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RESERVOIR DESCRIPTION BY USING A PIECEWISE CONSTANT LEVEL SET METHOD 被引量：3

RESERVOIR DESCRIPTION BY USING A PIECEWISE CONSTANT LEVEL SET METHOD
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摘要 We consider the permeability estimation problem in two-phase porous media flow. We try to identify the permeability field by utilizing both the production data from wells as well as inverted seismic data. The permeability field is assumed to be piecewise constant, or can be approximated well by a piecewise constant function. A variant of the level set method, called Piecewise Constant Level Set Method is used to represent the interfaces between the regions with different permeability levels. The inverse problem is solved by minimizing a functional, and TV norm regularization is used to deal with the ill-posedness. We also use the operator-splitting technique to decompose the constraint term from the fidelity term. This gives us more flexibility to deal with the constraint and helps to stabilize the algorithm. We consider the permeability estimation problem in two-phase porous media flow. We try to identify the permeability field by utilizing both the production data from wells as well as inverted seismic data. The permeability field is assumed to be piecewise constant, or can be approximated well by a piecewise constant function. A variant of the level set method, called Piecewise Constant Level Set Method is used to represent the interfaces between the regions with different permeability levels. The inverse problem is solved by minimizing a functional, and TV norm regularization is used to deal with the ill-posedness. We also use the operator-splitting technique to decompose the constraint term from the fidelity term. This gives us more flexibility to deal with the constraint and helps to stabilize the algorithm.
作者 Hongwei Li Center for Integrated Petroleum Research,University of Bergen,Norway Department of Mathematics,Capital Normal University,Beijing 100037,China Xuecheng Tai Department of Mathematics,University of Bergen,Norway Division of Mathematical Sciences,School of Physical and Mathematical Sciences,Nanyang Technological University,Singapore Sigurd Ivar Aanonsen Center for Integrated Petroleum Research,University of Bergen,Norway Department of Mathematics,University of Bergen,Norway
出处 《Journal of Computational Mathematics》 SCIE CSCD 2008年第3期365-377,共13页 计算数学（英文）
基金 the Norwegian Research Council,Petromaks Programme
关键词 Inverse problem Level set method Piecewise constant Operator splitting Reservoir description Inverse problem, Level set method, Piecewise constant, Operator splitting,Reservoir description
分类号 P618.13 [天文地球—矿床学]
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参考文献26

  • 1T. Chan and X.C. Tai, Identification of discontinuous coefficients from elliptic problems using total variation regularization, SIAM J. Sci. Comput., 25 (2003), 881-904.
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同被引文献14

  • 1T. K. Nilssen, X. C. Tai. Parameter Estimation with the Augmented Lagrangian Method for a Parabolic Equa- tion[ J ]. Journal of Optimization Theory and Applications, 2005, 124 (2) : 435 -453.
  • 2Johan Lie, Marius Lysaker, Xue - Cheng Tai. A Variant of the Level Set Method and Applications to Image Seg- mentation [ J ]. Mathematics of Computation, 2006, 75 (255) : 1155 - 1174.
  • 3Xue - Cheng Tai, Hongwei Li. A Piecewise Constant Level Set Method for Elliptic Inverse Problems [ J ]. Ap- plied Numerical Mathematics, 2007, 57 : 686,696.
  • 4K. van den Doel, U. M. Ascher. On Level Set Regularization for Highly Ill - posed Distribution Parameter Esti- mation Problems [ J ]. Journal of Computational Physics, 2006, 216:707 - 723.
  • 5Lie J, Lysaker M, Tai Xueeheng. A variant of the level set method and applications to image segmentation [ J ]. Mathe- matics of Computation, 2006, 75 ( 255 ) : 1155-1174.
  • 6Tai Xuecheng, Li Hongwei. A piecewise constant level set method for elliptic inverse problems [ J ]. Applied Numerical Mathematics, 2007, 57: 686-696.
  • 7Vogel C R. Sparse matrix computations arising in discon- tinuous parameter identification [ J ]. SIAM Journal on Matrix A- nalysis and Applications, 1999, 4(20) : 1027-1037.
  • 8Doel K, Ascher U M. On level set regularization for high- ly ill-posed distribution parameter estimation problems [ J ]. Journal of Computational Physics, 2006, 216:707-723.
  • 9Chan T F, Tai Xuecheng. Level set and total variation regularization for elliptic inverse problems with discontinues co- efficient [J]. Journal of Computational Physics, 2004, 193:40 -66.
  • 10Chan T F, Tai Xuecheng. Identification of discontinuous coefficients elliptic problems using total variation regularization [J]. Siam J Sci Comput, 2003, 3(25) : 881-904.

引证文献3

Journal of Computational Mathematics
2008年 第3期

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