CN111239828A - Multiple suppression method based on optimal hyperbolic integral path superposition - Google Patents
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Abstract
The invention belongs to the technical field of noise suppression in geophysical exploration, and relates to a multiple suppression method based on optimal hyperbolic integral path superposition. The invention optimizes and improves the conventional three-dimensional surface related multiple pressing method, utilizes the inner product of the cross survey line multiple contribution gather and the result obtained by parabolic Raon transformation of the cross survey line multiple contribution gather, determines the vertex coordinate of a hyperbola by picking up the local maximum value of the inner product result, performs statistics on the vertex coordinate, selects a few vertex coordinates with higher frequency as path superposition vertices, uses the vertex horizontal position coordinate as the offset selection result of the cross survey line multiple contribution gather to obtain a plurality of predicted multiple subsets, determines different intervals according to the time coordinate of the vertex position, selects and screens the multiple subsets according to the principle of maximum interval amplitude to obtain the final multiple prediction result, and finally realizes multiple pressing by matching and subtracting.
Description
Technical Field
The invention belongs to the technical field of noise suppression in geophysical exploration, particularly relates to a multiple suppression method in marine seismic exploration, and particularly relates to a multiple suppression method based on optimal hyperbolic integral path stacking.
Background
Multiples in marine seismic exploration reduce the signal-to-noise ratio of seismic data due to their periodicity and kinematic morphology, and are often referred to as coherent noise to be removed. Currently, the more common multiple suppression technique is the 2D SRME technique. However, in the case of a stratum inclination, the real propagation path is a three-dimensional space function, and the 2D method cannot depict the change of the direction of the contact survey line, so that the multiple prediction problem is converted into 3D, and 3D SRME needs to be introduced. However, 3D prediction is limited by sparse sampling of an observation system, and prediction artifacts are introduced by direct superposition to cause waveform distortion, so that multiple prediction generates serious spatial aliasing.
The 2D SRME method was proposed in 1992 by Berkhout and Verschuur et al (Verschuur D J, Berkhout AJ, Wapendaar C P A. adaptive surface-related multiple ionization [ J ]. GEOPHYSICS,1992,57(9):1166-1177.) by eliminating the influence of surface reflectivity in the data, designing the multiple removal as an inversion process in which the reflectivity characteristics of the source and the surface can be estimated, and the inversion residual is the predicted multiple, which is data-driven and only applicable to simple terrain conditions. With the increasing difficulty of seismic exploration, the 3D SRME method is proposed in 1999 by E.J.van Dedem (Dedem E J V.3D surface-related multiple evaluation and interplation [ J ]. SEG Technical Programme expanded Abstracts,1999,17(1):1321.) and introduces the direction of contact survey line on the basis of 2D SRME to adapt to more complex terrain. However, the 3D prediction process is limited by the sparsity of observation system crossline direction sampling, and therefore a series of solutions are proposed in succession. The method of dense sampling Data required for Data reconstruction to obtain 3D SRME was proposed in 1999 by automatic Baumstein et al (Baumstein A.3D SRME: Data retrieval and application field Data [ J ]. SEG Technical Program Expanded Abstracts,1999,23 (1)); then, a Multiple pressing method based on sparse inversion is proposed by Van Dedem and Verschuur (DedemE J V, Verschuur D J.3D Surface-related Multiple Prediction Using SparseInversion: Experience With Field Data [ J ]. Seg Technical Program expanding standards, 2002,21(1):2094.) in 2002, sparse inversion is utilized to reconstruct a sparse contact measuring line Multiple contribution channel set in a model space, and then correction and superposition are carried out through amplitude and phase to obtain predicted Multiple; separation of primary and multiple waves by curvelet transformation was proposed by Xiang Wu (Wu X, Hung b. adaptive primary-multiple separation 3D curvelet transform [ J ]. ASEG Extended extracts, 2015(1): 1155) in 2015; a three-dimensional surface multiple suppression method based on data regularization and sparse inversion is proposed in 2016 by a three-dimensional surface multiple suppression method [ J ] geophysical report, 2016, v.59(02):269-277.) based on data regularization and sparse inversion by a square cloud peak et al (square cloud peak, Nie-Remei, Zhang-Mei, et al), so that data distribution meets the requirements of three-dimensional SRME through data regularization and anti-regularization technologies, and then contact line multiple contribution gathers are replaced by sparse inversion. However, the sparse inversion method and data reconstruction or curvelet transformation adopted by the methods are weak in stability and have a large influence on different complex terrains.
