Accounting for uncertainties on the fault geometry in source inversion problems

The ill-posed nature of source estimation problems derives from several potential factors including the quality and quantity of available observations. Such observational errors are usually accounted for in the inversion process. However, epistemic errors, which relate to our simplified description of the forward problem, are rarely dealt with, despite their potential to bias the estimate of a source model. In this study, we explore the impact of uncertainties related to the fault geometry.In source inversion problems, the geometry of a fault structure is generally reduced to a set of fixed parameters, such as position, strike and dip, for one or a few planar fault segments. While some of these parameters can be solved for, more often they are fixed. We propose a practical framework to address this limitation, following on from the work of Duputel et al. (2014) which explored the impact of uncertainties on the Earth elastic properties. Here, we develop a sensitivity analysis to small perturbations of the fault geometry. We validate this approach with the simplified case of a fault that extends infinitely along strike, investigating fault dip and position uncertainty using both optimization and Bayesian approaches. We then apply our methodology to the co-seismic slip inversion of the 2016 Amatrice Mw6.1 earthquake, Italy. We find that inclusion of prediction uncertainties is critical to infer a robust source model and quantify the uncertainty on the inverted source parameters.