Renormalization group approach to earthquake scaling

A systematic way for deriving fundamental earthquake scaling relationships in their size-frequency distribution and high-frequency spectrum falloff based on the renormalization group method is presented for the model earthquakes. It is known that faults populations are broadly scale-invariant over several orders of magnitude. Applying the renormalization group method to the generalized Burrige–Knopoff earthquake model, we obtain the self-similar solution from which the scaling exponents of the size-frequency distribution and spectrum falloff are obtained. The obtained exponents are in agreement with the known values and the relation between these scaling exponents helps to bridge the gap between statistic and dynamical scalings. The present paper permits us to study the self-similar behavior and helps in understanding the basic ingredients underlying earthquake scaling.