CN108828670B - A kind of seismic data noise-reduction method - Google Patents
A kind of seismic data noise-reduction method Download PDFInfo
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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
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
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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
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
- G01V1/364—Seismic filtering
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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
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- 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
- G01V2210/324—Filtering
Abstract
The present invention discloses a kind of seismic data noise-reduction method, and for seismic data noise reduction problem, the present invention includes: S1, using the error term of steady Huber norm replacement objective function, obtains the objective function based on Huber norm；S2, schatter p- norm is introduced to the objective function obtained through step, obtains the objective function based on schatter p- norm；S3, the objective function obtained through step S2 is solved, obtains the robust iterative of Hankel matrix；Realization can effectively remove organized noise again while Attenuating Random Noise.
Description
Technical field
The invention belongs to seismic data process field, in particular to a kind of seismic data noise reduction technology.
Background technique
Seismic prospecting is to develop the important means of the resources such as mineral reserve, oil and natural gas.In the process of exploration, data
The influence that various factors can inevitably be will receive leads to can have a plurality of types of noises in the data being collected into: such as
Seismic signal amplitude and frequency in communication process gradually decay, and collect noise in data procedures and exist always, this will lead to very
The signal-to-noise ratio of real signal declines, so that useful signal is buried in noise, and then influences our analyses to geological information.Cause
We need a kind of effectively noise reduction means to improve the quality of seismic data this, improve the reliability of seismic prospecting.
Existing research work is mainly integrated on the noise reduction of random noise, and this respect has a large amount of research work, is summarized
To be segmented into two classes: (1) time-domain filtering method: such as classical architecture Steerable filter, median filtering, the filtering of guarantor side etc.；(1) become
It changes domain method: including common tau-p transformation, Radon transform, the filtering of the domain f-x, eigenimage filter, EMD, being based on small echo
Transformation is decomposed, and the domain radial trace and curvelet transformation are removed, and transform domain method on coefficient in transform domain due to grasping
Make, inverse transformation can generate after going back will appear apparent earthwormization in apparent side effect, such as filtered trace gather record
Phenomenon etc..More importantly two above frame can not remove organized noise very well, so needing in practically seismic data processing
A process flow is established to carry out gaussian sum non-Gaussian noise compacting: first removing white Gaussian noise with above method, then
Organized noise is removed with ad hoc approach again, is done so on the one hand very time-consuming and laborious；The smooth effect of still further aspect random noise
It will affect the removal of organized noise.
Summary of the invention
In order to solve the above-mentioned technical problem, the present invention proposes a kind of seismic data noise-reduction method, introduces steady Huber model
Number promotes non-gaussian noise removal capability, while retaining the noise reduction capability to Gaussian noise.
The invention adopts a technical scheme as: a kind of seismic data noise-reduction method, comprising:
S1, the error term that objective function is replaced using steady Huber norm, obtain the objective function based on Huber norm；
S2, schatter p- norm is introduced to the objective function obtained through step, obtained based on schatter p- norm
Objective function；
S3, the objective function obtained through step S2 is solved, obtains the robust iterative of Hankel matrix.
Further, step S1 is specifically included:
The model expression of the truncation SVD of S11, seismic data matrix X are as follows:
S.t.rank (D)=K
Wherein, K is expressed as the order of seismic data, | | | |FFor Frobenius norm, argmin expression finds a function value
Rank of matrix is sought in independent variable value when minimum, rank () expression；
S12, regular terms objective function form is converted by the expression formula of formula (1):
Wherein, γ is the first regularization coefficient；
S13, Huber norm is introduced to the error term of formula (2), obtains the objective function expression formula based on Huber norm are as follows:
Wherein, | | | |HFor lp- norm, X indicates that seismic data matrix, D indicate that additive noise, arg min () indicate
Rank of matrix is sought in independent variable value when function value minimum, rank () expression.
Further, objective function expression formula of the step S2 based on schatter p- norm are as follows:
Wherein, subscript SpIndicate schatter p- norm.
Further, step S3 specifically:
S31, generalIt is transformed to following formula:
S32, X, E, Z are solved using ADM algorithm respectively；
S33, X, E, the Z obtained according to step S32, obtain the robust iterative of Hankel matrix.
