CN108680953A - A kind of seismic data based on inverse proportion model interpolation and denoising method simultaneously - Google Patents
A kind of seismic data based on inverse proportion model interpolation and denoising method simultaneously Download PDFInfo
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Abstract
The present invention relates to a kind of seismic data based on inverse proportion model while interpolation and denoising method, steps：Initial irregularities Noise seismic data is inputted, positive Seislet transformation is carried out to the data of input, sparse expression has been obtained after input data is transformed to the domains Seislet；The Seislet coefficients that threshold value is remained larger than by threshold operator, will be less than the Seislet coefficient zero setting of threshold value；Anti- Seislet is carried out to the Seislet coefficients after threshold process and is transformed back to time-domain；Weighted factor is determined according to inverse proportion model；POCS algorithms are chosen as iterative algorithm, according to the value of iterative formula and weighted factor, the data that the time numeric field data that inverse transformation is obtained retains according to weighted factor selection, original observation data are returned according to the ratio of the weight of weighted factor in the data after being added to anti-Seislet transformation, and the reconstructed results of current iteration are obtained；Final reconstructed results are exported after successive ignition, so that the data of missing is reconstructed, noise is also suppressed.The present invention can reach preferable under different noise intensities and rebuild effect and ensure computational efficiency.
Description
Technical field
The present invention relates to a kind of Seismic Data Processing Technique fields, can adapt to different noise circumstances especially with regard to one kind
The seismic data based on inverse proportion model simultaneously interpolation and denoising method.
Background technology
The interpolation reconstruction of seismic data and denoising are a very important links in seismic data pre-stack processing flow.By
In barrier, weathered zone, the factors such as economic cost, the seismic data of field acquisition is typically irregular.Irregular earthquake number
According to the generation that can lead to alias, to which to follow-up processing flow such as SRME multiple removals, 3D offsets and imaging etc. cause not
Good influence.
In order to make seismic data regularization, our some commonly used mathematical algorithms come to the seismic channel of missing into row interpolation
It rebuilds.Interpolation method based on sparse transformation is widely used a kind of algorithm, and wherein POCS algorithms are with its easy spy
It puts and enjoys great popularity.POCS algorithms originate from image processing field, in 2006 by first Application to Reconstruction of seismic data field
(Abma and Kabir,2006).One of the shortcomings that POCS algorithms is exactly that noise immunity is poor.In order to reduce shadow of the noise to reconstruction
It rings, Oropeza and Sacchi (2011) introduces weight factor and seeks weight factor using a linear model.Gao
Et al (2013) further demonstrate weighting POCS algorithms advantage of tradition POCS algorithms relatively when rebuilding Noise Data.
Ge Zijian etc. (2015) is proposed calculates weight factor using data-driven model, but with the change of noise grade, it should
Method cannot be guaranteed the reconstruction data for obtaining high s/n ratio.
Since existing several methods of weighting do not have good noise adaptation, we have proposed one kind being based on inverse proportion
The method of the calculating weighted factor of model, applies it in weighting POCS algorithms and carries out weight to missing Noise seismic data
It builds.Changed with the value of iterations by controlling weighted factor, our method all achieves under different noise circumstances
Good reconstruction effect.
Invention content
In view of the above-mentioned problems, the object of the present invention is to provide a kind of seismic data based on inverse proportion model simultaneously interpolation with
Denoising method, energy Noise missing seismic data is rebuild, while suppressing noise, preferably adapts to different noises etc.
Grade, when ambient noise changes, good reconstruction effect still can be obtained by adjusting weighted factor.
To achieve the above object, the present invention takes following technical scheme：A kind of seismic data based on inverse proportion model is same
When interpolation and denoising method comprising following steps：1) input initial irregularities Noise seismic data, to the data of input into
The positive Seislet transformation of row, sparse expression has been obtained after input data is transformed to the domains Seislet；2) it is protected by threshold operator
The Seislet coefficients more than threshold value are stayed, it will be less than the Seislet coefficient zero setting of threshold value；3) to the Seislet systems after threshold process
Number carries out anti-Seislet and converts to obtain the data of time-domain；4) weighted factor is determined according to inverse proportion model；5) according to weighting
The iterative formula of POCS algorithms and the value of weighted factor, by the time numeric field data obtained in step 3) according to determining weighting because
Son retains according to the ratio of (I- α R), and original observation data are returned according to the ratio of the weight of weighted factor is added to anti-Seislet transformation
In data afterwards, the reconstructed results of current iteration are obtained；And judge whether k is less than preset maximum iteration N, it is less than
Then return to step 1), then using reconstructed results as the input of next iteration, continue iteration, it is on the contrary then export final reconstructed results,
The data of missing are made to be reconstructed, noise is also suppressed；Wherein, I is unit matrix；R is sampling matrix.
