Conditioning of Multiple-Point Statistics Facies Simulations to Tomographic Images
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Conditioning of Multiple-Point Statistics Facies Simulations to Tomographic Images Tobias Lochbühler · Guillaume Pirot · Julien Straubhaar · Niklas Linde
Received: 17 December 2012 / Accepted: 28 July 2013 © International Association for Mathematical Geosciences 2013
Abstract Geophysical tomography captures the spatial distribution of the underlying geophysical property at a relatively high resolution, but the tomographic images tend to be blurred representations of reality and generally fail to reproduce sharp interfaces. Such models may cause significant bias when taken as a basis for predictive flow and transport modeling and are unsuitable for uncertainty assessment. We present a methodology in which tomograms are used to condition multiple-point statistics (MPS) simulations. A large set of geologically reasonable facies realizations and their corresponding synthetically calculated cross-hole radar tomograms are used as a training image. The training image is scanned with a direct sampling algorithm for patterns in the conditioning tomogram, while accounting for the spatially varying resolution of the tomograms. In a post-processing step, only those conditional simulations that predicted the radar traveltimes within the expected data error levels are accepted. The methodology is demonstrated on a two-facies example featuring channels and an aquifer analog of alluvial sedimentary structures with five facies. For both cases, MPS simulations exhibit the sharp interfaces and the geological patterns found in the training image. Compared to unconditioned MPS simulations, the uncertainty in transport predictions is markedly decreased for simulations conditioned to tomograms. As an improvement to other approaches relying on classical smoothness-constrained geophysical tomography, the proposed method allows for: (1) reproduction of sharp interfaces, (2) incorporation of realistic geological constraints and (3) generation of multiple realizations that enables uncertainty assessment.
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T. Lochbühler ( ) · N. Linde Applied and Environmental Geophysics Group, Faculty of Geosciences and Environment, University of Lausanne, Lausanne, Switzerland e-mail: [email protected] G. Pirot · J. Straubhaar Center for Hydrogeology and Geothermics, University of Neuchâtel, Neuchâtel, Switzerland
Math Geosci
Keywords Multiple-point statistics · Multiple-point direct sampling · Geophysical tomography · Conditioning 1 Introduction Predictive modeling of subsurface flow and solute transport requires detailed models of the spatial distribution of hydraulic properties. A lot of recent research has focused on finding ways to use geophysical data for hydrological parameter estimation (e.g., Hubbard and Rubin 2000; Linde et al. 2006; Eppstein and Dougherty 1998; Dafflon and Barrash 2012). The benefit of geophysical techniques is that a high number of sensors can be used at rather low costs and with little invasive impact. Data sets of thousands of data points of high spatial density are easily acquired and when these data are inver
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