Power-Law Testing for Fault Attributes Distributions

Abstract

This paper is devoted to statistical analysis of faults’ attributes. The distributions of lengths, widths of damage zones, displacements and thicknesses of fault cores are studied. Truncated power-law (TPL) is considered in comparison with commonly used simple power-law (PL) (or Pareto) distribution. The maximal likelihood and the confidence interval of the exponent for both PL and TPL are estimated by appropriate statistical methods. The Kolmogorov–Smirnov (KS) test and the likelihood ratio test with alternative non-nested hypothesis for exponential distribution are used to verify the statistical approximation. Furthermore, the advantage of TPL is proved by Bayesian information criterion. Our results suggest that a TPL is more suitable for describing fault attributes, and that its condition is satisfied for a wide range of fault scales. We propose that using truncated power laws in general might eliminate or relax the bias related to sampling strategy and the resolution of measurements (such as censoring, truncation, and cut effect) and; therefore, the most reliable range of data can be considered for the statistical approximation of fault attributes.