On the mechanical work absorbed on faults during earthquake ruptures

In this paper we attempt to reconcile a theoretical understanding of the earthquake energy balance with current geologic understanding of fault zones, with seismological estimates of fracture energy on faults, and with geological measurements of surface energy in fault gouges. In particular, we discuss the mechanical work absorbed on the fault plane during the propagation of a dynamic earthquake rupture. We show that, for realistic fault zone models, all the mechanical work is converted in frictional work defined as the irreversible work against frictional stresses. We note that the γeffof Kostrov and Das (1988) is zero for cracks lacking stress singularities, and thus does not contribute to the work done on real faults. Fault shear tractions and slip velocities inferred seismologically are phenomenological variables at the macroscopic scale. We define the macroscopic frictional work and we discuss how it is partitioned into surface energy and heat (the latter includes real heat as well as plastic deformation and the radiation damping of Kostrov and Das). Tinti et al. (2005) defined and measured breakdown work for recent earthquakes, which is the excess of work over some minimum stress level associated with the dynamic fault weakening. The comparison between geologic measurements of surface energy and breakdown work revealed that 1–10% of breakdown work went into the creation of fresh fracture surfaces (surface energy) in large earthquakes, and the remainder went into heat. We also point out that in a realistic fault zone model the transition between heat and surface energy can lie anywhere below the slip weakening curve.