CN109782346A - A kind of acquisition footprint drawing method based on anatomic element analysis - Google Patents
A kind of acquisition footprint drawing method based on anatomic element analysis Download PDFInfo
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Abstract
The present invention discloses a kind of acquisition footprint drawing method based on anatomic element analysis, include: step 101: acquisition footprint wave configuration feature constructs two-dimentional local discrete cosine transform in the earthquake record being sliced according to the horizon slice of 3-d seismic data set or whens waiting, and combines with two-dimentional Stationary Wavelet Transform and constitute super complete dictionary；Step 102: in such a way that the initial data to earthquake tracer signal successively executes, the preliminary compacting that footprint is acquired based on the method that anatomic element is analyzed is utilized in each horizon slice or in slice whens waiting；Step 103: determining the low cut-off frequency of two dimension local discrete cosine transform；Step 104: repeating step 102-103 until the processing completion of all slice of data, the method analyzed based on anatomic element is utilized to carry out SNR estimation and compensation, suppress acquisition footprint noise, the final compacting realized to acquisition footprint noise in 3-d seismic data set.Footprint is acquired to 3-d seismic data set using the present invention to suppress, and has achieved the purpose that improve seismic data signal-to-noise ratio.
Description
Technical field
The invention belongs to technical field of data processing in seismic prospecting, in particular to foot is acquired in a kind of seismic acquisition data
The method of coining.
Background technique
Acquisition footprint is typically due to rolling arrangement mode and focus and the wave detector side line interval of seismic observation system
Caused by it is endless fully sampled and cause a kind of periodic amplitude illusion generated in seismic imaging, usually can be in 3-D seismics number
According to time or depth slice in observe.It is multiple in order to meet in the exploration process of the hidden-types oil-gas reservoir such as stratum-lithology
The demand of miscellaneous reservoir prediction needs to carry out seismic data fine interpretation of structure and depositional trap and explains.However, acquisition footprint
Noise meeting severe jamming seismic interpretation process, or even it can be mistaken for geologic structure or lithology exception, seriously affect earthquake money
Expect the precision and reliability explained.Therefore the method for research compacting and decaying acquisition footprint is particularly significant, has great theory
Meaning and market value.
With the development of signal sparsity theory, Starck et al. proposes the mixed signal decomposition side of anatomic element analysis
Method.Anatomic element analysis refers to, according to the constituent wave configuration feature of sophisticated signal, has different atomic features for two kinds
Transformation dictionary constitute super complete dictionary, realize that the representation more sparse to sophisticated signal and more effective information identify energy
Power realizes the separation of two kinds of ingredients.Dictionary is usually rule of thumb to select or construct from known mathematic(al) manipulation, and select
Dictionary whether sufficiently meet anatomic element analysis it is assumed that being the key that anatomic element analysis method success.Use shape
The method of state constituent analysis separates with harmonic noise realization to achieve the purpose that suppress harmonic noise signal, needs according to effectively
The wave configuration feature of signal and harmonic noise constructs suitable sparse transformation.Existing literature research selection is become using continuous wavelet
It is proper to bring rarefaction representation useful signal.But harmonic noise is complex, needs to construct more appropriate matched transformation and comes
Rarefaction representation, and select to determine the design parameter converted, presently relevant research is less.
The prior art:
Optimize acquisition method.Using the observation system of wide-azimuth, the uneven of data record azimuthal distribution can be reduced
Property, omnibearing observation is carried out on ground, so that seismic data has recorded the wave field characteristics in subsurface reflection point all directions, is obtained
Complete seismic wave field information；The observation system of wide-azimuth additionally aids the back-scattered noise for reducing shot point, improves quiet
Calibration result, these both contribute to weaken acquisition footprint.
The shortcomings that prior art:
Can only be for new acquisition data, the data acquired before can not handling；It needs to do difference for different acquisition system
Design, it is portable poor.
