Markov Chain Monte Carlo Simulation to Assess Uncertainty in Models of Naturally Deformed Rock

Abstract:

Field studies in tectonics and structural geology involve many kinds of data, such as foliation-lineation pairs, folded and boudinaged veins, deformed clasts, and lattice preferred orientations. Each data type can inform a model of deformation, for example by excluding certain geometries or constraining model parameters. In past work we have demonstrated how to systematically integrate a wide variety of data types into the computation of best-fit deformations. However, because even the simplest deformation models tend to be highly non-linear in their parameters, evaluating the uncertainty in the best fit has been difficult.

In this presentation we describe an approach to rigorously assessing the uncertainty in models of naturally deformed rock. Rather than finding a single vector of parameter values that fits the data best, we use Bayesian Markov chain Monte Carlo methods to generate a large set of vectors of varying fitness. Taken together, these vectors approximate the probability distribution of the parameters given the data. From this distribution, various auxiliary statistical quantities and conclusions can be derived. Further, the relative probability of differing models can be quantified.

We apply this approach to two example data sets, from the Gem Lake shear zone and western Idaho shear zone. Our findings address shear zone geometry, magnitude of deformation, strength of field fabric, and relative viscosity of clasts. We compare our model predictions to those of earlier studies.