The role of radiation damping in the modeling of repeated earthquake events

We have investigated the role of the radiation damping term (RDT) on repeated earthquake ruptures by modeling the faulting process through a single one-dimensional analog fault system governed by different constitutive laws. The RDT expresses the energy lost by the seismic waves. The RDT is inherently accounted for in more elaborated, fully dynamic models of extended fault, whereas it is neglected in one-dimensional fault models. In this study, we adopt various formulations of the laboratory-derived rate-dependent and state-dependent friction constitutive laws: the Dieterich-Ruina law, the Ruina-Dieterich law and the Chester and Higgs law. Our numerical results clearly indicate that the RDT significantly affects the system dynamics. More specifically, the more the RDT is effective, the more frequent the slip failures are (with a cycle-time reduction of ca. 30%). We also show that inclusion of the RDT tends to promote smaller but more frequent earthquake instabilities, irrespective of the choice of the governing law. Our data shed light on the limitations implied by the conventional formulation of the equation of motion for the spring system, in which the energy radiation is ignored.