CN107121701A - The multi-component earthquake data Corssline directions wave field method for reconstructing converted based on Shearlet - Google Patents
The multi-component earthquake data Corssline directions wave field method for reconstructing converted based on Shearlet Download PDFInfo
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Abstract
The present invention relates to a kind of multi-component earthquake data Corssline directions wave field method for reconstructing converted based on Shearlet, geological data reconstruct is attributed to the l based on Shearlet sparse constraints1Regularization；It is observed simultaneously using pressure in multi-component measurements and acceleration, gradient provides extra information for reconstruct geological data, can more accurately reconstruct data；By the way of alternating iteration, reconstruct P and acceleration wave field.This method is different from that other method is most basic to be to be extended to multi-component earthquake data interpolation on the basis of simple component geological data interpolation, because the addition of velocity component adds constraints, can obtain and preferably rebuild effect.Solve existing simple component earthquake Crossline directions seismic wave field method for reconstructing precision low, it is impossible to the problem of effectively reconstructing the tiny construction in underground, be difficult to rebuild.Solve the problem of Curvelet deep camber quality reconstructions are bad.Cost is reduced, precision is improved.
Description
Technical field
The present invention relates to a kind of geophysical exploration method, the sparse earthquake number especially arrived to offshore earthquake towing cable collection
According to the method rebuild, mainly the Crossline directions of the multi-component earthquake data of collection are rebuild.
Background technology
Current marine seismic data towing cable collection, due to the limitation of acquisition cost, is not advised typically in crossline directions
Then and be sparse, it is necessary to cover wider observation scope in limited acquisition cost, so Crossline directions are adopted
Collection spacing is typically inline directions more than 4 times.Cause to be difficult to the tiny construction of deep layer and space in crossline directions
Alias is extremely serious；Row interpolation is entered to this wave field in practice also difficult.
Conventional geological data interpolation requires that hypothesis geological data lineups are linear, and in time-space domain, seismic wave wavefront is recognized
To be the superposition of many plane waves, thus low-frequency information can be extrapolated on high-frequency information.In order that lineups are closer to
Linearly, the method for proposing dip moveout correction and azimuth TEC time error correction, but it is very big to be constrained to wave field amount of calculation.In addition it is based on
The geological data interpolation method of the method for Nyquist sampling thheorems, it is desirable to which sample frequency is at least two times of signal highest frequency,
Otherwise it is easy for fake frequency phenomenon occur, influences the reconstruction of data.This thought is applied in most of interpolation methods.But it is marine
In earthquake data acquisition, Crossline directions are typically especially sparse, and the interpolation method based on Nyquist sampling thheorems is simultaneously
It is inapplicable.
And the multi-component seismic of the measurement normal acceleration and Crossline directional accelerations beyond pressure component is adopted
Collection recent years are applied.High-quality vertical component can make pressure component be decomposed into upgoing wave and down going wave, because
This can improve the geological data frequency bandwidth of acquisition.The pressure component combination component of acceleration in Crossline directions causes very
3D earthquake data acquisitions are possibly realized.Vassallo andEt al. propose the multi-component seismic based on match tracing first
Data interpolating, its core concept is using sin basic functions function while representing pressure component and component of acceleration.
The present invention is different from Vassallo andTechnical method, we, which combine two kinds, can be based on sparse transformation
Method for reconstructing and multi -components method for reconstructing.
The content of the invention
The purpose of the present invention is that for above-mentioned the deficiencies in the prior art, is proposed a kind of based on many of Shearlet conversion
Component earthquake data Crossline wave-field reconstruction methods, to solve existing simple component earthquake Crossline directions seismic wave field weight
Construction method precision is low, it is impossible to the problem of effectively reconstructing the tiny construction in underground, be difficult to rebuild.
The present invention is achieved by the following technical solutions：
Idea of the invention is that：Geological data reconstruction is attributed to the l based on Shearlet sparse constraints first1Just
Then change problem；Secondly, make full use of in multi-component measurements, pressure and acceleration are observed simultaneously, in limited observation sequence, ladder
Spend and provide extra information for reconstruct geological data, can more accurately reconstruct data；It is simultaneously heavy by the way of alternating iteration
Structure P and acceleration wave field.
