CN108415076A - A kind of guarantor's width guarantor's boundary noise Enhancement Method based on linear inversion - Google Patents
A kind of guarantor's width guarantor's boundary noise Enhancement Method based on linear inversion Download PDFInfo
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- CN108415076A CN108415076A CN201810125340.5A CN201810125340A CN108415076A CN 108415076 A CN108415076 A CN 108415076A CN 201810125340 A CN201810125340 A CN 201810125340A CN 108415076 A CN108415076 A CN 108415076A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/30—Analysis
- G01V1/301—Analysis for determining seismic cross-sections or geostructures
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/30—Noise handling
- G01V2210/32—Noise reduction
Abstract
The invention discloses a kind of, and guarantor's width based on linear inversion protects boundary noise Enhancement Method, includes the following steps:1) prompt drop function structure smoothing weights μ is introducedx(t, x) and μt(t,x);2) it is based on protecting side denoising target structure object function;3) it utilizes least square method to solve the optimization problem of object function, derives the expression formula of u;4) rule of thumb artificial arrange parameter λ and k, then according to μx(t, x) and μtThe calculation formula of (t, x) calculates to obtain AtAnd Ax;Noisy seismic data d is input in the calculation formula of object function u, u is obtained;5) quality control is carried out by comparing the jamtosignal of seismic data before and after the processing and amplitude spectrum.Compared with prior art, method of the invention introduces prompt drop function using seismic data along the gradient information in the direction t, x; build smoothing weights; keep seismic data gradient smaller part smoothing weights big, gradient larger part smoothing weights are small, to realize enhancing signal-to-noise ratio and protect the purpose of tectonic information.In addition, the present invention is based on linear inversion, calculate simple and fast.
Description
Technical field
It is that one kind being based on line the present invention relates to oil geophysical exploration field, more particularly to seismic data process
Property inverting guarantor's width protect boundary noise Enhancement Method.
Background technology
In seismic data " high s/n ratio, high-resolution, high fidelity " three high requests, high s/n ratio is indoor data processing
Basic demand, the subsequent processes to seismic data and integrated interpretation important in inhibiting.How in the premise for protecting width
Lower compacting or removal noise are all one of the hot spot that scholars study all the time.As oil-gas exploration is constantly to earth's surface complex area
Domain promotes, and noise jamming is more serious.Due to the limitation of seismic prospecting intermediate-resolution and the presence of various noises, common place
Reason technology does not allow thin layer and complicated structure easy to identify, noise compacting imperative.
A major issue in seismic data noise attenuation is the protecting field how while removing noise, improving signal-to-noise ratio
Shake the useful signals such as boundary, the construction of data.For Approximation Theory angle, conventional denoising method is exactly to find a light relatively
Approximations of the sliding u as input seismic data d, this ill-posed problem can be solved by following regularization method.Wherein d is defeated
The noisy seismic data entered, u are the output data after denoising, and λ is regularization parameter, for balancing two effect effects
Fruit.
Though the conventional quick denoising method of calculating can achieve the effect that improve signal-to-noise ratio, often it is unfavorable for tectonic boundary
The protection of information influences the quality of seismic data, exploration work area especially complicated in construction, to the place of subsequent seismic data
It reason and explains and can all cause negative effect, therefore be often difficult in processing procedure to take into account high s/n ratio and high fidelity, this is just
It is required that carrying out further investigation to find equalization point between protection tectonic information and noise attentuation, in the premise for protecting width guarantor boundary
Under improve the signal-to-noise ratio of seismic data as far as possible.
Invention content
It is an object of the present invention to provide a kind of, and guarantor's width based on linear inversion protects boundary noise Enhancement Method.The party
Method using seismic data along the direction t, x gradient information, introduce prompt drop function, build smoothing weights, make seismic data gradient compared with
Small place's smoothing weights are big, and gradient larger part smoothing weights are small, to realize the guarantor boundary noise enhancing of seismic data.