Summary of the invention
The object of the present invention is to provide a kind of acquisition footprint drawing methods based on anatomic element analysis, on solving
State technical problem.The wave of acquisition footprint and significant wave signal whens for 3-d seismic data set horizon slice or waiting in slice
Shape morphological feature is different, constructs suitable rarefaction representation transformation, that is, choosing two-dimentional local discrete cosine transform indicates acquisition footprint,
Choosing two-dimentional Stationary Wavelet Transform indicates significant wave signal, and these two types of waveform morphology dictionaries joint is constituted super complete dictionary,
And it is selected to determine two-dimentional Stationary Wavelet Transform transformation parameter according to data characteristics, and real using coordinate Aries In The Block By Block Relaxation algorithmic method
Existing SNR estimation and compensation with reach the effectively horizon slice of compacting 3-d seismic data set or seismic data that while waiting are sliced in adopt
Collect the purpose of footprint.
To achieve the goals above, the present invention adopts the following technical scheme:
Acquisition footprint drawing method based on anatomic element analysis, comprising the following steps:
Step 101: acquisition footprint in the earthquake record being sliced according to the horizon slice of 3-d seismic data set or whens waiting
Wave configuration feature constructs two-dimentional local discrete cosine transform, and combines with two-dimentional Stationary Wavelet Transform and constitute super complete dictionary,
The decomposed class J of two-dimentional Stationary Wavelet Transform and the analysis window size W of two-dimentional local discrete cosine transform are determined simultaneously；
Step 102: in such a way that the initial data to earthquake tracer signal successively executes, in each horizon slice or
The preliminary compacting that footprint is acquired based on the method that anatomic element is analyzed is utilized whens equal in slice；
Step 103: determining the low cut-off frequency of two dimension local discrete cosine transform；
Step 104: repeating step 02-03 until the processing completion of all slice of data, utilize what is analyzed based on anatomic element
Method carries out SNR estimation and compensation, suppresses acquisition footprint noise, the final pressure realized to acquisition footprint noise in 3-d seismic data set
System.
Further, it is determined in step 101 according to useful signal wave configuration feature and acquisition footprint wave configuration feature
Two kinds of transformation dictionaries of anatomic element analysis, useful signal select two-dimentional Stationary Wavelet Transform, and acquisition footprint selects local Discrete
Cosine transform, and constitute super complete dictionary.
Using the ingredient that the object that anatomic element is analyzed is containing two kinds with different shape feature:
S=s1+s2,
In formula: s indicates signal to be analyzed；s1、s2Indicate two kinds of ingredients with different shape feature in signal；It mentions respectively
Take out s1、s2Both ingredients are the targets of anatomic element analysis；Assuming that s1And s2It can be respectively by dictionary Φ1And Φ2Effectively
Rarefaction representation, but use Φ2Rarefaction representation s1With with Φ1Rarefaction representation s2When sparsity it is poor；
Transformation dictionary of the two-dimentional Stationary Wavelet Transform as rarefaction representation useful signal ingredient is selected, wherein two dimension is steady small
Wave direct transform are as follows:
H in formulajAnd GjRespectively represent the filter group of jth layer decomposition.
The inverse transformation of two-dimentional Stationary Wavelet Transform are as follows:
In formulaWithRespectively represent HjAnd GjDual filter group.
Transformation dictionary of the two-dimentional local discrete cosine transform (IV type) as rarefaction representation acquisition footprint is selected, wherein two dimension
The direct transform of local discrete cosine transform are as follows:
In formula, f (i, j) indicates signal to be analyzed,Indicate that the two-dimentional local Discrete Cosine of signal to be analyzed becomes
Change coefficient, k1,k2=0,1 ... N-1.
The inverse transformation of two-dimentional local discrete cosine transform are as follows:
According to anatomic element analysis theories, with the dictionary Φ selected above1I.e. two-dimentional Stationary Wavelet Transform and Φ2It is i.e. two-dimentional
Local discrete cosine transform constitutes super complete dictionary, and rarefaction representation signal s calculates rarefaction representation coefficient:
In formula: x1For in reconstruction coefficients with Φ1Corresponding part；x2For in reconstruction coefficients with Φ2Corresponding part.For
Lagrange multiplier.
Further, cut along layer to original seismic data data using piecemeal coordinate relaxed algorithm in step 102
Piece or slicing treatment whens waiting, realize the compacting of acquisition footprint, which can solve by coordinate Aries In The Block By Block Relaxation algorithm.
