AVAZ inversion for fracture orientation and intensity: A physical modeling study. Faranak Mahmoudian Gary Margrave

Transcription

1 AVAZ inversion for fracture orientation and intensity: A physical modeling study Faranak Mahmoudian Gary Margrave

2 Objective Fracture orientation: direction of fracture planes Fracture intensity: number of fractures in unit volume times (mean diameter) 3 P-wave AVAZ inversion for fracture orientation and intensity Fracture orientation (Jenner, 00) AVAZ inversion using Rüger s equation for (ε (V), δ (V), γ), γ is directly related to fracture intensity

3 Outline HTI model Previous work on physical modeling Theory of AVAZ inversion Implementation on physical model data Conclusions Acknowledgements 3

4 HTI (horizontal transverse isotropy) Simple model to describe vertical fractures X Vertical isotropic plane Horizontal symmetry axis (α, β, ε (V), δ (V), γ) to describe the medium α = β = P-vertical velocity S-vertical velocity (S ) (Shear-wave splitting parameter) directly related to fracture intensity ε γ δ = V = Sx = V V Px Sz V V V Pz Sz Pz ( A A ) ( A A ) A ( A A )

5 Simulated fractured layer (00 work) Phenolic layer HTI Transmission shot gathers on single layer Traveltime inversion True (ε (V), δ (V), γ) x 3 -axis * x -axis x -axis 5

6 Azimuthal AVO from reflection data (0 work) Azimuth 90⁰ Acquisition coordinate system along fracture system Azimuth lines: 0⁰ to 90⁰ Large offset data phenolic top 6

7 Amplitudes top fracture corrected amplitudes 0.3 Azimuth 90 (isotropic plane) Azimuth 45 Azimuth 0 (symmetry axis) Amplitude Incident angle (degrees) 7

8 0 Oscillations on amplitude data Scaled time (s) Scaled offset (m) Scaled offset (m)

9 Smoothing the amplitude data Amplitude Az 90 Az 76 Az 63 Az 53 Az 45 Az 7 Az 37 Az 4 Az Incident angle (degrees) 9

10 HTI: PP reflection coefficient (Rüger, 997) ( known fracture orientation ) θ HTI HTI 0

11 HTI: PP reflection coefficient (Rüger, 997) ( known fracture orientation ) HTI R PP α 4β β 4β ρ ( θφ, ) sin θ + sin θ cos θ α α β α + ρ ( 4 ) 4β cos φsin θ tan θ ε + cos φsin θ γ + α ( cos φ sin θ + cos φ sin φ sin θ tan θ) δ θ : incident angle φ: angle between source-receiver azimuth and fracture symmetry axis φ

12 HTI R PP azimuthal dependent terms Rüger s approximation (Rüger, 997) Aki and Richard approximation α 4β β 4β ρ ( θϕ, ) sin θ + sin θ cos θ α α β + α ρ ( 4 ) 4β cos φsin θ tan θ ε + cos sin φ θ α γ + ( cos sin cos sin sin tan ) φ θ + φ φ θ θ δ α β ρ ( V) ( V) R A + B + C + D ε + E δ + F γ α β ρ At each offset, ray tracing using the overburden velocity model to obtain A, B, C, D, E, and F.

13 AVAZ inversion for six parameters Azimuth φ Azimuth φ m Aϕ B ϕ C ϕ D ϕ E ϕ F ϕ α / α A nϕ Bnϕ Cnϕ Dnϕ Enϕ F nϕ β / β ρ / ρ ε A ( ) B C D m m m E V m F ϕ ϕ ϕ ϕ ϕm ϕ δ m γ (6 ) A B C D E F nϕ nϕ nϕ nϕ nϕ nϕ m m m m m m ( nm 6) = R R R R n m nm ( nm ) G m d T T m = ( G G+ µ ) G d est 3

14 50 AVAZ inversion for six parameters (errors WRT traveltime inversion results) Max incident angle = 37 % error Δα/α Δ ββδ / / ρρ ε δ γ 4

15 50 AVAZ inversion for six parameters (errors WRT traveltime inversion results)) Max incident angle = 37 Max incident angle = 4 % error Δα/α Δ ββδ / / ρρ ε δ γ Δα/α Δ ββδ / / ρρ Max incident angle = 45 Max incident angle = 49 ε δ γ % error

16 AVAZ inversion for three-parameters (anisotropy parameters). Determine ( α/α, β/β, ρ/ρ ) from logs, or from conventional AVA inversion of isotropic plane direction.. Invert for ( ε (V), δ (V), γ ) using Rüger s equation constrained by results from step. 6