Disclosure of Invention
The invention aims to provide a multiple suppression method based on optimal hyperbolic integral path superposition so as to overcome the defect that a conventional three-dimensional surface related multiple suppression method generates spatial false frequency due to too sparse seismic data acquisition tie line direction.
The purpose of the invention is realized by the following technical scheme:
firstly, separating a common shot point gather and a common demodulator probe gather from data acquired by earthquake, convolving the common shot point gather and the common demodulator probe gather to obtain a vertical measuring line multiple contribution gather at different positions, summing the vertical measuring line multiple contribution gather along the vertical measuring line direction to obtain a contact measuring line multiple contribution gather, utilizing the contact measuring line multiple contribution gather and a result inner product obtained by parabolic Raon transformation of the contact measuring line multiple contribution gather, determining a hyperbolic vertex coordinate by picking up a local maximum value of an inner product result, counting the hyperbolic vertex coordinate, selecting a few vertex coordinates with higher frequency as a path superposition vertex, using a vertex horizontal position coordinate as a migration distance selection result of the contact measuring line multiple contribution gather to obtain a plurality of predicted multiple subsets, determining different intervals according to a time coordinate of the vertex position, and selecting and screening the multiple subsets at maximum according to an interval amplitude principle, and obtaining a final multiple prediction result, and finally, realizing multiple suppression through matching subtraction.
A multiple suppression method based on optimal hyperbolic integral path superposition comprises the following steps:
a. completing data acquired by three-dimensional marine seismic exploration through reciprocal theorem to obtain seismic data with the same shot channel, and extracting a gather according to a shot number (fldr) in channel head information to obtain a common shot point gather d (x)k,yk,t,xs,ys) (ii) a Extracting a gather according to the detection number (tracl) to obtain a common detection point gather r (x)r,yr,t,xk,yk) Wherein (x)k,yk) At any point location (shot or geophone), (x)s,ys) As the shot point coordinates, (x)r,yr) Is the coordinate of the demodulator probe and t is time.
b. For common shot gather d (x)k,yk,t,xs,ys) With common detection point gather r (x)r,yr,t,xk,yk) Fourier transform is carried out to obtain a common shot gather D (x) of a frequency domaink,yk,w,xs,ys) With common detection point gather R (x)r,yr,w,xk,yk) Where w is the angular frequency.
c. Gather D (x) common shot pointsk,yk,w,xs,ys) With common detection point gather R (x)r,yr,w,xk,yk) The product in the frequency domain yields corresponding different positions (x)k,yk) Longitudinal line multiple contribution gather Mxy(xr,yr,xs,ys,xk,yk,w)。
Mxy(xr,yr,xs,ys,xk,yk,w)＝r0R(xr,yr,w；xk,yk)D(xk,yk,w；xs,ys)
Wherein r is0Which represents the formation reflection coefficient and is typically-1.
d. Gather of traces M contributing to multiples of longitudinal measuring lines at different positionsxy(xr,yr,xs,ys,xk,ykW) summing along the longitudinal measuring line direction to obtain a cross measuring line multiple contribution gather My(xr,yr,xs,ys,ykW) and converted back to the time domain by inverse Fourier transform to obtain a cross-line multiple contribution gather m of the time domainy(xr,yr,xs,ys,yk,t)。
e. And (4) carrying out parabolic Radon transformation on the contact measuring line multiple contribution trace set, and carrying out inner product on the result of the parabolic Radon transformation and the contact measuring line multiple contribution trace set which is not subjected to the parabolic Radon transformation.
myradon(xr,yr,xs,ys,yk,t)＝Radon(my(xr,yr,xs,ys,yk,t))
myradon(xr,yr,xs,ys,ykT) is the result after Radon transformation, md(xr,yr,xs,ys,ykAnd t) is the result of the inner product.
f. And (4) picking up a local maximum value by utilizing findpeaks under a matlab platform through threshold limit contrast amplitude values, and acquiring hyperbolic vertex coordinates.
