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Reservoir Description Using a Binary Level Set Approach with Additional Prior Information About the Reservoir Model

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Image Processing Based on Partial Differential Equations

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References

  1. S.I. Aanonsen, I Aavatsmark, T Barkve, A Cominelli, R Gonard, O Gosselin, M Kolasinski, and H Reme. Effect of scale dependent data correlations in an integrated history matching loop combining production data and 4d seismic data. In Proceedings of the SPE Reservoir Simulation Symposium, Houston, Texas, Feb. 2003. SPE 79665, presented at the SPE Reservoir Simulation Symposium held in Houston, Texas.

    Google Scholar 

  2. S.I. Aanonsen, A Cominelli, O Gosselin, I Aavatsmark, and T Barkve. Integration of 4D Data in the History Match Loop by Investigating Scale dependent Correlations in the Acustic Impedance Cube. In Proceedings of the 8th European Conferance on the Mathematics of Oil Recovery, Freiberg, Germany, 3-6 Sept. 2002.

    Google Scholar 

  3. U. Ascher and E. Haber. Grid refinement and scaling for distributed parameter estimation problems. Inverse Problems, 17:571–590, 2001.

    Article  MathSciNet  Google Scholar 

  4. U. Ascher and E. Haber. Computational methods for large distributed parameter estimation problems with possible discontinuities. Symp. Inverse Problems, Design and Optimization, 2004.

    Google Scholar 

  5. U. Ascher, E. Haber, and H. Huang. On effective methods for implicit piecewise smooth surface recovery. Submitted 2004.

    Google Scholar 

  6. M. Burger. A level set method for inverse problems. Inverse problems, 17:1327–1355,2001.

    Article  MathSciNet  Google Scholar 

  7. M. Burger and S. Osher. A survey on level set methods for inverse problems and optimal design. UCLA, CAM-Report 04-02, 2004.

    Google Scholar 

  8. T. Chan and X.-C. Tai. Level set and total variation regularization for elliptic inverse problems with discontinous coefficients. Journal of Computational Physics, 193:40–66, 2003.

    Article  MathSciNet  Google Scholar 

  9. T. F. Chan and L. A. Vese. Active contours without edges. IEEE Trans. Image Processing, 10(2):266–277, 2001.

    Article  Google Scholar 

  10. E. Chung, Chan T., and X.-C. Tai. Electrical impedance tomography using level set representation and total variational regularization. submitted, 2004.

    Google Scholar 

  11. O. Dorn, E. Miller, and C. Rappaport. A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets. Inverse Problems, 16:1119–1156, 2000. Special issue on Electromagnetic Imaging and Inversion of the Earth’s Subsurface.

    Article  MathSciNet  Google Scholar 

  12. G. Chavent and J. Liu. Multiscale parameterization for the estimation of a diffusion coefficient in elliptic and parabolic problems. In Proceedings of the Fifth IFAC Symposium on Control of Distributed Parameter Systems, Perpignian, France, June 1987.

    Google Scholar 

  13. F. Gibou and R. Fedkiw. Fast hybrid k-means level set algorithm for segmentation. Stanford Technical Report, November 2002.

    Google Scholar 

  14. O. Gosselin, S.I. Aanonsen, I. Aavatsmark, A. Cominelli, R. Gonard, M. Kolasinski, F. Ferdinandi, and K. Kovacic, L. andNeylon. History matching Using Time-lapse Seismic (HUTS). In Proceedings of the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 30 Sept.-3 Oct. 2003. SPE 84464.

    Google Scholar 

  15. K. Ito, K. Kunisch, and Z. Li. Level-set function approach to an inverse interface problem. Inverse problems, 17:1225–1242, 2001.

    Article  MathSciNet  Google Scholar 

  16. M. Landrø and Ø Kvam. Pore Pressure Estimation - what can we learn from 4D. CSEG Recorder, September 2002.

    Google Scholar 

  17. R. Li, A.C. Reynolds, and D.S. Oliver. History matching of three-phase flow production data. SPE Journal, 8(4), December 2003.

    Google Scholar 

  18. J. Lie, M. Lysaker, and X.-C. Tai. A piecewise constant level set framework. url:“http://www.mi.uib.no/BBG/papers.html”, 2004.

  19. J. Lie, M. Lysaker, and X.-C. Tai. A piecewise constant level set level set framework. In Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering, Jyvskyl, July 2004.

    Google Scholar 

  20. J. Lie, M. Lysaker, and X.-C. Tai. A binary level set model and some applicaions to mumford-shah image segmentation. Accepted and to appear in IEEE Transection on image processing, 2005.

    Google Scholar 

  21. D.G. Luenberger. Optimization by Vector Space Methods. Wiley Professional Paperback Series. Wiley, 1969.

    Google Scholar 

  22. M. Lygren, K. Fagervik, T.S. Valen, A. Hetlelid, G. Berge, G.V. Dahl, L Snneland, H.E. Lie, and I. Magnus. A method for performing history matching of reservoir flow models using 4d seismic data. Petroleum Geoscience, 9:85–90, 2003.

    Article  Google Scholar 

  23. L.K. Nielsen. Reservoir Characterisation by a Binary Level Set Method and Adaptive Multiscale Estimation. PhD thesis, Department of Mathematics, University of Bergen, 2006.

    Google Scholar 

  24. L.K. Nielsen, X.-C. Tai, S. Aanonsen, and M. Espedal. A binary level set model for elliptic inverse problems with discontinuous coefficients. UCLA, CAM-Report 05-51, 2005.

    Google Scholar 

  25. L.K. Nielsen, X.-C. Tai, S.I. Aanonsen, and M. Espedal. Reservoir description using a binary level set model. UCLA, CAM-Report 05-50, 2005.

    Google Scholar 

  26. S. Osher and J.A. Sethian. Fronts propargating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations. J. Comput. Phys, 79(1):12–49,1988.

    Article  MathSciNet  Google Scholar 

  27. F. Santosa. A level-set approach for inverse problems involving obstacles. ESAIM: Contr. Optim. Calc. Var., 1:17–33, 1996.

    Article  MathSciNet  Google Scholar 

  28. B. Song and T. Chan. A fast algorithm for level set based optimization. UCLA CAM-Report 02-68, 2002.

    Google Scholar 

  29. X.-C. Tai and T. Chan. A survey on multiple level set methods with applications for identifying piecewise constant functions. Int. J. of numerical analysis and modeling, 1(1):25–47, 2004.

    MathSciNet  Google Scholar 

  30. X.-C. Tai, O. Christiansen, P. Lin, and I. Skjaelaaen. A remark on the mbo scheme and some piecewise constant level set methods. UCLA, CAM-Report 05-24, 2005.

    Google Scholar 

  31. O. Yilmaz and S.M. Doherty, editors. Seismic data analysis: processing, inversion, and interpretation of seismic data. Society of Exploration Geophysicists, Tulsa, 2001.

    Google Scholar 

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Nielsen, L.K., Tai, XC., Aanonsen, S.I., Espedal, M. (2007). Reservoir Description Using a Binary Level Set Approach with Additional Prior Information About the Reservoir Model. In: Tai, XC., Lie, KA., Chan, T.F., Osher, S. (eds) Image Processing Based on Partial Differential Equations. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33267-1_22

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  • DOI: https://doi.org/10.1007/978-3-540-33267-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33266-4

  • Online ISBN: 978-3-540-33267-1

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