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Porous media: recovering physical properties through dynamic forward modelling

Overpressure Mechanisms. Possible Scenarios. Fluid volume/mass increaseExternal stress = constant. Pore volume reductionExternal stress increase. . Overpressure. Mechanisms. A) Disequilibrium Compaction. B) Fluid Expansion. Bowers, 2002- TLE. Scientific motivation. Imaging subscale features through passive and active dynamic mechanical experiments and seismic resolutionImproving forward modellingImproving imaging techniques (often the first item is driven by the second one).

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Porous media: recovering physical properties through dynamic forward modelling

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    1. Porous media: recovering physical properties through dynamic forward modelling Louis de Barros Bastien Dupuy Stéphane Garambois Jean Virieux

    3. Scientific motivation Imaging subscale features through passive and active dynamic mechanical experiments and seismic resolution Improving forward modelling Improving imaging techniques (often the first item is driven by the second one)

    6. Pionner works: Biot (1941), Frenkel (1941), Gassmann (1951), Skempton (1954) Porous-elastodynamics: Biot (1956,1962), Biot et Willis (1957) Experimental validation: Plona (1980) Various improvements or justifications: Auriault et al. (1985), Johnson et al. (1987), Berryman et al. (1995), Pride (2005),… Forward problem solved by many authors following different strategies: Dai et al. (1995), Carcione et al. (1996), Haartsen et Pride (1997) both in frequency and time domains.

    7. 7 Equations of poroelastodynamics I

    8. 8

    9. 9 Main features

    10. 10

    11. 11 Seismic wave modelling

    12. 12 An example : the Sleipner of storage investigation in deep salt aquifer

    13. 13 Wave propagation in porous media

    14. 14 We may hope that the CO2 content could be estimated through wave signals (illumination k; broadband w) Deep storage of CO2

    15. Forward modelling Time versus frequency formulations Time : low memory requirement but integration stiffness (implicit integration) Frequency : high memory requirement but nicely suited for imaging (many forward problems)

    16. Motivation for DGPk Better description of the complexity of the medium Efficiency when smooth velocity variation

    17. Finite Volume approach

    18. Finite volume approach

    19. Complex free surface

    20. Complex Boundaries

    21. Extension to porous media Improve the time integration scheme Global time integration (RK) Local time integration (?) Other alternatives (?) Feasability of combining fluid & solid mechanics

    22. Frequency formulation Whatever is the numerical formulation, it boils down to an algebric linear equation A(m,w)p(x,w)=s(x,w) If A is LU-decomposed, solving many forward problems is very efficient

    27. Preliminary synthetic tests Synthetic model with body wave only Homogeneous medium 2 circular inclusions of 20% high velocity 40m x 40m model Spatial discretization step = 0.1m Rickers Source centered on 88Hz

    28. Preliminary synthetic tests Model and acquisition geometry 15 sources (Fz punctual forces) recorded by 36 receivers on the opposite side The same acquisition on 4 sides of model

    29. Preliminary synthetic tests Full wave inversion Initial model homogeneous Vp = 1 000 m/s Vs = 500m/s Inversion of 6 frequencies : 19.8 hz / 33.4 hz / 54.0 hz / 78.4 hz / 107.7 hz / 137.0 hz / 10 iterations per frequency

    31. Preliminary synthetic tests Model and acquisition geometry 15 sources (Fz punctual forces) recorded by 36 receivers on the same side The same acquisition on 4 sides of model

    32. Preliminary synthetic tests Full wave inversion Initial model homogeneous Vp = 1 000 m/s Vs = 500m/s Inversion of 5 frequencies : 19.8 hz / 33.4 hz / 54.0 hz / 78.4 hz / 107.7 hz 10 iterations per frequency

    34. WORK PLAN Formulation in 2D and 3D heterogeneous media (tuning theory through laboratory experiments) Investigation of the « best » numerical technique for imaging processing (frequency; 2D geometry: B. Dupuy work) Local imaging procedures (gradient; unicity: B. Dupuy work) Applications to real data sets (to be defined)

    35. Thank you

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