Bayesian Markov chain Monte Carlo methods for modeling rock deformation

Joshua Davis, Carleton College
Sarah Titus, Carleton College

When mathematically modeling a rock deformation such as a shear zone, the geologist's goal is to relate the parameters of the model to the observed data. A forward model takes parameter values as input and produces predicted data as output. An inverse model takes observed data as input and produces best-fit parameter values as output. In practice, the inverse model usually amounts to many computations of the forward model, for example in an iterative numerical optimization. The interpretation of results is often complicated by non-uniqueness and uncertainty in the best fit.

In this presentation, we inverse-model rock deformation using Bayesian Markov chain Monte Carlo simulation. The output of this method is a large set of parameter vectors, which approximates the probability distribution of the parameters given the data, giving rich insight into the uncertainty in the fit. Any kind of forward model can be plugged in, as long as suitable 'prior distributions' for its parameters can be identified.

To demonstrate these techniques, we focus on two kinds of data: foliation-lineation orientations, and shape preferred orientation (SPO) ellipsoids arising from rigid and deformable clasts. We compare two classes of forward model: homogeneous (kinematic) and heterogeneous (dynamic) triclinic transpression. We present numerical experiments about the coverage rates of statistical inference methods. These techniques can also be used to evaluate the relative probabilities of differing approaches, offering the geologist a way to evaluate which model is most appropriate in any given situation.


Cutting edge research in structural geology geophysics geochemistry and tectonics