Further, in the step 1), if it is the 1st iteration, then original observed data d is inputtedobs。
Further, in the step 2), using index hard -threshold model come the size of threshold value, threshold size is with iteration
Number and convert, the threshold tau selected by kth time iterationkFor：
τk=τiec(k-1)/(N-1), c=ln (τf/τi), k=1,2 ..., N.
Wherein, N is preset maximum iteration；K is iterations；τiFor initial threshold；τfTo terminate threshold value.
Further, in the step 4), the value of weighted factor is determined by following inverse proportion model：
Wherein, k is iterations, and the factor, controlling elements q are used for determining the fall off rate of weighted factor to q in order to control.
Further, the controlling elements q is determined according to the noise intensity of seismic data.
Further, in the step 5), the iterative formula of weighting POCS algorithms is：
In formula, mnIt is the reconstructed results after nth iteration；dobsIt is observation data；S is Seislet direct transforms；S-1For
Seislet inverse transformations；For hard -threshold operator；α is weighted factor, and size is between 0 and 1, specific value and ambient noise
Intensity it is related.
Further, the hard -threshold operatorFor：
Wherein, xkFor Seislet coefficients.
The invention adopts the above technical scheme, which has the following advantages：1, the present invention is used as weight using POCS algorithms
Algorithm is built, sparse transformation selects Seislet transformation, threshold model to use index threshold model.In order to be suppressed while rebuilding
Noise introduces weighted factor, and by inverse proportion model cootrol weighted factor with the fall off rate of iterations, to real
Seismic data interpolation and the denoising simultaneously that can adapt to ambient noise variation is showed.2, the present invention determines according to inverse proportion model and adds
Weight factor, can according to the substantially intensity of ambient noise come control weighted factor value change, relative to it is existing it is several plus
Power method can preferably adapt to different noise grades, when ambient noise changes, still can be taken by adjusting weighted factor
Obtain good reconstruction effect.3, the present invention determines weighted factor according to inverse proportion model, compensates for existing linear model, number
According to deficiency of the driving model in terms of noise adaptation, it can reach preferable under different noise intensities and rebuild effect and protect
Demonstrate,prove computational efficiency.4, the present invention introduces weighted factor to suppress noise, and the value of weighted factor is determined by inverse proportion model.
Description of the drawings
Fig. 1 is the overall flow schematic diagram of the present invention；
Fig. 2 is complete muting simulation seismic data；
Fig. 3 is the 50% irregular simulation seismic data for lacking and adding random noise；
Fig. 4 is to utilize the reconstructed results after the method for the present invention iteration 30 times to Fig. 3 data；
When Fig. 5 is that noise grade is higher, the signal-to-noise ratio recovery curve comparison diagram of each method of weighting reconstruction；
When Fig. 6 is that noise grade is medium, the signal-to-noise ratio recovery curve comparison diagram of each method of weighting reconstruction；
When Fig. 7 is that noise grade is relatively low, the signal-to-noise ratio recovery curve comparison diagram of each method of weighting reconstruction；
Fig. 8 is the actual seismic data of complete not Noise；
Fig. 9 is the 30% irregular actual seismic data for lacking and adding random noise；
Figure 10 is the result after being rebuild using the method for the present invention；
Figure 11 is the signal-to-noise ratio recovery curve comparison diagram after different weights method rebuilds Fig. 9 real data respectively.
Specific implementation mode
The present invention is described in detail below with reference to the accompanying drawings and embodiments.