Further, S32 solve X include it is following step by step:
A1, initialization stochastic variable Λ, Σ, E and Z；
A2, start while iterative cycles；
A3, fixed E and Z solve the subproblem expression formula of X are as follows:
Wherein, λ indicates the second regularization coefficient；
A4, X is updated according to the analytic solutions of expression formula in step A3；
Wherein,
A5, Λ is updated using Λ=Λ+μ (E-X+D), used Σ=Σ+μ (X-Z)；μ is updated using μ=ρ μ；
A6, A4 to A5 is repeated, until convergence.
Further, S32 solve E include it is following step by step:
B1, initialization stochastic variable Λ, Σ, E and Z；
B2, start while iterative cycles；
B3, fixed X and Z solve the subproblem expression formula of E are as follows:
Wherein, μ indicates third regularization coefficient,
B4, Λ is updated using Λ=Λ+μ (E-X+D), used Σ=Σ+μ (X-Z)；μ is updated using μ=ρ μ；
B5, B3 to B4 is repeated, until convergence.
Further, S32 solve E include it is following step by step:
C1, initialization stochastic variable Λ, Σ, E and Z；
C2, start while iterative cycles；
C3, fixed X and E solve the subproblem expression formula of Z are as follows:
Wherein, μ indicates third regularization coefficient；
C4, Λ is updated using Λ=Λ+μ (E-X+D), used Σ=Σ+μ (X-Z)；μ is updated using μ=ρ μ；
C5, C3 to C4 is repeated, until convergence.
Beneficial effects of the present invention: method of the invention replaces original truncation by the objective function based on Huber norm
The error term of F norm objective function used by SVD, then schattern p- norm to minimize item to the order of objective function
Regularization is carried out, the last iteration ADM estimation technique is used for objective function of the approximate solution based on schattern p- norm, to obtain
Obtain the robust iterative of Hankel matrix；Realization can effectively remove organized noise again while Attenuating Random Noise.
Detailed description of the invention
Fig. 1 is seismic data low-rank characteristic schematic diagram provided in an embodiment of the present invention；
Fig. 2 is Huber norm schematic diagram provided in an embodiment of the present invention；
Fig. 3 is program flow chart provided in an embodiment of the present invention；
Fig. 4 is original stacked seismic data figure one provided in an embodiment of the present invention；
Fig. 5 is the poststack sectional view one after noise reduction provided in an embodiment of the present invention；
Fig. 6 is the interference provided in an embodiment of the present invention removed through the method for the present invention section one；
Fig. 7 is original stacked seismic data figure two provided in an embodiment of the present invention；
Fig. 8 is the poststack section two after noise reduction provided in an embodiment of the present invention；
Fig. 9 is the interference provided in an embodiment of the present invention removed through the method for the present invention section two.
Specific embodiment
For convenient for those skilled in the art understand that technology contents of the invention, with reference to the accompanying drawing to the content of present invention into one
Step is illustrated.
Present invention aims at propose that a kind of seismic data noise-reduction method can have again while Attenuating Random Noise
Effect removal organized noise.Since there are two characteristics for seismic data tool: (1) as shown in Figure 1, clean seismic data has low-rank special
Property, and any noise will all destroy the correlation of seismic data, to destroy the low-rank structure of seismic data；(2) earthquake with
Machine noise is the white Gaussian noise with limit, can also be approximately the noise of Gaussian Profile, and organized noise can generally be considered as non-gaussian point
The noise of cloth.Based on two above characteristic, the present invention random minimizing technology problem synchronous with organized noise is innovated be changed into from
The technical issues of low-rank structure is extracted in noisy seismic data.