Based on Shearlet convert multi-component earthquake data Corssline directions wave field method for reconstructing, be by
Shearlet conversion is combined with threshold value iterative method, and geological data interpolation is attributed to l1Norm optimizes equation：
X%=Argminx||x||1s.t.||y-MS-1x||2≤ε (1)
M is observing matrix in above formula, and element is 0 to represent shortage of data in M, and element is 1 to represent that data are present, S-1For
Shearlet inverse transformations；X is one group of Shearlet coefficient；
Geological data interpolation is transformed into Shearlet domains and reconstructs geological data, one group of l is finally inversed by1Norm minimum
Shearlet coefficient x, formula (1) is using system for acquiring seismic data as observation system, and Shearlet conversion is used as compressed sensing
The sparse transformation that theory is implemented, constitutes the basis of multi-component earthquake data interpolation, in multi-component earthquake data interpolation, introduces
Vy components, due to
P andComponent is as mutual constraints, to provide each other with extra interpolation information, by P andConduct simultaneously
Interpolation is inputted, and pressure wavefield and acceleration wave field are rebuild, formula (1) are added with formula (2) and obtained simultaneously：
The pressure and component of acceleration observed is used as known input, xp,xvRespectively reconstruct pressure wavefield and acceleration
In the shearlet coefficients of wave field, each iterative process P andMutually update, asked for using P derivative Integration asks for P.
The multi-component earthquake data Corssline directions wave field method for reconstructing converted based on Shearlet, including following step
Suddenly：
A, initialization iterative parameter：Iterations N, threshold factor LmaxParameter lambda；
B, initialization pressure wavefield and gradient wave field P=0,
C, calculating primary iteration parameter δp=λp·Lmax, δv=λv·Lmax；
D, major cycle For i=1 to N do；
E, the geological data reconstructing method converted based on Shearlet is utilized to rebuild pressure field and gradient fields；
F, renewal threshold parameter δp andδv；
G、Ifλp≤λmin&λv≤λminTerminate .Else and return to D；
H, output:The pressure wavefield P and speed wave field of reconstruct
Reconstruction pressure field described in E steps, comprises the following steps：
1., pass throughUpdate Pi：
2. the residual error resp of P wave fields, is calculatedi=M (PM-Pi)
3., by thresholding algorithm, the Shearlet coefficients of pressure wavefield are solved
4. pressure wavefield P, is updated by Shearlet inverse transformationsi+1=Sxi+1。
Reconstruction gradient fields described in E steps, comprise the following steps：
I, pass through PiUpdate
IIth, the residual error of acceleration wave field is calculated
IIIth, by thresholding algorithm, the Shearlet coefficients of acceleration wave field are solved
IVth, acceleration wave field is updated by Shearlet inverse transformations
Beneficial effect：The present invention is to represent geological data using multiple dimensioned Shearlet conversion, due to Shearlet conversion
It is a kind of directive anisotropy small echo of tool, can effectively catches the textural characteristics of geological data, realize rarefaction representation.
And this method regard pressure component and Crossline directions velocity gradient component (i.e. component of acceleration) as input, speed simultaneously
Degree gradient provides extraneous information for pressure component, enables to the reconstruct of crossline directions more accurate.Solve existing single point
Measure earthquake Crossline directions seismic wave field method for reconstructing precision low, it is impossible to which effectively reconstruct underground is tiny constructs, is difficult to rebuild
The problem of.Solve the problem of Curvelet deep camber quality reconstructions are bad.Rebuild in the case where sampled data is especially sparse
Geological data；And due to the multi-direction characteristic of Shearlet conversion, the distribution of noise and signal in Shearlet conversion is not
Together, noise is sparse more dispersed and amplitude is smaller, and less demanding to data SNR；This method is different from other method most
It is to be extended to multi-component earthquake data interpolation on the basis of traditional simple component geological data interpolation at all, due to velocity component
Addition add constraints, can obtain preferably rebuild effect.Geophysical Data Processing and explain that personnel can be by
Program bag carries out seismic wave field reconstruct, with preferable value for applications.
