CN107589453B - A kind of comentropy filter and seismic data random noise attenuation method - Google Patents
A kind of comentropy filter and seismic data random noise attenuation method Download PDFInfo
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Abstract
The invention discloses a kind of comentropy filters and seismic data random noise attenuation method, comprising: 1) calculates gradient-structure tensor；2) stratum transverse direction discontinuity measurement is calculated；3) determination of threshold parameter；4) selection of structure adaptive filter scale parameter；5) comentropy filter process.The present invention is based on the decaying that can combine impulsive noise and random Gaussian white noise to set out; first define a kind of new filter; referred to as comentropy filter; in conjunction with gradient-structure tensor, line style confidence measure and structure adaptive filtering being capable of impulsive noise and random noises in effective attenuation seismic data; enhance the Space Consistency of seismic event; and the stratum edge such as useful signal and tomography, crack and detail signal structure, technical solution can be protected to be easily achieved, strong operability.
Description
Technical field
The invention belongs to seismic exploration technique fields, are related to noise attenuation technique, especially a kind of comentropy filter with
Seismic data random noise attenuation method.
Background technique
It is that seismic prospecting (such as data information processing) is very heavy in the process that noise attentuation and seismic data letter, which compare raising,
One of wanting for task, such as the acquisition data in field, subsequently seismic data processing, explanation each link in be need examine
The problem of worry.Random noise is usually usually the comprehensive generation of many factors by the random noise in more earthquake records in earthquake record
Random interference wave, the random distribution in the time of earthquake record, spatial domain, frequency band is relatively wide, has completely covered
Imitate the frequency range of wave.With the continuous improvement of Songliao basin, the explanation of seismic data by simple geologic structure interpretation gradually
Turn to fine interpretation of structure and reservoir prediction, it is desirable to which the structure interpretation and reservoir prediction work to seismic data are more smart
Carefully, and the low signal-to-noise ratio of seismic data be influence seismic interpretation and reservoir prediction reliability principal element.Common seismic data
Noise-removed technology used in processing has Noise Elimination from Wavelet Transform, the domain f-x predictive filtering, KL transformation, SVD decomposition etc., these methods are big
The spatial coherence characteristics of signal are utilized more, achieve the purpose that improve signal-to-noise ratio to sacrifice lateral resolution, be easy to make inclination and
Bending lineups are attenuated, and can obscure and suppress some subtle signal structures, such as small fracture, thin river, even
The incorrect link that can also cause the tomography two sides lineups of larger turn-off brings difficulty to fine seismic structural explanation.Thus,
It can preferably protect the poststack noise attenuation technique of the marginal textures such as fine structure and tomography, the crack of seismic data by ground
The attention of ball physicists.
Luo etc. (2002) proposes a kind of seismic data based on order statistics thought and protects side filtering (EPS, Edge-
Preserving Smoothing) algorithm, this method uses the more window analytical technologies of Kuwahara, calculates each around present analysis point
The mean value and variance of data in a sub- window export the mean value that minimum variance corresponds to sub- window as the filtering of current point.AlBin
This filter thought for protecting edge has been done further development by Hassan etc. (2006), and the sub- window for proposing 3D seismic data cuts open
Divide method, and the guarantor side that EPS algorithm is used for 3D seismic data is filtered.Lu etc. is promoted based on the thought of fitting of a polynomial
One-dimensional EPS algorithm, by calculating in a series of translations sub- window comprising present analysis point signal to the multinomial of given order
Formula error of fitting selects the estimated value of the corresponding sub- window signal of minimum error of fitting to export as the filtering of current point.Yang Peijie
The thought that this more windows analysis is also based on Deng (2010) gives a kind of directionality boundary and keeps tomography enhancing technology, it is usual this
Kind technology is applied to relevant volume data, and the display of faultage image can be made to be more clear.Liu et al. (2006) propose by structure forecast with
The method that (Low-Upper-Middle, LUM) filter combines in similitude median filter and low-high-carries out construction guarantor
Shield filtering, wherein LUM is a kind of broad sense median filter that weight coefficient is 1, embodies statistical characteristic, not due to this method
It is specific to seismic data design, therefore relatively limited treatment effect can only be obtained.
