Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/42002
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Type: Journal article
Title: Markov chain Monte Carlo implementation of rock fracture modelling
Author: Mardia, K.
Nyirongo, V.
Walder, A.
Xu, C.
Dowd, P.
Fowell, R.
Kent, J.
Citation: Mathematical Geosciences, 2007; 39(4):355-381
Publisher: Kluwer Academic/Plenum Publ
Issue Date: 2007
ISSN: 1874-8961
0882-8121
Statement of
Responsibility: 
K. V. Mardia , V. B. Nyirongo, A. N. Walder, C. Xu, P. A. Dowd, R. J. Fowell and J. T. Kent
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.
Keywords: Likelihood; Reversible jump; Markov chain Monte Carlo; Fracture planes
RMID: 0020070953
DOI: 10.1007/s11004-007-9099-3
Appears in Collections:Civil and Environmental Engineering publications

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