Markov Chain Monte Carlo Implementation of Rock Fracture Modelling |
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Authors: | K V Mardia V B Nyirongo A N Walder C Xu P A Dowd R J Fowell and J T Kent |
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Institution: | (1) Department of Statistics, University of Leeds, Leeds, West Yorkshire, LS2 9JT, UK;(2) School of Process, Environmental & Materials Engineering, University of Leeds, Leeds, West Yorkshire, LS2 9JT, UK;(3) Faculty of Engineering, Computer & Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia;(4) School of Civil, Environmental and Mining Engineering, University of Adelaide, Adelaide, SA, 5005, Australia |
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Abstract: | This paper deals with the problem of estimating fracture planes, given only the data at borehole intersections with fractures.
We formulate an appropriate model for the problem and give a solution to fitting the planes using a Markov chain Monte Carlo
(MCMC) implementation. The basics of MCMC are presented, with particular emphasis given to reversible jump, which is required
for changing dimensions. We also give a detailed worked example of the MCMC implementation with reversible jump since our
implementation relies heavily on this new methodology. The methods are tested on both simulated and real data. The latter
is a unique data set in the form of a granite block, which was sectioned into slices. All joints were located and recorded,
and the joint planes obtained by stacking strike lines.
This work is important in the risk assessment for the underground storage of hazardous waste. Problems and extensions are
discussed. |
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Keywords: | Markov chain Monte Carlo Likelihood Reversible jump Fracture planes |
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