided by the embodiment of the present invention is implemented specifically, the module for determining the nearest regular projection grid point index of the seismic source and the relative deviation between the actual seismic source plane position and the nearest grid projection direction is specifically configured to:

In an embodiment, when the irregular seismic source characterization device based on energy spectrum equivalence provided by the embodiment of the present invention is implemented specifically, the module for determining the nearest-to-regular projection grid point index of the seismic source and the relative deviation between the actual seismic source plane position and the nearest-to-regular projection grid point direction is further configured to determine the nearest-to-regular projection grid point index of the seismic source as follows:

i_x0＝NINT[(s_x-x₀)/Δx)]+1

i_y0＝NINT[(s_y-y₀)/Δy)]+1

In an embodiment, when the irregular seismic source characterization device based on energy spectrum equivalence provided by the embodiment of the present invention is implemented specifically, the module for determining the index of the nearest regular projection grid point of the seismic source and the relative deviation between the actual seismic source plane position and the nearest projection direction of the grid is further configured to determine the relative deviation between the actual seismic source plane position and the nearest projection direction of the grid as follows:

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence provided in the embodiment of the present invention is implemented specifically, the module for determining the index range of the regular grid points of the equivalent approximation of the seismic source and the weight function of the regular grid points of the equivalent approximation of the seismic source is specifically configured to:

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence provided by the embodiment of the present invention is implemented specifically, the module for determining the index range of the regular grid points of the equivalent approximation of the seismic source and the weight function of the regular grid points of the equivalent approximation of the seismic source is further configured to determine the index range of the regular grid points of the equivalent approximation of the seismic source according to the following manner:

i_x0-d_w≤i_x≤i_x0+d_w

i_y0-d_w≤i_y≤i_y0+d_w

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence provided by the embodiment of the present invention is implemented specifically, the module for determining the index range of the regular grid points of the seismic source equivalent approximation and the weight function of the regular grid points of the seismic source equivalent approximation is further configured to determine the unidirectional grid weight of the regular grid points of the seismic source equivalent approximation according to the following manner:

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence provided by the embodiment of the present invention is implemented specifically, the aforementioned regular grid point index range of seismic source equivalent approximation and the regular grid point weight function determination module of seismic source equivalent approximation are further configured to determine the regular grid point weight function of seismic source equivalent approximation according to the following manner:

C_xy(i_x,i_y)＝C_x(i_x)C_y(i_y)

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence is implemented specifically, the module for determining a regular grid point weight function two-dimensional space fourier spectrum is specifically configured to determine a regular grid point weight function two-dimensional space fourier spectrum according to the following manner:

wherein, F (kx)_l,ky_m) Two-dimensional spatial Fourier spectrum of a weight function of a regular grid point; c_xy(i_x,i_y) A regular grid point weight function that is an equivalent approximation of the seismic source; (i)_x,i_y) Index ranges in x-and y-directions for regular grid points, i, which are equivalent approximations of the seismic source_xAnd i_yIs a positive integer; (i)_x0,i_y0) Projecting a grid point index for the nearest rule of the seismic source; (e)_x，e_y) Relative deviation between the actual seismic source plane position and the projection direction of the nearest grid is obtained; (kx, ky) is a discretization wave number array in the x-axis direction and the y-axis direction, the dimensions are p and q respectively, and subscripts of corresponding array elements are represented by l and m respectively; j is a unit imaginary number; exp is an exponential function.

In an embodiment of the invention, when the irregular seismic source characterization device based on energy spectrum equivalence provided in the embodiment of the present invention is implemented specifically, the energy error determination module is specifically configured to compare an energy error of a two-dimensional fourier spectrum of a unit impulse function in space corresponding to an actual seismic source position with an energy error of a two-dimensional fourier spectrum of a weight function of a regular grid point according to the following manner:

