CN104849760A - Vector median filtering method based on Tau-p transformation - Google Patents
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Abstract
The invention discloses a vector median filtering method based on Tau-p transformation. The algorithm consists of two parts. In the first part, seismic data is transformed from a time-space domain to a Tau-p domain through Tau-p transformation, the instantaneous slopes of different waves are obtained in the Tau-p domain, the waves with different slopes are separated by windowing, and the data after separation is transformed to the time-space domain through Tau-p inverse transformation to obtain corresponding time-space domain data subsets; and in the second part, the moving direction of a filter time window is determined according to the instantaneous slopes obtained in the first part, vector median filtering is performed on the corresponding time-space domain data subsets, and finally, the data subsets after filtering are superposed to obtain seismic data after processing. By adopting the method of the invention, the problem that low-speed effective waves can be easily attenuated due to fixed window moving direction in a traditional vector median filtering method is solved, effective waves can be retained while noise is removed, and seismic data can be filtered and de-noised with high fidelity.
Description
Technical field
The present invention is a kind of Vector Median Filtering Method based on Tau-p conversion, realizes the high-fidelity filtering and noise reduction to geological data.
Background technology
In the wild in geological data, in order to eliminate the interference that direct wave and the reflection wave of refraction wave to shallow-layer cause.Conventional disposal route is directly excision, but while directly excising, excises the significant wave of offset distance far away possibly.At present, people more and more pay attention to the significant wave information of offset distance far away, and direct excision cannot reach the expectation of people.In order to while elimination direct wave and refraction wave interference, offset distance information far away can be protected not to be destroyed and excise even completely, the number of times using filter method to reach denoising object gets more and more.
Vector median filtering is a kind of multiparameter filtering based on sequence developed by medium filtering, and because it is at stress release treatment, there is good robustness on protection border, and it is relatively simple to realize structure, therefore in seismic data process, causes certain concern.But because Vector median filtering does not consider the velocity information of data, when processing the geological data containing low velocity ripple, seismic event gap time of arrival received due to each road wave detector is comparatively large, causes the problem of significant wave decay.
Before the object of this algorithm is Vector median filtering, Tau-p transfer pair geological data is used to carry out wave field separation, the geological data of different ripple can be obtained so respectively, the instantaneous slope to different ripple can be determined again, and then determine the direction of vector filtering window, make the correlativity of seismic event in vector filtering window the strongest, improve Vector median filtering to the filtering treatment effect of geological data.
Summary of the invention
This method can solve the problem that the lower significant wave of speed that in conventional vector median filtering algorithm, stationary window moving direction causes easily is attenuated, and can retain significant wave, realize the high-fidelity filtering and noise reduction to geological data while removal noise.
Basic performing step based on the Vector Median Filtering Method of Tau-p conversion is as follows:
Tau-p conversion fraction comprises:
Step one: the data d in temporal-spatial field territory is transformed to Frequency-Space Domain through FFT, obtains data D;
Step 2: the data D in Frequency-Space Domain is transformed to frequency-parameter field by Radon, obtains data M;
Step 3: the data M in frequency-parameter field is transformed to Tau-p territory by IFFT, obtains data DD;
Step 4: analyze the distribution form of DD in Tau-p territory, obtain the instantaneous slope of different ripple, and add window in Tau-p territory, different ripple is separated;
Step 5: by Tau-p inverse transformation by different ripple inverse transformation to temporal-spatial field, obtain the geological data X of different wavelength-division from rear correspondence
j, wherein j is the numbering of the geological data that different ripple is corresponding, and the total m of marking wave type;
Vector median filtering part comprises:
Step 6: from the wave field information be separated, select a jth geological data subset X
j, according to its instantaneous slope, design vector filtering window, wherein j corresponds to the numbering of geological data subset in step 5, and its initial value is 1;
Step 7: according to step 6 design vector filtering window from X
jmiddle taking-up data, and the mean value obtaining geological data in window;
Step 8: in calculation window, each data are to the distance of mean value is the intermediate value of data in this window apart from minimum data, and replaces window Central Plains central value to export, and moving window, until process X
jin all data;
Step 9: add 1 to j, repeats step 6 to step 8, until j is the sum of ripple type, namely all completes filtering to all ripples, all filtered geological data subsets superposed afterwards, obtain the geological data after final filtering process.
