Vallianatos, F; Tzanis, A; (1999) On possible scaling laws between electric earthquake precursors (EEP) and earthquake magnitude. Geophysical Research Letters , 26 (13) 2013 - 2016. 10.1029/1999GL900406.

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Abstract

We assume, without reference to any particular electrification mechanism, that a pre-seismic, time dependent polarization appears in a number of spherical volumes distributed in some earthquake preparation zone embedded in a half space of constant resistivity. We estimate the resulting transient electric and magnetic fields in the quasi-static approximation. On assuming that the number of polarized spheres N is scaling with their radii I as N proportional to l/l(D), we show that at some distance r from the zone, the electric field and the magnitude of the earthquake are related as LogE=alpha M+C, where alpha=(3-D)/2 and similarly for the magnetic field. Fragmentation experiments and theoretical simulations indicate that 2.2 less than or equal to D less than or equal to 2.6, yielding 0.4>alpha>0.2. The lower fractal dimensions correspond to the case of dynamic crack propagation. Letting D approximate to 2.3, yields alpha approximate to 0.35 which is comparable to the experimental value of 0.35 given by Varotsos and Alexopoulos, (1984) on the basis of a few earthquake sequences in Greece. This indicates that electric and magnetic earthquake precursors may obey scaling laws that are direct consequence of the fractal distribution of their generators and also implies that transient precursors may result from microfracturing and fragmentation processes in the earthquake preparation zone.

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