WAVELET PHASE ESTIMATION WITHOUT
ACCURATE TIME-DEPTH CONVERSION
JIANGBO YU
ADVISOR: DR. JOHN CASTAGNA
AGL UPDATE MEETING
MAY 2, 2012
CONTENT
• Introduction
• Theory
• Results
• Conclusion
INTRODUCTIONSEISMIC-TO-WELL-TIE
CONVOLUTION
Statistical wavelet from seismic
Reflectivity series from well logs
Phase rotate wavelet until
maximum correlation is found
QC initial tie
Final tie
Edgar and van der Baan, 2009
PROBLEMS OF SONIC
LOG CALIBRATION
• P-wave velocity from sonic log is different with seismic
velocity
• Short logging runs, or gaps in sonic log coverage
• Inaccurate time-depth conversion
• Aggressively forcing a well tie will affect the estimated
wavelet
THEORY-HISTOGRAM MATCHING PHASE ESTIMATION
1. Zero-phase wavelet estimation
Zero-phase wavelet from seismic
Normalized Amplitude Spectrum
0.3
Normalized spectral amplitude
0.25
0.2
0.15
0.1
0.05
-50
0
50
0
20
40
60
Frequency (Hz)
80
THEORY – HISTOGRAM MATCHING
2. Frequency domain deconvolution
Deconvolution output
Narrow-band reflectivity
0
0
500
500
1000
1000
1500
1500
2000
2000
Amplitude spectrum
Normalized spectral amplitude
Normalized spectral amplitude
Amplitude spectrum
0.2
0.15
0.1
0.05
0
20
40
60
Frequency (Hz)
0.2
0.15
0.1
0.05
80
0
20
40
60
Frequency (Hz)
80
Amplitude histogram of narrow-band reflectivity
Amplitude histogram of inverted reflectivity
2.5
2
2
Density
Density
1.5
1.5
1
0.5
0.5
0
1
-0.4
-0.2
0
0.2
Data
0.4
0.6
0
-0.4
-0.2
0
0.2
Data
0.4
0.6
THEORY – HISTOGRAM MATCHING
True phase 90degree
32
30
28
Misfit
26
24
22
20
97
-150
-100
-50
0
Phase Rotation
Estimated
Estimated wavelet
Wavelet
50
100
True wavelet
Phase rotated wavelet
-60
-60
-40
-40
-20
-20
Time (ms)
Time (ms)
18
-200
0
0
20
20
40
40
60
60
13-Oct-2011 10:26:46
13-Oct-2011 10:26:46
150
200
THEORY – HISTOGRAM MATCHING
Assumption:
Major part of the difference between inverted reflectivity
amplitude distribution with well log derived reflectivity
amplitude distribution is caused by the incorrect phase of
wavelet
Advantage:
Will not be affected by inaccurate time-depth conversion
REAL DATA
Correlation:
0.924
REAL DATA
7
1.615
x 10
1.61
1.605
Misfit
1.6
1.595
1.59
1.585

-89
1.58
-200
-150
-100
-50
Estimated from seismic-to-well tie (-86 degree)
0
Phase rotation
50
100
150
200
Estimated from histogram matching (-89 degree)
RESULT– REAL REFLECTIVITY
RESULT– ACCURATE TIME-DEPTH CONVERSION
Histogram
matching
Estimated
Wavelet
Wiener
filter
Wiener Filter
-60
-40
-40
-40
-20
-20
-20
0
Time (ms)
-60
Time (ms)
Time (ms)
True
wavelet
Phase
rotated
wavelet
-60
0
0
20
20
20
40
40
40
60
60
60
13-Oct-2011 10:26:46
13-Oct-2011 10:26:46
07-Mar-2012 17:41:13
RESULT– BULK SHIFT
Synthetic trace (black) vs. Bulk shifted synthetic trace (w)
100
Time (ms)
200
300
400
500
600
TrueTrue
wavelet
wavelet
Histogram
matching
Estimated
Wavelet
-60
-40
-40
-20
0
-20
Time (ms)
Time (ms)
Time (ms)
-60
-40
-20
0
Wiener
filter
Wiener
Filter
-60
0
20
20
20
40
40
40
60
60
60
RESULT– DYNAMIC SHIFT
Synthetic trace (black) vs. Dynamic shifted synthetic trace (w)
100
Time (ms)
200
300
400
500
600
Histogram
matching
Estimated
Wavelet
Wiener
filter
Wiener Filter
-60
-40
-40
-40
-20
-20
-20
0
0
20
20
40
40
60
60
Time (ms)
-60
Time (ms)
Time (ms)
TrueTrue
wavelet
wavelet
-60
0
20
40
60
CONCLUSION
• Inaccurate time-depth conversion will affect seismic
wavelet estimation through well-tie
• Histogram matching could estimate wavelet phase
correctly even with a wrong time-depth conversion