Dynamic and quasi-dynamic modelling of earthquake cycles under rate-and-state friction from zero to three dimensions

Abstract:

Understanding earthquake sequences is fundamental to ultimately better assess seismic hazard. Numerical models are well-suited to overcome limited spatiotemporal observations and facilitate evaluations of key processes and parameters. However, 3D fully dynamic models are computational time and memory consuming. In this study we aim to provide an overview of the similarities and differences of simulated earthquake sequences from 0D to 3D.

To readily build models varying in dimension we exploit the flexibility of a recently developed C++ non-linear multi-physics library GARNET with a fully staggered grid finite difference scheme. We present numerical models of an infinitely thin strike-slip fault under rate-and-state friction embedded in an elastic medium. This model setup follows that established by the SCEC SEAS benchmarks (Erickson et al., SRL, 2020) to facilitate the comparison with other modelers for validation. We also include an adaptive grid configuration and adaptive time stepping to study the spatial and temporal resolutions.

We have validated our code against SCEC benchmarks BP1-3 (2D) and are perfecting our results of BP4 (3D). By adding one dimension at a time, we also verified lower dimensional models against higher dimensional ones. Our results indicate that some important observables, such as the event recurrence interval, max-/minimum stress and slip rate, are accurately calculated in 0/1D models which run hundreds to millions times faster. However, lacking velocity-weakening/-strengthening transitions and seismogenic fault widths limits their ability to explore earthquake nucleation and arrest mechanisms. For similar reasons, our 0/1D models favor growing/decaying oscillations over periodic slow slip events with respect to 2D and particularly 3D models where periodic events are more generally observed under same rate-and-state friction parameters. Our study with adaptive grid sizes in 2D shows that a thin layer near the velocity-weakening fault requires a fine, constant resolution to reduce numerical errors and oscillations, while coarser grid can be configured far away. This overview in terms of quantification and understanding of the limitations and advantages of each dimension facilitates future studies in result interpretations and can guide dimensional model choices.