E(kx_l,ky_m)＝|F(kx_l,ky_m)|²-1

To sum up, the irregular seismic source characterization method and device based on energy spectrum equivalence provided by the embodiment of the invention firstly establish a regular gridding model and obtain the plane projection parameters of the seismic source; then, according to the plane projection parameters of the seismic source, determining the nearest regular projection grid point index of the seismic source and the relative deviation between the actual plane position of the seismic source and the nearest grid projection direction; then inputting a minimum approximate grid half-width parameter, and determining a regular grid point index range of equivalent approximation of the seismic source and a regular grid point weight function of equivalent approximation of the seismic source according to the index of the nearest regular projection grid point of the seismic source and the relative deviation of the actual plane position of the seismic source and the nearest grid projection direction; determining a two-dimensional space Fourier spectrum of the regular grid point weight function according to the discretization wave number array, the regular grid point index range of the seismic source equivalent approximation and the regular grid point weight function of the seismic source equivalent approximation; then comparing the energy error of the space unit pulse function two-dimensional Fourier spectrum corresponding to the actual seismic source position with the energy error of the regular grid point weight function two-dimensional space Fourier spectrum, and judging whether the energy error meets a preset energy error threshold value; and finally, when the energy error does not meet a preset energy error threshold, modifying the minimum approximate grid half-width parameter for iteration, and determining a grid node index and a corresponding node weight function value participating in the rule discretization representation until the energy error meets the preset energy error threshold. The embodiment of the invention establishes a regular discretization equivalent characterization method of an irregular excitation seismic source based on an energy spectrum equivalent principle, utilizes a method for characterizing the irregular seismic source by utilizing a regular discretization grid combined seismic source, finally generates a regular grid index and grid point weight which can be used for approximating the equivalent characterization, and can better reduce space positioning errors. For actual local sparse points, larger space positioning errors possibly caused are reduced, and adverse effects caused by subsequent imaging, illumination analysis and full waveform inversion are reduced. The method can calculate the weighting function of the seismic source combination in the corresponding rule discretization format under the condition of the given rule grid parameters and the plane coordinates of any seismic source, so that the error between the spectral energy of the corresponding equivalent seismic source combination and the actual seismic source spectral energy meets the given precision requirement.

The irregular seismic source characterization method and device based on energy spectrum equivalence have wide application prospect because the irregular seismic source characterization method and device based on energy spectrum equivalence is an important basic step in the current data processing in the seismic data processing, which is caused by the deep application of more and more nodes receiving, pile number-free excitation and compressed sensing. The feasibility of the method and the device is proved through theoretical data simulation verification.

As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims

1. An irregular seismic source characterization method based on energy spectrum equivalence is characterized by comprising the following steps:

2. The method of claim 1, wherein establishing a regular gridding model to obtain source plane projection parameters comprises:

3. The method of claim 2, wherein obtaining the source plane projection parameters according to a regular gridding model comprises:

4. The method of claim 3, wherein determining, from the source plane projection parameters, a source nearest neighbor regular projection grid point index and a relative deviation of an actual source plane location from a nearest neighbor grid projection direction comprises:

5. The method of claim 4, wherein the source nearest-neighbor regular projection grid point index is determined as follows:

i_x0＝NINT[(s_x-x₀)/Δx)]+1

i_y0＝NINT[(s_y-y₀)/Δy)]+1

wherein (i)_x0,i_y0) Is the nearest neighbor of the seismic sourceRegularly projecting grid point indexes; (s)_x,s_y) Projecting coordinates for the seismic source plane; (x)₀,y₀) As reference origin coordinates; (Δ x, Δ y) is the planar grid spacing; NINT is rounded according to rounding.

6. The method of claim 4, wherein the relative deviation of the actual source plane location from the nearest grid projection direction is determined as follows:

7. The method of claim 1, wherein inputting a minimum approximation grid half-width parameter, determining a range of regular grid point indices for the source equivalent approximation and a regular grid point weight function for the source equivalent approximation based on the source nearest regular projection grid point index and a relative deviation of an actual source plane position from a nearest grid projection direction comprises:

8. The method of claim 7, wherein the range of regular grid point indices for the equivalent approximation of the seismic source is determined as follows:

i_x0-d_w≤i_x≤i_x0+d_w

i_y0-d_w≤i_y≤i_y0+d_w

9. The method of claim 7, wherein the unidirectional grid weights for the regular grid points of the equivalent approximation of the seismic source are determined as follows:

wherein, C_x(i_x) And C_y(i_y) A one-way grid weight of a regular grid point which is equivalent and approximate to the seismic source; (i)_x,i_y) Index ranges in x-and y-directions for regular grid points, i, which are equivalent approximations of the seismic source_xAnd i_yIs a positive integer; d_wIs a minimum approximate grid half-width parameter; (i)_x0,i_y0) Is a vibrationProjecting grid point indexes by using a source nearest rule; (e)_x，e_y) Relative deviation between the actual seismic source plane position and the projection direction of the nearest grid is obtained; sinc is a sine function notation; cos is the cosine function notation.

