Document Details
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Document Type |
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Article In Journal |
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Document Title |
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Modelling subsurface heterogeneity by coupled Markov chains: Directional dependency, Walther's law and entropy نمذجة عدم التجانس للطبقات تحت السطحية باستخدام سلاسل ماركوف المزدوجة : الإعتماد على الاتجاه وقانون ولتر والإنتروبيا |
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Document Language |
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English |
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Abstract |
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Modelling subsurface heterogeneity by
coupled Markov chains: Directional dependency,
Walther’s law and entropy
A.M.M. ELFEKI1, ? and F.M. DEKKING2
Water Resources Section, Faculty of Civil Engineering and Geosciences, Delft University of
Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands. e-mail: a.m.elfeki@citg.tudelft.nl
2Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Probability
and Statistics, Delft University of Technology, P.O. Box 5031, 2600GA Delft, The
Netherlands. e-mail: f.m.dekking@math.tudelft.nl
Abstract. This paper is an extension of the two-dimensional coupled Markov chain model
developed by Elfeki and Dekking (2001) supplemented with extensive simulations. We focus
on the development of various coupled Markov chains models: the so-called fully forward
Markov chain, fully backward Markov chain and forward–backward Markov chain models.
We addressed many issues such as: sensitivity analysis of optimal sampling intervals in horizontal
and lateral directions, directional dependency, use of Walther’s law to describe lateral
variability, effect of conditioning on number of boreholes on the model performance, stability
of the Monte Carlo realizations, various implementation strategies, use of cross validation
techniques to evaluate model performance and image division for statistically non-homogeneous
deposits are addressed. The applications are made on three sites; two sites are located in
the Netherlands, and the third is in the USA. The purpose of these applications is to show
under which conditions the Markov models can be used, and to provide some guidelines for
the practice. Entropy maps are good tools to indicate places where high uncertainty is present,
so can be used for designing sampling networks to reduce uncertainty at these locations.
Symmetric and diagonally dominant horizontal transition probabilities with proper sampling
interval show plausible results (fits with geologists prediction) in terms of delineation of
subsurface heterogeneous structures. Walther’s law can be utilised with a proper sampling
interval to account for the lateral variability.
Key words. Markov chains, Walthers’ law, conditional simulations, entropy, stochastic
modelling, subsurface heterogeneity. |
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ISSN |
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2233 |
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Journal Name |
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Journal of Geotechnical and Geological Engineering |
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Volume |
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23 |
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Issue Number |
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1 |
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Publishing Year |
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1426 AH
2005 AD |
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Article Type |
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Article |
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Added Date |
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Monday, March 12, 2012 |
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Researchers
| عمرو محمد الفقي | Elfeki, Amro Mohamed | Investigator | Doctorate | aelfeki@kau.edu.sa |
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