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

The scaling of displacement as a function of length is important for a vari ety 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 cha nge significantly at a characteristic length for a variety of reasons, for example when cracks begin to interact, or when faults grow to a length comp arable to a characteristic size in the brittle layer. Such a break of slope requires a second straight line, requiring two extra model parameters. Her e we present a new method for analysing such data, which penalises the extr a 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 I celand, and find a significant break of slope, from nu approximate to 3/2 t o nu approximate to 2/3, at a characteristic length of 12 m.