The basic thought of coordinate Aries In The Block By Block Relaxation algorithm is the calculating x of alternating iteration1And x2.Its main contents step are as follows:
Initialization: primary iteration step number k=0, initial solution
For indicating signal component s1Coefficient initial solution,For indicating signal component s2Coefficient initial solution；
Iteration: iterative steps k increases by 1 when every step iteration, and calculates:
In formula, TλFor hard threshold function；With Φ1A pair of positive inverse transformation is constituted,With Φ2Constitute a pair of positive inverse transformation；
Termination condition: whenWhen less than preset value, when influence of the continuation iteration to result is sufficiently small, iteration
It terminates；
Output:
For isolated signal component s1Final transformation coefficient,For isolated signal component s2Final transformation series
Number；
In piecemeal coordinate relaxed algorithm, hard threshold function formula is as follows:
In formula:For hard threshold function, λ is hard -threshold,For coefficient matrixElement, k=1,
2 ..., N, N are the size of coefficient matrix.
Further, step 103 is in determining that the low cut-off frequency of two-dimentional local discrete cosine transform is realized, to specifically include:
Step 301: being sliced whens taking M to wait 3-d seismic data set according to interval time Δ T for testing local cosine
The low cut-off frequency parameter of the restructuring transformation of transformation, their position is respectively t0,tΔT,t2ΔT,…,t(M-1)ΔT；
Step 302: for position tkΔT, k=0,1 ..., M-1 provide the restructuring transformation of two-dimentional local discrete cosine transform
A series of low cut-off frequency parameters, and be directed to each low cut-off frequency parameter, solve and obtain significant wave signal and acquisition footprint noise
Separation；It is determined by the SNR estimation and compensation effect under comparison parameters and obtains best SNR estimation and compensation effect in current time location
Low cut-off frequency parameter fkΔT；
Step 303: linear interpolation method is utilized, according to time location tkΔT, k=0,1 ..., M-1 and its is corresponding low
Cut-off frequency parameter fkΔT, k=0,1 ..., M-1 are obtained more than the two-dimentional local Discrete of position of entire 3-d seismic data set other time
The low cut-off frequency parameter of the restructuring transformation of string transformation；
Further, it is cut in step 04 according to each time for successively handling 3-d seismic data set from shallow-layer to deep layer
Piece, by solving formula
Obtain the expression vector x of significant wave signal and acquisition footprint noiseeAnd xf, gone to obtain being sliced from current time
The acquisition footprint noise s removedf=ΦfxfAnd corresponding significant wave signal is se=s-sf。
Further, preset value takes 10-6。
Further, hard -threshold λ takesAccording to arranged from big to smallA value.
Compared with the existing technology, the invention has the following advantages:
The present invention utilizes anatomic element analysis theories, also regards acquisition footprint noise as one of poststack seismic wave field letter
Number component constructs the i.e. two-dimentional local discrete cosine transform of suitable rarefaction representation transformation, constitutes and surpass with two-dimentional Stationary Wavelet Transform
Complete dictionary, and selected to determine two-dimentional Stationary Wavelet Transform parameter according to data characteristics, and use coordinate Aries In The Block By Block Relaxation algorithm
Method realizes that SNR estimation and compensation achievees the purpose that suppress harmonic noise.The present invention can not only effectively suppress acquisition footprint, removal
Part random noise and migration processing illusion, and useful signal has compared with hi-fi.
Detailed description of the invention
Fig. 1 is Part and whole time domain waveform；
Fig. 2 is bell window function (k=0)；
Fig. 3 is two-dimentional 8 × 8 discrete cosine transform atoms；
Fig. 4 is two-dimentional Stationary Wavelet Transform atom；
Fig. 5 is the flow chart that the method for the present invention handles data；
Fig. 6 is the flow chart for determining the low cut-off frequency parameter of Local Cosine Transform restructuring transformation；
Fig. 7 A is one main profile section of real data；Fig. 7 B is the significant wave letter that the method for the present invention is separated from Fig. 7 A
Number；Fig. 7 C is the acquisition footprint noise that the method for the present invention is removed from Fig. 7 A；
Fig. 8 A is the isochronous surface of 1.7s in real data body；The significant wave letter that Fig. 8 B the method for the present invention is separated from Fig. 8 A
Number；The acquisition footprint noise that Fig. 8 C the method for the present invention is removed from Fig. 8 A.