Median filter has excellent noise attentuation performance, and the peak value for being particularly suitable for eliminating in non-stationary signal is made an uproar
Sound.(2012,1995) median filter method is used for seismic data process by Bednar, Duncan and Beresford, achieves ratio
Conventional treatment method has the effect of excellent random noise attenuation and envelope eapsulotomy.In the processing of Liu et al. (2008) application image
Two-dimensional multistage median filter eliminates earthquake random noise, and analyzes filter scales parameter selection to noise attentuation and signal
The influence of details protection.Liu et al. (2011) provides a kind of non-stationary median filtering technology, according to useful signal, random noise
A kind of window of the one-dimensional median filter of adaptive threshold policy control of characteristic Design is long, in random noise attenuation and can have
Effect signal obtains compromise between keeping.Liu Yang etc. by Weighted median filtering technology respectively with the structure forecast information of seismic data and
Dip direction information combines, and proposes two kinds of local correlation weighted median filters that can protect tectonic information, guarantees tomography
Protection and noise attentuation between balance.Wang Weis etc. (2012) portray seismic reflection layer using gradient-structure Tensor Method and locally tie
Structure feature provides a kind of adaptive intermediate value filter of two-dimensional structure in conjunction with line style in seismic profile and lateral discontinuity confidence measure
Wave method, so that median filtering operation window function is adaptively made according to signal partial structurtes feature, direction extends and scale is stretched
Contracting, thus can Removing Random No and the stratum such as effective protection useful signal and tomography marginal texture to the maximum extent.
The above prior art has the disadvantages that
Conventional filtering operation method is usually predominantly the noise attentuation for a kind of type, when simultaneously containing there are two types of make an uproar
When sound, the above method can not combine the decaying of two kinds of noises.
Summary of the invention
The purpose of the present invention is achieved through the following technical solutions:
Present invention firstly provides a kind of comentropy filters: the information first in a given analysis window, calculates every
Then point value respective in analysis window is multiplied by the power of a point by being normalized to the weight coefficient of each point with the weight coefficient of each point
Summation, output valve of the value as comentropy filter.The comentropy filter specifically:
If X is the set of stochastic variable x, s0For a stochastic variable in stochastic variable x, then X Shannon entropy H (X) is as follows
Formula indicates:
Wherein N is the number of stochastic variable x, and P (x) is probability density function；
Defining W (x) is stochastic variable x power shared in set X, is calculate by the following formula gained:
W (x)=- P (x) log2[P(x)]-(1-P(x))log2[1-P(x)] (2)
Then, by after stochastic variable x power W (x) normalization, the weight coefficient for obtaining each point is denoted as w (x), such as following formula:
It will sum after the stochastic variable product of obtained each point weight coefficient and each point, such as following formula:
Use s'0Instead of stochastic variable s in set X0, then this process is defined as comentropy filter.
Based on above- mentioned information entropy filter, the present invention also proposes a kind of seismic data random noise attenuation method: this method
Using the regular degree of earth formation in gradient-structure tensor analysis neighborhood, regulate and control the scale and shape of filtering window, so that
Filtering window most matches the earth formation information in neighborhood to be treated, while being protected using the method for structure adaptive
The detailed information of structure, realization carries out random noise attenuation to seismic data, and protects earthquake useful signal, tomography, crack
The structure at equal stratum edge and detail signal.