Further, in described step one, the concrete formula of FFT conversion and Fast Fourier Transform (FFT) is:
D＝Wd
Wherein d is the data matrix of the geological data composition of temporal-spatial field, and column vector represents the sequence of time-domain samples of per pass geological data, and row vector represents the sample sequence of each sampling instant not people having a common goal, and matrix dimension is N × Q, N is sampling number, and Q is earthquake number of channels; D is the Frequency-Space Domain data matrix after FFT conversion, and column vector represents the frequency domain sequence of per pass geological data, and row vector represents the sample sequence of not people having a common goal on each Frequency point, and matrix dimension is N × Q; W is Fourier transform matrix, and to be each element in this matrix of N × N be dimension
wherein n is positive integer, represents that time domain is counted and n=1,2 ... .N, k is positive integer, represents that frequency domain is counted and k=1,2 ... .N.
Further, in described step 2, use damped least square method, the data matrix D in Frequency-Space Domain is transformed to frequency-parameter field by Radon and obtains data matrix M, concrete form is:
Wherein λ
2for damping factor, I is the diagonal matrix of P × P, D
tthe transposition of D,
l
ktransposition, L
kfor conversion coefficient matrix corresponding to a kth Frequency point, its dimension are element in P × Q, matrix be
f
kfor the frequency values that a f-x territory kth Frequency point is corresponding, k=1,2 ..., N, p
ibe i-th ray parameter, i=1,2 ..., P, P are total number of ray parameter, x
qfor the spatial offset in q road in f-x territory, q=1,2 ..., Q.
Further, in described step 3, described IFFT is transformed to the inverse transformation of FFT conversion, and its concrete formula is:
Wherein W
hbe the conjugate transpose of W, counting of IFFT is consistent with FFT, and the data matrix DD obtained after inverse transformation is the Tau-p domain representation of geological data.
Further, in described step 4, in Tau-p territory, the geometric meaning of horizontal ordinate p is the instantaneous slope of corresponding point on the time-distance graph that shows before seismic event in temporal-spatial field, and the geometric meaning of ordinate Tau is the intercept that the time-distance graph that shows before seismic event in temporal-spatial field is corresponding; If the time-distance graph that in temporal-spatial field, seismic event wavefront shows is straight line, show as a point after conversion in Tau-p territory, the slope of straight line is different, and the abscissa positions that point is corresponding is also different; If the time-distance graph shown before seismic event in temporal-spatial field is hyperbolic curve, after conversion, in Tau-p territory, show as an ellipse; Because the time-distance graph of wavefront in temporal-spatial field is different, the instantaneous slope showed is also different, after adding window, various wavelength-division can be left in Tau-p territory.
Further, in described step 5, utilize window added in Tau-p territory, data in different ripple place windows are carried out Tau-p inverse transformation to temporal-spatial field, the concrete steps of its inverse transformation are, the conversion of FFT conversion-Radon inverse transformation-IFFT, after inverse transformation, obtain different wavelength-division from after geological data subset X
j, wherein j is the numbering of the geological data subset that dissimilar ripple is corresponding, and the total m of marking wave type.
Further, in described step 6, geological data subset X
jthe directivity of vector filtering window determined by the instantaneous slope of these data in Tau-p territory.
Further, in described step 7, in vector filtering window to data along from left to right, top-down order peek, and obtain the geological data subset X in window
jmean value
wherein x
ifor the data in vector filtering window, i=1,2 ..., n
1, n
1for the length that odd number is vector filtering window.