Brief description of the drawings：
Fig. 1 is to enter row interpolation test effect to generated data to compare figure
(a) complete seismogram, (b) lacks 75% geological data figure, the Reconstruction of seismic data of (c) based on wavelet transformation
Figure, the Reconstruction of seismic data figure that (d) is converted based on Curvelet, the Reconstruction of seismic data figure of (e) based on wavelet transformation, (f) base
The multi-component earthquake data interpolation graphs converted in Shearlet；
Fig. 2 be to the 3D data of synthesis along Crossline directional interpolation figures,
Four wave field time-slice maps before a interpolation, b insert after before four wave field slice map c interpolation wave field four frequencies
Rate slice map, d insert after four wave field frequency slice figure e be interpolation before all-wave field data figure f based on this method rebuild it is complete
Wave field figure；
Fig. 3 is to handle comparison diagram to three kinds of methods of actual seismic data,
A is the geological data figure of before processing, and b is the geological data figure that Curvelet converts reconstruct, and c is become based on Shearlet
The geological data figure of reconstruct is changed, the Shearlet sparse constraints that d adds component of acceleration constraint rebuild figure；
Fig. 4 is flow chart of the invention.
Embodiment：
It is described in further detail with reference to the accompanying drawings and examples：
Based on Shearlet convert multi-component earthquake data Corssline directions wave field method for reconstructing, be by
Shearlet conversion is combined with threshold value iterative method, and geological data interpolation is attributed to l1Norm optimizes equation：
X%=Argminx||x||1s.t.||y-MS-1x||2≤ε (1)
M is observing matrix in above formula, and element is 0 to represent shortage of data in M, and element is 1 to represent that data are present, S-1For
Shearlet inverse transformations；X is one group of Shearlet coefficient；
Geological data interpolation is transformed into Shearlet domains and reconstructs geological data, one group of l is finally inversed by1Norm minimum
Shearlet coefficient x, formula (1) is using system for acquiring seismic data as observation system, and Shearlet conversion is used as compressed sensing
The sparse transformation that theory is implemented, constitutes the basis of multi-component earthquake data interpolation, in multi-component earthquake data interpolation, introduces
Vy components, due to
P andComponent is as mutual constraints, to provide each other with extra interpolation information, by P andConduct simultaneously
Interpolation is inputted, and pressure wavefield and acceleration wave field are rebuild, formula (1) are added with formula (2) and obtained simultaneously：
The pressure and component of acceleration observed is used as known input, xp,xvRespectively reconstruct pressure wavefield and acceleration
In the shearlet coefficients of wave field, each iterative process P andMutually update, asked for using P derivative Integration asks for P.
The multi-component earthquake data Corssline directions wave field method for reconstructing converted based on Shearlet, including following step
Suddenly：
A, initialization iterative parameter：Iterations N, threshold factor LmaxParameter lambda；
B, initialization pressure wavefield and gradient wave field P=0,
C, calculating primary iteration parameter δp=λp·Lmax, δv=λv·Lmax；
D, major cycle For i=1toN do；
E, the geological data reconstructing method converted based on Shearlet is utilized to rebuild pressure field and gradient fields；
F, renewal threshold parameter δp andδv；
G、Ifλp≤λmin&λv≤λminTerminate .Else and return to D；
H, output:The pressure wavefield P and speed wave field of reconstruct
Reconstruction pressure field described in E steps, comprises the following steps：
1., pass throughUpdate Pi：
2. the residual error resp of P wave fields, is calculatedi=M (PM-Pi)
3., by thresholding algorithm, the Shearlet coefficients of pressure wavefield are solved
4. pressure wavefield P, is updated by Shearlet inverse transformationsi+1=Sxi+1。
Reconstruction gradient fields described in E steps, comprise the following steps：
I, pass through PiUpdate
IIth, the residual error of acceleration wave field is calculated
IIIth, by thresholding algorithm, the Shearlet coefficients of acceleration wave field are solved
IVth, acceleration wave field is updated by Shearlet inverse transformations
In multi -components offshore acquisition, acceleration information is used for supplementing pressure data, and the equation of motion discloses pressure P
With the proportionate relationship of acceleration：Δ P=- ρ a
ρ is the density of medium in formula,
In inline and crossline directions, just have：
In formula：Vx, VyPoint on the respectively speed in inline directions and crossline directions, scalar represents gradient, i.e.,For inline directional accelerations,For Crossline directional accelerations.
