Multifractals and Local Singularity Analysis - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 447

Fig. 11.27 Geological map of northwestern Zhejiang Province, China (Source: Xiao et al. 2012 ,
Fig. 1)

numerous successful applications of this relatively simple model including many
to solve solid Earth problems (also see, e.g., Cheng 1994 ; Cheng and Agterberg
1996 ;Agterberg 2007a , b ;Cheng 2008 ). Although various departures from the
model have been described in these papers and elsewhere, the binomial/ p model
basically is characterized by a single parameter. In the original model of de Wijs
( 1951 ), this parameter is the dispersion index d . In Sect. 6.2 it was discussed that
the absolute dispersion index of Matheron satisfies A ) 2 /log e 16, and

¼ (log e ʷ

ʷ ¼ (1 + d )/(1 d ). When the parameter p is used as in Evertsz and Mandelbrot

( 1992 ): p d ). The multifractal spectrum of this model, which shows

the fractal dimensions f (

¼ 0.5(1

α ) as a function of the singularities, has its maximum

f ( α ) ¼ 1 r E ¼ 1) at α ¼ 1, and f ( α ) ¼ 0 at two points with:

α min ¼ log 2 (1 p ); α max ¼ log 2 p . Another parameter that can be used to