CN109541687B - A kind of entropy constrained data-driven normalized tight frame seismic data rule method - Google Patents
A kind of entropy constrained data-driven normalized tight frame seismic data rule method Download PDFInfo
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Abstract
The invention discloses a kind of entropy constrained data-driven normalized tight frame seismic data rule methods, comprising the following steps: handles original irregular earthquake data grayization；Seismic data after gray processing is divided into data subset, calculates the entropy of each data subset；The key assignments of each data subset is calculated according to the entropy of each data subset；It chooses the biggish data subset of key assignments and forms training set, carry out dictionary training, seek self-adapting dictionary basic function；Using the relative error of iterative approximation result and maximum number of iterations as convergence, interpolation encryption is carried out to irregular seismic data using finally trained self-adapting dictionary basic function；By the interpolation seismic data output on regular grid, seismic data regularization is completed.The present invention is using based on prior information --- and entropy constrained training set Selection Strategy realizes efficient application of the self-adapting dictionary learning method in terms of Reconstruction of seismic data under the premise of guaranteeing to encrypt interpolation seismic channel precision.
Description
Technical field
The present invention relates to Exploration of Oil And Gas technical fields, and in particular to a kind of entropy constrained data-driven normalized tight frame earthquake
Data normalization method.
Background technique
In outer seismic data acquisition process out of office, due to the barriers such as reservoir, embankment, village, mining site or the shadow in taboo exploiting field
It rings, the distribution of seismic data spatially is often irregular.Since most seismic data process algorithms are with rule
Premised on the seismic data of grid distribution, if these seismic processing algorithms just can not be into without seismic data regularization
Row.Meanwhile the scrambling of seismic data also will affect velocity analysis precision and relevant Noise Elimination effect, therefore seismic data is advised
Then change has particularly important meaning in seismic prospecting.
Common seismic data rule method is to encrypt seismic channel by interpolation algorithm, later by will be on regular grid
Seismic channel export to realize seismic data regularization, regularization approach is as shown in Fig. 1 a, Fig. 1 b, Fig. 1 c.Common earthquake is inserted
Value method mainly include the interpolation method based on predictive filtering, the interpolation method based on wave equation and it is compressed sensing based insert
Value method.Interpolation method based on predictive filtering has Frequency-Space Domain predictive filtering, frequency wavenumber domain predictive filtering etc., such
Method can only be irregular sampling data as rule sampling data processing, and interpolation error is often relatively large.Based on fluctuation side
The interpolation method of journey realizes Trace Interpolation by positive inverse operator, and such method is limited to the order of accuarcy and all-wave of velocity field
The field huge calculation amount of operation bring.Data space need to be projected to the model space by compressed sensing based interpolation method, protected
Under the premise of model of a syndrome space factor is sparse, realize that Trace Interpolation is encrypted by seeking indirect problem, the key of this method exists
In sparse transformation, sparse transformation includes two class of fixed basis sparse transformation and adaptive base function sparse transformation, fixed base letter
Number sparse transformation can not adaptively be adjusted according to seismic data, have the defects that interpolation precision is not high；Adaptive base function
Sparse transformation is to generate redundant dictionary by dictionary learning (K_ singular value decomposition, structuring dictionary learning etc.) algorithm, can be adaptive
Data characteristics should be extracted, the defect of fixed basis sparse transformation is effectively avoided, improves the interpolation precision of seismic channel, but training is superfluous
Remaining dictionary requires a great deal of time.
Summary of the invention
The purpose of the present invention is to overcome above-mentioned the deficiencies in the prior art, provide a kind of entropy constrained data-driven normalized tight frame
Seismic data rule method, for this method in compressed sensing interpolation method, adaptive base function time consumption for training is huge, application
The shortcomings that low efficiency, using based on prior information --- entropy constrained training set Selection Strategy is guaranteeing to encrypt interpolation seismic channel
Under the premise of precision, the training process of adaptive base function is accelerated, realizes self-adapting dictionary learning method in seismic data
Rebuild the efficient application of aspect.
