Fluctuations, trends and scaling of the energy radiated by heterogeneous seismic sources

Abstract

SUMMARY Computer simulations, based on a heterogeneous seismic source model governed by the overdamped dynamics, reproduce essential aspects of seismicity, both on ‘microscopic’ (local functions, such as slip velocity), and ‘macroscopic’ (global functions, such as seismic energy) level. The present work focuses on relations between these two description levels, using formulation of the seismic energy rate implied by the same model. It is shown that the apparent stress, defined as the seismic energy and the seismic moment ratio, represents the correlation integral of the slip velocity distribution. An auxiliary, simplified, kinematic model of an averaged, pulse-like rupture process is used to derive the scaling relationship for the apparent stress as a function of other ‘macroscopic’ quantities: The seismic moment, MO, the rupture area, A, and the average slip acceleration, g, treated as independent variables. These results explain observed fluctuations and statistical trends of the apparent stress, characterizing both real and simulated earthquake populations.