1 avo inversion of long-offset synthetic pp data based on effective reflection coefficients 10 april...
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AVO INVERSION OF LONG-OFFSET SYNTHETIC PP DATA
BASED ON EFFECTIVE REFLECTION
COEFFICIENTS
10 April 2008
Lyubov Skopintseva
Milana Ayzenberg, Martin Landrø
Tatyana Nefedkina, Arkady Aizenberg
AVO-analysis. What is that?
Conventional AVO analysis:
•Range of incidence angles: 0-400
•Weak contrasts at reflector
0 10 20 30 40 50 60 70 80 900
0.2
0.4
0.6
0.8
1
incidence angle, degree
amp
litu
de
Pre-critical region
Critical angle
Post-critical region
2 2( ) (Re ( )) (Im ( ))A x K x K x
1
1 2
sin 1
Vp Vp
Plane-wave reflection coefficient
Effective reflection coefficient (ERC)
Incident wave
Plane-wave decomposition
Division by incident wave
Multiplying by plane-wave reflection
coefficient (PWRC)
Summation
ERC versus PWRC
• PWRC valid for plane waves
• ERC generalize PWRC for point sources
- incidence angle - frequency
- wavefront curvature - wave velocity
K x K x
;R x
x xV
2 f
V R x
x
ERC versus PWRC
0
0,2
0,4
0,6
0,8
1
1,2
1,4
0 50 100 150 200 250 300 350 400Offsets, km
Am
pli
tud
e
PWRCERC(2 Hz)ERC (5 Hz)ERC (10 Hz)ERC (20 Hz)
Model parameters
0 1250 2500 3750 5000
1000
0
H=1000 m
L=5000 m
x=25 m
Vp1=2000 m/s
Vs1=1100 m/s
1=1800 kg/m3
Vp2=2800 m/s
Vs
2=1600 m/s
2=2100 kg/m3
Offset, m
Dep
th, m
Wavelet: F(t)=-sin(2ft)e-(2ft)
Dominant frequency (f): 32 Hz
Z-component from reflectivity modeling
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0 1000 2000 3000 4000 5000
offsets, m
tim
e,
s
AVO response
0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Offsets,m
Am
plit
ud
e
SpectrogramF
requ
ency
, H
z
Offsets,m
1000 2000 3000 4000 5000
10
20
30
40
50
60
2
4
6
8
10
12
14
16
x 10-3
AVO response comparison with ERC and PWRC
0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Offsets,m
Am
plit
ud
e
AVO-response
AVO-function (29-44Hz)
AVO-function (22-51Hz)AVO-function (all frequencies)
AVO function based on PWRC
Vs1
Vp1
1 600 2 000 2 400900
1000
1100
1200
1300
0 0.2 0.4 0.6 0.8
ro1
Vp1
1600 2000 24001400
1600
1800
2000
0 0.2 0.4 0.6 0.8
ro1
Vs1
900 1100 13001400
1600
1800
2000
0.2 0.4 0.6 0.8
ro2
Vs2
1400 1600 1800
1800
2000
2200
2400
0 0.2 0.4 0.6 0.8
Vs1
Vp1
1500 2000 2500
800
1000
1200
1400
0.2 0.4 0.6 0.8
ro1
Vp1
1500 2000 2500
1500
2000
2500
0.2 0.4 0.6 0.8
ro1
Vs1
800 1100 1 400
1500
2000
2500
0.2 0.4 0.6 0.8ro
2
Vs2
1000 1500 2000
1500
2000
2500
0.2 0.4 0.6 0.8
Plane-wave reflection coefficient
Effective reflection coefficient
Cost functions comparison (pre-critical offsets)
Vs1
Vp1
1600 2000 2400900
1000
1100
1200
1300
0 0.2 0.4 0.6 0.8
ro1
Vp1
1600 2000 24001400
1600
1800
2000
0 0.2 0.4 0.6 0.8
ro1
Vs1
900 1100 13001400
1600
1800
2000
0 0.2 0.4 0.6 0.8
ro2
Vs2
1400 1600 1800
1800
2000
2200
2400
0 0.2 0.4 0.6 0.8
Vs1
Vp1
1500 2000 2500
800
1000
1200
1400
0.2 0.4 0.6 0.8
ro1
Vp1
1500 2000 2500
1500
2000
2500
0.2 0.4 0.6 0.8
ro1
Vs1
800 1100 1400
1500
2000
2500
0.4 0.6 0.8ro
2
Vs2
1000 1500 2000
1500
2000
2500
0.5 0.6 0.7 0.8 0.9
Cost functions comparison (all offsets)
Effective reflection coefficient
Plane-wave reflection coefficient
AVO inversion results
ERC solution PWRC solution
Pre-critical offsets Post-critical offsets 0
2
4
6
8
10
12
14
16
18
20
22
24
Rel
ativ
e er
ror
in e
last
ic p
aram
eter
s, %
Vp1
Vs1
1
Vp2
Vs2
2
Pre-critical offsets Post-critical offsets0
2
4
6
8
10
12
14
16
18
20
22
24
Rel
ativ
e er
ror
in e
last
ic p
aram
eter
s, %
Vp1
Vs1
1
Vp2
Vs2
2
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