To achieve the above object, the present invention adopts the following technical solutions: a kind of entropy constrained data-driven normalized tight frame earthquake
Data normalization method, comprising the following steps:
Step 1: original irregular earthquake data grayization is handled；
Step 2: the seismic data after gray processing is divided into data subset, calculates the entropy of each data subset；
Step 3: the key assignments of each data subset is calculated according to the entropy of each data subset；
Step 4: it chooses the biggish data subset of key assignments and forms training set, carry out dictionary training, seek self-adapting dictionary base
Function；
Step 5: interpolation encryption is carried out to irregular seismic data using the self-adapting dictionary basic function that training obtains；
Step 6: step 1 is repeated to five, until the number of iterations reaches preset value or relative error less than some
Stop iteration when threshold value；
Step 7: the interpolation seismic data on regular grid is exported, and completes seismic data regularization.
Preferably, in the step 1, gray processing processing is carried out according to formula (1) to original irregular seismic data:
In formula (1), INT is bracket function, and A is the seismic amplitude value at current time, AmaxFor maximum earthquake amplitude, Amin
For minimum earthquake amplitude, G is gray value corresponding to amplitude A.
Preferably, in the step 2, integral number power that the size of each data subset is 2.
Preferably, in the step 2, the entropy of each data subset is calculated according to formula (2):
In formula 2, HiFor the entropy of i-th of data subset, wherein 1≤i≤n, n are the total number of data subset；pjIt is by gray scale
The probability that the gray scale j that histogram obtains occurs in i-th of data subset.
Preferably, in the step 3, the key assignments of each data subset is calculated according to formula (3):
In formula (3), Key (i) is the key assignments of i-th of data subset；riFor between one 0 to 1 equal-probability distribution it is random
Number；HiFor the entropy of i-th of data subset, wherein 1≤i≤n, n are the total number of data subset.
Preferably, in the step 4, key value Key (i) is subjected to descending arrangement, the biggish data of M key assignments before choosing
Subset forms training set, and the iterative step of training self-adapting dictionary basic function is as follows:
(4-1) keeps self-adapting dictionary basic function D constant, solves coefficient vector x by the objective function of formula (4):
x(k+1)=arg minx(||x-(D(k))TW||2+ε||x||0) (4)
In formula (4), objective function argminxIndicate | | x- (D(k))TW||2+ε||x||0Value minimum when corresponding be
Number vector x；K is the number of iterations；||·||2、||·||0It is 2 norms and 0 norm respectively；ε is given weight coefficient；W is preceding M
The biggish data subset of key assignments forms training set；D is self-adapting dictionary basic function；
(4-2) retention coefficient vector x is constant, solves self-adapting dictionary basic function D by the objective function of formula (5):
D(k+1)=arg minD||x(k+1)-DTW||2s.t.DTD=I (5)
In formula (5), objective function argminDIt indicates in normalized tight frame DTUnder D=I constraint, make | | x(k+1)-DTW||2Value
Reach self-adapting dictionary basic function D corresponding when minimum；K is the number of iterations；I is unit battle array；W is that preceding M key assignments is biggish
Data subset forms training set；||·||2It is 2 norms.
Preferably, in the step 5, interpolation encryption is carried out to irregular seismic data using self-adapting dictionary basic function
The step of it is as follows:
The self-adapting dictionary basic function D and original irregular seismic data y that (5-1) input dictionary training obtains；
(5-2) constructs sampling matrix φ according to the distribution situation of original irregular seismic data y, wherein there is the position of data
It is set as 1, the position of no data is set as 0；
(5-3) iteratively solves the objective function of formula (6), obtains the sparse bayesian learning factor alpha of complete seismic data
α=arg minα(||y-Φα||2+ε||α||0) (6)
In formula (6), objective function arg minαIndicate | | y- Φ α | |2+ε||α||0Value minimum when corresponding factor alpha；
Φ=φ D, wherein φ is sampling matrix, and D is self-adapting dictionary basic function；Y is original irregular seismic data；ε is given
Weight coefficient；||·||2、||·||0It is 2 norms and 0 norm respectively；
(5-4) carries out interpolation calculation to irregular seismic data using formula (7):
S=D α (7)
In formula (7), s is the seismic data after interpolation, and D is self-adapting dictionary basic function.
