CN107589453A - A kind of comentropy wave filter and seismic data random noise attenuation method - Google Patents
A kind of comentropy wave filter and seismic data random noise attenuation method Download PDFInfo
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Abstract
The invention discloses a kind of comentropy wave filter and seismic data random noise attenuation method, including：1) gradient-structure tensor is calculated；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 set out based on the decay that can take into account impulsive noise and random Gaussian white noise simultaneously; first define a kind of new wave filter; referred to as comentropy wave filter; with reference to gradient-structure tensor, line style confidence measure and structure adaptive filtering being capable of impulsive noise and random noises in effective attenuation seismic data; strengthen the Space Consistency of seismic event; and the stratum edge such as useful signal and tomography, crack and detail signal structure, technical scheme can be protected to be easily achieved, it is workable.
Description
Technical field
The invention belongs to seismic exploration technique field, is related to noise attenuation technique, especially a kind of comentropy wave filter with
Seismic data random noise attenuation method.
Background technology
Noise attentuation and seismic data letter than raising be during seismic prospecting (such as data information processing) it is very heavy
One of wanting for task, such as gathered data in the wild, it is subsequently to need to examine in seismic data processing, each link explained
The problem of worry.Random noise is typically that many factors synthesis produces generally by the random noise in more earthquake records in earthquake record
Random interference ripple, random distribution in the time, spatial domain in earthquake record, its frequency band is relatively wide, completely covers
Imitate the frequency range of ripple.With the continuous improvement of Songliao basin, the explanation of seismic data by simple geologic structure interpretation progressively
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 is the principal element for influenceing seismic interpretation and reservoir prediction reliability.Common seismic data
The noise-removed technology used in processing has Noise Elimination from Wavelet Transform, f-x domains predictive filtering, KL conversion, SVD decomposition etc., and these methods are big
The spatial coherence characteristics that make use of signal more, reached with to sacrifice lateral resolution and improve the purpose of signal to noise ratio, easily make inclination and
It is attenuated to bend lineups, and can obscure and suppress some trickle signal structures, such as small fracture, thin river course, even
The incorrect link of the tomography both sides lineups of larger turn-off can also be caused, explained to fine seismic structural and bring difficulty.Thus,
The poststack noise attenuation technique of the marginal textures such as fine structure and tomography, the crack of geological data can preferably be protected by ground
The attention of ball physicists.
Luo etc. (2002) proposes a kind of geological 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 average and variance of data in individual sub- window, the average that minimum variance is corresponded to sub- window export as the filtering of current point.AlBin
The filter thought at this guarantor edge has been done further development by Hassan etc. (2006), it is proposed that the sub- window of 3D seismic data cuts open
Divide method, and EPS algorithms are used for the guarantor side filtering process of 3D seismic data.The thought based on fitting of a polynomial such as Lu is promoted
One-dimensional EPS algorithms, by calculating in a series of translations sub- window comprising present analysis point signal to giving the multinomial of order
Formula error of fitting, the estimate of sub- window signal corresponding to minimum error of fitting is selected to be exported 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 border and keeps tomography enhancing technology, it is usual this
Kind technology is applied to relevant volume data, can become apparent from the display of faultage image.Liu etc. (2006) propose by structure forecast with
Similitude median filter and low-high-in the method that is combined of (Low-Upper-Middle, LUM) wave filter carry out construction guarantor
Shield filtering, wherein LUM are the broad sense median filters that a kind of weight coefficient is 1, embody statistical characteristic, due to this method not
Geological data design is specific to, therefore relatively limited treatment effect can only be obtained.