Specific embodiment
It is right with reference to the accompanying drawings and detailed description in order to which the purpose of the present invention, technical solution is more clearly understood
The present invention is further described in detail.Here, exemplary embodiment and its explanation of the invention is used to explain the present invention, but
It is not intended as restriction of the invention.
In embodiments of the present invention, propose it is a kind of based on anatomic element analysis acquisition footprint drawing method, including with
Lower step:
Step 101: acquisition footprint in the earthquake record being sliced according to the horizon slice of 3-d seismic data set or whens waiting
Wave configuration feature constructs two-dimentional local discrete cosine transform, and combines with two-dimentional Stationary Wavelet Transform and constitute super complete dictionary,
The decomposed class J of two-dimentional Stationary Wavelet Transform and the analysis window size W of two-dimentional local discrete cosine transform are determined simultaneously；
Step 102: in such a way that the initial data to 3-d seismic data set successively executes, in each horizon slice or
The preliminary compacting that footprint is acquired based on the method that anatomic element is analyzed is utilized in being sliced whens person etc.；
Step 103: determining the low cut-off frequency of two dimension local discrete cosine transform；
Step 104: repeating step 102-103 until the processing of all slice of data is completed, using based on anatomic element analysis
Method carry out SNR estimation and compensation, suppress acquisition footprint noise, it is final to realize to acquisition footprint noise in 3-d seismic data set
Compacting.
In step 01 according to 3-D seismics record in acquisition footprint wave configuration feature construct two-dimentional local Discrete Cosine and become
It changes, and constitutes super complete dictionary with two-dimentional Stationary Wavelet Transform, specifically include:
Transformation dictionary of the two-dimentional local discrete cosine transform as rarefaction representation acquisition footprint is selected, in discrete cosine transform
Common Part and whole has I type and two kinds of IV, and the present invention mainly uses IV type cosine basis, local I V-type cosine-basis function
(LCB-IV) it is defined as follows:
In above formula, bmn(x) Part and whole with wave number index m and positioning index n is indicated, as shown in Figure 1, wherein
For section initial position,For section final position,For siding-to-siding block length.Bell window function BnIt (x) is definition
In closed intervalSmooth function, andε and ε ' is respectively the weight of section arranged on left and right sides
Folded radius,
Wherein β (x) is profile function (increasing or decreasing transformation), and expression formula is by recursive definition
Here k >=0, and
Profile function βk+1(x) smooth degree will increase with the increase of k, such as profile function when k=0 is
It is illustrated in figure 2 bell window function corresponding at this time.
For function f ∈ CN, discrete IV type cosine transform (DCT-IV) is defined as follows:
And its inverse transformation (IDCT-IV) is defined as:
Transformation dictionary of the two-dimentional Stationary Wavelet Transform as rarefaction representation useful signal is selected, for giving one-dimensional scale
Function phi (t) and wavelet function ψ (t), the scaling function and wavelet function of two-dimentional Stationary Wavelet Transform by φ (t) and ψ (t) with
The mode of tensor product obtains:
Two dimensional scaling function φ (x, y): φ (x, y)=φ (x) φ (y)；
Two-dimensional level direction wavelet function ΨH(x, y): ψH(x, y)=φ (x) ψ (y)；
Second vertical direction wavelet function ψV(x, y): ψV(x, y)=ψ (x) φ (y)；
Two-dimentional diagonal direction wavelet function ψD(x, y): ψD(x, y)=ψ (x) ψ (y).
Two-dimentional Stationary Wavelet Transform by the signal low frequency part of jth layer be decomposed into+1 layer of jth low frequency part and vertical, water
The high frequency section of gentle diagonal direction, the signal that wherein low frequency part of signal corresponds to behavior low frequency, is classified as low frequency；The water of signal
The signal that flat high frequency section corresponds to behavior low frequency, is classified as high frequency；The vertical high frequency part of signal corresponds to behavior high frequency, is classified as low frequency
Signal；The signal that the diagonal high frequency section of signal corresponds to behavior high frequency, is classified as high frequency.It is realized using A'trous algorithm steady small
Wave conversion defines filter group H and G, then HjAnd GjThe filter group for respectively representing the decomposition of jth layer, by each of H and G
2 are inserted between coefficientj- 1 zero obtains, for any j >=0, the direct transform of the Stationary Wavelet Transform of jth layer are as follows:
If HjAnd GjDual filter group be respectivelyWithThe Stationary Wavelet Transform of so available jth layer
Inverse transformation are as follows:
As shown in Figure 3 and Figure 4, the respectively discrete cosine transform atom of two dimension 8 × 8 and two-dimentional Stationary Wavelet Transform is former
Son, wherein the frequency of two-dimension discrete cosine transform atom in Fig. 3 its horizontal direction from left to right gradually rises, and from
The frequency of top to its following vertical direction gradually rises；Fig. 4 is that the two-dimentional Stationary Wavelet Transform of three different decomposition scales is former
Son has horizontal, vertical and diagonal three directions in each scale, complies fully with the requirement of anatomic element analysis theories, take
Obtain expected rarefaction representation and desired separating effect to unlike signal component.
