Markov chain Monte Carlo implementation of rock fracture modelling
Date
2007
Authors
Mardia, K.
Nyirongo, V.
Walder, A.
Xu, C.
Dowd, P.
Fowell, R.
Kent, J.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Mathematical Geosciences, 2007; 39(4):355-381
Statement of Responsibility
K. V. Mardia , V. B. Nyirongo, A. N. Walder, C. Xu, P. A. Dowd, R. J. Fowell and J. T. Kent
Conference Name
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.