Transcript 幻灯片 1 - University of Houston

Advisor: John P. Castagna
nd
May 2 2012
 Background---STFT, CWT and MPD
 Fractional Matching Pursuit Decomposition
 Computational Simulation
 Results: MPD versus FMPD
 Conclusion
2
 Background---STFT, CWT and MPD
 Fractional Matching Pursuit Decomposition
 Computational Simulation
 Results: MPD versus FMPD
 Conclusion
3
THE NEED FOR TIME FREQ ANALYSIS
1. Localized information is valuable
2. Fourier Transform: information of stationary signals
3. Seismic Signals: NON-STATIONARY
Stationary Signal: constant statistical parameters over time
Short Time Fourier Transform(STFT): Primary solution
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SHORT TIME FOURIER TRANSFORM(STFT)
1. Break into segments
2. Applied FT on each segment
3. Lay out the spectrum along time
4. Display all the spectra
Assumption: truncated signals are stationary
Con: window determine combined resolution
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WAVELET TRANSFORM(WT)
1. Cross correlation
2. Display the coefficients
Continuous WT: sliding wavelet
Discrete WT: segments (correlate the segments with
wavelet at the same time)
How much does the trace resemble the adjusted
mother wavelet
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MATCHING PURSUIT(MP)
1.
Cross correlation
2.
Subtract best matched wavelet
3.
Iteration
4.
FT on matched wavelet and project along time
5.
Display
Matching Pursuit: a combination of WT & STFT
Easy reconstruction
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 Background---STFT, CWT and MPD
 Fractional Matching Pursuit Decomposition
 Computational Simulation
 Results: MPD versus FMPD
 Conclusion
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FRACTIONAL MPD
1. Regression: stability problem
2. Subtract the matched wavelet with a portion of the
coefficient
 FMPD: much more laterally stable
 Mitigate the interference effect
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 Background---STFT, CWT and MPD
 Fractional Matching Pursuit Decomposition
 Computational Simulation
 Results: MPD versus FMPD
 Conclusion
10
ALGORITHM
Input seismic
trace
correlation
Wavelet Dictionary
Wavelet=Ricker(f)
Best Matched
Wavelet
energy>threshold
subtraction
Residual
Trace
energy<threshold
Residual
summation
Reconstructed
trace 11
 Background---STFT, CWT and MPD
 Fractional Matching Pursuit Decomposition
 Computational Simulation
 Results: MPD versus FMPD
 Conclusion
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Ricker Criterion
Rayleigh Criterion
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Ricker Criterion
Rayleigh Criterion
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wedgemodel pos+neg
50
100
time sample
150
200
250
300
350
400
0
5
10
15
20
25
30
trace number
35
40
45
50
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section 50Hz inline 30 MPD
section 50Hz inline 30 FMPD
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timeslice 34 50Hz MPD
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timeslice 34 50Hz FMPD
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 Background---STFT, CWT and MPD
 Fractional Matching Pursuit Decomposition
 Computational Simulation
 Results: MPD versus FMPD
 Conclusion
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CONCLUSION
Matching Pursuit Decomposition is laterally unstable
Fractional Matching Pursuit Decomposition solves the problem
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60Hz Ricker
Questions? Comments?
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MOTIVATION
1. Alternative time frequency analysis method
2. New representation provides new perspective new attributes
3. Convolution model base
4. Extracted wavelet---Ricker like
5. Application: Gas Brine differentiation; channel detection
6. Simple representation---more to discover
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windowed cos wavelet by bell function/window size=200
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
amplitude
amplitude
windowed cos wavelet by bell function/window size=80
1
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
-0.25 -0.2 -0.15 -0.1 -0.05
0
0.05 0.1 0.15 0.2
time(s)
spectrum of windowed wavelet/window size=80
-1
0.25
-0.25 -0.2 -0.15 -0.1 -0.05
0
0.05
time(s)
0.1
0.15
0.2
0.25
spectrum of windowed wavelet/window size=200
90
200
80
180
160
60
140
50
120
amplitude
amplitude
70
40
100
80
30
60
20
40
10
0
20
0
5
10
15
20
25
30
Frequency(Hz)
35
40
45
50
0
0
5
10
15
20
25
30
Frequency(Hz)
35
40
33
45
50
wedgemodel pos+pos
50
100
time sample
150
200
250
300
350
400
0
5
10
15
20
25
30
trace number
35
40
45
50
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