According to anatomic element analysis theories, with the dictionary Φ selected above1I.e. two-dimentional Stationary Wavelet Transform and Φ2It is i.e. two-dimentional
Local discrete cosine transform constitutes super complete dictionary rarefaction representation signal s, calculates rarefaction representation coefficient:
In formula: x1For in reconstruction coefficients with Φ1Corresponding part；x2For in reconstruction coefficients with Φ2Corresponding part.For
Lagrange multiplier.The optimization problem is solved by coordinate Aries In The Block By Block Relaxation algorithm.
Using piecemeal coordinate relaxed algorithm to carrying out horizon slice to original seismic data data or whens waiting in step 02
Slicing treatment realizes the compacting of acquisition footprint, which is solved by coordinate Aries In The Block By Block Relaxation algorithm.Coordinate Aries In The Block By Block Relaxation is calculated
The basic thought of method is the calculating x of alternating iteration1And x2.Its main contents step are as follows:
Initialization: primary iteration step number k=0, initial solution
For indicating the coefficient initial solution of signal component 1,For indicating the coefficient initial solution of signal component 2；
Iteration: iterative steps k increases by 1 when every step iteration, and calculates:
In formula, TλFor hard threshold function；With Φ1A pair of positive inverse transformation is constituted,With Φ2Constitute a pair of positive inverse transformation；
Termination condition: whenWhen less than preset value, when influence of the continuation iteration to result is sufficiently small, iteration
It terminates；
Output:
For the final transformation coefficient of isolated signal component 1,For the final transformation coefficient of isolated signal component 2；
In piecemeal coordinate relaxed algorithm, hard threshold function formula is as follows:
In formula:For hard threshold function, λ is hard -threshold, is usually takenAccording to arranged from big to small
A value,For coefficient matrixElement, k=1,2 ..., N, N be coefficient matrix size, Φ be transformation dictionary, s
For time-domain signal.
As shown in fig. 6, the low cut-off frequency of the restructuring transformation of two dimension local discrete cosine transform is determined in step 103, it is main to wrap
Include following steps:
Step 301: being sliced whens taking M to wait 3-d seismic data set according to interval time Δ T for testing local cosine
The low cut-off frequency parameter of the restructuring transformation of transformation, their position is respectively t0,tΔT,t2ΔT,…,t(M-1)ΔT；
Step 302: for position tkΔT, k=0,1 ..., M-1 provide the restructuring transformation of two-dimentional local discrete cosine transform
A series of low cut-off frequency parameters, and be directed to each low cut-off frequency parameter, solve above-mentioned optimization problem obtain significant wave signal and
The separation of acquisition footprint noise；It is determined by the SNR estimation and compensation effect under comparison parameters and is obtained most preferably in current time location
The low cut-off frequency parameter of SNR estimation and compensation effect；
Step 303: linear interpolation method is utilized, according to time location tkΔT, k=0,1 ..., M-1 and its is corresponding low
Cut-off frequency parameter fkΔT, k=0,1 ..., M-1 are obtained more than the two-dimentional local Discrete of position of entire 3-d seismic data set other time
The low cut-off frequency parameter of the restructuring transformation of string transformation.
In the present embodiment, a kind of acquisition footprint drawing method based on anatomic element analysis is proposed, to reach
Effectively acquisition footprint purpose in compacting 3D seismic data.The invention has the following advantages:
Footprint is acquired to 3-d seismic data set using method of the invention to suppress, and can not only effectively be suppressed and be adopted
Collect footprint, removes part random noise and migration processing illusion, and useful signal has compared with hi-fi.