A kind of guarantor's width guarantor's boundary noise Enhancement Method based on linear inversion, includes the following steps:
S1:Using seismic data along the gradient information in the direction t, x, prompt drop function structure smoothing weights μ is introducedx(t, x) and μt
(t,x);Keep seismic data gradient smaller part smoothing weights big, gradient larger part smoothing weights are small, to realize that seismic data is protected
The purpose of side denoising;Wherein, t, x represent time location and the spatial position of seismic data sampled point;μx(t, x) and μt(t's, x)
Calculation formula is as follows;
S2:While in order to protect the tectonic boundary information in seismic data, make enough without borderline region seismic data
Smoothly to improve the signal-to-noise ratio of seismic data, therefore it is as follows to construct the calculation formula without the data u that makes an uproar:
Wherein, d is the noisy seismic data of input, and u is the output data after denoising,;First item [u (t, x)-d
(t,x)]2It is to approach item, in order to make output seismic data as close possible to input data, to reach protection efficiency frontier information
Effect, Section 2 are regularization terms, and it is smooth to realize to export the partial derivative of seismic data u by minimum;μ in Section 2t、μx
Respectively represent the smoothing weights in the direction t, x, μt、μxThe change of the partial derivative of t, x is changed with input seismic data respectively;λ is
Regularization parameter, for balancing two function and effect;
S3:Based on side denoising target is protected, the calculation formula that object function u is solved using least square method is as follows:
U=(I+ λ Ld)-1D (formula 4);
Wherein, I indicates unit matrix, Ld=Dt TAtDt+Dx TAxDx, DtAnd DxThe difference operator in the direction t, x is represented, difference is calculated
Son expression formula be:AtAnd AxIt includes smoothing weights μ to be respectivelyt(t,x)、μxPair of (t, x)
Angular moment battle array;
S4:Rule of thumb artificial arrange parameter λ and k, then according to μx(t, x) and μtThe calculation formula of (t, x) calculates to obtain At
And Ax;Noisy seismic data d is input in the calculation formula of object function u, u is obtained;
S5:According to the d and u in step S4, matter is carried out by comparing the jamtosignal of seismic data before and after the processing and amplitude spectrum
Amount control.
Further, the present invention has selected a prompt drop functionTo define refinement weight mut、μx, such as (formula 2) institute
Show;In the region without tectonic information, the gradient of seismic data is smaller, brings Grad into prompt drop function, obtains larger put down
Sliding weight, smooth great efforts can effectively remove the noise in the region;In the region containing tectonic boundary, the gradient of seismic data
It is larger, Grad is brought into prompt drop function at this time, it will obtain smaller smoothing weights, smooth dynamics is small, in denoising
Achieve the effect that protect tectonic boundary in processing procedure.
Further, method of the invention is under the premise of taking into account high s/n ratio and high fidelity, two contradiction targets it
Between find it is balanced.For noisy seismic data d, on the one hand, to protect the tectonic boundary information in seismic data as far as possible;
On the other hand, to make without borderline region seismic data enough smoothly to improve the signal-to-noise ratio of seismic data.Side is protected based on above
Denoising target, the calculating without the data u that makes an uproar are equivalent to solution minimization problem, (formula 3) are expressed as with matrix form
J (u)=(u-d)T(u-d)+λ(uTDt TAtDtu+uTDx TAxDxU) (formula 5);
Wherein, d is the noisy seismic data of input, and u is the output data after denoising, AtAnd AxIt is comprising flat respectively
Sliding weight mut(t,x)、μxThe diagonal matrix of (t, x), matrix DtAnd DxIt is discrete differential operator respectively.Seek the minimum in (formula 5)
Change can be converted into following problem
It can be obtained by formula (6)
U=(I+ λ Ld)-1D (formula 4);
Wherein, Ld=Dt TAtDt+Dx TAxDx;Thus the minimum in (formula 6) is converted into the solution of a linear problem.It solved
Cheng Zhong, DtAnd DxIt is forward-difference operator, Dt TAnd Dx TIt is backward difference operator, LdIt is five space of points anisotropy La Pula
This matrix.
Further, the selection of parameter lambda and k are most important for denoising result.For example, when λ is too small, then in seismic data
Many noises will be remained, the effect for improving signal-to-noise ratio is unable to reach, if when λ is bigger than normal, after excess smoothness in seismic data
Detail information will lose.The selection of k is a tradeoff for improving signal-to-noise ratio and protecting tectonic boundary;When k is bigger than normal, ground
It is less to shake data configuration information loss, when k is too small, more noises in seismic data can be removed.Therefore the present invention needs basis
The artificial arrange parameter λ and k of experience.
