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

4

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

9

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

11

Background---STFT, CWT and MPD

Fractional Matching Pursuit Decomposition

Computational Simulation

Results: MPD versus FMPD

Conclusion12

Contents

1313

1414

15

Ricker Criterion

Rayleigh Criterion

16

Ricker Criterion

Rayleigh Criterion

17

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

19

20

21

section 50Hz inline 30 FMPD

section 50Hz inline 30 MPD

22

timeslice 34 50Hz MPD

23

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

25

26

Questions? Comments?

60Hz Ricker

27

28

29

3030

3131

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

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)

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