The concrete thought that the method for the present invention solves the above technical problem is as follows: (1) schatten p- norm regularization is promoted
Low-rank structural stability: since the non-Gaussian noises such as organized noise show as collective's outlier, if using conventional nuclear norm
Method can not overcome outlier to influence, so the present invention innovatively replaces nuclear norm to eliminate off using schatten p- norm
Group's value influences；(2) Huber norm steadily and surely removes non-Gaussian noise from waveform angle: Huber norm as shown in Figure 2 is L1 norm
With the norm of L2 norm fusion, the advantages of having both L1 norm and L2 norm, it is non-to eliminate gaussian sum from waveform in an iterative process
Gaussian noise influences；(3) Hankel matrix promotes seismic data low-rank structure: the structured matrix such as Hankel matrix are usually used to
The order of lifting matrixes, the rank of matrix the low, restores better, so Hankel matrix is the expression-form of data in the present invention.
The seismic data noise reduction basic principle based on Hankel matrix is briefly introduced in the present embodiment, is based on Hankel matrix
Seismic noise decay visible with the detailed content of Reconstruction of seismic data document " Oropeza, V., and M.D.Sacchi,
2011,Simultaneous seismic data denoising and reconstruction via multichannel
singular spectrum analysis:Geophysics,76,no.3,V25–V32,doi:10.1190/1.3552706”。
Seismic data noise reduction based on Hankel matrix is specifically mainly segmented into two steps:
(1) the seismic data Hankel transformation based on sliding window
The present embodiment is mainly illustrated by taking the realization in the two dimension of reduced-rank filtering (t-x) seismic data as an example, but is dropped
Order filtering can also be in the seismic data for being widely applied to three peacekeepings five dimension.Reduced-rank filtering mainly utilizes the low-rank of seismic data
Property, the low-rank of ideal seismic signal can be further decreased by Hankel transformation, raise simultaneously the order of noisy seismic data.
Hankel transformation relates generally to two steps:
Step 1: carry out Fourier transformation to seismic data: the seismic data in wicket can pass through frequency-space
The superposition of domain inner plane wave obtains:
Wherein,J=1,2 ..., N are the seismic channel set index values in spatial axes, and ω indicates temporal frequency.It is false
If seismic data is by with different ray parameter PkThe linear events composition of K.Here, AkThe multiple vibration of (ω) expression kth plane wave
Width, Δ x indicate the space interval between seismic profile.
Step 2: Hankel transformation: reduced-rank filtering is by single-frequency D (ω)=(D1(ω), D2(ω) ..., DN(ω))TInsertion
Signal constructs following Hankel matrix:
WhereinIndicate Hankel operator.
For ease of calculation, it is selected in the present embodimentMake Hankel matrix approximation square matrix,Ellipsis ω, and all frequencies are analyzed.Superposition for K plane wave can obtain rank
(MX)=K.
(2) low-rank based on the domain Hankel approaches
Since additive noise D will will increase the order of matrix X, reduced-rank filtering device is by reducing order, to reach the mesh of noise reduction
's.Reduced-rank filtering can be expressed as:
Wherein,It is to oppose angle averaging operator,It is contraction operator, it approaches M by order K matrix,It is
Hankel operator.OperatorHankel form is converted into vector by average diagonal line.Block is then used for multidimensional signal
Hankel matrix and the diagonal averaging operator of damping.Contraction operationThe SVD of truncation, random SVD or use can be passed through
The fast algorithm of Lanczos bidiagonalization method and efficient matrix-vector multiplication realizes that fast algorithm uses fast Fourier
Transformation.
Based on the above principles, the technical solution of the present invention is as follows: a kind of seismic data noise-reduction method, as shown in Figure 1, include with
Lower step:
S1, the error term that objective function is replaced using steady Huber norm, obtain the objective function based on Huber norm；
Specifically include it is following step by step:
The truncation low-rank decomposition model of S11, seismic data noise reduction
Clean seismic data is found after SVD is decomposed: most of energy of seismic signal concentrates on a small amount of several spies
Above value indicative, most of energy is concentrated in the several characteristic values in front, and such characteristic is known as the low-rank characteristic of seismic data.
It further promotes, on the fractions of low-rank, noise is then distributed in addition to low-rank the Energy distribution of effective seismic data
On ingredient in addition.Therefore noise reduction can be carried out to seismic data using truncation SVD method.
More specifically, the model of the truncation SVD of seismic data matrix X can be expressed as follows:
S.t.rank (D)=K
Wherein, K is expressed as the order of seismic data, | | | |FFor Frobenius norm,For
MatrixOptimization problem is fundamentally based on the convex optimization of Frobenius norm in formula (1).