Beneficial effects of the present invention are as follows:
1, compared with prior art, method of the invention introduces prompt drop using seismic data along the gradient information in the direction t, x
Function builds smoothing weights, keeps seismic data gradient smaller part smoothing weights big, and gradient larger part smoothing weights are small, to real
Show enhancing signal-to-noise ratio and protects the purpose of tectonic information.
2, the present invention is based on guarantor's width of linear inversion to protect boundary noise Enhancement Method, includes smoothing weights coefficient by structure
Space anisotropic Laplacian Matrix, realize the linear solution of minimization problem, calculate simple and fast;Suitable for extensive
The processing of seismic data.
Description of the drawings
The specific implementation mode of the present invention is preferably described in detail below in conjunction with the accompanying drawings.
Fig. 1:The comparison before and after the denoising of side is protected for 1 seismic data of embodiment;(a) it is seismic synthetic profile figure;(b) it is
Add the seismic profile of 50% random noise;(c) it is conventional linear denoising method treated seismic profile;(d) it is conventional line
Property denoising method removal noise;(e) it is using the method for the present invention treated seismic profile;(f) it is using the method for the present invention
The noise of removal.
Fig. 2:The smoothing weights during the denoising of side are protected for embodiment 1;(a) it is smoothing weights At;(b) it is smooth power
Weight Ax, AtAnd AxIndicate to include smoothing weights μ respectivelyt(t,x)、μxThe diagonal matrix of (t, x).
Fig. 3:For the comparison of seismic data amplitude spectrum before and after 1 denoising of embodiment;Wherein, double-crossed is represented without earthquake of making an uproar
The amplitude spectrum of data, dotted line represent the amplitude spectrum of the seismic data after 50% random noise of addition, and solid line, which represents, utilizes the present invention
The amplitude spectrum of the method for proposition treated seismic data, chain-dotted line represent smoothing weights and are equal to 1, i.e., conventional denoising method processing
The amplitude spectrum of seismic data afterwards.
Fig. 4:The comparison before and after the denoising of side is protected for 2 seismic data of embodiment;(a) it is noisy field seismic profile;
(b) it is conventional denoising method treated seismic profile;(c) noise for indicating removal, is made by the seismic profile in (a) and (b)
Difference obtains;(d) it is method proposed by the present invention treated seismic profile;(e) noise for indicating removal, by (a) and (d)
Seismic profile subtracts each other acquisition.
Fig. 5:The smoothing weights during the denoising of side are protected for embodiment 2;(a) it is smoothing weights At;(b) it is smooth power
Weight Ax, AtAnd AxIndicate to include smoothing weights μ respectivelyt(t,x)、μxThe diagonal matrix of (t, x).
Fig. 6:For the comparison of 2 seismic data noise attenuation of embodiment amplitude spectrum before and after the processing;Wherein, dotted line represents noisy earthquake number
According to amplitude spectrum, solid line represents the amplitude spectrum using method proposed by the present invention treated seismic data, and chain-dotted line represents flat
Sliding weight is equal to 1, i.e., the amplitude spectrum of conventional denoising method treated seismic data.
Specific implementation mode
In order to illustrate more clearly of the present invention, the present invention is done further with reference to preferred embodiments and drawings
It is bright.It will be appreciated by those skilled in the art that specifically described content is illustrative and be not restrictive below, it should not be with this
It limits the scope of the invention.
In order to examine the application effect of the method for the present invention, we have used 1 poststack model data and 1 prestack reality respectively
Border data are tested the denoising effect of the present invention;The validity of method proposed by the invention is demonstrated, can carried
Achieve the effect that protect boundary information while high seismic data signal-to-noise ratio.
Embodiment 1
It makes an uproar seismic data as shown in Figure 1, Fig. 1 a are a nothing, Fig. 1 b are the earthquake number after 50% random noise of addition
According to;It is utilized respectively conventional linear denoising method and guarantor's width proposed by the present invention based on linear inversion protects boundary noise Enhancement Method
Noisy seismic data is handled.
In conventional linear denoising method, the calculation formula without the data u that makes an uproar is as follows
The calculation formula that object function u is solved using least square method is as follows
U=(I+ λ (Dt TDt+Dx TDx))-1D (formula 7);
Wherein, I indicates unit matrix, DtAnd DxIt is forward-difference operator, Dt TAnd Dx TIt is backward difference operator.