The invention has the following advantages:
The present invention is to use data entropy to be constrained as prior information to choose training set under compressed sensing framework, pass through
Data-driven normalized tight frame is trained training set, generates adaptive dictionary basis functions；Then self-adapting dictionary base letter is utilized
It is several that the encryption of high-precision interpolation is carried out to irregular seismic data, realize seismic data regularization.
The present invention feature larger according to entropy at seismic data special tectonic (pinching point, breakpoint) position, utilizes earthquake
For the entropy of data as prior information, selected data subset includes more effective informations.
The present invention can be improved seismic data interpolation precision compared to having no prior-constrained random dictionary learning method, add
Application efficiency of the adaptive base function in terms of seismic data regularization is greatly improved in fast dictionary training process.
Detailed description of the invention
Fig. 1 a is irregular distribution seismic data；
Fig. 1 b is the encrypted seismic data of interpolation；
Fig. 1 c is by the result of the seismic data output on regular grid；
Fig. 2 is medium entropy bound data driving normalized tight frame seismic data regularization flow chart of the present invention；
Fig. 3 a is without model seismic data of making an uproar；
Fig. 3 b is the comentropy section calculated using the method for the present invention data in Fig. 3 a；
Fig. 3 c is the training set randomly selected for data in Fig. 3 a；
Fig. 3 d is the training set for data in Fig. 3 a using the entropy constrained selection in the method for the present invention；
Fig. 4 a is the data that data add after gaussian noise in Fig. 3 a；
Fig. 4 b is the comentropy section calculated using the method for the present invention data in Fig. 4 a；
Fig. 4 c is the training set randomly selected for data in Fig. 4 a；
Fig. 4 d is the training set for data in Fig. 4 a using the entropy constrained selection in the method for the present invention；
Fig. 5 a is seismic traces collection；
Fig. 5 b is 50% random lack sampling trace gather data；
Fig. 5 c is the result for randomly selecting training set interpolation；
Fig. 5 d is the seismic data interpolation result using the method for the present invention；
Fig. 6 a is the F-K spectra of the original trace gather of Fig. 5 a；
Fig. 6 b is the F-K spectra of the random lack sampling data of Fig. 5 b；
Fig. 6 c is the F-K spectra using the method for the present invention interpolation reconstruction result；
Fig. 7 is the number of iterations and signal-to-noise ratio for choosing mode interpolation using different training sets for Fig. 5 a original earthquake data
Relational graph.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
A kind of entropy constrained data-driven normalized tight frame seismic data rule method, comprising the following steps:
Step 1: original irregular earthquake data grayization is handled；
Wherein, in the step 1, gray processing processing is carried out according to formula (1) to original irregular seismic data:
In formula (1), INT is bracket function, and A is the seismic amplitude value at current time, AmaxFor maximum earthquake amplitude, Amin
For minimum earthquake amplitude, G is gray value corresponding to amplitude A.
Step 2: the seismic data after gray processing is divided into data subset, calculates the entropy of each data subset；
Wherein, in the step 2, integral number power that the size of each data subset is 2.
Wherein, in the step 2, the entropy of each data subset is calculated according to formula (2):
In formula 2, HiFor the entropy of i-th of data subset, wherein 1≤i≤n, n are the total number of data subset；pjIt is by gray scale
The probability that the gray scale j that histogram obtains occurs in i-th of data subset.
Step 3: according to the entropy of each data subset, the key assignments of each data subset is calculated；
Wherein, in the step 3, the key assignments of each data subset is calculated according to formula (3):
In formula (3), Key (i) is the key assignments of i-th of data subset；riFor between one 0 to 1 equal-probability distribution it is random
Number；HiFor the entropy of i-th of data subset, wherein 1≤i≤n, n are the total number of data subset.
