On the relations between fracture energy and physical observables in dynamic earthquake models

Abstract
We explore the relationships between the fracture energy density (EG) and the key parameters characterizing earthquake sources, such as the rupture velocity (vr), thetotal fault slip (utot), and the dynamic stress drop (?td). We perform several numerical experiments of three-dimensional, spontaneous, fully dynamic ruptures developing on planar faultsof finite width, obeying different governing laws and accounting for both homogeneous and heterogeneous friction. Our results indicate that EG behaves differently, depending on theadopted governing law and mainly on the rupture mode (pulselike or cracklike, sub- or supershear regime). Subshear,
homogeneous ruptures show a general agreement with thetheoretical prediction of EG , but for ruptures that accelerate up to supershear speeds it is difficult to infer a clear dependence of fracture energy density on rupture speed, especially inheterogeneous configurations. We see that slip pulses noticeably agree with the theoretical prediction of EG utot2, contrarily to cracklike solutions, both sub- and supershear andboth homogeneous and heterogeneous, which is in agreement with seismological inferences, showing a scaling exponent roughly equal to 1. We also found that the proportionality betweenEG and ?td2, expected from theoretical predictions, is somehow verified only in the case of subshear, homogeneous ruptures with RD law. Our spontaneous rupture models confirm thatthe total fracture energy (the integral of EG over the whole fault surface) has a power law dependence on the seismic moment, with an exponent nearly equal to 1.13, in generalagreement with kinematic inferences of previous studies. Overall, our results support the idea that EG should not be regarded as an intrinsic material property. Author: Andrea Bizzarri