Arriving at estimates of a rate and state fault friction model parameter using Bayesian inference and Markov chain Monte Carlo

The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few me-ters depending on the length scale of the critically stressed fault. This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed ac-celeration at the seismogram. To eventually construct a framework that takes noisy seismogram acceleration data as input and spits out robust estimates of critical slip distance as the output, we first present the performance of the framework for synthetic data. The framework is based on Bayesian inference and Markov chain Monte Carlo methods. The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.