Further, in described step 8, in filter window, ask each data to the distance of mean value
represent and ask L norm, by the result of L norm as distance result of calculation, apart from geological data value in minimum corresponding vector filtering window as geological data intermediate value in this vector filtering window, the former central value in this vector filtering window is replaced to export, then this vector filtering window is moved a vector distance, until complete X by instantaneous slope direction
jthe filtering process of interior all data.
Further, in described step 9,1 is added to j, repeat step 6 to step 8, until j is ripple sum m, namely all filtering is completed to all geological datas, afterwards all filtered geological data subsets are superposed, obtain the geological data after final filtering process.
Technical scheme of the present invention, converted by Tau-p, first geological data is separated into the geological data subset with friction speed field information, and utilize the window direction of the instantaneous slope information design Vector median filtering of gained in Tau-p territory, medium filtering process is carried out to corresponding geological data subset, velocity of wave can be avoided to cross the situation causing useful signal to decay slowly, thus improve filter quality, realize high-fidelity filtering process.
Accompanying drawing explanation
Fig. 1 is the FB(flow block) of the Vector median filtering based on Tau-p conversion;
Fig. 2 is forward model and forming process thereof, wherein Fig. 2 (a) is a Tau-p numeric field data containing two pulses, Fig. 2 (b) is for just to drill by Fig. 2 (a) geological data obtained, and Fig. 2 (c) is for adding the Seismic forward data of random noise;
Fig. 3 for conventional vector filter method to add make an uproar after Seismic forward data with 3 × 3 filter window carry out the effect after filtering process, wherein Fig. 3 (a) is for carrying out once filtered effect, and Fig. 3 (b) is for carrying out five filtered effects;
Fig. 4 be with the Vector median filtering method converted based on Tau-p to add make an uproar after Seismic forward data with 3 × 3 filter window carry out the effect after filtering process, wherein Fig. 4 (a) is for carrying out once filtered effect, and Fig. 4 (b) is for carrying out five filtered effects.
Embodiment
Be described principle of the present invention below in conjunction with concrete method implementation process, example, only for explaining the present invention, is not intended to limit scope of the present invention.
Based on a Vector Median Filtering Method for Tau-p conversion, embodiment can be:
Step one: the data d in temporal-spatial field territory is transformed to Frequency-Space Domain through FFT, obtains data D;
Step 2: the data D in Frequency-Space Domain is transformed to frequency-parameter field by Radon, obtains data M;
Step 3: the data M in frequency-parameter field is transformed to Tau-p territory by IFFT, obtains data DD;
Step 4: analyze the distribution form of DD in Tau-p territory, obtain the instantaneous slope of different ripple, and add window in Tau-p territory, different ripple is separated;
Step 5: by Tau-p inverse transformation by different ripple inverse transformation to temporal-spatial field, obtain the geological data X of different wavelength-division from rear correspondence
j, wherein j is the numbering of the geological data that different ripple is corresponding, and the total m of marking wave type;
Step 6: from the wave field information be separated, select a jth geological data X
j, according to its instantaneous slope, design vector filtering window, wherein j corresponds to the numbering of geological data in step 5, and its initial value is 1;
Step 7: in vector filtering window to data along from left to right, top-down order peek, and obtain the geological data X in window
jmean value
wherein x
ifor the data in vector filtering window, i=1,2 ..., n
1, n
1for the length that odd number is vector filtering window.
Step 8: in calculation window, each vector is to the distance of mean vector is the vector median in this window apart from minimum vector, and replaces center vector to export, moving window, until process X
jin all data;
Step 9: add 1 to j, repeats step 6 to step 8, until j is the sum of ripple type, namely all completes filtering to all ripples, superposed by all filtered T-X curves afterwards, obtain the geological data after final filtering process.