Above-mentioned transition structure and parameter determination method are specifically described below with reference to a specific embodiment, and the reality
Example is applied merely to more preferably illustrating the present invention, is not constituted improper limitations of the present invention.
Fig. 7 A is a main profile section of the marine three dimensional seismic data in certain oil field, and the acquisition time of the data is more early,
Due to being limited by acquisition technique at that time and acquisition instrument, the acquisition quality between different surveys line differs greatly, remote cable acquisition
Poor quality so that offset data influenced by acquisition footprint it is very serious；In addition, at sea earthquake-capturing process, often by
In the influence of seasonal law and ocean current, the temperature and salinity of seawater can all have a greater change, and be easy to cause the propagation of seismic wave
Speed changes to generate apparent acquisition footprint in method for marine seismic data.
As shown in Fig. 7 B and Fig. 7 C, this is contained at the earthquake record (Fig. 7 A) of acquisition footprint by the method for the invention
Reason, obtains the acquisition footprint noise of corresponding useful signal and removal.The method of the present invention can be effectively to acquisition footprint noise
It is suppressed, also removes part random noise and migration processing illusion, data that treated becomes more fully apparent, lineups
Continuity is stronger, so that having confirmed the method for the present invention has preferable significant wave signal fidelity.
The isochronous surface of 1.7s in Fig. 8 A 3-d seismic data set, it can be seen that acquisition footprint in the 3D data volume
Mainly along main profile directional spreding, and acquisition footprint phenomenon is clearly, causes to be difficult to determine this from original time slice
Kind of amplitude anomaly is to be caused by underground medium cross directional variations or the influence of acquisition footprint.
As shown in Fig. 8 B- Fig. 8 C, using method of the invention to the 3D data volume handled as a result, side of the present invention
Method has suppressed footprint noise well, and preferably maintains the various fine structure features of the significant wave signal in section.
In above model and real data example, become using the rarefaction representation of method construct acquisition footprint of the invention
It changes, footprint compacting is acquired to seismic data, can not only effectively suppress acquisition footprint noise, and useful signal
With compared with hi-fi, lay the foundation for the analysis of subsequent data.
Finally, it should be noted that model above and real data example be to the purpose of the present invention, technical solution and have
Beneficial effect provides further verifying, this only belongs to specific implementation example of the invention, the guarantor being not intended to limit the present invention
Protect range.All within the spirits and principles of the present invention, any modification made, improvement or equivalent replacement etc., should all be in this hair
In bright protection scope.
Claims (6)
1. a kind of acquisition footprint drawing method based on anatomic element analysis, which comprises the following steps:
Step 101: acquisition footprint waveform in the earthquake record being sliced according to the horizon slice of 3-d seismic data set or whens waiting
Morphological feature constructs two-dimentional local discrete cosine transform, and combines with two-dimentional Stationary Wavelet Transform and constitute super complete dictionary, simultaneously
Determine the decomposed class J of two dimension Stationary Wavelet Transform and the analysis window size W of two-dimentional local discrete cosine transform；
Step 102: in such a way that the initial data to 3-d seismic data set successively executes, in each horizon slice or waiting
When slice in using being acquired the preliminary compacting of footprint based on the method that anatomic element is analyzed；
Step 103: determining the low cut-off frequency of two dimension local discrete cosine transform；
Step 104: repeating step 102-103 until the processing completion of all slice of data, utilize the side analyzed based on anatomic element
Method carries out SNR estimation and compensation, suppresses acquisition footprint noise, the final compacting realized to acquisition footprint noise in 3-d seismic data set.