Shearlet conversion is combined with threshold value iterative method, then sum up following l the problem of geological data interpolation1Model
Number optimizes equation：
X%=Argminx||x||1s.t.||y-MS-1x||2≤ε (1)
M is observing matrix in above formula, and element is 0 to represent shortage of data in M, and element is 1 and represents that data are present.S-1For
Shearlet inverse transformations；X is one group of Shearlet coefficient.
Geological data interpolation is transformed into Shearlet domains and reconstructs geological data, one group of l is finally inversed by1Norm minimum
Shearlet coefficient x, formula 3 is using system for acquiring seismic data as observation system, and Shearlet conversion is used as compressed sensing
The sparse transformation that theory is implemented, the purpose of the reconstruct to geological data is reached by optimization.Method for solving structure above
Into the basis of multi-component earthquake data interpolation.In multi-component earthquake data interpolation, we introduce Vy components, due to
P andComponent can be as mutual constraints, to provide each other with extra interpolation information, so we are by P
WithSimultaneously as the input of interpolation, pressure wavefield and acceleration wave field are rebuild, formula (1) are added in formula (2) simultaneously,
：
In above-mentioned optimization, the pressure and component of acceleration observed is used as known input, xp,xvRespectively reconstruct pressure
In Reeb and the shearlet coefficients of acceleration wave field, each iterative process P andMutually update, asked for using P derivativeIntegration asks for P.
Specific implementation step based on the Shearlet multi-component earthquake data Corssline directions wave field method for reconstructing converted
It is rapid as follows：
A, initialization iterative parameter：Iterations N, threshold factor LmaxParameter lambda；
B, initialization pressure wavefield and gradient wave field P=0,Calculate primary iteration parameter δp=λp·Lmax, δv=
λv·Lmax；
D, major cycle For i=1 to N do；
E, the geological data reconstructing method converted based on Shearlet is utilized to rebuild pressure field and gradient fields；
1. pressure field, is rebuild
1st, pass throughUpdate Pi：
2nd, the residual error resp of P wave fields is calculatedi=M (PM-Pi)
3rd, by thresholding algorithm, the Shearlet coefficients of pressure wavefield are solved
4th, pressure wavefield P is updated by Shearlet inverse transformationsi+1=Sxi+1
2. gradient fields, are rebuild
1st, P is passed throughiUpdate
2nd, the residual error of acceleration wave field is calculated
3rd, by thresholding algorithm, the Shearlet coefficients of acceleration wave field are solved
4th, acceleration wave field is updated by Shearlet inverse transformations
F, renewal threshold parameter δp andδv.
G、Ifλp≤λmin&λv≤λminTerminate .Else and return to D.
H, output:The pressure wavefield P and speed wave field of reconstruct
Fig. 1 is to enter row interpolation test to generated data, (a) complete earthquake record, and (b) lacks 75% geological data, (c) base
The Reconstruction of seismic data method converted in the Reconstruction of seismic data method of wavelet transformation, (d) based on Curvelet, (e) is based on small
The Reconstruction of seismic data method of wave conversion, the multi-component earthquake data interpolation method that (f) is converted based on Shearlet
Fig. 2 enters road after row interpolation, the preceding road spacing 150m of interpolation, interpolation for the 3D data to synthesis along Crossline directions
Four wave field isochronous surfaces before spacing 25m, (a) interpolation, after (b) is inserted four of wave field before four wave fields section (c) interpolation
Frequency slice, what four wave field frequency slices (e) after (d) is slotting were rebuild for all-wave field data (f) before interpolation based on this method
All-wave.
Fig. 3 is to handle comparison diagram to three kinds of methods of actual seismic data, and (a) is the geological data of before processing, and (b) is
The geological data (c) of Curvelet conversion reconstruct adds component of acceleration based on the Shearlet geological datas (d) for converting reconstruct
The Shearlet sparse constraint method for reconstructing of constraint.
Fig. 1 c are the result reconstructed through wavelet transformation, and lineups continuity is bad, and quality reconstruction is general；Fig. 1 d are warp
The result of Curvelet conversion reconstruct, quality reconstruction has larger lifting compared with wavelet transformation, but in 0.4s lineups curvature
Big part less effective；Fig. 1 e are the result that reconstruct is converted through Shearlet, are that three kinds of conversion quality reconstructions are best, solve
The problem of Curvelet deep camber quality reconstructions are bad.Shown by Fig. 1 c-e, Shearlet shows best to earthquake tables of data.And
The geological data reconstructing method that Fig. 1 f constrain for addition acceleration, it can be seen that add after acceleration constraint, reconstruction accuracy is obtained
To significantly being lifted.