S12, regular terms objective function form is converted by formula (1):
Wherein γ is regularization coefficient.
S13, ability of making an uproar in order to further enhance the pressure to non-Gaussian noise, it is steady that the present invention introduces formula (2) error term
Norm is also required to retain the noise reduction capability to Gaussian noise to promote the noise removal capability to non-gaussian.It then will be by formula (2)
It is converted into the matrix decomposition mode based on steady Huber norm:
Wherein, | | | |HFor lp- norm, since Huber norm is also convex function, so the introducing of Huber norm will not
The property for changing objective function (3), remains convex function.
S2, schatter p- norm is introduced to the objective function obtained through step, obtained based on schatter p- norm
Objective function；Detailed process are as follows:
Since there are Gaussian noises and non-Gaussian noise for actual seismic data, in addition to being needed in objective function error term
The case where considering non-gaussian and Gaussian noise, it is also desirable to the case where non-gaussian is considered when low-rank approaches, schatten 1- model
Number can minimize method than common order and can preferably approach low-rank, and steady to outlier.The schatten 1- of matrix
Norm is nuclear norm Optimized model described in formula (4), is expanded to schatten p- norm (0 < p < ∞), then
There is following Optimized model:
As p=1, schatter p- norm is nuclear norm.If defining σ0=0, then it can be by schattern p-
Norm expands to the case where p=0, as rank function.After introducing schatter p- norm, formula (3) objective function is variable
Are as follows:
S3, the objective function obtained through step S2 is solved, obtains the robust iterative of Hankel matrix.Detailed process
Are as follows:
The problem of for solution formula (3), the present invention are selected using a kind of new Alternating Direction
Method (ADM) (is specifically referred to: Lin Z, Liu R, Su Z.Linearized alternating direction
method with adaptive penalty for low-rank representation[C]//Advances in
neural information processing systems.2011:612-620.).In order to which ADM is solved conveniently, by formula
(5) it indicates are as follows:
According to ADM algorithm, formula (5) and (6) can be resolved into following subproblem and solved.
A, when fixed E and Z then solves following subproblem:
WhereinWithTo the subproblem of formula (7), it is easy to get following parsing
Solution:
B, as fixation X, Z, we alternately can solve following subproblem:
Wherein,
C, as fixation X, E, we alternately can solve another subproblem:
WhereinG is the approximate evaluation value of X.Formula (9) and (10) belong to classical optimization problem and ask
Solution can be solved using existing ripe algorithm, such as conjugate gradient algorithms.
To sum up, for solving X, the solution process of step S3 are as follows:
A1, initialization stochastic variable Λ, Σ, E and Z；
A2, start while iterative cycles；
A3, X is updated using formula (8)；
A4, Λ is updated using Λ=Λ+μ (E-X+D), used Σ=Σ+μ (X-Z)；
A5, μ is updated using μ=ρ μ；Those skilled in the art should know the value of ρ here according to required precision in practice
Setting.
A6, A3 to A5 is repeated, until convergence.The condition of convergence is that iterative target functional value is less than pre-determined threshold twice for front and back
When, expression reaches the condition of convergence.Thresholding is set to be calculated according to the required precision in practical application, it is generally secondary in order to reduce iteration
Number, it is also feasible for being set as 0.001.
Step S33 in above-mentioned solution process is replaced with and updates E using formula (9)；The process of E is then obtained solving；
Step S33 in above-mentioned solution process is replaced with and updates Z using formula (10)；The process of Z is then obtained solving.
Fig. 4 to fig. 6 is the treatment process of original stacked seismic data figure one provided in this embodiment；Fig. 4 is original poststack
Seismic cross-section one, Fig. 5 are the poststack section one after noise reduction, and Fig. 6 is the interference removed through the method for the present invention section one；Fig. 7
Fig. 9 is the treatment process of original stacked seismic data figure two provided in this embodiment；Fig. 7 is original stacked seismic data figure two,
Fig. 8 is the poststack section two after noise reduction, and Fig. 9 is the interference removed through the method for the present invention section two；As can be seen that practical denoising knot
Fruit meets theoretical hypothesis, and actual effect is very good, and noise reduction effect is apparent.Rows of the Fig. 4 into Fig. 9 indicates row,
Columns indicates column.