If arrange parameter λ=1.6, is calculated by formula (7) using conventional linear denoising method and obtain treated seismic data
U, as illustrated in figure 1 c;The noise data of removal is made difference by Fig. 1 b and Fig. 1 c and is obtained, as shown in Figure 1 d;It follows that conventional linear
Denoising method is while removing noise along with the loss of useful signal.
The seismic data after width protects boundary noise Enhancement Method calculation processing is protected using the present invention is based on linear inversion, if
Then arrange parameter λ=2.5 and k=1.5 are calculated by (formula 4) and are obtained treated seismic data u as shown in fig. le;Removal
Noise data is made difference by Fig. 1 b and Fig. 1 e and is obtained, as shown in Figure 1 f;It follows that being compared with Fig. 1 b, the noise in Fig. 1 e obtains
Compacting, the signal-to-noise ratio of seismic data are remarkably reinforced, and in Fig. 1 f and are free of apparent tectonic information, in the mistake for improving signal-to-noise ratio
Cheng Zhong, the tectonic boundary information in seismic data are effectively protected.Jamtosignal is to weigh seismic data noise attenuation processing effect
An important evidence for fruit, calculation formula areWherein d represents noisy seismic data, and u is represented without earthquake number of making an uproar
According to.Use the present invention is based on guarantor's width of linear inversion protect the signal-to-noise ratio of boundary noise Enhancement Method treated seismic data for
5.82%.
Fig. 2 is the smoothing weights A during Fig. 1 guarantor's side denoisingstAnd Ax, AtAnd AxIndicate to include smoothing weights μ respectivelyt
(t,x)、μxThe diagonal matrix of (t, x) can be calculated by formula (3).Fig. 2 is, it is apparent that the smoothing weights containing structure realm
The smoothing weights of smaller (darker regions), atectonic area domain are larger (light areas), therefore using the present invention is based on linear inversions
Guarantor's width protect boundary noise Enhancement Method handle, effective information is protected during denoising.
Fig. 3 is the comparison of seismic data amplitude spectrum before and after denoising.Wherein, double-crossed represents the amplitude without seismic data of making an uproar
Spectrum, dotted line represent the amplitude spectrum of the seismic data after 50% random noise of addition, and solid line representative is based on using proposed by the present invention
The amplitude spectrum of the guarantor boundary noise Enhancement Method of linear inversion treated seismic data, chain-dotted line represent smoothing weights and are equal to 1
(regularization parameter λ takes 1.6 at this time), i.e., the amplitude spectrum of conventional denoising method treated seismic data.The calculation shows that, this hair
The jamtosignal of the guarantor boundary noise Enhancement Method based on linear inversion of bright proposition treated seismic data is 5.82%, is passed through
The jamtosignal of conventional Denoising Algorithm treated seismic data is 5.25%.By Fig. 3 Comparative results it is found that with conventional denoising method phase
Than method proposed by the present invention has achieved the effect that certain protection effective information while improving signal-to-noise ratio.
Embodiment 2
As shown in figure 4, Fig. 4 a are a noise-containing field seismic datas, it is utilized respectively conventional linear denoising method
The noisy seismic data is handled with the noise Enhancement Method proposed by the present invention based on linear inversion.
In conventional linear denoising method, the calculation formula without the data u that makes an uproar is as follows
The calculation formula that object function u is solved using least square method is as follows
U=(I+ λ (Dt TDt+Dx TDx))-1D (formula 7);
Wherein, I indicates unit matrix, DtAnd DxIt is forward-difference operator, Dt TAnd Dx TIt is backward difference operator.
Using the seismic data after conventional linear denoising method calculation processing, if arrange parameter λ=3, then counted by (formula 7)
It calculates and obtains that treated that seismic data u is as shown in Figure 4 b;The noise data of removal by Fig. 4 a and Fig. 4 b make that difference obtains such as Fig. 4 c
It is shown;It follows that after the processing of conventional denoising method, the signal-to-noise ratio of seismic data has obtained certain raising, but on construction side
Occurs blooming at edge.
