Inference of discontinuity trace length distributions using statistical graphical models

The characterization of discontinuities within rock masses is often accomplished using stochastic discontinuity network models, in which the stochastic nature of the discontinuity network is represented by means of statistical distributions. We present a flexible methodology for maximum likelihood inference of the distribution of discontinuity trace lengths based on observations at rock outcrops. The inference problem is formulated using statistical graphical models and target distributions with several Gaussian mixture components. We use the Expectation–Maximization algorithm to exploit the relations of conditional independence between variables in the maximum likelihood estimation problem. Initial results using artificially generated discontinuity traces show that the method has good inference capabilities, and inferred trace length distributions closely reproduce those used for generation. In addition, the convergence of the algorithm is shown to be fast.