幻灯片 1 - University of Houston
Download
Report
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
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
Conclusion
8
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
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
12
13
13
14
14
15
Ricker Criterion
Rayleigh Criterion
16
Ricker Criterion
Rayleigh Criterion
17
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
18
19
20
section 50Hz inline 30 MPD
section 50Hz inline 30 FMPD
21
timeslice 34 50Hz MPD
22
timeslice 34 50Hz FMPD
23
Background---STFT, CWT and MPD
Fractional Matching Pursuit Decomposition
Computational Simulation
Results: MPD versus FMPD
Conclusion
24
CONCLUSION
Matching Pursuit Decomposition is laterally unstable
Fractional Matching Pursuit Decomposition solves the problem
25
60Hz Ricker
Questions? Comments?
26
27
28
29
30
30
31
31
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
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
34