Post on 23-Feb-2016
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Fractional Matching Pursuit Decomposition
(FMPD)Mingyong Chen
May 2nd 2012Advisor: John P. Castagna
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion2
Contents
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion3
Contents
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
THE NEED FOR TIME FREQ ANALYSIS
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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 5
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 6
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 7
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion8
Contents
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
Conclusion10
Contents
ALGORITHMInput
seismic trace
Wavelet Dictionary
Wavelet=Ricker(f)
Best Matched Wavelet
ResidualReconstruct
ed trace
Residual Trace
correlation
subtractionenergy>threshold
energy<threshold
summation
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Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion12
Contents
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Ricker Criterion
Rayleigh Criterion
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Ricker Criterion
Rayleigh Criterion
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180 5 10 15 20 25 30 35 40 45 50
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wedgemodel pos+neg
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section 50Hz inline 30 FMPD
section 50Hz inline 30 MPD
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timeslice 34 50Hz MPD
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timeslice 34 50Hz FMPD
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion24
Contents
CONCLUSION
Matching Pursuit Decomposition is laterally unstable
Fractional Matching Pursuit Decomposition solves the problem
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Questions? Comments?
60Hz Ricker
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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 32
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