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One slope or two? Detecting statistically significant breaks of slope in geophysical data, with application to fracture scaling relationships
Author(s) -
Main I. G.,
Leonard T.,
Papasouliotis O.,
Hatton C. G.,
Meredith P. G.
Publication year - 1999
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 - 10.1029/1999gl005372
Subject(s) - scaling , exponent , geology , power function , displacement (psychology) , fracture (geology) , function (biology) , geotechnical engineering , mathematics , geometry , mathematical analysis , psychology , philosophy , linguistics , psychotherapist , evolutionary biology , biology
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 ν which has been found to characterise 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 ν ≈ 3/2 to ν ≈ 2/3, at a characteristic length of 12m.