Structural model of the relation between seismic scalings and the generalized scaling law of seismicity

A mathematical model has been proposed to match scalings of two multifractal fields induced by multiplicative cascades. Relations between the parameters of local and global scalings of such fields have been derived. The model has been applied to describe the relation of scalings of spatial distributions of epicenters of micro-earthquakes and their seismic energy, as well as the scaling of recurrence of earthquakes. It has been shown that the derived relations are satisfied for real seismic distributions simulated by multifractal fields. These relations between all known forms of seismic scalings (except for the time scaling) have been proposed to be considered as a new seismic law, a generalized scaling law of seismicity.