[xm,tm]＝findpeaks(md(xr,yr,xs,ys,yk,t))
[xm,tm]Is a matrix composed of the transverse coordinates of the vertices of the same phase axis.
g. And (4) counting the vertex coordinates of all the same-phase axes, and selecting a plurality of the vertex coordinates (generally 3-5, determined according to actual conditions) with the highest occurrence frequency as the vertices of the path superposition.
h. Respectively selecting x of a plurality of vertexes with superposed pathsmax(i)As offset (offset) of Radon transform, Radon transform is performed, and the result of Radon transform is superimposed to obtain a plurality of predicted multiples m(i)(xr,yr,xs,ysT), comparing tmax(i)Find different intervals in the time direction
my(i)(xr,yr,xs,ys,yk,t)＝Radon(xmax(i))(my(xr,yr,xs,ys,yk,t))
i. In different intervals
And selecting the part with larger amplitude in the plurality of predicted multiples to form a final multiple prediction result.
j. And subtracting by adopting time domain matching to obtain the seismic data without multiple waves.
Further, in step g, the number of the vertices is typically 3-5, depending on the actual situation.
Compared with the prior art, the invention has the beneficial effects that:
the invention realizes the multiple suppression technology by selecting the optimal hyperbolic integral path superposition. The method comprises the steps of utilizing an interconnection survey line multiple contribution gather and a result inner product obtained by parabolic Raon transformation of the interconnection survey line multiple contribution gather, determining a hyperbolic vertex coordinate by picking up a local maximum value of an inner product result, carrying out statistics on the internal product result, selecting a few vertex coordinates with high frequency of occurrence as a path superposition vertex, using a vertex horizontal position coordinate as an offset selection result of the interconnection survey line multiple contribution gather to obtain a plurality of predicted multiple subsets, determining different intervals according to time coordinates of vertex positions, selecting and screening the multiple subsets according to the principle that the interval amplitude is the maximum to obtain a final multiple prediction result, and finally realizing multiple suppression through matching subtraction, so that the accuracy and precision of the multiple suppression are remarkably improved.
The invention has the following advantages:
1. the multiple suppression technology is realized based on the superposition of optimal hyperbolic integral paths, belongs to a data driving method, does not need the hypothesis and prior information of an underground medium, only needs the information of a seismic source and a wave detection point, and can realize the purposes of effectively predicting and suppressing multiple.
2. The method effectively solves the problem that the 3D SRME requires intensive data acquisition, and can obtain the multiple suppression effect with high precision and high stability aiming at different geological models.
3. Compared with a multiple suppression method based on sparse inversion, the method has higher calculation efficiency and reduces the cost of seismic data processing and interpretation.
Drawings
FIG. 1 is a flow chart of a multiple pressing method based on stacking of optimal hyperbolic integral paths.
FIG. 2 is a schematic diagram of a three-dimensional marine seismic survey data acquisition and observation system.
Fig. 3 is a three-dimensional effect path propagation diagram.
FIG. 4 is a schematic diagram of the propagation path of surface multiples.
FIG. 5 is a schematic view of an inline multiple contribution gather.
FIG. 6 is a schematic diagram of a cross-line multiple contribution gather.
FIG. 7 is a diagram of the Radon transform results for a line-of-sight multiple contribution gather.
FIG. 8 is a schematic diagram of the inner product of the cross-line multiple contribution gather and its Radon transform result
FIG. 9 three-dimensional simulation data; fig. 9a is a schematic diagram of a simulated geological model, fig. 9b is an Offset-500 diagram of a multiple for path-stacked vertex prediction, fig. 9c is an Offset-300 diagram of a multiple for path-stacked vertex prediction, fig. 9d is an Offset-0 diagram of a multiple for path-stacked vertex prediction, fig. 9e is a diagram of a multiple prediction result, fig. 9f is a diagram of raw data, and fig. 9g is a diagram of a multiple compression result.
Detailed Description
The invention is described in further detail below with reference to the figures and examples.
The invention optimizes and improves a conventional three-dimensional surface-related multiple suppression method (3D surface-related multiple selection, 3D SRME), utilizes the inner product of a contact measuring line multiple contribution gather and a result obtained by parabolic Raon transformation, determines a hyperbolic vertex coordinate by picking up a local maximum value of the inner product result, statistically selects a few vertex coordinates with higher frequency as a path superposition vertex, uses a vertex horizontal position coordinate as an offset selection result of the contact measuring line multiple contribution gather to obtain a plurality of predicted multiple subsets, determines different intervals according to a time coordinate of a vertex position, selects and screens the multiple subsets according to the principle of maximum interval amplitude to obtain a final multiple prediction result, and finally realizes multiple suppression by matching and subtracting. The multiple pressing method based on the superposition of the optimal hyperbolic integral paths is realized by a Seismic Unix platform and an MATLAB platform.
