One slope or two? Detecting statistically significant breaks of slope in geophysical data, with application to fracture scaling relationships

Details One slope or two? Detecting statistically significant breaks of slope in geophysical data, with application to fracture scaling relationships One slope or two? Detecting statistically significant breaks of slope in geophysical data, with application to fracture scaling relationships

Sep 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999georl..26.2801m&link_type=abstract

Geophysical Research Letters, Volume 26, Issue 18, p. 2801-2804

Physics

Geophysics

22

Mathematical Geophysics, Structural Geology: Fractures And Faults, Physical Properties Of Rocks: Fracture And Flow, Mathematical Geophysics: General Or Miscellaneous

Scientific paper

The scaling of displacement as a function of length is important for a variety of applications which depend on the mechanical and hydraulic properties of faults and fractures. Recently it has been suggested that the power-law exponent v which has been found to characterize this relationship may change significantly at a characteristic length for a variety of reasons, for example when cracks begin to interact, or when faults grow to a length comparable to a characteristic size in the brittle layer. Such a break of slope requires a second straight line, requiring two extra model parameters. Here we present a new method for analysing such data, which penalises the extra parameters using a modified form of Schwarz's Information Criterion, and a Bayesian approach which represents uncertainty in the unknown parameters. We apply the method to data from the Krafla fissure zone in the north of Iceland, and find a significant break of slope, from v~3/2 to v~2/3, at a characteristic length of 12 m.

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