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Inversion of Sw and Porosity from Seismic AVO
Xin-Gong Li
De-hua Han Jiajin Liu
Donn McQuire
Nov 7, 2005 SEG
Rock Physics Lab, University of Houston IntSeis Inc Rock Physics Lab, University of Houston Anadarko Petroleum Corp
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Objectives • To build relationships between reservoir properties
(Sw and porosity) and AVO attributes
• To directly invert Sw and porosity
• To improve the fluid prediction (to detect low saturation gas)
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Outline
• Review • AVO crossplot • Impedance and density inversion
• Sw and porosity inverison
• Example
• Conclusion and future
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Bayesian formulation
nmd += )(f
⎥⎦
⎤⎢⎣
⎡ −−−−∝ ))(())((21
21exp( dmCdmmCmd|m -1
mT ffp 1-
dT)
))) m|dmd|m ((( ppp ∝
The problem
Bayes rule
))(())((21
21 dmCdmmCm -1
mT −−+=Φ ff 1-
dT
Posterior density
Objective function
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Simultaneous inversion for P and S impedance and density
ρρ
θθθθ
θΔ
−+Δ
−Δ+
= )tan21sin2(sin
2tan1
)( 2222
KIIK
II
Rs
s
p
ppp
Gidlow et al, 1992
( )
⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
Δ
Δ
Δ
⎥⎥⎦
⎤
⎢⎢⎣
⎡−−
+=
ρρ
θθθθ
θs
s
p
p
IIII
KK 2222
tan21sin2sin
2tan1
d
A K=(Vs/Vp)2
( ) Amd =θ
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New vs Conventional Methods
),( φSwfd =
),,( ρΔΔΔ= IsIpfd
))(())((21
21 dmCdmmCm -1
mT −−+=Φ ff 1-
dT
Objective function
( )BA,
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King Kong and Lisa Anne data
Based on O’Brien, 2004 • Both have Strong reflections • Both structures are not closed • Both amplitude anomalies do not fit to structures
Patch A: Gas
Patch B: LSG
April 2002 - Mariner Energy have said that its third well in the King Kong/Yosemite complex in the US Gulf of Mexico commenced production this month, with total production increasing to a gross rate of approximately 160 million cf/d of natural gas. - from http://www.oilvoice.com/
• Water depth 4100
ft
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Amplitudes: top sand
Patch A
Patch B
Patch A Patch B PA/PB
Top -14 -10 1.4/1
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Time Domain Amplitudes
Tuning Thin layers
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Steps • Define fluid, rock properties • Compute AVO attributes• AVO modeling based on well log• Scale AVO attributes• Invert Sw and porosity
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Relation #1 • (Sw, phi) ~ (Vp, VS, rho)
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
Saturation (V/V)
Vel
ocity
(km
/s) &
den
sity
(g/c
c)
Vp Vs Density
0
0.5
1
1.5
2
2.5
3
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Porosity (V/V)
Velo
city
(km
/s) &
den
sity
(g/c
c)
Vp Vs Density
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(A, B) ~ (Sw, Porosity) • Non-linear (A,B) ~ Sw• Only approximately orthogonal
Sw=0Phi=0.3
Sw =1Phi=0.3Phi=0.4
Sw =0.9
Phi=0.15Sw=0.9 -0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0-0.3 -0.2 -0.1 0
A
B
VarySw VaryPhi
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AVO Attributes
Wet
FizzGas
Rho (A/B) Gr (A/B)Vp (A/B)
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Scaling
Sw=1Phi=0.3
Sw=0Phi=0.3
Phi=0.15Sw=0.9
Phi=0.4Sw=0.9
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1
A
B
VarySw VaryPhi KK LA
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Inverted Sw Patch A
Patch B
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Inverted Porosity Patch A
Patch B
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Computed Density • Rhof = Sw*rhob +
(1-Sw)*rhog• Rho = phi*rhof +
(1 - phi)*rho0
• Low density due to hydrocarbon at well A
• No density change at prospect
Patch A
Patch B
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Conclusions
• New method directly can invert for Sw and porosity (can derive density)
• Example shows the new method correctly distinguish LSG from commercial gas
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Future work (1) • Thickness
estimation, for scaling
• Volume inversion with seismic wavelet
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Acknowledgements
• Members of Fluids/DHI Consortium at UH/CSM
• WesternGeco and Anadarko for permission to show the data
• Hampson and Russell and IntSeis for Software
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THANK YOU FOR YOUR ATTENTION