Further, the above seismic data random noise attenuation method specifically includes the following steps:
1) gradient-structure tensor is calculated
The gradient-structure tensor for calculating two-dimension earthquake section according to the definition of gradient-structure tensor first, obtains gradient-structure
Tensor
Wherein, u (x, t) is expressed as two-dimensional seismic profile, in formula:- gradient operator；Gρ- two-dimensional Gaussian function Gρ
(x, t)=exp (- (x2+t2)/2ρ2), ρ is scale parameter；- convolution operator；T-matrix transposed operator；
2) the lateral discontinuity measurement of lineups is calculated
The line style signal structure confidence measure defined according to Bakker (2002) calculates the confidence of seismic data linear structure
Measure CL:
Wherein, μ1With μ2Respectively gradient-structure tensorTwo characteristic values, CL be linear structure confidence measure,
Pass through the confidence level magnitude CI of formula (6) computational representation information transverse energy change intensity:
CI=(1-CL) μ2 (7)
The value of CI value between section [0,1]；
3) determination of threshold parameter
Marginal texture retentivity is controlled by threshold parameter β, passes through the adaptively selected strategy of the threshold parameter of region segmentation
β is calculated, is shown below:
Wherein: α-percentage Dynamic gene is determined according to the requirement overall situation for protecting edge filter；Thr-ground noise threshold
Value, is determined by the overall noise interference level of section；
4) structure adaptive comentropy filter scales parameter selection
According to the requirement of structure adaptive filtering operation, filtering window is the oval window comprising target point, in conjunction with
Linear structure confidence measure CL and lateral confidence measure CI, the scale parameter of filter is determined by filtering scale parameter selection strategy
σ1And σ2, it is shown below:
Wherein, x=(x, t) is two-dimension earthquake data space, time location, RmaxFor the maximum ruler of oval filter window
It is very little, σ1And σ2The long axis and short axle of respectively oval analysis window, g () are the monotonous descending function about CI (x), value model
Enclose and be limited to (0,1], wherein g () is exponential function
In formula, the rate of decay of β control exponential function, β value is smaller, and the decline of exponential function is faster；Conversely, index letter
Several decaying slow down；
5) comentropy filter process
See the data in oval analysis window as a seismic data set F,
W (f)=- P (f) log2[P(f)]-(1-P(f))log2[1-P(f)] (11)
Wherein, f is the seismic data value in window, and P (f) is the probability density function in analysis window, and N is the earthquake number in window
According to number；
The realization of each data point is traversed through the above steps to decay to the noise of entire seismic data.
The invention has the following advantages:
The present invention is capable of the random noise of effective attenuation seismic data, i.e. impulsive noise and white Gaussian noise, utilizes gradient
Judgement of the structure tensor to stratum degree of structuration amount can enhance the Space Consistency of seismic event, and can adaptively protect
Protect the stratum edge such as useful signal and tomography, crack and detail signal structure feature；Using comentropy filter gram of the invention
The deficiency of single type noise attentuation is taken, can decay the seismic data containing impulsive noise and white Gaussian noise, and the present invention is easy
In realization, strong operability；In summary step and characteristic are realized to the effective random noise attenuation of seismic data.
Detailed description of the invention
Fig. 1 comentropy filter schematic；Wherein (a) is the data of simulation, (b) is the data of target point plus noise, (c)
The weight coefficient value of each point of analysis window；
The flow chart of Fig. 2 the method for the present invention；
Fig. 3 model data test chart；Wherein (a) test model section, (b) structure adaptive comentropy is filtered cuts open
Face；(c) structure adaptive median filtering difference section, (d) structure adaptive mean filter difference section, (e) structure adaptive information
Entropy filters poor section.
Specific embodiment
Referring to Fig. 1, invention defines a kind of new filters, referred to as comentropy filter, which can be simultaneously
Take into account decaying impulsive noise (salt-pepper noise is otherwise referred to as in image procossing) and the two kinds of random noise of white Gaussian noise.
For comentropy filter of the invention specifically, according to Information Statistics theory, Shannon entropy is most common comentropy, if
X is the set of stochastic variable x, s0For a stochastic variable in stochastic variable x, then X Shannon entropy H (X) such as following formula indicates:
Wherein N is the number of stochastic variable x, and P (x) is probability density function.