Adopt Vector Median Filtering Method respectively below, and adopt the Vector Median Filtering Method based on Tau-p conversion of the present invention to add to make an uproar to one and just drill data and carry out filtering, and result is compared:
One, just data are drilled
Just drilling linear events different containing 2 slopes in data, they intersect a point of crossing, is just drilling data as shown in Fig. 2 (a).This is shown as two points, as shown in Fig. 2 (b) after just drilling data Tau-p conversion in Tau-p territory.Data in Fig. 2 (a) add random noise, obtain adding just drilling data, as shown in Fig. 2 (c) after making an uproar.
Two, conventional vector median-filtered result
With the filter window of 3 × 3, filtering process is carried out to adding the forward model after making an uproar with conventional vector median filtering method, as shown in Figure 3, wherein Fig. 3 (a) is for carrying out once filtered effect for result, and Fig. 3 (b) is for carrying out five filtered effects.
Three, based on the Vector median filtering result of Tau-p conversion
With the filter window of 3 × 3, filtering process is carried out to adding the Seismic forward data after making an uproar according to by the Vector median filtering method converted based on Tau-p, the geological data subset wherein obtained in step 5 is 2, length of window in step 7 is 3 × 3=9, result after filtering process as shown in Figure 4, wherein Fig. 4 (a) is for carrying out once filtered effect, and Fig. 4 (b) is for carrying out five filtered effects.
Analysis and summary:
Conventional vector medium filtering and based on Tau-p conversion Vector median filtering result as shown in Figure 3 and Figure 4, relatively two figure, we can find out, Vector median filtering effect based on Tau-p conversion obviously will be better than the appropriate medium filtering of tradition, after comparison diagram 3 (b) and Fig. 4 (b), we can find out, the robustness based on the Vector median filtering of Tau-p conversion obviously will be better than the appropriate medium filtering of tradition.
To sum up, the Vector median filtering based on Tau-p conversion is a kind of effective novel filtering method of one improving Vector median filtering, can realize the high-fidelity filtering process to geological data.
The foregoing is only and realize preferred embodiments of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.
Claims (10)
1. the Vector Median Filtering Method based on Tau-p conversion, for seismic data process, realize, to the high-fidelity filtering and noise reduction of geological data, it is characterized in that, comprise Tau-p conversion fraction and Vector median filtering two parts, wherein said Tau-p conversion fraction comprises:
Step one: the data d in temporal-spatial field territory is transformed to Frequency-Space Domain through FFT, obtains data D;
Step 2: the data D in Frequency-Space Domain is transformed to frequency-parameter field by Radon, obtains data M;
Step 3: the data M in frequency-parameter field is transformed to Tau-p territory by IFFT, obtains data DD;
Step 4: analyze the distribution form of DD in Tau-p territory, obtain the instantaneous slope of different ripple, and add window in Tau-p territory, different ripple is separated;
Step 5: by Tau-p inverse transformation by different ripple inverse transformation to temporal-spatial field, obtain the geological data subset X of different wavelength-division from rear correspondence
j, wherein j is the numbering of the geological data subset that different ripple is corresponding, and the total m of marking wave type;
Described Vector median filtering part comprises:
Step 6: from the wave field information be separated, select a jth geological data subset X
j, according to its instantaneous slope, design vector filtering window, wherein j corresponds to the numbering of geological data subset in step 5, and its initial value is 1;
Step 7: according to step 6 design vector filtering window from X
jmiddle taking-up data, and the mean value obtaining geological data in window;
Step 8: in calculation window, each data are to the distance of mean value is the intermediate value of data in this window apart from minimum data, and replaces window Central Plains central value to export, and moving window, until process X
jin all data;
Step 9: add 1 to j, repeats step 6 to step 8, until j equals the total m obtained in step 5, namely all completes filtering to all ripples, superposed by all filtered T-X curves afterwards, obtain the geological data after final filtering process.
