A modern regression approach to determining fault displacement-length scaling relationships

A number of studies have supported the hypothesis that fault displacement is systematically related to fault size by a power law. The relationship is important for estimating bulk strain in faulted terrains. However, the exponent of this relation has been the subject of some dispute: in particular as to whether the exponent is unity (i.e. a linear relationship exists between displacement and length) or larger. The techniques used to determine the exponent have been inconsistent and far from rigorous in their application of statistical tests and terminology. We have re-analysed several of the data sets using more careful techniques. We find that the power law with an exponent of unity explains most sets of data when analysed separately. We also applied a weighted joint regression analysis to combined data covering nearly 6 orders of magnitude. The best estimate of the common slope (slope in log-log space = exponent of a power law in linear space) is 0.946 with a standard error of 0.0426. Statistical tests confirm that this exponent is consistent with a value of unity, implying a linear relationship between fault displacement and length within each data set, However, the different data sets have varying intercepts in the log-log space, indicating differing slopes for the linear relation.