On the Spatial Scaling of Seismicity Rate

Scaling analysis of seismicity in the space-time-magnitude domain very often starts from the relation N(m,L)=a(L)*10**(-bm)*L**c for the rate of seismic events of magnitude M>m in an area of size L. There is some evidence in favor 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 c's are related to different types of spatial averaging applied to N(m,L) and what are the c's for which the distributions of a(L) best agree for small L. Theoretical analysis is tested using California data.