As shown in Figure 1, the present invention provides a kind of seismic data based on inverse proportion model interpolation and denoising method simultaneously, it should
Method uses convex set projection algorithm for reconstructing, in each iteration, changes commanders input signal in Seislet by Seislet changes first
It is sparse in domain to show, the coefficient of threshold value is remained larger than by threshold operator, then anti-Seislet is carried out to the coefficient of reservation
It is transformed back to time-domain, according to the intensity of ambient noise, determines the value of a suitable controlling elements q, according to inverse proportion model,
Determine the value of the weighted factor of each iteration.Further according to the iterative formula of weighting POCS algorithms, corresponding data reservation is carried out
It returns and adds with the part of former observation data, obtain the reconstructed results of the secondary iteration, next iteration is carried out as input.By
The reconstruction of missing seismic data and the compacting of noise may be implemented in enough iteration.
The present invention specifically includes following steps：
1) initial irregularities Noise seismic data is inputted, positive Seislet transformation is carried out to the data of input, number will be inputted
According to having obtained sparse expression after transforming to the domains Seislet；Wherein, if it is the 1st iteration, then original observed data is inputted
dobs；
2) threshold process：The Seislet coefficients that threshold value is remained larger than by threshold operator, will be less than the Seislet of threshold value
Coefficient zero setting；
In the present embodiment, using index hard -threshold model come the size of threshold value, threshold size with iterations and
It converts, the threshold tau selected by kth time iterationkCalculation formula be：
τk=τiec(k-1)/(N-1), c=ln (τf/τi), k=1,2 ..., N.
Wherein, N is preset maximum iteration；K is iterations；τiFor initial threshold, generally select maximum
Coefficient is as initial threshold；τfTo terminate threshold value, it is usually chosen to a small value close or equal to zero.With iterations going on,
Threshold size exponentially decays to termination threshold value from initial threshold.
3) anti-Seislet is carried out to the Seislet coefficients after threshold process to convert to obtain the data of time-domain
4) good reconstructed results in order to obtain, need that the value of weighted factor is allowed as iteration is descending to successively decrease, then root
The value of weighted factor is determined according to inverse proportion model；
The specific value of weighted factor is determined by following inverse proportion model：
Wherein, k is iterations, and the factor, controlling elements q are used for determining the fall off rate of weighted factor to q in order to control, generally
From the value for selecting q between 0 and 1.
The noise intensity according to seismic data is needed to determine the value of q：If noise intensity is higher, selection one is needed
A larger q values (such as 0.8 or so), so striked weighted factor can rapidly decline in preceding iteration several times；If
Noise intensity is medium, then the accordingly value (substantially being chosen between 0.3-0.6) of adjustment q, makes weighted factor with slightly gentle
Rate decline；If noise intensity is weaker, the smaller q values (such as 0.15 or so) of corresponding selection, make weighted factor with
More gentle rate declines.It should be noted that judgement only qualitatively estimation of this method to environmental noise level, therefore
The selection of q values may be needed to attempt and adjust several times, q value selection ranges are not limited to the aforementioned selection range provided.
After selected q values, the weighted factor of each iteration can also be determined by inverse proportion model.
5) according to the value of the iterative formula and weighted factor of weighting POCS algorithms, the time-domain number that will be obtained in step 3)
According toRetained according to the ratio of (I- α R) according to the weighted factor determined in step 4), original observation data are according to weighting
The ratio of the weight of factor-alpha is returned in the data after being added to anti-Seislet transformation, and the reconstructed results of current iteration are obtained；And judge k
Whether it is less than preset maximum iteration N, is less than then return to step 1), then using reconstructed results as the defeated of next iteration
Enter, continues iteration, it is on the contrary then export final reconstructed results；By enough iteration, the data of missing are reconstructed, and noise also obtains
To compacting.
Above-mentioned steps 5) in, the iterative formula of weighting POCS algorithms is：
In formula, mnIt is the reconstructed results after nth iteration；dobsIt is observation data；I is unit matrix；R is sampling matrix；
S is Seislet direct transforms；S-1For Seislet inverse transformations；For hard -threshold operator；α is weighted factor, size between 0 and 1 it
Between, specific value is related with the intensity of ambient noise.
Wherein, hard -threshold operatorExpression formula it is as follows：
Wherein, xkFor Seislet coefficients.
