Markov chain Monte Carlo inversion for the rheology of olivine single crystals

We present major modifications to the Markov chain Monte Carlo inversion method of Korenaga and Karato (2008), which was developed to analyze rock deformation data and determine a corresponding flow law and its uncertainty. The uncertainties of state variables, e.g., temperature, pressure, and stress, are now taken into account by data randomization, to avoid parameter bias that could be introduced by the original implementation of the cost function. Also, it is now possible to handle a flow law composed of both parallel and sequential deformation mechanisms, by using conjugate gradient search to determine scaling constants. We test the new inversion algorithm extensively using synthetic data as well as the high-quality experimental data of Bai et al. (1991) on the deformation of olivine single crystals. Our reanalysis of this experimental data set reveals that a commonly adopted value for the stress exponent (approximate to 3.5) is considerably less certain than previously reported, and we offer a detailed account for the validity of our new estimates. The significance of fully reporting parameter uncertainties including covariance is also discussed with a worked example on flow law prediction under geological conditions.