Essay: Seismic noise attenuation using 2D F-X Prediction Design Levinson-Durbin filter mode

Abstract:
The Seismic noise attenuation is very important for seismic data interpretation and analysis. In our paper, we propose a 2D F-X Prediction Design Levinson-Durbin filter mode method for2D seismic land data random noise attenuation by applying Design Levinson-Durbin filter The key idea of this paper is to consider that The FXDecon works on each frequency slice in the frequency spatial domain. And because the filter is based on a linear prediction theory, the filter is desired for linear events. Therefore, FXDecon is applied to a window of data with the assumption that inside the window the seismic events are approximately linear. The effects of F–X prediction are harsher on smaller windows when fewer traces and short time intervals. The big disadvantage of F–X is of course the inability to handle conflicting dips such as curving” structure, so split the data into sections each containing only consistent dips prior to inputting to F–X prediction. Our way is to improve the signal through using 2D F-X Prediction Design Levinson-Durbin filter mode and also compare the effect of the parameters on our signal .we took raw data then applied filter twice. The amplitude for was applying this filter was getting higher ,but when applied more than three times the single started effect and losing clear frequency .
Key words: FXDecon, Design Levinson-Durbin filter, Signal Enhancement
INTRODUCTION:
The f-x prediction technique was introduced by Canales (1984) and further developed by Gulunay (1986). The f-x domain prediction technique is also referred as f-x deconvolution by Gulunay (1986). Sacchi and Kuehl (2001) utilized the autoregressive-moving average (ARMA) structure of the signal to estimate a prediction error filter (PEF) and the noise sequence is estimated by self-deconvolving the PEF from the filtered data. Hodgson et al. (2002).
FXDecon calculates the filter that is based on filter theory (Canales, L.L. 1984, Random Noise Reduction, 54th Annual SEG meeting, Atlanta.)The FX-decon is a simple process that predicts linear events by making predictions in the (frequency-space) domain. FX-decon prediction process depends on the form of linear events in frequency versus x, x being the space direction. Given a linear event, the Fourier transform of this event is or . In x, the function is clearly periodic. To predict a linear event, a least squares prediction filter is calculated, using where f is the prediction filter, d is the desired output, and X is a matrix filled with shifted versions of the input series in x. indicates the transpose conjugate.
Following the nomenclature of Gulunay1986, d is the data shifted by one sample, or .The input data, forms the matrix X below:
X being a matrix of size (2n-1) by n. While d may be built with a longer shift, a shift of one sample is typically used. Process of applying the FX-decon starts by partitioning the data into windows small enough so events of interest appear linear. The data within each window are then Fourier transformed. For each frequency, a prediction filter is calculated and applied twice; once forward in space and once backwards. The two predictions are summed, the inverse Fourier transform applied, and the windows merged back into the output. The operations within each frequency are independent of other frequencies. This allows a large degree of freedom in the prediction of the output. Another interesting feature of the FX-decon process pointed out by Spitz 1991 involves the relationships of the response of a dip at one frequency to that at another frequency. A single dipping event is shown in time and after Fourier transformation of the time axis. It can be seen that the events are periodic both in frequency and in space. The periodicity at low frequency may be used to predict the shape of the higher frequency components and may be used to guide interpolation of events that are aliased in the high frequency components, but not aliased at low frequencies.
WORK METHOD
The Levinson–Durbin algorithm was proposed first by Norman Levinson in 1947, improved by James Durbin in 1960, and subsequently improved to 4n2 and then 3n2multiplications by W. F. Trench and S. Zohar, respectively.
Levinson recursion or Levinson–Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix. The algorithm runs in Θ(n2) time, which is a strong improvement over Gauss–Jordan elimination, which runs in Θ(n3).
Newer algorithms, called asymptotically fast or sometimes superfast Toeplitz algorithms, can solve in Θ(n logpn) for various p . Levinson recursion remains popular for several reasons; for one, it is relatively easy to understand in comparison; for another, it can be faster than a superfast algorithm for small n (usually n < 256).
Levinson solves the symmetric Toeplitz system of linear equations:
Where r = [r(1) … r(n+1)] is the input autocorrelation vector, and r(i)* denotes the complex conjugate of r(i). The input r is typically a vector of autocorrelation coefficients where lag 0 is the first element r(1). The algorithm requires O(n2) flops.
Here we are applying Levinson–Durbin filter and also see the effect of changing the parameter .The parameters can be display in following table (1).we can see the effect on raw data (fig (1)(a), (b) Amplitude spectral) after applying the filter on (fig 2, 3) and we comparing between raw 2d land data and after applying Levinson–Durbin algorithm difference can be seen on (fig2 (c) ).We applied same filter twice and the single amplitude increased on some prates and frequencies becomes more regular fig(6).
