From antimoment to moment: Plane-strain models of earthquakes that stop

Abstract

Some simple cases of the seismic gap model are examined in plane strain. Numerical solutions are found for near-field elastodynamic motion coupled to frictional sliding on a fault. Rupture velocity is specified, but the dynamic solution is otherwise dependent only on the initial state. The initial seismic gap is a non-uniformity of past slip on the fault plane. It is termed an antidislocation and is characterized by its antimoment and its energy. Sliding stops naturally in this model, even with uniform material properties. The moment of the calculated earthquake is dependent on the difference between the kinetic friction level and the background shear-stress level and is independent of rupture velocity. If initial states are scaled to have equal antimoments, and if the stress scale is normalized according to the initial energy, then the earthquake moment is nearly independent of the shape of the initial antidislocation. The ratio of radiation reaction stress (apparent stress) to weighted mean stress drop is 0.36±0.04 for all cases calculated. Non-dependence of earthquake moment on rupture velocity and the shape of the initial antidislocation is expected to carry over to three-dimensional cases. The final fault dislocation is smoother than the initial dislocation in every case calculated. Nonuniform friction or a nonplanar fault is required to get a dislocation rough enough to produce succeeding earthquakes.