The invention relates to a multiple suppression method based on optimal hyperbolic integral path superposition, which comprises the following steps of:
a. complementing data acquired by a three-dimensional marine seismic exploration observation system (figure 2) through reciprocal theorem to obtain seismic data with the same shot channel, and extracting a gather according to a shot number (fldr) in channel head information to obtain a common shot point gather d (x)k,yk,t,xs,ys) (ii) a Extracting a gather according to the detection number (tracl) to obtain a common detection point gather r (x)r,yr,t,xk,yk) Wherein (x)k,yk) At any point location (shot or geophone), (x)s,ys) As the shot point coordinates, (x)r,yr) Is the coordinate of the demodulator probe and t is time.
b. For common shot gather d (x)k,yk,t,xs,ys) With common detection point gather r (x)r,yr,t,xk,yk) Fourier transform is carried out to obtain a common shot gather D (x) of a frequency domaink,yk,w,xs,ys) With common detection point gather R (x)r,yr,w,xk,yk) Where w is the angular frequency.
c. Considering three-dimensional effect influence (figure 3), according to wave field motion characteristics of multiple wave propagation paths (figure 4), collecting D (x) common shot pointsk,yk,w,xs,ys) With common detection point gather R (x)r,yr,w,xk,yk) The product in the frequency domain yields corresponding different positions (x)k,yk) Longitudinal line multiple contribution gather Mxy(xr,yr,xs,ys,xk,ykW) (fig. 5).
Mxy(xr,yr,xs,ys,xk,yk,w)＝r0R(xr,yr,w；xk,yk)D(xk,yk,w；xs,ys)
Wherein r is0Which represents the formation reflection coefficient and is typically-1.
d. Gather M of contributions to multiples of longitudinal linexy(xr,yr,xs,ys,xk,ykW) summing along the longitudinal measuring line direction to obtain a cross measuring line multiple contribution gather My(xr,yr,xs,ys,ykW) and converted back to the time domain by inverse Fourier transform to obtain a cross-line multiple contribution gather m of the time domainy(xr,yr,xs,ys,ykT) (fig. 6).
e. Parabolic Radon transform is performed on the contact log multiple contribution gather, and the result of the parabolic Radon transform (FIG. 7) is integrated with the contact log multiple contribution gather without the parabolic Radon transform (FIG. 8).
myradon(xr,yr,xs,ys,yk,t)＝Radon(my(xr,yr,xs,ys,yk,t))
myradon(xr,yr,xs,ys,ykT) is the result after Radon transformation, md(xr,yr,xs,ys,ykAnd t) is the result of the inner product.
f. And (4) picking up a local maximum value by utilizing findpeaks under a matlab platform through threshold limit contrast amplitude values, and acquiring hyperbolic vertex coordinates.
[xm,tm]＝findpeaks(md(xr,yr,xs,ys,yk,t))
[xm,tm]Is a matrix composed of the transverse coordinates of the vertices of the same phase axis.
g. And (4) counting the vertex coordinates of all the same-phase axes, and selecting a plurality of the vertex coordinates with the highest occurrence frequency (generally 3-5, determined according to the actual situation) as the vertices of the path superposition.
h. respectively selecting x of a plurality of vertexes with superposed pathsmax(i)As offset (offset) of Radon transform, Radon transform is performed, and the result of Radon transform is superimposed to obtain a plurality of predicted multiples m(i)(xr,yr,xs,ysT), comparing tmax(i)Find different intervals in the time direction
my(i)(xr,yr,xs,ys,yk,t)＝Radon(xmax(i))(my(xr,yr,xs,ys,yk,t))
i. In different intervals
And selecting the part with larger amplitude in the plurality of predicted multiples to form a final multiple prediction result.
j. And subtracting the predicted multiples from the original data in time domain matching to obtain the seismic data without the multiples.
