On the spatial scaling of seismicity rate

Abstract

Scaling analysis of seismicity in the space-time-magnitude domain very often starts from the relation λ(m, L) = aL 10-bm Lc for the rate of seismic events of magnitude M > m in an area of size L. There is some evidence in favour of multifractality being present in seismicity. In this case, the optimal choice of the scale exponent c is not unique. It is shown how different values of c are related to different types of spatial averaging applied to λ(m, L) and what are the values of c for which the distributions of aL best agree for small L. Theoretical analysis is tested using the California data. © 2005 RAS.