Statistical Analysis of Fault Attributes

The statistical analysis of fault attributes scaling relationships is discussed. Dependences of length, width of damage zone and thickness of fault core on displacement were studied assuming power-law relations. The approximation forms a piecewise-linear function with few slopes in log-log scale. The Bayesian Information Criterion (BIC) was used to find the best fit for an optimal number of parameters. Numerical tests show that the best fit was obtained when using power-law relations with two slopes. Bayesian analysis of model parameters’ probability distribution was performed. The second part of this work is devoted to statistical analysis of single faults' attributes. Truncated power-law (TPL) is considered in comparison with commonly used simple power-law (PL) (or Parreto) distribution. The maximal likelihood and the confidence interval of the exponent for both PL and TPL are estimated by appropriate statistical methods. Kolmogorov-Smirnov (KS) test and likelihood ratio test (LRT) with alternative non-nested hypothesis for exponential distribution are used to verify the statistical approximation. Our results suggest that a truncated power-law is more suitable for describing fault attributes and its condition is satisfied for a wide range of fault scales. Furthermore, advantage of TPL is proved by BIC.