MCMC implementation of rock fracture modelling

Mardia, K.V., Walder, A.N., Xu, C., Dowd, P.A., Fowell, R.J., Nyirongo, V.B. & Kent, J.T.

This paper deals with the problem of estimating fracture planes, given only the data at boreholes. We formulate an appropriate model for the problem, and give a solution to fitting the planes using a Markov chain Monte Carlo implementation. The basics of MCMC are given, with particular emphasis given to reversible jump, which is required for changing dimension. (A detailed worked example is given as an appendix). 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: Markov chain Monte Carlo; likelihood; reversible jump; fracture planes