Numerical modelling of earthquake cycles based on Navier-Stokes
equations with Viscoelastic-plasticity rheology
Abstract
Visco-elastic-plastic modelling approaches for long-term tectonic
deformation assume that co-seismic fault displacement can be integrated
over 1,000s-10,000s years (tens of earthquake cycles) with the
appropriate failure law, and that short-timescale fluctuations in the
stress field due to individual earthquakes have no effect on long-term
behavior. Models of the earthquake rupture process generally assume that
the tectonic (long-range) stress field or kinematic boundary conditions
are steady over the course of multiple earthquake cycles. In this study,
we develop a numerical framework that embeds earthquake rupture dynamics
into a long-term tectonic deformation model by adding inertial terms and
using highly adaptive time-stepping that can capture deformation at
plate-motion rates as well as individual earthquakes. We reproduce
benchmarks at the earthquake timescale to demonstrate the effectiveness
of our approach. We then discuss how these high-resolution models
degrade if the time-step cannot capture the rupture process accurately
and, from this, infer when it is important to consider coupling of the
two timescales and the level of accuracy required. To build upon these
benchmarks, we undertake a generic study of a thrust fault in the crust
with a prescribed geometry. We find that lower crustal rheology affects
the periodic time of characteristic earthquake cycles and the
inter-seismic, free-surface deformation rate. In particular, the
relaxation of the surface of a cratonic region (with a relatively strong
lower crust) has a characteristic double-peaked uplift profile that
persists for thousands of years after a major slip event. This pattern
might be diagnostic of active faults in cratonic regions.