WAVELET PHASE ESTIMATION WITHOUT ACCURATE TIME-DEPTH CONVERSION

J IANGBO YU

ADVISOR: DR. JOHN CASTAGNA

AGL UPDATE MEETING

MAY 2, 2012

CONTENT• Introduction

• Theory

• Results

• Conclusion

INTRODUCTION-SEISMIC-TO-WELL-TIE

Edgar and van der Baan, 2009

Statistical wavelet from seismic Reflectivity series from well logs

QC initial tie

Phase rotate wavelet until maximum correlation is found

Final tie

CONVOLUTION

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

-50 0 50

Zero-phase wavelet from seismic

0 20 40 60 80

0.05

0.1

0.15

0.2

0.25

0.3

Frequency (Hz)

Nor

mal

ized

spe

ctra

l am

plitu

de

Normalized Amplitude Spectrum

1. Zero-phase wavelet estimation

THEORY – HISTOGRAM MATCHING

0

500

1000

1500

2000

Deconvolution output0

500

1000

1500

2000

Narrow-band reflectivity

0 20 40 60 80

0.05

0.1

0.15

0.2

Frequency (Hz)

Nor

mal

ized

spe

ctra

l am

plitu

de

Amplitude spectrum

0 20 40 60 80

0.05

0.1

0.15

0.2

Frequency (Hz)

Nor

mal

ized

spe

ctra

l am

plitu

de

Amplitude spectrum

-0.4 -0.2 0 0.2 0.4 0.60

0.5

1

1.5

2

2.5

Data

Den

sity

Amplitude histogram of inverted reflectivity

-0.4 -0.2 0 0.2 0.4 0.60

0.5

1

1.5

2

Data

Den

sity

Amplitude histogram of narrow-band reflectivity

2. Frequency domain deconvolution

THEORY – HISTOGRAM MATCHING

13-Oct-2011 10:26:46

-60

-40

-20

0

20

40

60

Tim

e (m

s)

Phase rotated waveletTrue wavelet

13-Oct-2011 10:26:46

-60

-40

-20

0

20

40

60

Tim

e (m

s)

Estimated WaveletEstimated wavelet

-200 -150 -100 -50 0 50 100 150 20018

20

22

24

26

28

30

32

97

Phase Rotation

Mis

fit

True phase 90degree

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

-200 -150 -100 -50 0 50 100 150 2001.58

1.585

1.59

1.595

1.6

1.605

1.61

1.615x 10

7

-89

Phase rotation

Mis

fit

Estimated from seismic-to-well tie (-86 degree) Estimated from histogram matching (-89 degree)

RESULT– REAL REFLECTIVITY

07-Mar-2012 17:41:13

-60

-40

-20

0

20

40

60

Tim

e (m

s)

Wiener Filter

RESULT– ACCURATE TIME-DEPTH CONVERSION

 

13-Oct-2011 10:26:46

-60

-40

-20

0

20

40

60

Tim

e (m

s)

Phase rotated waveletTrue wavelet

13-Oct-2011 10:26:46

-60

-40

-20

0

20

40

60

Time (

ms)

Estimated WaveletHistogram matching Wiener filter

RESULT– BULK SHIFT

100

200

300

400

500

600

Tim

e (m

s)

Synthetic trace (black) vs. Bulk shifted synthetic trace (w)

-60

-40

-20

0

20

40

60

Tim

e (m

s)

True wavelet

-60

-40

-20

0

20

40

60

Tim

e (m

s)

Wiener Filter

13-Oct-2011 10:26:46

-60

-40

-20

0

20

40

60

Time (

ms)

Estimated WaveletHistogram matching Wiener filter

True wavelet

RESULT– DYNAMIC SHIFT

100

200

300

400

500

600

Tim

e (

ms)

Synthetic trace (black) vs. Dynamic shifted synthetic trace (w)

-60

-40

-20

0

20

40

60

Tim

e (m

s)

Wiener Filter

13-Oct-2011 10:26:46

-60

-40

-20

0

20

40

60

Time (

ms)

Estimated WaveletHistogram matching-60

-40

-20

0

20

40

60

Tim

e (m

s)

True waveletTrue wavelet Wiener filter

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