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AVO INVERSION OF LONG-OFFSET
SYNTHETIC PP DATA
BASED ON EFFECTIVE REFLECTION
COEFFICIENTS
Lyubov Skopintseva
Milana Ayzenberg, Martin Landrø
10 April 2008
AVO-analysis. What is that?
Conventional AVO analysis:
•Range of incidence angles: 0-400
•Weak contrasts at reflector
Plane-wave reflection coefficient
Post-critical region
1
A( x)  (Re K ( x)) 2  (Im K ( x)) 2
amplitude
0.8
0.6
Critical angle
0.4
sin 1
1

Vp1
Vp2
Pre-critical region
0.2
0
0
10
20
30
40
50
60
incidence angle, degree
70
80
90
Effective reflection coefficient
(ERC)
Incident wave
Plane-wave decomposition
Multiplying by planewave reflection
coefficient (PWRC)
Summation
Division by incident wave
ERC versus PWRC
• PWRC valid for plane waves
K  x   K   x  
• ERC generalize PWRC for point sources
R  x 

  x      x  ;

V


  x
- incidence angle
R  x
- wavefront curvature
  2 f
- frequency
V - wave velocity
ERC versus PWRC
1,4
PWRC
ERC(2 Hz)
ERC (5 Hz)
ERC (10 Hz)
ERC (20 Hz)
1,2
Amplitude
1
0,8
0,6
0,4
0,2
0
0
50
100
150
200
250
Offsets, km
300
350
400
Model parameters
0
H=1000 m
Vp1=2000 m/s
L=5000 m
Vs1=1100 m/s
Depth, m
x=25 m
1=1800 kg/m3
1000
Wavelet: F(t)=-sin(2 ft)e-(2ft)
Vp2=2800 m/s
Dominant frequency (f): 32 Hz
Vs2=1600 m/s
2=2100 kg/m3
0
1250
2500
Offset, m
3750
5000
1.0
Z-component from reflectivity
modeling
1.2
1.4
1.6
time, s
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0
1000
2000
3000
offsets, m
4000
5000
AVO response
1.8
1.6
Amplitude
1.4
1.2
1
0.8
0.6
0.4
0.2
0
500
1000
1500
2000
2500
3000
Offsets,m
3500
4000
4500
5000
Spectrogram
x 10
60
16
14
50
Frequency, Hz
12
40
10
30
8
6
20
4
10
2
1000
2000
3000
Offsets,m
4000
5000
-3
AVO response comparison with
ERC and PWRC
2
1.8
1.6
Amplitude
1.4
1.2
1
0.8
AVO-response
AVO-function (29-44Hz)
AVO-function (22-51Hz)
AVO-function (all frequencies)
AVO function based on PWRC
0.6
0.4
0.2
0
500
1000
1500
2000
2500
3000
Offsets,m
3500
4000
4500
5000
Cost functions comparison
(pre-critical offsets)
Effective reflection coefficient
1300
1000
1800
ro2
ro1
Vs1
1100
2400
2000
ro1
2000
1200
1800
1600
1600
1400
1600
1400
900
2200
2000
1800
900
1 600
2 000
2 400
Vp1
2000
2400
Vp1
0 0.2 0.4 0.6 0.8
1100
1300
1400 1600 1800
Vs1
0 0.2 0.4 0.6 0.8
Vs2
0.2 0.4 0.6 0.8
0 0.2 0.4 0.6 0.8
Plane-wave reflection coefficient
2500
2500
2000
2000
1400
1500
ro2
1000
ro1
ro1
Vs1
2500
1200
2000
1500
800
1500
1500 2000 2500
1500 2000 2500
800
1100
1 400
1000
1500
2000
Vp1
Vp1
Vs1
Vs2
0.2 0.4 0.6 0.8
0.2 0.4 0.6 0.8
0.2 0.4 0.6 0.8
0.2 0.4 0.6 0.8
Cost functions comparison
(all offsets)
Effective reflection coefficient
1300
1000
1800
ro2
ro1
Vs1
1100
2400
2000
ro1
2000
1200
1800
1600
1600
1400
1600
1400
900
2200
2000
1800
900
1600
2000
2400
Vp1
2000
2400
Vp1
0 0.2 0.4 0.6 0.8
1100
1300
1400 1600 1800
Vs1
0 0.2 0.4 0.6 0.8
Vs2
0 0.2 0.4 0.6 0.8
0 0.2 0.4 0.6 0.8
Plane-wave reflection coefficient
2500
2500
2000
2000
1400
1500
ro2
1000
ro1
ro1
Vs1
2500
1200
2000
1500
800
1500
1500 2000 2500
1500 2000 2500
Vp1
Vp1
0.2 0.4 0.6 0.8
0.2 0.4 0.6 0.8
800
1100
1400
Vs1
0.4
0.6
1000
1500
2000
Vs2
0.8
0.5 0.6 0.7 0.8 0.9
AVO inversion results
24
22
20
Vp1
18
Vs1
16
1
14
Vp2
12
Vs2
10
2
8
6
4
2
0
Pre-critical offsets
Post-critical offsets
PWRC solution
Relative error in elastic parameters, %
Relative error in elastic parameters, %
ERC solution
24
22
20
Vp1
18
Vs1
16
1
14
Vp2
12
Vs2
10
2
8
6
4
2
0
Pre-critical offsets
Post-critical offsets
15
Conclusion
• ERC give better estimates than PWRC
• Rapid variations in reflection amplitude for
post-critical offsets improve inversion
results
• Long-offset data allow accurate estimation
of Vp and Vs
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