2. a kind of acquisition footprint drawing method based on anatomic element analysis as described in claim 1, which is characterized in that step
101, comprising:
Using the ingredient that the object that anatomic element is analyzed is containing two kinds with different shape feature:
S=s1+s2,
In formula: s indicates signal to be analyzed；s1、s2Indicate two kinds of ingredients with different shape feature in signal；It extracts respectively
s1、s2Both ingredients are the targets of anatomic element analysis；Assuming that s1And s2It can be respectively by dictionary Φ1And Φ2It is effective sparse
It indicates, but uses Φ2Rarefaction representation s1With with Φ1Rarefaction representation s2When sparsity it is poor；
Transformation dictionary of the two-dimentional Stationary Wavelet Transform as rarefaction representation useful signal ingredient is selected, wherein two-dimentional stationary wavelet is just
Transformation are as follows:
H in formulajAnd GjRespectively represent the filter group of jth layer decomposition；
The inverse transformation of two-dimentional Stationary Wavelet Transform are as follows:
In formulaWithRespectively represent HjAnd GjDual filter group；
Transformation dictionary of the two-dimentional local discrete cosine transform as rarefaction representation acquisition footprint is selected, wherein more than two-dimentional local Discrete
The direct transform of string transformation are as follows:
F (i, j) indicates signal to be analyzed in formula,Indicate the two-dimentional local discrete cosine transform system of signal to be analyzed
Number, k1,k2The total line number or total columns that=0,1 ... N-1, N are signal f to be analyzed；
The inverse transformation of two-dimentional local discrete cosine transform are as follows:
According to anatomic element analysis theories, with the dictionary Φ selected above1And Φ2, constitute super complete dictionary, rarefaction representation signal
S calculates rarefaction representation coefficient:
In formula: x1For in reconstruction coefficients with Φ1Corresponding part；x2For in reconstruction coefficients with Φ2Corresponding part；It is bright for glug
Day multiplier；The optimization problem is solved by coordinate Aries In The Block By Block Relaxation algorithm.
3. a kind of acquisition footprint drawing method based on anatomic element analysis as described in claim 1, which is characterized in that step
102 specifically include:
The step of piecemeal coordinate relaxed algorithm are as follows:
Initialization: primary iteration step number k=0, initial solution
For indicating the coefficient initial solution of signal component 1,For indicating the coefficient initial solution of signal component 2；
Iteration: iterative steps k increases by 1 when every step iteration, and calculates:
In formula, TλFor hard threshold function；With Φ1A pair of positive inverse transformation is constituted,With Φ2Constitute a pair of positive inverse transformation；
Termination condition: whenWhen less than preset value, when influence of the continuation iteration to result is sufficiently small, iteration is whole
Only；
Output:
For the final transformation coefficient of isolated signal component 1,For the final transformation coefficient of isolated signal component 2；
In piecemeal coordinate relaxed algorithm, hard threshold function formula is as follows:
In formula:For hard threshold function, λ is hard -threshold,For coefficient matrixElement, k=1,2 ..., N,
N is the size of coefficient matrix, and Φ is transformation dictionary, and s is time-domain signal.
4. a kind of acquisition footprint drawing method based on anatomic element analysis as described in claim 1, which is characterized in that step
103 specifically include:
Step 301: being sliced whens taking M to wait 3-d seismic data set according to interval time Δ T for testing Local Cosine Transform
Restructuring transformation low cut-off frequency parameter, their position is respectively t0,t∧T,t2ΔT,…,t(M-1)ΔT；
Step 302: for position tkΔT, k=0,1 ..., M-1 provide the one of the restructuring transformation of two-dimentional local discrete cosine transform
The low cut-off frequency parameter of series, and it is directed to each low cut-off frequency parameter, solve the separation for obtaining significant wave signal and acquisition footprint noise；
It is determined by the SNR estimation and compensation effect under comparison parameters and obtains low section of best SNR estimation and compensation effect in current time location
Frequency parameter fkΔT；
Step 303: linear interpolation method is utilized, according to time location tkΔT, k=0,1 ..., M-1 and its corresponding low cut-off frequency
Parameter fkΔT, k=0,1 ..., M-1 obtain the two-dimentional local Discrete Cosine change of position of entire 3-d seismic data set other time
The low cut-off frequency parameter of the restructuring transformation changed.
5. a kind of acquisition footprint drawing method based on anatomic element analysis as claimed in claim 3, which is characterized in that default
Value take 10-6。
6. a kind of acquisition footprint drawing method based on anatomic element analysis as claimed in claim 3, which is characterized in that hard threshold
Value λ takesAccording to arranged from big to smallA value.
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| CN112329595A (en) * | 2020-11-02 | 2021-02-05 | 中南大学 | Rock joint surface geometric morphology spectrum analysis and reconstruction method |
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