Median filter has excellent noise attentuation performance, and the peak value eliminated in non-stationary signal that is particularly suitable for use in 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 etc. (2008) application image
Two-dimensional multistage median filter eliminates earthquake random noise, and analyzes the selection of filter scales parameter to noise attentuation and signal
The influence of details protection.Liu etc. (2011) provides a kind of non-stationary median filtering technology, according to useful signal, random noise
A kind of window length of one-dimensional median filter of adaptive threshold policy control of characteristic Design, 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 geological data and
Dip direction information is combined, and proposes two kinds of local correlation weighted median filters that can protect tectonic information, ensures tomography
Protection and noise attentuation between balance.Wang Weis etc. (2012) portray seismic reflection layer using gradient-structure Tensor Method and locally tied
Structure feature, with reference to line style in seismic profile and horizontal discontinuity confidence measure, provide a kind of adaptive intermediate value filter of two-dimensional structure
Wave method, median filtering operation window function is adaptively made direction extension according to signal partial structurtes feature and stretched with yardstick
Contracting, so as to Removing Random No, and can effectively protect the stratum such as useful signal and tomography marginal texture to greatest extent.
Above prior art has the disadvantages that：
Conventional filtering operation method, it is usually predominantly the noise attentuation for a kind of type, is made an uproar when simultaneously containing two kinds
During sound, the above method can not take into account the decay of two kinds of noises simultaneously.
The content of the invention
The purpose of the present invention is achieved through the following technical solutions：
Present invention firstly provides a kind of comentropy wave filter：Information first in a given analysis window, calculate every
The power of individual point, by being normalized to the weight coefficient of each point, then respective point value in analysis window is multiplied with the weight coefficient of each point
Summation, output valve of its value as comentropy wave filter.Described information entropy wave filter is specially：
If X is stochastic variable x set, s0For a stochastic variable in stochastic variable x, then X Shannon entropies H (X) is as follows
Formula represents：
Wherein N is stochastic variable x number, and P (x) is probability density function；
It is stochastic variable x power shared in set X to define W (x), as obtained by calculating following formula：
W (x)=- P (x) log2[P(x)]-(1-P(x))log2[1-P(x)] (2)
Then, after stochastic variable x being weighed into W (x) normalization, the weight coefficient for obtaining each point is designated as w (x), such as following formula：
It will be summed 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 be defined as comentropy wave filter.
Based on above- mentioned information entropy wave 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 yardstick and shape of filtering window so that
Filtering window most matches the earth formation information needed in neighborhood to be processed, while is protected using the method for structure adaptive
The detailed information of structure, realize and random noise attenuation is carried out to seismic data, and protect earthquake useful signal, tomography, crack
Deng the structure at stratum edge and detail signal.
Further, above seismic data random noise attenuation method specifically includes following steps：
1) gradient-structure tensor is calculated
The gradient-structure tensor of two-dimension earthquake section is calculated according to the definition of gradient-structure tensor first, obtains gradient-structure
Tensor
Wherein, u (x, t) is expressed as the seismic profile of two dimension, 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 horizontal discontinuity measurement of lineups is calculated
The line style signal structure confidence measure defined according to Bakker (2002), calculate the confidence of geological data linear structure
Measure CL：
Wherein, μ1With μ2Respectively gradient-structure tensorTwo characteristic values, CL is linear structure confidence measure,
Pass through the confidence level value CI of formula (6) computational representation information transverse energy change intensity：
CI=(1-CL) μ2 (7)
CI value 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, determined according to the requirement for protecting edge filter is global；Thr-ground noise threshold
Value, is determined by the overall noise interference level of section；
4) structure adaptive comentropy filter scales parameter selects
According to the requirement of structure adaptive filtering operation, filtering window is the oval window comprising target point, with reference to
Linear structure confidence measure CL and horizontal confidence measure CI, the scale parameter of wave filter is determined by filtering scale parameter selection strategy
σ1And σ2, it is shown below：
Wherein, x=(x, t) be two-dimension earthquake data space, time location, RmaxFor the maximum chi of oval filter window
It is very little, σ1And σ2The major axis and short axle of respectively oval analysis window,For the monotonous descending function on CI (x), its span
Be defined to (0,1], whereinFor exponential function
In formula, the rate of decay of β control characteristic functions, β values are smaller, and the decline of exponential function is faster；Conversely, index letter
Several decay 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 geological 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；
Travel through each data point by above-mentioned steps and realize and the noise of whole seismic data is decayed.