Example 1
a. The simulated data model is a three-dimensional tilted formation model (fig. 9 a). The observation system is set to be 11 seismic prospecting data with the same shot-detection on the central measuring line, wherein the distance between every two measuring lines is 100 meters and is approximately distributed in parallel (-500 m), receivers are uniformly distributed on every measuring line at intervals of 25 meters for receiving (0 m-2000 m), seismic waves are excited by the seismic sources at the horizontal position of the central cable along with the towing ship at intervals of 25 meters, and the data is supplemented through a reciprocal theorem. Extracting a gather according to the shot number (fldr, 1-81) in the track head information to obtain a common shot point gather d (x)k,yk,t,xs,ys) (ii) a Extracting a gather according to the detection number (tracl, (1-81, 1-11)) to obtain a common detection point gather r (x)r,yr,t,xk,yk) Wherein (x)k,yk) At any point location (shot or geophone), (x)s,ys) As the shot point coordinates, (x)r,yr) Is the coordinate of the demodulator probe and t is time.
b. For common shot gather d (x)k,yk,t,xs,ys) With common detection point gather r (x)r,yr,t,xk,yk) Fourier transform is carried out to obtain a common shot gather D (x) of a frequency domaink,yk,w,xs,ys) With common detection point gather R (x)r,yr,w,xk,yk) Where w is the angular frequency.
c. Gather D (x) common shot pointsk,yk,w,xs,ys) With common detection point gather R (x)r,yr,w,xk,yk) The product in the frequency domain yields corresponding different positions (x)k,yk) Longitudinal line multiple contribution gather Mxy(xr,yr,xs,ys,xk,ykW) (total 81 x 11).
Mxy(xr,yr,xs,ys,xk,yk,w)＝r0R(xr,yr,w；xk,yk)D(xk,yk,w；xs,ys)
Wherein r is0Which represents the formation reflection coefficient and is typically-1.
d. Gather M of contributions to multiples of longitudinal linexy(xr,yr,xs,ys,xk,ykW) summing along the longitudinal measuring line direction to obtain a cross measuring line multiple contribution gather My(xr,yr,xs,ys,ykW) (81 in total) and converted back to the time domain by inverse fourier transform to obtain a time domain crossline multiple contribution gather my(xr,yr,xs,ys,yk,t)。
e. And (3) carrying out parabolic Radon transformation on the channel set contributing to the multiple waves of the contact survey line, wherein the reference maximum offset distance in parameter setting is 2000m, the minimum time difference is 200, and the maximum time difference is 1000. And (4) performing inner product of the parabolic Radon transform result and the cross-line multiple contribution trace gather without the parabolic Radon transform.
myradon(xr,yr,xs,ys,yk,t)＝Radon(my(xr,yr,xs,ys,yk,t))
myradon(xr,yr,xs,ys,ykT) is the result after Radon transformation, md(xr,yr,xs,ys,ykT) is
The result of the inner product.
f. Local maximum values are picked up by using findpeaks under a matlab platform through threshold limit contrast amplitude values, and hyperbolic vertex coordinates (table 1) are obtained, wherein the amplitude threshold is set to be 0.01.
[xm,tm]＝findpeaks(md(xr,yr,xs,ys,yk,t))
[xm,tm]Is a matrix composed of the transverse coordinates of the vertices of the same phase axis.
g. And (4) counting the vertex coordinates of all the same-phase axes, and selecting 3 with the highest occurrence frequency as the vertices of path superposition, wherein x is-500, -300 and 0.
h. Respectively selecting x of 3 vertexes with superposed paths1＝-500，x2＝-300，x3The Radon transform is performed with 0 as the offset (offset) of the Radon transform, the results of the Radon transform are superimposed to obtain 3 predicted multiples (fig. 9b, c, d), and t is compared with tmax(i)Find different intervals in the time direction
my(i)(xr,yr,xs,ys,yk,t)＝Radon(xmax(i))(my(xr,yr,xs,ys,yk,t))
i. In different intervals
In the method, the part with larger amplitude in the 3 predicted multiples is selected to form the final multiple prediction result, and the final prediction result (shown in figure 9e) is found to be better than the prediction results with different offset distances, accurate in predicted arrival time and high in precision and resolution.
j. Time domain matching subtraction from the raw data (fig. 9f) yields seismic data (fig. 9g) without multiples that are effectively suppressed.
