The correlation between b-value and fractal dimension (D) for seismicity 

                                        Wang Wei-Chian

                                     Abstract

            Seismicity has fractal structures in space, time, and magnitude
         distributions, as expressed by the fractal dimension D of the epicenter
         distributions, Omori’s exponent p of the aftershocks, and the b value of the
         Gutenberg and Richter relation, respectively. There are correlations
         among these scaling parameters in different way. Aki’s relation of D=3b/c is
         only a speculation and has not been supported by observation data.
         However, Turcotte explained and described the relation by b=D/2
         (1986b). Then, Hirata (1989) found the negative correlation (D=2.3-0.73b)
         between b and D from the analysis of the real earthquake catalogue in the
         Tohoku region. The correlation between b and D need to explore, so
         Wang (1993) used an one-dimensional mass-spring model with fractal
         distribution of breaking strengths for the simulation of seismicity. The
         relations from synthetic seismicity show that b-values for events with
         intermediate magnitudes are close to 1, while those for larger events are
         from 1.68 to 2.52. For small events, the logN values are almost constant.

                                          Reference

               Hirata, T., A correlation between the b value and the fractal dimension of 
               earthquakes, J. Geophys. Res., 94, 7507-7414, 1989.

                                           (Abstract)(Full text)

               Wang J. H., A note on the correlation between b-value and fractal dimension 
               from synthetic seismicity, TAO, vol.4, No.4, 1993. 

                                           (Abstract)(Full text) 

               Turcotte, D.L., A fractal model for crustal deformation, Tectonophysics, 
               132, 261-269, 1986. 

                                           (Abstract)(Full text)