The invention has the advantages that：
The present invention is capable of the random noise of effective attenuation seismic data, i.e. impulsive noise and white Gaussian noise, utilizes gradient
The judgement that structure tensor is measured to earth formation, the Space Consistency of seismic event can be strengthened, and can adaptively protected
Protect the stratum edge such as useful signal and tomography, crack and detail signal architectural feature；Using the comentropy wave filter gram of the present 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 easily
It is workable in realization；Summary step and characteristic are realized to the effective random noise attenuation of seismic data.
Brief description of the drawings
Fig. 1 comentropy filter schematics；Wherein (a) be simulation data, (b) be target point plus noise data, (c)
The weight coefficient value of each point of analysis window；
The flow chart of Fig. 2 the inventive method；
Fig. 3 model data test charts；Wherein (a) test model section, (b) structure adaptive comentropy is filtered to be cutd open
Face；(c) structure adaptive medium filtering difference section, (d) structure adaptive mean filter difference section, (e) structure adaptive information
Entropy filters poor section.
Embodiment
Referring to Fig. 1, invention defines a kind of new wave filter, referred to as comentropy wave filter, the wave filter can be simultaneously
Take into account decay 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 the comentropy wave filter of the present invention specifically, theoretical according to Information Statistics, Shannon entropy is the most frequently used comentropy, if
X is stochastic variable x set, s0For a stochastic variable in stochastic variable x, then X Shannon entropies H (X) such as following formula expressions：
Wherein N is stochastic variable x number, and P (x) is probability density function.
It is stochastic variable x power shared in set X to define W (x), as obtained by calculating following formula：
W (x)=- P (x) log2[P(x)]-(1-P(x))log2[1-P(x)] (2)
Then, after stochastic variable x being weighed into W (x) normalization, the weight coefficient for obtaining each point is designated as w (x), such as following formula：
It will be summed 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 be defined as comentropy wave filter.
The calculation procedure of comentropy wave 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 to aiming spot, the letter in Fig. 1 (b) after aiming spot (at stain) plus noise
Breath, the power each put is calculated,, 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 its value as comentropy wave filter.The operation principle of wave 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, is made an uproar after filtering process
The influence of sound value is smaller, and noise figure is smaller, and its weight coefficient is bigger, the big maximum of proportion, and the value after filtering process is got over actual value
Closely.
Invention also proposes a kind of seismic data random noise attenuation method based on information above entropy wave filter, in this method
In, comentropy wave filter can take into account the characteristic of the decay to impulsive noise and white Gaussian noise, utilize gradient-structure tensor analysis
The regular degree of earth formation in neighborhood, regulate and control the yardstick and shape of filtering window so that filtering window is as far as possible most
Matching needs the earth formation information in neighborhood to be processed, while is believed using the method for structure adaptive come the details of protection structure
Breath, realize and random noise attenuation is carried out to seismic data, and earthquake useful signal can be protected, the stratum side such as tomography, crack
The structure of edge and detail signal, the technical scheme is easily achieved, workable.The seismic data random noise attenuation of the present invention
Method, according to implementing procedure figure (referring to Fig. 2), specifically include following steps：
1) gradient-structure tensor is calculated
The systematicness analysis of earth formation has a variety of implementation methods, and gradient-structure tensor is exactly one of them；If u (x, y)
For two-dimension earthquake section, then gradient-structure tensorFor：
Wherein,- gradient operator；T- is transposed operator；- represent convolution algorithm；Gρ- represent the dimensional Gaussian that yardstick is ρ
Function Gρ(x, y)=exp (- (x2+y2)/2ρ2)。
2) the horizontal confidence measure (i.e. confidence measure) of lineups is calculated
In the definition of gradient-structure tensor, by gradient vectorAnd its tensor matrix and yardstick that transposed vector is formed
