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Experimental discovery of scaling laws relating fractal dimensions and the length distribution exponent of fault systems
Author(s) -
Davy Philippe,
Sornette Anne,
Sornette Didier
Publication year - 1992
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 - 10.1029/91gl02711
Subject(s) - fractal , fractal dimension , exponent , scaling , fault (geology) , statistical physics , distribution (mathematics) , fractal dimension on networks , scaling law , scale (ratio) , geology , geometry , physics , mathematics , fractal analysis , mathematical analysis , seismology , philosophy , linguistics , quantum mechanics
A series of experiments scaled for gravity on the formation of faults in a laboratory model of the earth's lithosphere have shown that the obtained fault patterns are self‐similar and can be characterized by various fractal dimensions. By analyzing a large set of experimental results, we discover a remarquable scaling law relating the generalized fractal dimensions D q the fault barycenter fractal dimension ‘b’ and the exponent ‘a’ of the fault length distribution. : D 0 ≈b is independent of ‘a’ whereas D q≥1 =b+2−a, for 2≤a≤3 as found in our experiments.