10. The method of claim 7, wherein the regular grid point weight function for the equivalent approximation of the seismic source is determined as follows:

C_xy(i_x,i_y)＝C_x(i_x)C_y(i_y)

11. The method of claim 1, characterized in that the regular grid point weight function two-dimensional spatial fourier spectrum is determined in the following manner:

12. The method of claim 1, wherein the energy error of the two-dimensional space fourier spectrum of the unit impulse function in space corresponding to the actual source location is compared to the two-dimensional space fourier spectrum of the weight function of the regular grid points by:

E(kx_l,ky_m)＝|F(kx_l,ky_m)|²-1

13. An irregular seismic source characterization device based on energy spectrum equivalence, which is characterized by comprising:

14. The apparatus of claim 13, wherein the source plane projection parameters acquisition module is specifically configured to:

15. The apparatus of claim 14, wherein the source plane projection parameters acquisition module is further to:

16. The apparatus of claim 15, wherein the source nearest regular projected grid point index and the relative deviation of the actual source plane position from the nearest grid projection direction determination module are specifically configured to:

17. The apparatus of claim 16, wherein the source nearest regular projected grid point index and the relative deviation of the actual source plane location from the nearest grid projection direction determination module are further configured to determine the source nearest regular projected grid point index as follows:

i_x0＝NINT[(s_x-x₀)/Δx)]+1

i_y0＝NINT[(s_y-y₀)/Δy)]+1

18. The apparatus of claim 16, wherein the source nearest regular projected grid point index and actual source plane position relative deviation from nearest grid projection direction determination module is further configured to determine the actual source plane position relative deviation from nearest grid projection direction as follows:

19. The apparatus of claim 13, wherein the index range of regular grid points for the source equivalent approximation and the weight function determination module for the regular grid points for the source equivalent approximation are specifically configured to:

20. The apparatus of claim 19, wherein the regular grid point index range for the source equivalent approximation and the regular grid point weight function determination module for the source equivalent approximation are further configured to determine the regular grid point index range for the source equivalent approximation as follows:

i_x0-d_w≤i_x≤i_x0+d_w

i_y0-d_w≤i_y≤i_y0+d_w

21. The apparatus of claim 19, wherein the index range of regular grid points for the source equivalent approximation and the function determination module for weights of regular grid points for the source equivalent approximation are further configured to determine unidirectional grid weights for regular grid points for the source equivalent approximation as follows:

22. The apparatus of claim 19, wherein the index range of regular grid points for the source equivalent approximation and the weight function determination module for regular grid points for the source equivalent approximation are further configured to determine the weight function for regular grid points for the source equivalent approximation as follows:

C_xy(i_x,i_y)＝C_x(i_x)C_y(i_y)

wherein, C_xy(i_x,i_y) A regular grid point weight function that is an equivalent approximation of the seismic source; c_x(i_x) And C_y(i_y) Regular grid point list for equivalent approximation of seismic sourceAnd weighting to the grid.

23. The apparatus according to claim 13, wherein the regular grid point weight function two-dimensional spatial fourier spectrum determining module is specifically configured to determine the regular grid point weight function two-dimensional spatial fourier spectrum in the manner:

24. The apparatus according to claim 13, wherein the energy error determination module is specifically configured to compare the energy error of the two-dimensional space fourier spectrum of the unit impulse function in space corresponding to the actual source location with the two-dimensional space fourier spectrum of the weight function of the regular grid points, as follows:

E(kx_l,ky_m)＝|F(kx_l,ky_m)|²-1

25. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method of any of claims 1 to 12 when executing the computer program.

26. A computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program for executing a method according to any one of claims 1 to 12.