The roles of baseline Earth elastic properties and time-lapse changes in determining difference AVO. Shahin Jabbari Kris Innanen

Transcription

1 The roles of baseline Earth elastic properties and time-lapse changes in determining difference AO hahin Jabbari Kris Innanen

2 Outline Introduction and review A framework for time-lapse AO alidation of results with a physical model ummary Conclusions Future work Acknowledgments

3 Time-lapse 3 Monitoring changes in reservoir: production, EOR Repeated seismic surveys over calendar time The baseline and monitor survey Changes in seismic parameters CO storage in the leipner gas field (image courtesy of tatoilhydro)

4 AO : Amplitude ersus Offset 4 Baseline and time-lapse changes Baseline b b b = = = b b b I 0 φ0 R R 0, 0, 0 Time lapse = = = m m m b b b φ,, T T

5 Time lapse changes (Landrø, 00) 5 Large time lapse changes in are possible Linearized equation is inaccurate for large contrast tan sin ) ( R Relative change in versus pressure changes ( Landrø et al., 00)

6 A general framework for time-lapse AO 6 Deriving ΔR() from Zoeppritz equations Linear or Aki-Richards approximation Nonlinear correction Examine linear and nonlinear terms for: Agreement with Landrø at small contrast Behaviour of approximations at large contrast

7 A time-lapse problem 7 0, 0,0 b, b, b 0, 0,0 m, m, m Baseline urvey Monitor urvey Baseline perturbation Time-lapse perturbation = b 0, + b 0 = m b, + m b = b 0, + b 0 = m b, + m b 0 = b + b 0 m = b m + b

8 8 Time-lapse AO Zoeppritz equations for baseline and monitoring targets: R R = b RBL( ) = BL T BL T det( ) det( ) R R det( ) = b RM ( ) = M T M det( ) T Expand ΔR() in orders of perturbation parameters R ( ) = RM ( ) RBL( )

9 R for the Baseline and Monitor survey and ΔR 9 R, ΔR Baseline Monitor ΔR Incident angle (degree) More details in modeled data (Jabbari and Innanen, 0)

10 Examining linear and nonlinear terms 0 ( ) ( ) ( )... R R R R = (3) () () ) ( sin sin ) ( () R = +Γ +Γ +Γ +Γ +Γ +Γ +Γ +Γ = Γ R ) ( ()

11 Agreement of linear term in ΔR with Landrø s work sin sin ) ( () R = tan sin ) ( R Our first order term Landrø s approximation

12 ΔR for the exact, linear, second and third order approximation ΔR Exact ΔR Linear ΔR econd order ΔR Third order ΔR Incident angle (degree) More details in modeled data (Jabbari and Innanen, 0)

13 hysical modelling 3 Array of transducers for sources and detectors The model contains water and different material blocks Common midpoint (CM) gathers are recorded on EG-Y files caling factor of 0,000: mm 0 m MHz 00 Hz The University of Calgary eismic hysical Modelling Facility (J. Wong and Lawton, 009)

14 Modeling a time-lapse problem 4 More details in modeled data (Jabbari and Innanen, 0)

15 CM (common mid point) gather 5 Corrections (Mahmoudian et al. 0) Geometrical spreading Emergence angle Free surface Transmission loss ource/receiver directivity CM gather along the plexiglas- phenolic interface in monitor survey model

16 Time-lapse difference data in the physical model 6 R, ΔR Baseline-Model Monitor-Model ΔR-Model Incident angle (degree) More details in modeled data (Jabbari and Innanen, 0)

17 ΔR for the model, linear, second and third order approximation 7 ΔR Modeled ΔR Linear ΔR econd order ΔR Third order ΔR Incident angle (degree) More details in modeled data (Jabbari and Innanen, 0)

18 ummary 8 A framework for linear and non linear time-lapse AO analysis is formulated. Agreement of linear term in ΔR with Landrø s work. Higher order approximations made corrections in ΔR. hysical model validated the importance of low order interpretable nonlinear corrections.

19 Conclusions 9 In plausible large contrast time-lapse scenarios Landrø s approximation requires correction. hysical modeling study validates nonlinear framework with real data in controlled settings.

20 Future work 0 Further numerical, analytical examination of ΔR, ΔR, ΔR alidation of time-lapse AO formula using physical modeling data Modeling of inversion of field data example

21 Acknowledgments Dr Joe Wong Faranak Mahmoudian CREWE tudents and taffs CREWE ponsors

22 Questions

23 More details of the time-lapse model 3 Material (m/sec) (m/sec) (g/cm 3 ) Water exiglas C henolic

24 4 HTI Medium

25 5 Ghost Raypath (Mahmoudian et al. 0)

26 6 ource/receiver directivity (Mahmoudian et al. 0)

27 Zoeppritz matrix- Elastic parameters b T T R R = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) DX X AD DX AC BX X B BX DX AD CX X AD BX B X X B DX CX BX X DX CX BX X ( ) BX X X B X X b F, E, D, C, B, A, 0 in X ) ( = ) det( ) det( ) 0 ( R =

28 8 econd order correction (Jabbari and Innanen, 0)

29 9 Third order correction (Jabbari and Innanen, 0)