Embodiment：
It is further illustrated below by the example of numerical simulation and real data.As shown in Fig. 2, being original complete simulation
Seismic channel carries out 50% missing at random to it and adds random noise (as shown in Figure 3), with the weighting based on inverse proportion model
POCS algorithms rebuild it, and the reconstructed results after iteration 30 times are as shown in Figure 4, it can be seen that the seismic channel of missing is weighed
It builds, and most of noise is suppressed.Continue reconstruction knot of more several different weights models under 3 kinds of different noise circumstances
Fruit.Reconstruction quality is compared by calculating signal-to-noise ratio and drawing SNR curves.From Fig. 5, Fig. 6 and Fig. 7 can be seen that by adjusting
The value of controlling elements q, method of the invention has under 3 kinds of different noise circumstances rebuilds effect well.It is observed that
Although linear model can finally obtain the reconstructed results of high s/n ratio, under the higher environment of noise intensity, convergence
Speed ratio inverse proportion model is many slowly, and data-driven model is good in the higher reconstruction quality of noise intensity, still
When noise intensity is relatively low, reconstructed results are undesirable.Finally, it is verified by real data.As shown in figure 8, being
Whole noiseless actual seismic data remove 30% seismic channel and add random noise (as shown in Figure 9), are added respectively with four kinds
Power method rebuilds it；As shown in Figure 10, it is the reconstructed results of method proposed by the present invention, it can be seen that it is good to rebuild effect
It is good.The method of weighting based on inverse proportion model, which is can be seen that, from the signal-to-noise ratio recovery correlation curve in Figure 11 compares other methods,
Higher signal-to-noise ratio can be reached.
The various embodiments described above are merely to illustrate the present invention, and each step may be changed, in the technology of the present invention
On the basis of scheme, all improvement carried out to separate step according to the principle of the invention and equivalents should not be excluded in this hair
Except bright protection domain.
Claims (7)
1. a kind of seismic data based on inverse proportion model while interpolation and denoising method, it is characterised in that include the following steps：
1) initial irregularities Noise seismic data is inputted, positive Seislet transformation is carried out to the data of input, input data is become
Sparse expression has been obtained after changing to the domains Seislet；
2) the Seislet coefficients that threshold value is remained larger than by threshold operator, will be less than the Seislet coefficient zero setting of threshold value；
3) anti-Seislet is carried out to the Seislet coefficients after threshold process to convert to obtain the data of time-domain；
4) weighted factor is determined according to inverse proportion model；
5) according to the value of the iterative formula and weighted factor of weighting POCS algorithms, the time numeric field data root that will be obtained in step 3)
Retain according to the ratio of (I- α R) according to determining weighted factor, original observation data are returned according to the ratio of the weight of weighted factor to be added
In data after being converted to anti-Seislet, the reconstructed results of current iteration are obtained；And judge k whether be less than it is preset most
Big iterations N, is less than then return to step 1), then using reconstructed results as the input of next iteration, continue iteration, it is on the contrary then defeated
Go out final reconstructed results, so that the data of missing is reconstructed, noise is also suppressed；Wherein, I is unit matrix；R is sampling square
Battle array.
2. method as described in claim 1, it is characterised in that：In the step 1), if it is the 1st iteration, then input original
Observe data dobs。
3. method as described in claim 1, it is characterised in that：In the step 2), threshold is determined using index hard -threshold model
The size of value, threshold size are converted with iterations, the threshold tau selected by kth time iterationkFor：
τk=τiec(k-1)/(N-1), c=ln (τf/τi), k=1,2 ..., N.
Wherein, N is preset maximum iteration；K is iterations；τiFor initial threshold；τfTo terminate threshold value.
4. method as described in claim 1, it is characterised in that：In the step 4), the value of weighted factor is by following inverse proportion
Model determines：
Wherein, k is iterations, and the factor, controlling elements q are used for determining the fall off rate of weighted factor to q in order to control.
5. method as claimed in claim 4, it is characterised in that：The controlling elements q is according to the noise intensity of seismic data come really
It is fixed.
6. method as described in claim 1, it is characterised in that：In the step 5), the iterative formula of weighting POCS algorithms is：
In formula, mnIt is the reconstructed results after nth iteration；dobsIt is observation data；S is Seislet direct transforms；S-1For Seislet
Inverse transformation；For hard -threshold operator；α is weighted factor, and between 0 and 1, the intensity of specific value and ambient noise has size
It closes.
7. method as claimed in claim 6, it is characterised in that：The hard -threshold operatorFor：
Wherein, xkFor Seislet coefficients.
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