A macroscopic approach towards earthquake physics: the meaning of the apparent stress

Some theoretical results concerning earthquake parameters are based on simplified seismic source models with uniform distributions of slips along a fault. Here two such results, the meaning of the apparent stress and the seismic energy vs. seismic moment relation, are revised by taking into account fault heterogeneity and interactions related to slip gradients. A theoretical microscopic model of a seismic source, formulated in terms of slip and stress fields, is studied by computer simulations. Formulation of the seismic energy rate implied by the microscopic model, together with an auxiliary kinematic model of a pulse-like rupture process, is used to derive a scaling relationship for the seismic energy as a function of other 'macroscopic' quantities: the seismic moment, rupture area, and the average slip acceleration, treated as independent variables. This result explains observed fluctuations and statistical trends of the seismic energy in both real and simulated earthquake populations.