Step 4: it chooses the biggish data subset of key assignments and forms training set, carry out dictionary training, seek self-adapting dictionary base
Function；
Wherein, in the step 4, key value Key (i) is subjected to descending arrangement, biggish data of M key assignments before choosing
Collection composition training set, the iterative step of training self-adapting dictionary basic function are as follows:
(4-1) keeps self-adapting dictionary basic function D constant, solves coefficient vector x by the objective function of formula (4):
x(k+1)=arg minx(||x-(D(k))TW||2+ε||x||0) (4)
In formula (4), objective function argminxIndicate | | x- (D(k))TW||2+ε||x||0Value minimum when corresponding be
Number vector x；K is the number of iterations；||·||2、||·||0It is 2 norms and 0 norm respectively；ε is given weight coefficient；W is preceding M
The biggish data subset of key assignments forms training set；D is self-adapting dictionary basic function；
(4-2) retention coefficient vector x is constant, solves self-adapting dictionary basic function D by the objective function of formula (5):
D(k+1)=arg minD||x(k+1)-DTW||2s.t.DTD=I (5)
In formula (5), objective function argminDIt indicates in normalized tight frame DTUnder D=I constraint, make | | x(k+1)-DTW||2Value
Reach self-adapting dictionary basic function D corresponding when minimum；K is the number of iterations；I is unit battle array；W is that preceding M key assignments is biggish
Data subset forms training set；||·||2It is 2 norms.
Step 5: interpolation encryption is carried out to irregular seismic data using the self-adapting dictionary basic function that training obtains；
Wherein, in the step 5, interpolation encryption is carried out to irregular seismic data using self-adapting dictionary basic function
Steps are as follows:
The self-adapting dictionary basic function D and original irregular seismic data y that (5-1) input dictionary training obtains；
(5-2) constructs sampling matrix φ according to the distribution situation of original irregular seismic data y, wherein there is the position of data
It is set as 1, the position of no data is set as 0；
(5-3) iteratively solves the objective function of formula (6), obtains the sparse bayesian learning factor alpha of complete seismic data
α=arg minα(||y-Φα||2+ε||α||0) (6)
In formula (6), objective function arg minαIndicate | | y- Φ α | |2+ε||α||0Value minimum when corresponding factor alpha；
Φ=φ D, wherein φ is sampling matrix, and D is self-adapting dictionary basic function；The original irregular seismic data of y；ε is given power
Coefficient；||·||2、||·||0It is 2 norms and 0 norm respectively；
(5-4) carries out interpolation calculation to irregular seismic data using formula (7):
S=D α (7)
In formula, s is the seismic data after interpolation, and D is self-adapting dictionary basic function.
Step 6: step 1 is repeated to five, until the number of iterations reaches preset value or relative error less than some
Stop iteration when threshold value.
Step 7: the interpolation seismic data on regular grid is exported, and completes seismic data regularization.
Wherein, Fig. 2 is medium entropy bound data driving normalized tight frame seismic data regularization flow chart of the present invention, You Tuzhong
Find out, original irregular seismic data is subjected to gray processing processing first, is carried out being divided into multiple data subsets later, and count
Calculate the entropy of each data subset；It is more big according to data subset entropy more the principle of training set should be selected by more high probability, choose instruction
Practice collection；Dictionary training is carried out using the training set and data-driven normalized tight frame of selection, obtains self-adapting dictionary basic function；With repeatedly
Relative error and maximum number of iterations for reconstructed results is as convergence, the adaptive base function obtained using final training
High-precision interpolation is carried out to irregular data.Finally the seismic data on regular grid is exported, completes the rule of seismic data
Change process.
The method of the present invention and the comparison for randomly selecting trained set method difference result:
1, the method for the present invention is compared with randomly selecting method for the advantage without model seismic data selection training set of making an uproar.
Fig. 3 a is without model seismic data of making an uproar, wherein the bending comprising tomography, pinching, horizontal lineups and similar trace gather
Lineups.
Fig. 3 b is the comentropy section calculated using the method for the present invention data in Fig. 3 a, it can be seen that the letter at lineups
It is larger to cease entropy；Entropy at special tectonic is maximum, such as at pinching point, at breakpoint；It, should since the entropy at special tectonic is maximum
The data subset at place then has greater probability to choose in training set, this is provided for the special tectonic accurate reconstruction that seismic data includes
It may.
Fig. 3 c is the training set randomly selected for data in Fig. 3 a, and each data subset is not poor for randomly selecting
Not, the probability being selected into training set is identical；Since a large amount of invalid subsets are selected in training set, it is suppressed that effective subset
The rarefaction representation of information is unfavorable for data details information reconstruction.
Fig. 3 d is the training set for data in Fig. 3 a using the entropy constrained selection in the method for the present invention, due to choosing
The data subset for having used entropy as prior information in the process, therefore having chosen all includes substantially effective information, makes institute in seismic data
The detailed information for including is able to rarefaction representation, is conducive to accelerate training effectiveness.
