Pure and Applied Geophysics

, Volume 170, Issue 12, pp 2173–2183 | Cite as

Power-Law Testing for Fault Attributes Distributions

  • Dmitry KolyukhinEmail author
  • Anita Torabi


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.


Faults power-law distribution likelihood ratio test non-nested hypotheses Bayesian information criterion 



The financial support from Statoil-VISTA, and research cooperation between the Norwegian Academy of Science and Letters and Statoil to the first author is acknowledged. His research was carried out as part of the Impact of Fault Envelope Architecture on Reservoir Fluid Flow Project at the Centre for Integrated Petroleum Research (CIPR), Uni Research. We are grateful to Jan Tveranger for his comments on the earlier version of the manuscript. The second author is grateful to CIPR, centre of excellence and the Research Council of Norway for supporting her research.


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© Springer Basel 2013

Authors and Affiliations

  1. 1.Uni CIPRBergenNorway

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