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An empirical evolution law of fractal size frequency of fault population and its similarity law
Author(s) -
Otsuki Kenshiro
Publication year - 1998
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/98gl00380
Subject(s) - power law , exponent , dissipative system , fractal , fault (geology) , law , statistical physics , range (aeronautics) , physics , mathematics , statistics , mathematical analysis , materials science , geology , thermodynamics , seismology , philosophy , linguistics , political science , composite material
Size (displacement) frequencies of 10 fault populations follow a power‐law associated with cut‐off in the range smaller than a characteristic size. They are depicted by five geometrical parameters of fault population; cut‐off size, sharpness of cut‐off, fault number density, fault displacement density and the power‐law exponent. The former three are rock properties related to dissipative energy density and constitute the similarity law of the size frequency. The fault displacement density is a measure of total input energy density. The power‐law exponent decreases as the − 1/4 power of total input energy density normalized by dissipative energy density.