Our original parameters were filter length/traces, DESIGN TRACE WINDWO /TRACES, DESING TIME WINDOW/MS, End Frequency/HZ, Taper End Frequency/HZ as shows in tab(1). Then we increased the values of parameters to be twice of original parameters in first case fig (2 (c), (d)) and to be half of original parameters as second case also shows in tab (1) FIG(2,(e),(f)).The End Frequency/HZ should be only (0-10 HZ).
FX FILTER MODE FIKTER
LENGTH/TRACES DESIGN TRACE WINDWO /TRACES DESING
TIME WINDOW/MS End Frequency/
HZ Taper
End Frequency/HZ
Levinson-Durbin
3 100 200 100 10
6 200 400 200 10
1 50 100 50 10
TAB (1) SHOW Parameters used for FX filter Levinson–Durbin
(a) (b)
Fig (1) (a) Input data 2d crocked line, shot point N 16 with 300 traces, (b) Amplitude spectral for Input data 2d crocked line
(a) (b)
(©) (d)
(e) (f)
Fig (2), (a) Applying Levinson-Durbin, 1, FIKTER LENGTH/TRACES 3, (b) Amplitude spectral display in dB for Input data 2d crocked line after Applying Levinson-Durbin, FIKTER LENGTH/TRACES 3, (c) Applying Levinson-Durbin, 1, FIKTER LENGTH/TRACES 5,(d) Amplitude spectral for fig(c) ,(e) Applying Levinson-Durbin, 1, FIKTER LENGTH/TRACES 1 second case (f) Amplitude spectral for fig (e ).
(a) (b)
(c)
Fig (3) (a)Applying Levinson-Durbin, 1, FIKTER LENGTH/TRACES 3 for second time, (b)Difference between raw data and after applying Levinson-Durbin, 1, FIKTER LENGTH/TRACES 3, second time applied ,(c) Amplitude spectral display in dB ,and after applying Levinson-Durbin, FIKTER LENGTH/TRACES 3, second time applied.
Now to see the effect on amplitude we will compare the raw data with data after applied the Levinson–Durbin filter on analysis windows.
As we can see in amplitude –frequency window from 20H to 80 H ON frequency the single becomes more regular and at frequencies 20H TO 40 H it appeared to increase amplitude
Fig (4) Frequency analysis for 2d raw data
Fig (5) Frequency analysis after applying, Levinson-Durbin, 1, FIKTER LENGTH/TRACES 3
Fig (6) Frequency analysis after applying, Levinson-Durbin, 1, FIKTER LENGTH/TRACES 3
Second time applied filter.
(a) (b)
(c) (d)
Fig (7) (a) Difference Amplitude spectral display in dB between input data and after Applying Levinson-Durbin, (b) Difference Amplitude spectral dB between input data and after Applying Levinson-Durbin for second time. (c ) Difference Amplitude spectral display in dB between input data and after Applying Levinson first case ,(d) Difference Amplitude spectral display in dB between input data and after Applying Levinson second case.
CONCLUSIONS
In this paper, our way is to improve the signal through using 2D F-X Prediction Design Levinson-Durbin filter mode and also compare the effect of the filter to the raw data on our signal .we took raw data then applied throw flow unite and changing our parameters to see the difference and we find also As a general rule, the effects of F–X prediction are harsher on smaller windows – when was fewer traces and short time intervals. The big disadvantage of F–X is of course the inability to handle conflicting dips such as “curving” structure, so split the data into sections each containing only consistent dips prior to inputting to F–X prediction. The number of traces to use in design and application of the filter. In fact a 2–sided filter is used so that a value of 3 here would use 3 traces on each side of the trace being computed. Default = 3. As a rule of thumb make this number equal to the number of distinct sets of dipping events in the design window. It will usually be in the range of 3 to 5.
Number of traces in the design window this usually less than the total number of traces in the data set. And filters should be redesigned every 50 to 100 traces.
The End Frequency value acts as a high–cut filter, And It can also shorten the run time by only computing up to this value. As a result, in the same computation time, the algorithm in this paper can enhance the single and the effect can be see when applying frequency analysis window. Filter gave good result when we applied same filter for second time but then started effect to single frequencies and amplitude fig (6).
Acknowledgements
I would like to thank CREWES Project – University of Calgary for giving me permission to use their raw data.
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MOHAMED MHMOD, PHD, Jilin university Geoexploration science and technology ,Geophysics.
E-MAIL:baveciwan-23@hotmail.com