On possible scaling laws between electric earthquake precursors (EEP) and earthquake magnitude

We assume, without reference to any particular electrification mechanism, t hat a pre-seismic, time dependent polarization appears in a number of spher ical volumes distributed in some earthquake preparation zone embedded in a half space of constant resistivity. We estimate the resulting transient ele ctric and magnetic fields in the quasi-static approximation. On assuming th at the number of polarized spheres N is scaling with their radii I as N pro portional to l/l(D), we show that at some distance r from the zone, the ele ctric 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 equ al to D less than or equal to 2.6, yielding 0.4>alpha>0.2. The lower fracta l dimensions correspond to the case of dynamic crack propagation. Letting D approximate to 2.3, yields alpha approximate to 0.35 which is comparable t o 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 e lectric and magnetic earthquake precursors may obey scaling laws that are d irect consequence of the fractal distribution of their generators and also implies that transient precursors may result from microfracturing and fragm entation processes in the earthquake preparation zone.