The seismic data after width protects boundary noise Enhancement Method calculation processing is protected using the present invention is based on linear inversion, if
Then arrange parameter λ=3 and k=2.5 are calculated by (formula 4) and are obtained treated seismic data u as shown in figure 4d;Removal is made an uproar
Sound data make the difference acquisition by Fig. 4 a and Fig. 4 d, as shown in fig 4e;It follows that after denoising, the signal-to-noise ratio of seismic data is bright
It is aobvious to improve, and useful signal unobvious in the noise removed, the validity of this method is demonstrated with Fig. 4 c comparative analyses.
Fig. 5 is the smoothing weights μ during Fig. 4 guarantor's side denoisingst(t, x) and μx(t, x) can be obtained by formula (3) calculating
.It is smaller in seismic data partial derivative larger part smoothing weights, it is larger in partial derivative smaller part smoothing weights, thus reach and protects side
The effect of boundary's noise enhancing.
Fig. 6 is the comparison of seismic data amplitude spectrum before and after denoising.The amplitude spectrum of the noisy seismic data of where the dotted line signifies that, it is real
Line indicates the amplitude for protecting the seismic data after the enhancing technical finesse of boundary noise based on linear inversion using proposed by the present invention
Spectrum, chain-dotted line indicate that smoothing weights are equal to 1 (regularization parameter λ takes 3 at this time), i.e., conventional denoising method treated seismic data
Amplitude spectrum.As seen from contrast in Figure 6, solid line and chain-dotted line high band amplitude decrease, and both of which effectively improves
The signal-to-noise ratio of seismic data, but in effective frequency range of seismic data, compared with chain-dotted line, amplitude and the dotted line phase of solid line
Closely, it was demonstrated that compared with conventional denoising method, denoising method proposed by the present invention taken into account high s/n ratio during the treatment
With Hi-Fi requirement.
Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair
The restriction of embodiments of the present invention may be used also on the basis of the above description for those of ordinary skill in the art
To make other variations or changes in different ways, all embodiments can not be exhaustive here, it is every to belong to this hair
Row of the obvious changes or variations that bright technical solution is extended out still in protection scope of the present invention.
Claims (1)
1. a kind of guarantor's width based on linear inversion protects boundary noise Enhancement Method, which is characterized in that include the following steps:
S1:Using seismic data along the gradient information in the direction t, x, prompt drop function structure smoothing weights μ is introducedx(t, x) and μt(t,
x);Keep seismic data gradient smaller part smoothing weights big, gradient larger part smoothing weights are small, to realize that seismic data protects side
The purpose made an uproar;Wherein, t, x respectively represent time location and the spatial position of seismic data sampled point;μx(t, x) and μt(t's, x)
Calculation formula is as follows:
S2:In order to realize while protecting earthquake data configuration boundary information, make flat enough without borderline region seismic data
It slides to improve the signal-to-noise ratio of seismic data, therefore constructs following object function:
Wherein, d is the noisy seismic data of input, and u is the output data after denoising, first item [u (t, x)-d (t, x)]2
It is to approach item, in order to make output seismic data as close possible to input data, to achieve the effect that protect efficiency frontier information, the
Binomial is regularization term, and it is smooth to realize to export the partial derivative of seismic data u by minimum;μ in Section 2t、μxIt respectively represents
T, the smoothing weights in the directions x, μt、μxThe change of the partial derivative of t, x is changed with input seismic data respectively;λ is regularization ginseng
Number, for balancing two function and effect;
S3:Based on side denoising target is protected, object function is solved using least square method, is derived by the calculation formula of u, following institute
Show:
U=(I+ λ Ld)-1D (formula 4);
Wherein, I indicates unit matrix, Ld=Dt TAtDt+Dx TAxDx, DtAnd DxIt is forward-difference operator, Dt TAnd Dx TIt is backward difference
Operator, AtAnd AxIt includes smoothing weights μ to be respectivelyt(t,x)、μxThe diagonal matrix of (t, x);
S4:Rule of thumb artificial arrange parameter λ and k, then according to μx(t, x) and μtThe calculation formula of (t, x) calculates to obtain AtAnd Ax;
Noisy seismic data d is input in the calculation formula of object function u, u is obtained;
S5:According to the d and u in step S4, quality control is carried out by comparing the jamtosignal of seismic data before and after the processing and amplitude spectrum
System.
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