Fractional Matching Pursuit Decomposition (FMPD)
description
Transcript of Fractional Matching Pursuit Decomposition (FMPD)
![Page 1: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/1.jpg)
Fractional Matching Pursuit Decomposition
(FMPD)Mingyong Chen
May 2nd 2012Advisor: John P. Castagna
![Page 2: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/2.jpg)
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion2
Contents
![Page 3: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/3.jpg)
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion3
Contents
![Page 4: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/4.jpg)
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
4
![Page 5: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/5.jpg)
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
![Page 6: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/6.jpg)
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
![Page 7: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/7.jpg)
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
![Page 8: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/8.jpg)
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion8
Contents
![Page 9: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/9.jpg)
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
9
![Page 10: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/10.jpg)
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion10
Contents
![Page 11: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/11.jpg)
ALGORITHMInput
seismic trace
Wavelet Dictionary
Wavelet=Ricker(f)
Best Matched Wavelet
ResidualReconstruct
ed trace
Residual Trace
correlation
subtractionenergy>threshold
energy<threshold
summation
11
![Page 12: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/12.jpg)
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion12
Contents
![Page 13: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/13.jpg)
1313
![Page 14: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/14.jpg)
1414
![Page 15: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/15.jpg)
15
![Page 16: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/16.jpg)
Ricker Criterion
Rayleigh Criterion
16
![Page 17: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/17.jpg)
Ricker Criterion
Rayleigh Criterion
17
![Page 18: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/18.jpg)
180 5 10 15 20 25 30 35 40 45 50
50
100
150
200
250
300
350
400
wedgemodel pos+neg
trace number
time
sam
ple
![Page 19: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/19.jpg)
19
![Page 20: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/20.jpg)
20
![Page 21: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/21.jpg)
21
section 50Hz inline 30 FMPD
section 50Hz inline 30 MPD
![Page 22: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/22.jpg)
22
timeslice 34 50Hz MPD
![Page 23: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/23.jpg)
23
timeslice 34 50Hz FMPD
![Page 24: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/24.jpg)
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion24
Contents
![Page 25: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/25.jpg)
CONCLUSION
Matching Pursuit Decomposition is laterally unstable
Fractional Matching Pursuit Decomposition solves the problem
25
![Page 26: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/26.jpg)
26
Questions? Comments?
60Hz Ricker
![Page 27: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/27.jpg)
27
![Page 28: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/28.jpg)
28
![Page 29: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/29.jpg)
29
![Page 30: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/30.jpg)
3030
![Page 31: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/31.jpg)
3131
![Page 32: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/32.jpg)
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
![Page 33: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/33.jpg)
33
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1windowed cos wavelet by bell function/window size=200
ampl
itude
time(s)-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1am
plitu
de
time(s)
windowed cos wavelet by bell function/window size=80
0 5 10 15 20 25 30 35 40 45 500
20
40
60
80
100
120
140
160
180
200
Frequency(Hz)
ampl
itude
spectrum of windowed wavelet/window size=200
0 5 10 15 20 25 30 35 40 45 500
10
20
30
40
50
60
70
80
90spectrum of windowed wavelet/window size=80
ampl
itude
Frequency(Hz)
![Page 34: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/34.jpg)
340 5 10 15 20 25 30 35 40 45 50
50
100
150
200
250
300
350
400
wedgemodel pos+postim
e sa
mpl
e
trace number
![Page 35: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/35.jpg)
![Page 36: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/36.jpg)
![Page 37: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/37.jpg)
![Page 38: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/38.jpg)
![Page 39: Fractional Matching Pursuit Decomposition (FMPD)](https://reader030.fdocuments.in/reader030/viewer/2022033103/56816333550346895dd3b986/html5/thumbnails/39.jpg)