Random fluctuations of the apparent stress among heterogeneous seismic sources

The apparent stress, Τa, defined as the ratio of seismic energy, Es, and seismic moment, Mo, has been formulated as the average stress associated with radiation resistance of a sliding fault during an earthquake. The overdamped dynamics approximation of a seismic source implies that the seismic energy rate at a given time is proportional to the square of the slip velocity integrated over the rupture area, Es(t) ∝ ∫A q2dA. This result allows us to interpret the apparent stress as a correlation integral of the slip velocity field over space and time. Consequently, other macroscopic parameters, such as momentary and local apparent stress, Τm and Τ1, are proposed to characterize spatial and temporal heterogeneity of complex seismic sources. This approach is used to understand fluctuations of the apparent stress, and other macroscopic parameters in earthquake populations, in terms of their microscopic representation.