2, the method for the present invention chooses noisy model seismic data compared with randomly selecting method the advantage of training set.
Fig. 4 a is the data that data add after gaussian noise in Fig. 3 a；
Fig. 4 b is the comentropy section calculated using the method for the present invention data in Fig. 4 a, and without making an uproar seismic data result one
It causes, the comentropy at lineups is bigger；Entropy at special tectonic is maximum, such as at pinching point, at breakpoint.
Fig. 4 c is the training set randomly selected for data in Fig. 4 a, and Fig. 4 d is using the entropy constrained choosing in the method for the present invention
The training set for data in Fig. 4 a taken；Comparison diagram 4c and Fig. 4 d can be seen that for the seismic data containing noise, be based on entropy
The training set of selection is remained to comprising most effective informations, can to use dictionary training progress data interpolating encryption to provide
Energy.
3, the method for the present invention is compared with randomly selecting method for the advantage of seismic data interpolation.
Fig. 5 a is seismic traces collection, and Fig. 5 b is 50% random lack sampling trace gather data, and Fig. 5 c is to randomly select training set
Interpolation as a result, Fig. 5 d be using the method for the present invention seismic data interpolation result.For the accurate journey of quantitatively characterizing interpolation result
Degree, introduces two evaluation parameters: signal-to-noise ratioAnd relative errorWherein UtFor original earthquake data, U is the seismic data after rebuilding.Signal-to-noise ratio is higher, relatively
Error is smaller, shows that interpolation result and reality are closer, interpolation is more ideal.The SNR of Fig. 5 c is 35.5225dB, and original
Data relative error is 1.6721%, interpolation processing used time 190.8918s, and the SNR of Fig. 5 d is 37.7755dB, with original number
It is 0.5919% according to relative error, the interpolation processing used time is 103.5708s.It can thus be seen that the more random selection instruction of the present invention
Dictionary training process can be accelerated by practicing collection interpolation method, while promote the precision of Reconstruction of seismic data result.Circle in Fig. 5 c, Fig. 5 d
Also it can illustrate that the present invention restores more acurrate to detailed information contained by seismic data at circle.
Fig. 6 a is the F-K spectra of the original trace gather of Fig. 5 a, and Fig. 6 b is the frequency-wavenumber of the random lack sampling data of Fig. 5 b
Spectrum, the space aliasing that visible random lack sampling generates from Fig. 6 b show as Whole frequency band and are concerned with by a narrow margin to make an uproar on F-K spectra
Sound；Fig. 6 c is the F-K spectra using the method for the present invention interpolation reconstruction result, it is seen that frequency-wave of processing result of the present invention
Number spectrum is consistent with the F-K spectra of Fig. 5 a initial data, and the relevant noise in Fig. 6 b is effectively eliminated.
Fig. 7 is the number of iterations and signal-to-noise ratio for choosing mode interpolation using different training sets for Fig. 5 a original earthquake data
Relational graph；As shown in Figure 7, entropy constrained method signal-to-noise ratio after iteration 4 times is very high, and as the increase of the number of iterations is protected substantially
Hold it is constant, so 4 iteration of entropy constrained method.And randomly select mode its signal-to-noise ratio and gradually increased with the number of iterations, it needs
It iterates to 10 times to be just basically unchanged, and its value is always below the method for the present invention.Therefore, the present invention can not only promote reconstruction knot
The precision of fruit, and the number of iterations can be reduced, accelerate training process.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not to limit of the invention
System, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art do not need to pay
The various modifications or changes that creative work can be made out are still within protection scope of the present invention.
Claims (7)
1. a kind of entropy constrained data-driven normalized tight frame seismic data rule method, characterized in that the following steps are included:
Step 1: original irregular earthquake data grayization is handled；
Step 2: the seismic data after gray processing is divided into data subset, calculates the entropy of each data subset；
Step 3: the key assignments of each data subset is calculated according to the entropy of each data subset；
Step 4: it chooses the biggish data subset of key assignments and forms training set, carry out dictionary training, seek self-adapting dictionary base letter
Number；
Step 5: interpolation encryption is carried out to irregular seismic data using the self-adapting dictionary basic function that training obtains；
Step 6: step 1 is repeated to five, until the number of iterations reaches preset value or relative error less than some threshold value
When stop iteration；
Step 7: the interpolation seismic data on regular grid is exported, and completes seismic data regularization.
