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