17 AVAZ inversion 6-parameter vs. 3-parameter % error Δα α Δβ β Δρ ρ Max incident angle = 4⁰ ε δ γ ε δ Favourable results compared to those obtained previously by traveltime inversion Directly related to fracture intensity γ 7

18 Fracture symmetry axis not known X φ φ 0 X : fracture system : acquisition coordinate φ : source-receiver azimuth φ 0 : fracture symmetry direction HTI R PP X 3 α 4β β 4β ρ ( θφ, ) sin θ + sin θ cos θ α α β + α ρ ( 4 ) 4β cos ( φ φ0 )sin θ tan θ ε + cos ( 0)sin φ φ θ γ α + ( cos ( φ φ0 )sin θ + cos ( φ φ0 )sin ( φ φ0 ) ) sin θ tan θ δ 8

19 R HTI PP HTI: PP reflection coefficient Small incident angle ( θ < 35⁰ ) α 4β β 4β ρ ( θφ, ) sin θ + sin θ cos θ α α β + α ρ AVO intercept 4β + γ + δ cos ( )sin α Q = AVO gradient φ φ0 θ HTI RPP ( θϕ, ) I + G Gcos ( φ φ0) + sin θ Isotropic gradient Anisotropic gradient gradient non-linear with respect to (G,G, φ 0 ) G 4β = γ + δ α 9

20 Estimate fracture orientation ( Grechka and Tsvankin (998); Jenner (00) ) Q = G + G cos ( ϕ ϕ ) 0 ϕ ϕ0 ϕ ϕ0 cos cos sin sin = ( G + G )cos ( ) + G sin ( ) = W φ+ W φ φ+ W φ Acquisition coordinate system x = rcosφ x = rsinφ + + Q = W x W xx W x [ x x ] W W x = W W x λ y λ y λ, e Q = + ( : igenvalues) tan( φ ) = 0 W W W x Q = ( G + G) y + Gy Coordinate system aligned with fractures y = rcos( φ φ0) y = rsin( φ φ0). φ φ 0 0 x

21 Estimate fracture orientation ( Grechka and Tsvankin (998); Jenner (00) ) φ φ W W + ( W W ) + 4W () 0 = tan W W W ( W W ) + 4W () 0 = tan W φ () () 0 φ0 = + π Accurate prediction of fracture orientation requires extra geological info, or azimuthal NMO velocity.

22 AVAZ inversion for fracture orientation ( small incident angle, θ < 35⁰ ) ( ) R( θφ, ) = I + W cos φ+ W cosφsinφ+ W sin φ sin θ cos φ sin θ cosφ sinφ sin θ sin φ sin θ R I cos φsin θn cosφsinφsin θn sin φsin θn Rn I W W = W (3 ) cos φmsin θm cosφmsinφmsin θm sin φmsin θ R m m I cos φmsin θnm cosφmsinφmsin θm sin φmsin θ Rnm I m ( nm 3) ( nm ) Least squares inversion for (W, W, W 33 )

23 Test on physical model data, AVAZ inversion φ 0 = 30⁰ φ 0 : fracture symmetry axis azimuth φ 0 X True φ 0 30⁰ Estimate φ 0 8.5⁰ and 8.5⁰ 3

24 Testing different fracture orientations φ 0 : fracture symmetry axis azimuth True φ 0 0⁰ 0⁰ 0⁰ 40⁰ 60⁰ 80⁰ 90⁰ Estimate φ 0 -.5⁰ 8.5⁰ 8.5⁰ 38.5⁰ 58.5⁰ 78.5⁰ 88.5⁰ 88.5⁰ 98.5⁰ 08.5⁰ 8.5⁰ 48.5⁰ 68.5⁰ 78.5⁰ 4

25 Conclusions Rüger equation for HTI, PP reflection coefficient, can be used in an inversion for anisotropy parameters, but fracture orientation must be known. Knowing the fracture orientation, fracture intensity can be estimated from AVAZ inversion of large-offset data. Fracture orientation can be determined from AVAZ inversion of small incident angle data, but with 90⁰ ambiguity. Implementation on physical model data gives results consistent with these theories. 5

26 Acknowledgments CREWES sponsors Dr. Joe Wong Xinxiang Li Dr. P.F. Daley Dr. Kris Innanen David Henley Marcus Wilson Mahdi Al-Mutlaq 6