Acted on for ρ gauss low frequency filter, determine 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 ν2It is characterized vector, μ2≥μ1>=0, characteristic value is anti-
The Gauss neighborhood G of the position (x, t) of signal is answeredρThe intensity of interior edge characteristic direction amplitude variations, characteristic vector ν1And v2To striking out
Portion's orthogonal orientation, ν1Corresponding to the gradient direction in local amplitude change maximum direction, i.e. signal, and v2Corresponding to local amplitude
Change the trend in minimum direction, i.e. reflection line-ups, according to the two of gradient-structure tensor characteristic value μ1And μ2Value feelings
Condition, calculate the confidence measure CL that Bakker (2002) etc. introduces line style signal structure：
In formula, CL span is [0,1], for weighing the similarity degree of the feature of local signal and linear structure,
The order of accuarcy of local signal orientation estimation is also characterized simultaneously, when CL → 1, represents that local signal feature tends to linear structure, phase
Instead, when CL → 0, representing that partial signal construction has deviated from linear structure, such case is likely to be by noise jamming or tomography,
The horizontal discontinuity such as crack causes, and the confidence measure CL according to linear structure can identify local signal into linear structure well
Reflection line-ups, this confidence level value may determine that the relative intensity of variation of signal, but be vulnerable to the interference of noise.Wang Wei
A kind of putting containing signal transverse energy change intensity information is given on the basis of linear structure confidence measure Deng (2012)
Reliability value CI, for identifying the horizontal discontinuous structure such as tomography, crack：
CI=(1-CL) μ2 (14)
Wherein, (1-CL) describes signal partial structurtes feature opposite linear structure and deviates from degree, μ2It is characterized in given degree
In amount field mean square error least meaning under energy variation intensity of the signal along the consistent direction of partial structurtes, due to confidence
Transverse energy changes μ2Presence, in the case of noise energy is weaker than signal energy, CI has good anti-noise ability, in addition
CI can also differentiate the region of no clear signal structure, and this is particularly important to using CI filterings, can avoid some filtering
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, determined according to the requirement for protecting edge filter is global；Thr-ground noise threshold
Value, is determined by the overall noise interference level of section.
4) structure adaptive comentropy filter scales parameter selects
According to the requirement of structure adaptive filtering operation, filtering window is the oval window comprising target point, with reference to
Linear structure confidence measure CL and horizontal confidence measure CI, the scale parameter of wave filter is determined by filtering scale parameter selection strategy
σ1And σ2, it is shown below：
Wherein, x=(x, t) be two-dimension earthquake data space, time location, RmaxFor the maximum chi of oval filter window
It is very little, σ1And σ2The major axis and short axle of respectively oval analysis window, together decided on the filter scale of structure adaptive filter with
And the set direction of filtering operation,For the monotonous descending function on CI (x), its span be defined to (0,1], whereinFor exponential function
In formula, the rate of decay of β control characteristic functions, β values are smaller, and the decline of exponential function is faster；Conversely, index letter
Several decay 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 geological 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.
Travel through each data point by the step of foregoing invention method and realize and the noise of whole seismic data is declined
Subtract.
According to the specific implementation step of invention, tested by model data, realized using the method for the present invention to Noise
Data carry out noise attentuation, and Fig. 3 (a) be original two dimensional model data, the two dimensional model after method noise attentuation (b) of the invention
Data, (c) are based on structure adaptive medium filtering difference section, and (d) is based on the adaptive mean filter difference section of mechanism, (e)
For the poor section of the application present invention, it can be seen that the present invention has preferable protective effect for details fault information from (b),
By being compared to poor section, it can be found that with reference to the noise reduction method of median filter and mean filter to tiny disconnected
Layer is smaller compared to protection more of the invention.