2. the method for claim 1, is characterized in that, in described step one, the concrete formula of FFT conversion and Fast Fourier Transform (FFT) is:
D＝Wd
Wherein d is the data matrix of the geological data composition of temporal-spatial field, and column vector represents the sequence of time-domain samples of per pass geological data, and row vector represents the sample sequence of each sampling instant not people having a common goal, and matrix dimension is N × Q, N is sampling number, and Q is earthquake number of channels; D is the Frequency-Space Domain data matrix after FFT conversion, and column vector represents the frequency domain sequence of per pass geological data, and row vector represents the sample sequence of not people having a common goal on each Frequency point, and matrix dimension is N × Q; W is Fourier transform matrix, and to be each element in this matrix of N × N be dimension
wherein n is positive integer, represents that time domain is counted and n=1,2 ... .N, k are positive integer, represent that frequency domain is counted and k=1,2 ... .N.
3. the method for claim 1, is characterized in that, in described step 2, use damped least square method, the data matrix D in Frequency-Space Domain is transformed to frequency-parameter field by Radon and obtains data matrix M, concrete form is:
Wherein λ
2for damping factor, I is the diagonal matrix of P × P, D
tthe transposition of D,
l
ktransposition, L
kfor conversion coefficient matrix corresponding to a kth Frequency point, its dimension are element in P × Q, matrix be
f
kfor the frequency values that a f-x territory kth Frequency point is corresponding, k=1,2 ..., N, p
ibe i-th ray parameter, i=1,2 ..., P, P are total number of ray parameter, x
qfor the spatial offset in q road in f-x territory, q=1,2 ..., Q.
4. the method for claim 1, is characterized in that, in described step 3, described IFFT is transformed to the inverse transformation of FFT conversion, and its concrete formula is:
Wherein W
hbe the conjugate transpose of W, counting of IFFT is consistent with FFT, and the data matrix DD obtained after inverse transformation is the Tau-p domain representation of geological data.
5. the method for claim 1, it is characterized in that, in described step 4, in Tau-p territory, the geometric meaning of horizontal ordinate is the instantaneous slope of corresponding point on the time-distance graph that shows before seismic event in temporal-spatial field, and the geometric meaning of ordinate is the intercept that this curve is corresponding; If the time-distance graph that in temporal-spatial field, seismic event wavefront shows is straight line, show as a point after conversion in Tau-p territory, the slope of straight line is different, and the abscissa positions that point is corresponding is also different; If the time-distance graph shown before seismic event in temporal-spatial field is hyperbolic curve, after conversion, in Tau-p territory, show as an ellipse; Because the time-distance graph of wavefront in temporal-spatial field is different, the instantaneous slope showed is also different, after adding window, various wavelength-division can be left in Tau-p territory.
6. the method for claim 1, it is characterized in that, in described step 5, utilize window added in Tau-p territory, data in the window of various ripple places are carried out Tau-p inverse transformation to temporal-spatial field, and the concrete steps of its inverse transformation are, FFT conversion-Radon inverse transformation-IFFT conversion, after inverse transformation, obtain the geological data subset X of dissimilar wavelength-division from rear all kinds of ripple
j, wherein j is the numbering of the geological data that dissimilar ripple is corresponding, and the total m of marking wave type.
7. the method for claim 1, is characterized in that, in described step 6, and geological data subset X
jthe directivity of vector filtering window determined by the instantaneous slope of these data in Tau-p territory.
8. the method for claim 1, is characterized in that, in described step 7, in vector filtering window to data along from left to right, top-down order peek, and obtain the geological data subset X in window
jmean value.
9. the method for claim 1, it is characterized in that, in described step 8, in filter window, ask each data to the distance of mean value, be geological data intermediate value in this filter window apart from minimum data value, replace the former central value in this filter window to export, then this filter window is moved a vector distance, until complete X by slope direction
jthe filtering process of interior all data.
10. the method for claim 1, is characterized in that, in described step 9,1 is added to j, repeats step 6 to step 8, until j equals the total m in step 5, all filtered geological data subsets are superposed, obtains the geological data after final filtering process.
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