Main, IG; Leonard, T; Papasouliotis, O; Hatton, CG; Meredith, PG; (1999) One slope or two? Detecting statistically significant breaks of slope in geophysical data, with application to fracture scaling relationships. Geophysical Research Letters , 26 (18) 2801 - 2804. 10.1029/1999GL005372.

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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 nu 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 nu approximate to 3/2 to nu approximate to 2/3, at a characteristic length of 12 m.

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