Automated fault model discretization for inversions for coseismic slip distributions

Geoscientists increasingly rely on coseismic slip distributions inferred from geodetic observations to drive sophisticated models of the seismic cycle. To date, little work has been done on optimizing the parameterization of these fault models so that they reflect the resolving power of observed surface displacements. The locations of noisy surface displacement observations are often widely scattered far from features we wish to analyze in the subsurface and result in highly variable model resolution with depth. The few attempts to produce variably discretized fault planes are arduously constructed by hand and may not correctly reflect the ability of the data to resolve slip features. Motivated by the increasing size of geodetic data pools and the need for distributed slip models that accurately represent features the data can resolve, we present a fully automated algorithm that iteratively adjusts the sizes of dislocations in a fault model. We use the concept of smoothing scales, derived from the model resolution matrix, to resize dislocations so that each dislocation is sized appropriately given the area over which slip in that region of the fault would be smoothed. We present a series of synthetic tests that utilize both sparse and dense data sets, and we compare our variably discretized inversions to traditional regularly discretized inversions. We also use our approach to invert for slip from geodetic observations of the 2004 M-w 6.0 Parkfield, California, earthquake and the 1995M(w) 8.1 Antofagasta, Chile, earthquake.