Constraining Moment Deficit Rate on Crustal Faults from Geodetic Data

Abstract:

Constraining moment deficit rates on crustal faults using geodetic data is currently an under-utilized but powerful method for estimating the potential seismic hazard presented by crustal faults. Two previous approaches to moment-bounding, bootstrapping and Metropolis-Hastings sampling, can both fail catastrophically when estimating the probability distribution of moment given data, p(M_o|d). Straightforward application of traditional Metropolis-Hastings sampling with uniform prior probabilities on slip leads to a mesh-dependent estimate of moment with a variance inversely related to the number of model elements. Moment thus estimated exhibits an “effective prior” on p(M_O) that tends toward a delta function halfway between the bounds as the fault discretization becomes finer! Thus, it is incorrect to estimate the uncertainty in moment directly from the uncertainty in slip. Bootstrapping can produce optimistic bounds and give biased results. A third approach is functional moment bounding (FMB), which obtains bounds on moment by minimizing the data misfit over slip for all possible values of M_o and accepting only those values with a total misfit less than some threshold. We present a modified version of this method that creates a probability distribution function on M_o from the misfit and uses this pdf to obtain confidence bounds. We also present a fourth method that we term Probabilistic Moment Bounding (PMB) that we derive within a Bayesian framework and incorporate a smoothed slip prior. Both of these approaches produce conservative results and do not exhibit mesh dependence. We compare the results from FMB and PMB to those obtained from other methods and assess the results.