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
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
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)
Outline
• Review • AVO crossplot • Impedance and density inversion
• Sw and porosity inverison
• Example
• Conclusion and future
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
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
New vs Conventional Methods
),( φSwfd =
),,( ρΔΔΔ= IsIpfd
))(())((21
21 dmCdmmCm -1
mT −−+=Φ ff 1-
dT
Objective function
( )BA,
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
Amplitudes: top sand
Patch A
Patch B
Patch A Patch B PA/PB
Top -14 -10 1.4/1
Time Domain Amplitudes
Tuning Thin layers
Steps • Define fluid, rock properties • Compute AVO attributes• AVO modeling based on well log• Scale AVO attributes• Invert Sw and porosity
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
(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
AVO Attributes
Wet
FizzGas
Rho (A/B) Gr (A/B)Vp (A/B)
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
Inverted Sw Patch A
Patch B
Inverted Porosity Patch A
Patch B
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
Conclusions
• New method directly can invert for Sw and porosity (can derive density)
• Example shows the new method correctly distinguish LSG from commercial gas
Future work (1) • Thickness
estimation, for scaling
• Volume inversion with seismic wavelet
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
THANK YOU FOR YOUR ATTENTION