Fig. 2 e enter row interpolation for the 3D seismic data to synthesis along Crossline directions, are cut from Fig. 2 a four times
Wave field is very sparse before piece can be seen that interpolation, and wave field collection density is very high in Fig. 2 b after interpolation, and precision has aobvious
Write lifting.The corresponding FKK spectral spaces alias of Fig. 2 a is extremely serious, and the wave field frequency spectrum after rebuilding effectively has suppressed alias letter
Breath.Fig. 2 e-f illustrate comparison diagram before and after wave-field reconstruction of the invention.
Fig. 3 a are converted with Curvelet, and shearlet conversion enters row interpolation to its pressure component and obtains Fig. 3 b, Fig. 3 c.Figure
3d is to insert the result that component of acceleration constraint is obtained.From result, the multi-component seismic converted based on Shearlet
Data interpolating effect is best.
Embodiment 1：
First by the 3D data of a synthesis in the embodiment of the present invention, row interpolation, interpolation are entered along Crossline directions
Road spacing 25m after preceding road spacing 150m, interpolation, crossline directions have 17 cables, 750 sampled points, pressure wavefield such as to scheme before rebuilding
Shown in 1a.1 is carried out to it with the present invention：6 reconstruction.Specifically implementation steps are：
The input that A, the pressure section for extracting crossline directions and acceleration are cut into slices as the present invention, setting changes
Generation number is 50 times, threshold factor 0.99.
B, according to the data of input calculate iterative parameter λ, δp=λp·LmaxAnd δv=λv·Lmax；
C, according to 1:6 ratio builds a missing matrix M, and size is 750*102；I.e. 17 cables are reconstructed into 102 cables；
D, according to the pressure in crossline directions cut into slices, acceleration section and missing matrix M, to the pressure wave of input
Field and acceleration wave field do shearlet conversion；
E, first, Shearlet conversion is carried out to pressure wavefield, is carried out shearlet threshold values alternative manner and is updated pressure wave
Field shearlet coefficientsInverse transformation is carried out to coefficient and obtains new pressure wavefield, passes through public affairs
Formula Δ P=- ρ a obtain updating acceleration wave field, and wherein ρ is the density of water；
F, secondly, carries out threshold value iteration by acceleration wave field after renewal, Shearlet is carried out to acceleration wave field
New pressure wavefield is obtained by formula Δ P=- ρ a；
G, repeat step E-F are until meet error condition output pressure wave field and acceleration wave field；
H, reconstruct the section of crossline directional pressure and carry out next crossline sections and rebuild, until whole
Wave field is rebuild.
Fig. 1 illustrates comparison diagram before and after wave-field reconstruction of the invention.Fig. 2 a are the 3D seismic data edge to synthesis
Crossline enters row interpolation in direction, and wave field is very sparse before can be seen that interpolation from Fig. 2 a four isochronous surfaces, and inserts
Wave field collection density is very high in Fig. 2 b after value, and precision, which has, to be obviously improved.The corresponding FKK spectral spaces alias of Fig. 2 a is very tight
Weight, and the wave field frequency spectrum after rebuilding effectively has suppressed alias information.
Embodiment 2：By taking certain marine measured data as an example, altogether provided with 40 roads, road spacing is 150m, is first become with Curvelet
Change, then enter row interpolation to its pressure component with shearlet conversion and obtain Fig. 3 b, Fig. 3 c.Fig. 3 d are sparse into component of acceleration
Obtained result is constrained, finally, the multi-component earthquake data interpolation converted based on Shearlet is best.
Specific implementation step is as follows：
A, the pressure section in extraction crossline directions and acceleration section are as input, and setting iterations is
50 times, threshold factor 0.99.
