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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... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Research Letters Wiley

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

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References (11)

Publisher
Wiley
Copyright
Copyright © 1999 by the American Geophysical Union.
ISSN
0094-8276
eISSN
1944-8007
DOI
10.1029/1999GL005372
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Geophysical Research LettersWiley

Published: Sep 15, 1999

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