2. a kind of entropy constrained data-driven normalized tight frame seismic data rule method as described in claim 1, characterized in that
In the step 1, gray processing processing is carried out according to formula (1) to original irregular seismic data:
In formula (1), INT is bracket function, and A is the seismic amplitude value at current time, AmaxFor maximum earthquake amplitude, AminFor most
Small earthquake amplitude, G are gray value corresponding to amplitude A.
3. a kind of entropy constrained data-driven normalized tight frame seismic data rule method as claimed in claim 2, characterized in that
In the step 2, integral number power that the size of each data subset is 2.
4. a kind of entropy constrained data-driven normalized tight frame seismic data rule method as claimed in claim 3, characterized in that
In the step 2, the entropy of each data subset is calculated according to formula (2):
In formula 2, HiFor the entropy of i-th of data subset, wherein 1≤i≤n, n are the total number of data subset；pjIt is by intensity histogram
The probability that the gray scale j that figure obtains occurs in i-th of data subset.
5. a kind of entropy constrained data-driven normalized tight frame seismic data rule method as claimed in claim 4, characterized in that
In the step 3, the key assignments of each data subset is calculated according to formula (3):
In formula (3), Key (i) is the key assignments of i-th of data subset；riFor the random number of equal-probability distribution between one 0 to 1；Hi
For the entropy of i-th of data subset, wherein 1≤i≤n, n are the total number of data subset.
6. a kind of entropy constrained data-driven normalized tight frame seismic data rule method as claimed in claim 5, characterized in that
In the step 4, key value Key (i) is subjected to descending arrangement, the biggish data subset of M key assignments forms training set before choosing,
The iterative step of training self-adapting dictionary basic function is as follows:
(4-1) keeps self-adapting dictionary basic function D constant, solves coefficient vector x by the objective function of formula (4):
x(k+1)=argminx(||x-(D(k))TW||2+ε||x||0) (4)
In formula (4), objective function argminxIndicate | | x- (D(k))TW||2+ε||x||0Value minimum when corresponding coefficient vector
x；K is the number of iterations；||·||2、||·||0It is 2 norms and 0 norm respectively；ε is given weight coefficient；W be preceding M key assignments compared with
Big data subset forms training set；D is self-adapting dictionary basic function；
(4-2) retention coefficient vector x is constant, solves self-adapting dictionary basic function D by the objective function of formula (5):
D(k+1)=argminD||x(k+1)-DTW||2s.t.DTD=I (5)
In formula (5), objective function argminDIt indicates in normalized tight frame DTUnder D=I constraint, make | | x(k+1)-DTW||2Value reach
Corresponding self-adapting dictionary basic function D when minimum；K is the number of iterations；I is unit battle array；W is the preceding biggish data of M key assignments
Subset forms training set；||·||2It is 2 norms.
7. a kind of entropy constrained data-driven normalized tight frame seismic data rule method as claimed in claim 6, characterized in that
In the step 5, using self-adapting dictionary basic function to irregular seismic data carry out interpolation encryption the step of it is as follows:
The self-adapting dictionary basic function D and original irregular seismic data y that (5-1) input dictionary training obtains；
(5-2) constructs sampling matrix φ according to the distribution situation of original irregular seismic data y, wherein there is the position of data to be set as
1, the position of no data is set as 0；
(5-3) iteratively solves the objective function of formula (6), obtains the sparse bayesian learning factor alpha of complete seismic data
α=argminα(||y-Φα||2+ε||α||0) (6)
In formula (6), objective function argminαIndicate | | y- Φ α | |2+ε||α||0Value minimum when corresponding factor alpha；Φ=
φ D, wherein φ is sampling matrix, and D is self-adapting dictionary basic function；Y is original irregular seismic data；ε is given power system
Number；||·||2、||·||0It is 2 norms and 0 norm respectively；
(5-4) carries out interpolation calculation to irregular seismic data using formula (7):
S=D α (7)
In formula (7), s is the seismic data after interpolation, and D is self-adapting dictionary basic function.
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