B, using the pressure wavefield of real data and acceleration wave field as this example input
C, according to the data of input calculate iterative parameter λ, δp=λp·LmaxAnd δv=λv·Lmax；
D, according to 1:6 ratio builds a missing matrix M, and size is 750*102；I.e. 17 cables are reconstructed into 102 cables；
E, according to the pressure in crossline directions cut into slices, acceleration section and missing matrix M, to the pressure wave of input
Field and acceleration wave field do shearlet conversion；
F, first, Shearlet conversion is carried out to pressure wavefield, is carried out shearlet threshold values alternative manner and is updated pressure wave
Field shearlet coefficientsInverse transformation is carried out to coefficient and obtains new pressure wavefield, passes through public affairs
Formula Δ P=- ρ a obtain updating acceleration wave field, and wherein ρ is the density of water；
G, secondly, carries out threshold value iteration by acceleration wave field after renewal, Shearlet changes is carried out to acceleration wave field
Change, the shearlet coefficients for obtaining acceleration wave field are updated also according to shearlet threshold values alternative mannerInverse transformation is carried out to the shearlet coefficients after renewal and obtains new acceleration, passes through public affairs
Formula Δ P=- ρ a obtain new pressure wavefield；
H, repeat step E-F are until meet error condition output pressure wave field and acceleration wave field；Output:The pressure of reconstruct
Reeb P and speed wave field
Claims (4)
1. a kind of multi-component earthquake data Corssline directions wave field method for reconstructing converted based on Shearlet, its feature is existed
In, be by Shearlet conversion be combined with threshold value iterative method, geological data interpolation is attributed to l1Norm optimizes equation：
M is observing matrix in above formula, and element is 0 to represent shortage of data in M, and element is 1 to represent that data are present, S-1For Shearlet
Inverse transformation；X is one group of Shearlet coefficient；
Geological data interpolation is transformed into Shearlet domains and reconstructs geological data, one group of l is finally inversed by1Norm minimum
Shearlet coefficient x, formula (1) is using system for acquiring seismic data as observation system, and Shearlet conversion is used as compressed sensing
The sparse transformation that theory is implemented, constitutes the basis of multi-component earthquake data interpolation, in multi-component earthquake data interpolation, introduces
Vy components, due to
P andComponent is as mutual constraints, to provide each other with extra interpolation information, by P andIt is simultaneously defeated as interpolation
Enter, pressure wavefield and acceleration wave field are rebuild simultaneously, formula (1) is added with formula (2) and obtained：
The pressure and component of acceleration observed is used as known input, xp,xvRespectively reconstruct pressure wavefield and acceleration wave field
Shearlet coefficients, in each iterative process P andMutually update, asked for using P derivative Integration asks for P.
2. a kind of multi-component earthquake data Corssline directions wave field method for reconstructing converted based on Shearlet, its feature is existed
In comprising the following steps：
A, initialization iterative parameter：Iterations N, threshold factor LmaxParameter lambda；
B, initialization pressure wavefield and gradient wave field P=0,
C, calculating primary iteration parameter δp=λp·Lmax, δv=λv·Lmax；
D, major cycle For i=1 to N do；
E, the geological data reconstructing method converted based on Shearlet is utilized to rebuild pressure field and gradient fields；
F, renewal threshold parameter δp andδv；
G、Ifλp≤λmin&λv≤λminTerminate .Else and return to D；
H, output:The pressure wavefield P and speed wave field of reconstruct
3. according to the multi-component earthquake data Corssline directions wave field weight converted based on Shearlet described in claim 2
Construction method, it is characterised in that the utilization described in E steps rebuilds pressure based on the geological data reconstructing method that Shearlet is converted
, comprise the following steps：
1., pass throughUpdate Pi：
2. the residual error resp of P wave fields, is calculatedi=M (PM-Pi)
3., by thresholding algorithm, the Shearlet coefficients of pressure wavefield are solved
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4. according to the multi-component earthquake data Corssline directions wave field weight converted based on Shearlet described in claim 2
Construction method, it is characterised in that the utilization described in E steps rebuilds gradient based on the geological data reconstructing method that Shearlet is converted
, comprise the following steps：
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IIth, the residual error of acceleration wave field is calculated
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IVth, acceleration wave field is updated by Shearlet inverse transformations
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| CN110490219A (en) * | 2019-07-02 | 2019-11-22 | 中国地质大学（武汉） | A method of the U-net network based on texture constraint carries out Reconstruction of seismic data |
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| CN112946741A (en) * | 2021-02-03 | 2021-06-11 | 中国石油大学(华东) | Azimuth anisotropy weak information extraction method based on sparse reconstruction theory |
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