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Scaling and statistical trends of the apparent stress for heterogeneous seismic sources

Senatorski P.

Acta Geophysica Polonica

2003

Vol. 51, nr 2

125-134

The apparent stress can be understood as the correlation integral of the slip velocity field over an earthquake rupture area (Senatorski, 2003). This means that the apparent stress is a macroscopic function, which can be expressed as an average of microscopic quantities describing details of the rupture process. Here it is shown, using this statistical mechanics approach and a view of the slip velocity pulse-like rupture propagation, that the apparent stress can be formulated as a function of three other macroscopic parameters - the seismic moment, the rupture area and the slip acceleration 0 treated as independent variables. Moreover, the scaling relationship for these quantities is derived. This relationship is used to explain statistical trends of the apparent stress and other macroscopic earthquake parameters observed in earthquake populations.

Random fluctuations of the apparent stress among heterogeneous seismic sources

Senatorski P.

Acta Geophysica Polonica

2003

Vol. 51, nr 1

23-36

The apparent stress, (tau)a, defined as the ration of seismic energy, Es, and seismic moment, M0, has been formulated as the average stress associated with radiation resistance of a sliding fault during as earthquake. The over damped 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 integrates over the rupture area. 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, (tau)m and (tau)l, 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.