TABLE 1 local maximum value acquisition hyperbolic vertex coordinate table
| Serial number | x(m) | t(s) |
| 1 | -300 | 3.05 |
| 2 | 0 | 3.70 |
| 3 | -500 | 3.80 |
| 4 | 0 | 3.81 |
| 5 | -300 | 4.19 |
| 6 | 0 | 4.37 |
| 7 | -300 | 4.83 |
| 8 | -500 | 5.30 |
| 9 | -100 | 5.33 |
| 10 | -300 | 5.63 |
| 11 | -300 | 5.77 |
Claims (2)
1. A multiple suppression method based on optimal hyperbolic integral path superposition is characterized in that the problem that the 3D SRME requires intensive data acquisition is solved without the assumption and prior information of underground media, high-precision and high-stability multiple suppression effects can be obtained for different geological models, higher calculation efficiency is achieved compared with a multiple suppression method based on sparse inversion, and the cost of seismic data processing and interpretation is reduced, and the method comprises the following steps:
a. complementing data acquired by three-dimensional marine seismic exploration through reciprocal theorem to obtain seismic data with the same shot channel, and extracting a gather according to the shot number in the channel head information to obtain a common shot point gather d (x)k,yk,t,xs,ys) (ii) a Extracting a gather according to the detection number to obtain a common detection point gather r (x)r,yr,t,xk,yk) Wherein (x)k,yk) At any point location (shot or geophone), (x)s,ys) As the shot point coordinates, (x)r,yr) Is the coordinate of the wave detection point, and t is time;
b. for common shot gather d (x)k,yk,t,xs,ys) With common detection point gather r (x)r,yr,t,xk,yk) Fourier transform is carried out to obtain a common shot gather D (x) of a frequency domaink,yk,w,xs,ys) With common detection point gather R (x)r,yr,w,xk,yk) Wherein w is the angular frequency;
c. gather D (x) common shot pointsk,yk,w,xs,ys) With common detection point gather R (x)r,yr,w,xk,yk) The product in the frequency domain yields corresponding different positions (x)k,yk) Longitudinal line multiple contribution gather Mxy(xr,yr,xs,ys,xk,yk,w)；
Mxy(xr,yr,xs,ys,xk,yk,w)＝r0R(xr,yr,w；xk,yk)D(xk,yk,w；xs,ys)
Wherein r is0The reflection coefficient of the stratum is represented as-1;
d. gather of traces M contributing to multiples of longitudinal measuring lines at different positionsxy(xr,yr,xs,ys,xk,ykW) summing along the longitudinal measuring line direction to obtain a cross measuring line multiple contribution gather My(xr,yr,xs,ys,ykW) and converted back to the time domain by inverse Fourier transform to obtain a cross-line multiple contribution gather m of the time domainy(xr,yr,xs,ys,yk,t)，
e. Making parabolic Radon transform on the contact measuring line multiple contribution trace set, and making the inner product of the parabolic Radon transform result and the contact measuring line multiple contribution trace set without parabolic Radon transform,
myradon(xr,yr,xs,ys,yk,t)＝Radon(my(xr,yr,xs,ys,yk,t))
myradon(xr,yr,xs,ys,ykt) is the result after Radon transformation, md(xr,yr,xs,ys,ykT) is the result of the inner product;
f. picking up a local maximum value through a threshold limit contrast amplitude value, and acquiring a hyperbolic vertex coordinate;
[xm,tm]＝findpeaks(md(xr,yr,xs,ys,yk,t))
[xm,tm]a matrix formed by the horizontal coordinates of the vertex of the same phase axis;
g. counting the vertex coordinates of all the same phase axes, selecting a plurality of vertexes with the highest frequency of occurrence as the path superposition,
h. respectively selecting x of a plurality of vertexes with superposed pathsmax(i)Performing Radon transformation as offset of Radon transformation, and superposing the Radon transformation results to obtain a plurality of predicted multiples m(i)(xr,yr,xs,ysT), comparing tmax(i)Find different intervals in the time direction
i. In different intervals
Selecting a part with larger amplitude in the plurality of predicted multiples to form a final multiple prediction result;
j. and subtracting by adopting time domain matching to obtain the seismic data without multiple waves.
2. The method for multiple suppression based on superposition of optimal hyperbolic integral paths according to claim 1, wherein the method comprises the following steps: and g, the number of the vertexes is 3-5.
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