An Objective Mechanical Modelling Approach For Estimating the Distribution of Fault Creep and Locking From Geodetic Data
Abstract:We present a Markov Chain Monte Carlo method that can be used to find the extents of creeping fault areas, an important input to seismic hazard models, from mechanical boundary element modelling of geodetic data. In our scheme, the surface of a partially-creeping fault is represented as a mesh of triangular elements, each of which is modelled as either locked or creeping (freely-slipping) using the boundary element code poly3d. Slip on the creeping elements of our fault mesh, and therefore elastic deformation of the surface, is driven by stresses imparted by semi-infinite faults beneath the base of the mesh (and any other surface faults) that slip at the geodetic slip rate of the faults. Starting from a random distribution of locked and unlocked patches, a modified Metropolis algorithm is used to propose changes to the locking state (i.e. from locked to creeping, or vice-versa) of randomly selected elements, retaining or discarding these based on a geodetic data misfit criterion; the succession of accepted models forms a Markov chain of model states. After a ‘burn-in’ period of a few hundred samples, these Markov chains sample a region of parameter space close to the minimum misfit configuration. By running multiple Markov chains, we can realise multiple such well-fitting models, and look for robustly resolved features (i.e. features common to a majority of the models, and/or present in the mean of those models).
We apply this method to a combination of persistent scatterer InSAR and GPS data covering the Hayward fault in northern California. Preliminary results show strong agreement between all models on the presence of regions of creep across the full down-dip extent of the fault at its northwest and southeast ends. The central portion of the fault, thought to be the source of the M~7 1868 Hayward earthquake, shows less consistent patterns. Most elements in this area are locked in around half of the models, with only a few locked in all models, indicating that the fault is likely partially locked here, and that multiple possible configurations of locked and creeping elements can fit the data approximately equally well. Additional observations, e.g. from surface creep measurements or characteristic repeating earthquakes, will be used to further refine these results in future.