Defining W (x) is stochastic variable x power shared in set X, is calculate by the following formula gained:
W (x)=- P (x) log2[P(x)]-(1-P(x))log2[1-P(x)] (2)
Then, by after stochastic variable x power W (x) normalization, the weight coefficient for obtaining each point is denoted as w (x), such as following formula:
It will sum after the stochastic variable product of obtained each point weight coefficient and each point, such as following formula:
Use s'0Instead of stochastic variable s in set X0, then this process is defined as comentropy filter.
The calculating step of comentropy filter of the present invention is, first the information in a given analysis window, such as Fig. 1
(a) shown in, wherein stain position is to be set as aiming spot, the letter in Fig. 1 (b) after aiming spot (at stain) plus noise
Breath, calculates the power of each point,, then will be respective in analysis window as shown in Fig. 1 (c) by being normalized to the weight coefficient of each point
Point value is multiplied summation with the weight coefficient of each point, output valve of the value as comentropy filter.The working principle of filter is, right
It is inversely proportional in the corresponding weight coefficient of the size of target spot noise figure, the bigger weight coefficient of noise figure is smaller, makes an uproar after filtering processing
The influence of sound value is smaller, and noise figure is smaller, and weight coefficient is bigger, and the big maximum of proportion, the value after filtering processing is got over true value
Closely.
Invention also proposes a kind of seismic data random noise attenuation method based on information above entropy filter, in this method
In, comentropy filter can take into account the characteristic of the decaying to impulsive noise and white Gaussian noise, utilize gradient-structure tensor analysis
The regular degree of earth formation in neighborhood, regulates and controls the scale and shape of filtering window, so that filtering window is as far as possible most
The earth formation information in neighborhood to be treated is matched, while protecting the details of structure to believe using the method for structure adaptive
Breath, realization carries out random noise attenuation to seismic data, and can protect earthquake useful signal,
The structure at the stratum edge and detail signal such as tomography, crack, the technical solution are easily achieved, strong operability.This
The seismic data random noise attenuation method of invention, according to implementation flow chart (referring to fig. 2), specifically includes the following steps:
1) gradient-structure tensor is calculated
There are many implementation method, gradient-structure tensor is exactly one of them for the systematicness analysis of earth formation；If u (x, y)
For two-dimension earthquake section, then gradient-structure tensorAre as follows:
Wherein,Gradient operator；T- is transposed operator；Indicate convolution algorithm；GρIndicate that scale is the dimensional Gaussian of ρ
Function Gρ(x, y)=exp (- (x2+y2)/2ρ2)。
2) the lateral confidence measure (i.e. confidence measure) of lineups is calculated
In the definition of gradient-structure tensor, by gradient vectorAnd its tensor matrix and scale that transposed vector is formed
It is acted on for the gauss low frequency filter of ρ, determines the out to out of the mensurable signal characteristic of gradient-structure tensor, this is symmetrical
Positive semidefinite matrixDo matrix- eigenvector-decomposition:
Wherein, μ1And μ2For positive definite matrixCharacteristic value, ν1And ν2For feature vector, μ2≥μ1>=0, characteristic value is anti-
The Gauss neighborhood G of the position (x, t) of signal is answeredρThe interior intensity along characteristic direction amplitude variations, feature vector ν1And v2To striking out
Portion's orthogonal orientation, ν1Change maximum direction, the i.e. gradient direction of signal corresponding to local amplitude, and v2Corresponding to local amplitude
Change the smallest direction, the i.e. trend of reflection line-ups, according to the two of gradient-structure tensor characteristic value μ1And μ2Value feelings
Condition calculates the confidence measure CL that Bakker (2002) etc. introduce line style signal structure:
In formula, the value range of CL is [0,1], for measuring the feature of local signal and the similarity degree of linear structure,
Also the order of accuarcy that characterization local signal orientation is estimated simultaneously indicates that local signal feature tends to linear structure, phase when CL → 1
Instead, when CL → 0, indicating that partial signal construction has deviated from linear structure, such case is likely to be by noise jamming or tomography,
The transverse direction discontinuity such as crack causes, and the confidence measure CL according to linear structure can identify well local signal at linear structure
Reflection line-ups, this confidence level magnitude may determine that the opposite variation degree of signal, but the interference vulnerable to noise.Wang Wei
A kind of setting containing signal transverse energy change intensity information is given on the basis of linear structure confidence measure Deng (2012)
Reliability magnitude CI, the lateral discontinuous structure such as tomography, crack for identification:
CI=(1-CL) μ2 (14)
Wherein, (1-CL) describe signal partial structurtes feature opposite linear structure deviate from degree, μ2It is characterized in given degree
In amount field mean square error least meaning under signal along the consistent direction of partial structurtes energy variation intensity, due to confidence
Transverse energy changes μ2Presence, the case where being weaker than signal energy for noise energy, CI has good anti-noise ability, furthermore
CI can also differentiate the region of no clear signal structure, this, can be to avoid some filtering to using CI filtering particularly important
The generation of illusion.