Claims (4)
1. a kind of comentropy wave filter, it is characterised in that the information first in a given analysis window, calculate what is each put
Power, by being normalized to the weight coefficient of each point, then respective point value in analysis window is multiplied summation with the weight coefficient of each point, its
It is worth the output valve as comentropy wave filter.
2. comentropy wave filter according to claim 1, it is characterised in that described information entropy wave filter is specially：
If X is stochastic variable x set, s0For a stochastic variable in stochastic variable x, then X Shannon entropies H (X) such as following formula table
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Use s'0Instead of stochastic variable s in set X0, then this process be defined as comentropy wave filter.
A kind of 3. seismic data random noise attenuation method based on claim 2 described information entropy wave filter, it is characterised in that
This method utilizes the regular degree of earth formation in gradient-structure tensor analysis neighborhood, regulates and controls the yardstick and shape of filtering window
Shape so that filtering window most matches the earth formation information needed in neighborhood to be processed, while utilizes the side of structure adaptive
Method carrys out the detailed information of protection structure, realizes and carries out random noise attenuation to seismic data, and protects earthquake useful signal, breaks
The structure at the stratum edge such as layer, crack and detail signal.
4. seismic data random noise attenuation method according to claim 3, it is characterised in that specifically include following step
Suddenly：
1) gradient-structure tensor is calculated
The gradient-structure tensor of two-dimension earthquake section is calculated according to the definition of gradient-structure tensor first, obtains gradient-structure tensor
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Wherein, u (x, t) is expressed as the seismic profile of two dimension, 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 horizontal discontinuity measurement of lineups is calculated
The line style signal structure confidence measure defined according to Bakker (2002), calculate the confidence measure of geological data linear structure
CL：
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<mi>C</mi>
<mi>L</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>&mu;</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>&mu;</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, μ1With μ2Respectively gradient-structure tensorTwo characteristic values, CL is linear structure confidence measure, is passed through
The confidence level value CI of formula (6) computational representation information transverse energy change intensity：
CI=(1-CL) μ2 (7)
CI value 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, it is shown below：
Wherein：α-percentage Dynamic gene, determined according to the requirement for protecting edge filter is global；Thr-ground noise threshold value, by
The overall noise interference level of section is determined；
4) structure adaptive comentropy filter scales parameter selects
According to the requirement of structure adaptive filtering operation, filtering window is the oval window comprising target point, with reference to line style
Structure confidence measure CL and horizontal confidence measure CI, the scale parameter σ of wave filter is determined by filtering scale parameter selection strategy1With
σ2, it is shown below：
Wherein, x=(x, t) be two-dimension earthquake data space, time location, RmaxFor the full-size of oval filter window, σ1
And σ2The major axis and short axle of respectively oval analysis window,For the monotonous descending function on CI (x), its span limits
For (0,1], whereinFor exponential function；
<mrow>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>C</mi>
<mi>I</mi>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mfrac>
<mrow>
<mi>C</mi>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
<mi>&beta;</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, the rate of decay of β control characteristic functions, β values are smaller, and the decline of exponential function is faster；Conversely, exponential function
Decay 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)
<mrow>
<mi>w</mi>
<mrow>
<mo>(</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>W</mi>
<mrow>
<mo>(</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>f</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mi>W</mi>
<mrow>
<mo>(</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, f is the geological data value in window, and P (f) is the probability density function in analysis window, and N is the geological data in window
Number；
<mrow>
<msubsup>
<mi>s</mi>
<mn>0</mn>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>f</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mi>w</mi>
<mrow>
<mo>(</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
<mi>s</mi>
<mrow>
<mo>(</mo>
<mi>f</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
Travel through each data point by above-mentioned steps and realize and the noise of whole seismic data is decayed.
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| CN111929732A (en) * | 2020-07-28 | 2020-11-13 | 中国石油大学(北京) | Seismic data denoising method, device and equipment |
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