Population scaling biases in map samples of power-law fault systems

Fault population power-law exponents derived from maps are subject to sampling biases, yet simple methods do not exist for estimating quantitatively the unbiased population characteristics from the measured (biased) ones. Fault length, maximum throw and geometric moment populations measured in different sized maps of the same natural fault system are used to test new analytical results. In the analytical treatment, scale-specific probability density functions of the different measures of fault size are derived by calculating the probability of sampling faults censored to particular sizes within a small-scale sample area of a power-law population. The best-fit power-law exponents of these analytically biased populations match closely the average exponents observed at the same scales in both natural and synthetic fault maps. The exponents are less at smaller scales, with the maximum throw population showing the greatest bias and the length population the least. Exponents deduced from fault maps representative of many published ones are unlikely to be biased by more than 0.1 for the length population, but scaling biases of 0.3 or more are likely for maximum throw populations. Population exponents measured at particular scales can be used to estimate those at different scales using a maximum likelihood estimation procedure. (C) 2009 Elsevier Ltd. All rights reserved.