Abstract
We study the dynamics of the seismic activity in Mexico within a framework of dynamic scaling approach to time series fluctuations, recently suggested by Balankin (Phys. Rev. E, 76 (2007) 056120). We found that the relative seismic activity and the long-sampled fluctuations of seismic activity both display a self-affine invariance within a wide range of consecutive seismic evens. Furthermore, we found that the long-sampled fluctuations of seismic activity obey the dynamic scaling ansatz analogous to the Family-Vicsek dynamic scaling ansatz in the theory of kinetic roughening of moving interfaces. These findings imply that the records of recurrent seismic events possess hidden, long-term correlations associated with the scaling dynamics of seismic activity fluctuations.