3) determination of threshold parameter
Marginal texture retentivity is controlled by threshold parameter β, passes through the adaptively selected strategy of the threshold parameter of region segmentation
β is calculated, is shown below:
Wherein: α-percentage Dynamic gene is determined according to the requirement overall situation for protecting edge filter；Thr-ground noise threshold
Value, is determined by the overall noise interference level of section.
4) structure adaptive comentropy filter scales parameter selection
According to the requirement of structure adaptive filtering operation, filtering window is the oval window comprising target point, in conjunction with
Linear structure confidence measure CL and lateral confidence measure CI, the scale parameter of filter is determined by filtering scale parameter selection strategy
σ1And σ2, it is shown below:
Wherein, x=(x, t) is two-dimension earthquake data space, time location, RmaxFor the maximum ruler of oval filter window
It is very little, σ1And σ2The long axis and short axle of respectively oval analysis window, codetermined the filter scale of structure adaptive filter with
And the direction selection of filtering operation, g () are monotonous descending function about CI (x), value range be limited to (0,1],
Middle g () is exponential function
In formula, the rate of decay of β control exponential function, β value is smaller, and the decline of exponential function is faster；Conversely, index letter
Several decaying slow down.
5) comentropy filter process
See the data in oval analysis window as a seismic data set F, then the power of each point and weight coefficient are
W (f)=- P (f) log2[P(f)]-(1-P(f))log2[1-P(f)] (18)
Wherein, f is the seismic data value in window, and P (f) is the probability density function in analysis window, and N is the earthquake number in window
According to number.
The realization of each data point is traversed by the step of foregoing invention method to decline to the noise of entire seismic data
Subtract.
It according to the specific implementation step of invention, is tested by model data, is realized using method of the invention to Noise
Data carry out noise attentuation, and Fig. 3 (a) is original two dimensional model data, (b) two dimensional model after method noise attentuation of the invention
Data are (c) based on structure adaptive median filtering difference section, are (d) based on the adaptive mean filter difference section of mechanism, (e)
For apply poor section of the invention, from (b) it can be seen that the present invention for details fault information have preferable protective effect,
By being compared to poor section, it can be found that in conjunction with the noise reduction method of median filter and mean filter to tiny disconnected
Layer is smaller compared to protection more of the invention.
Claims (3)
1. a kind of comentropy filter, which is characterized in that first against the information in a given analysis window, calculate each point
Power, by normalization obtain the weight coefficient of each point, point value respective in analysis window is multiplied with the weight coefficient of each point then and is asked
With output valve of the value as comentropy filter；
The comentropy filter specifically:
If X is the set of stochastic variable x, s0For a stochastic variable in stochastic variable x, then X Shannon entropy H (X) such as following formula table
Show:
Wherein N is the number of stochastic variable x, and P (x) is probability density function；
Defining W (x) is stochastic variable x power shared in set X, is calculate by the following formula gained:
W (x)=- P (x) log2[P(x)]-(1-P(x))log2[1-P(x)] (2)
Then, by after stochastic variable x power W (x) normalization, the weight coefficient for obtaining each point is denoted as w (x), such as following formula:
It will sum after the stochastic variable product of obtained each point weight coefficient and each point, such as following formula:
Use s'0Instead of stochastic variable s in set X0, then this process is defined as comentropy filter.
