Reconsideration of the energy balance in earthquake faulting, Progress in Earth and Planetary Science

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The occurrence of earthquakes is now understood as brittle shear fracture releasing the elastic potential energy stored in the earth. Since the 1950s, many studies on the energy balance in earthquake faulting have been done, but there seems to be some incoherence among them. The essential reason is because various changes in conceptual framework happened during the last six decades, specifically the introduction of the new paradigm of plate tectonics in the 1960s, the concept of moment tensor as source representation in the 1970s, and the fault constitutive law governing rupture growth in the 1990s. Therefore, it will be worthwhile to reconsider the energetics of earthquake faulting from a current perspective. For this purpose, first of all, we summarize the basic concepts of elastic potential energy and moment tensor and review the general representation of earthquake sources and the origin of background crustal stress to confirm that the effect of earth’s self-gravitation is negligible in the energetics of shear faulting. Next, as a starting point for discussion, we directly derive a basic equation of mechanical energy balance in dynamic shear faulting from the equation of motion for an elastic body subjected to tectonic-origin deviatoric stress. Then, we review the widely accepted formula for indirectly evaluating radiated seismic energy from a simplified energy balance equation and compare with the direct evaluation based on the analytical solution of displacement fields for a point dislocation source in order to call attention to inconsistency between them. The inconsistency comes from the omission of the effects of rupture growth rate in the simplified energy balance equation. So, finally, we review the energy balance at the tips of a propagating shear crack, which naturally leads to the introduction of the slip-weakening fault constitutive law as a fundamental equation governing earthquake rupture. Then, we discuss the whole process of earthquake rupture, consisting of initiation, acceleration, steady propagation, deceleration, and termination from the viewpoint of energy balance.