Those of ordinary skill in the art will understand that the embodiments described herein, which is to help reader, understands this hair
Bright principle, it should be understood that protection scope of the present invention is not limited to such specific embodiments and embodiments.For ability
For the technical staff in domain, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made
Any modification, equivalent substitution, improvement and etc. should be included within scope of the presently claimed invention.
Claims (6)
1. a kind of seismic data noise-reduction method characterized by comprising
S1, the error term that objective function is replaced using steady Huber norm, obtain the objective function based on Huber norm；
S2, schatter p- norm is introduced to the objective function obtained through step S1, obtained based on schatter p- norm
Objective function；Objective function expression formula of the step S2 based on schatter p- norm are as follows:
Wherein, subscript SpIndicate schatter p- norm, X indicates that seismic data matrix, D indicate that additive noise, γ are first just
Then change coefficient；
S3, the objective function obtained through step S2 is solved, obtains the robust iterative of Hankel matrix.
2. a kind of seismic data noise-reduction method according to claim 1, which is characterized in that step S1 is specifically included:
The model expression of the truncation SVD of S11, seismic data matrix X are as follows:
S.t.rank (D)=K
Wherein, K is expressed as the order of seismic data, | | | |FFor Frobenius norm, when argmin expression finds a function value minimum
Independent variable value, rank () expression seek rank of matrix；
S12, regular terms objective function form is converted by the expression formula of formula (1):
Wherein, γ is the first regularization coefficient；
S13, Huber norm is introduced to the error term of formula (2), obtains the objective function expression formula based on Huber norm are as follows:
Wherein, | | | |HFor Huber norm, X indicates that seismic data matrix, D indicate that additive noise, arg min () indicate letter
Rank of matrix is sought in independent variable value when number value minimum, rank () expression.
3. a kind of seismic data noise-reduction method according to claim 2, which is characterized in that step S3 specifically:
S31, generalIt is transformed to following formula:
E and Z indicates stochastic variable；
S32, X, E, Z are solved using ADM algorithm respectively；
S33, X, E, the Z obtained according to step S32, obtain the robust iterative of Hankel matrix.
4. a kind of seismic data noise-reduction method according to claim 3, which is characterized in that it includes following substep that S32, which solves X,
It is rapid:
A1, initialization stochastic variable Λ, Σ, E and Z；
A2, start while iterative cycles；
A3, fixed E and Z solve the subproblem expression formula of X are as follows:
Wherein, λ indicates the second regularization coefficient；
A4, X is updated according to the analytic solutions of expression formula in step A3；
X=N
Wherein,
A5, Λ is updated using Λ=Λ+μ (E-X+D), used Σ=Σ+μ (X-Z)；μ is updated using μ=ρ μ；
A6, A4 to A5 is repeated, until convergence.
5. a kind of seismic data noise-reduction method according to claim 3, which is characterized in that it includes following substep that S32, which solves E,
It is rapid:
B1, initialization stochastic variable Λ, Σ, E and Z；
B2, start while iterative cycles；
B3, fixed X and Z solve the subproblem expression formula of E are as follows:
Wherein, μ indicates third regularization coefficient,
B4, Λ is updated using Λ=Λ+μ (E-X+D), used Σ=Σ+μ (X-Z)；μ is updated using μ=ρ μ；
B5, B3 to B4 is repeated, until convergence.
6. a kind of seismic data noise-reduction method according to claim 3, which is characterized in that it includes following substep that S32, which solves E,
It is rapid:
C1, initialization stochastic variable Λ, Σ, E and Z；
C2, start while iterative cycles；
C3, fixed X and E solve the subproblem expression formula of Z are as follows:
Wherein, μ indicates third regularization coefficient；
C4, Λ is updated using Λ=Λ+μ (E-X+D), used Σ=Σ+μ (X-Z)；μ is updated using μ=ρ μ；
C5, C3 to C4 is repeated, until convergence.
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