Inversion of CSEM Data for Subsurface Structure Identification and Numerical Assessment of the Upstream Mobility Scheme
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Part I In this part of the thesis, two different methodologies for solving the inverse problem of mapping the subsurface electric conductivity distribution using controlled source electromagnetic (CSEM) data are presented. The two inversion methodologies are based on a classical and a Bayesian approach for solving inverse problems, respectively. In the classical approach, we regularize the inverse problem by incorporating structural prior information available from, e.g., interpreted seismic data. In many cases, the outcome of an interpretation of seismic data cannot be well approximated by a Gaussian distribution. Hence, to incorporate non-Gaussian prior information we have applied the shape prior technique. Here, an implicit transformation of variables facilitates the incorporation of non-Gaussian prior information, at the expense of an applicationdependent kernel function. In the Bayesian approach, a combination of prior knowledge and observed data results in a solution given as a posterior probability density function (PDF). To sample from the posterior PDF, a sequential Bayesian method, the ensemble Kalman filter (EnKF), is applied. Structural prior information is naturally incorporated as a part of the Bayesian framework. To represent large-scale subsurface structures two model-based, composite parameterizations based on the level-set representation are applied in the inversion methodologies. By using a reduced number of parameters in the representation, a regularization of the inverse problem is achieved. Moreover, it enables the use of second-order gradientbased optimization algorithms in the classical approach. Part II In this part of the thesis, a numerical investigation of the upstream mobility scheme for calculating fluid flow in porous media is presented. Previous studies have shown that the upstream mobility scheme experienced erroneous behaviour when approximating pure gravity segregation flow in 1D heterogeneous porous media. The errors shown, however, were small in magnitude. In this work, numerical experiments, where we include both advection and gravity segregation, are conducted. It is shown that the errors produced in this case may be larger in magnitude than for pure gravity segregation, but are only found for countercurrent flow situations.
Has partsPaper I: S. Tveit, S. A. Bakr, M. Lien, and T. Mannseth, Identification of subsurface structures using electromagnetic data and shape priors, submitted to Journal of Computational Physics, 2014. The article is available at: http://hdl.handle.net/1956/9612.
Paper II: S. Tveit, S. A. Bakr, M. Lien, and T. Mannseth, Ensemble-based, Bayesian inversion of CSEM data using structural prior information, in proceedings of the 76th EAGE Conference & Exhibition, Amsterdam, the Netherlands, 2014. Full text not available in BORA due to publisher restrictions. The article is available at: http://dx.doi.org/10.3997/2214-4609.20141558.
Paper III: S. Tveit, S. A. Bakr, M. Lien, and T. Mannseth, Ensemble-based Bayesian inversion of CSEM data for subsurface structure identification, resubmitted to Geophysical Journal International, 2014. Full text not available in BORA.
Paper IV: S. Tveit and I. Aavatsmark, Errors in the upstream mobility scheme for countercurrent two-phase flow in heterogeneous porous media, Computational Geosciences 16(3), 809-825, 2012. Full text not available in BORA due to publisher restrictions. The article is available at: http://dx.doi.org/10.1007/s10596-012-9289-z.