2. a kind of seismic data random noise attenuation method based on comentropy filter described in claim 1, which is characterized in that
This method regulates and controls the scale and shape of filtering window using the regular degree of earth formation in gradient-structure tensor analysis neighborhood
Shape so that filtering window most matches the earth formation information in neighborhood to be treated, while utilizing the side of structure adaptive
Method protects the detailed information of structure, realizes and carries out random noise attenuation to seismic data, and protect earthquake useful signal, breaks
The structure at stratum edge and detail signal including layer, crack.
3. seismic data random noise attenuation method according to claim 2, which is characterized in that specifically include following step
It is rapid:
1) gradient-structure tensor is calculated
The gradient-structure tensor for calculating two-dimension earthquake section according to the definition of gradient-structure tensor first, obtains gradient-structure tensor
Wherein, u (x, t) is expressed as two-dimensional seismic profile, in formula:- gradient operator；Gρ- two-dimensional Gaussian function Gρ(x,t)
=exp (- (x2+t2)/2ρ2), ρ is scale parameter；- convolution operator；T-matrix transposed operator；
2) the lateral discontinuity measurement of lineups is calculated
The line style signal structure confidence measure defined according to Bakker (2002) calculates the confidence measure of seismic data linear structure
CL:
Wherein, μ1With μ2Respectively gradient-structure tensorTwo characteristic values, CL be linear structure confidence measure, pass through
The confidence level magnitude CI of formula (6) computational representation information transverse energy change intensity:
CI=(1-CL) μ2 (7)
The value of CI value between section [0,1]；
3) determination of threshold parameter
Marginal texture retentivity is controlled by threshold parameter β, passes through the adaptively selected policy calculation of the threshold parameter of region segmentation
β is shown below:
Wherein: α-percentage Dynamic gene is determined according to the requirement overall situation for protecting edge filter；Thr-ground noise threshold value, by
The overall noise interference level of section is determined；
4) structure adaptive comentropy filter scales parameter selection
According to the requirement of structure adaptive filtering operation, filtering window is the oval window comprising target point, in conjunction with line style
Structure confidence measure CL and lateral confidence measure CI, the scale parameter σ of filter is determined by filtering scale parameter selection strategy1With
σ2, it is shown below:
Wherein, x=(x, t) is two-dimension earthquake data space, time location, RmaxFor the full-size of oval filter window, σ1
And σ2The long axis and short axle of respectively oval analysis window, g () are the monotonous descending function about CI (x), value range limit
Be set to (0,1], wherein g () is exponential function；
In formula, the rate of decay of β control exponential function, β value is smaller, and the decline of exponential function is faster；Conversely, exponential function
Decaying slows down；
5) comentropy filter process
See the data in oval analysis window as a seismic data set F,
W (f)=- P (f) log2[P(f)]-(1-P(f))log2[1-P(f)] (11)
Wherein, f is the seismic data value in window, and P (f) is the probability density function in analysis window, and N is the seismic data in window
Number；
The realization of each data point is traversed through the above steps to decay to the noise of entire seismic data.
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| CN104678288A (en) * | 2015-02-07 | 2015-06-03 | 长沙学院 | Information entropy and wavelet transform-based switched current circuit failure dictionary acquisition method |
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| CN102496162A (en) * | 2011-12-21 | 2012-06-13 | 浙江大学 | Method for evaluating quality of part of reference image based on non-tensor product wavelet filter |
| CN104678288A (en) * | 2015-02-07 | 2015-06-03 | 长沙学院 | Information entropy and wavelet transform-based switched current circuit failure dictionary acquisition method |
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