On the nature, scaling and spectral properties of pre-seismic ULF signals

Earlier work by the authors (Vallianatos and Tzanis, 1999b), has proposed a model for the propagation and scaling of electric earthquake precursors, according to which the pre-seismic electric field emission is due to some time dependent polarisation appearing in an ensemble of electrified crustal volumes within the seismogenic source, which are distributed according to a fractal power law. Herein, we extend this formulation to the analysis of ULF magnetic precursors. We calculate the resulting transient magnetic field, which turns out to be mainly vertical and observable only if the seismogenic process generates a source with polarization rate perpendicular to the vertical plane through the source and the receiver. Furthermore, a scaling law between the vertical magnetic field and the magnitude of the associated earthquake is provided. We also investigate the spectral distribution law expected from such a set of emitters. To this effect, we assume that the evolution of the precursory polarisation process is quasi-incoherent over the exited ensemble, i.e. there is no unique relaxation time, but rather a spectrum of these with energy dependence expressed by an Arrhenius law with uniformly distributed energies. We show that the macroscopic ULF field resulting from the superposition of such an ensemble of sources has a power density spectrum distributed proportionally to 1/f . The above theoretical prediction appears to be consistent with independent observations by other investigators.