Faulting occurs over a large range of which are sampled by various techniques (e.g., microscopy, outcrop measurement, mapping, seismic reflection and other forms of remote sensing). Use of a single technique to measure displacement or strain will not sample faults at all scales and hence will give a biased estimate. In order to assess this bias, a knowledge of the distribution over all scales is needed. Many samples of fault displacement appear to follow a power-low distribution, with departures which can be attributed to sampling effects. The number of faults with a displacement greater-than-or-equal-to u is given by N(u) = cu(-D). The power-law distribution of displacement is consistent with similar distributions of other fault parameters and earthquake magnitudes. When sampling along a line (e.g., a bedding trace on a map or section), a self-similar fault population would have D = 1, whereas self-affine geometries yield D not-equal 1. Displacement and extension are dominated by small faults when D > 1 and by large faults when D < 1. When sampling over areas or volumes these critical values are 2 and 3, respectively. A set of strike-slip faults from the Badajoz-Cordoba Shear Zone, Spain, were sampled at two different scales using 1:50000 maps and outcrop measurements. Displacement ranges over 6 orders of magnitude. These and other fault populations typically have D ranging from 0.6 to 1.5. The power-law relationship may be integrated to yield estimates of the displacement (or extension) for faults which lie beyond the resolution of the sampling system. For example, a knowledge of D allows the extension measured on a map or seismic section to be "corrected" for faults whose displacement is below the resolution of the survey- Based on an overall estimate of D = 0.9 for the Badajoz-Cordoba data, only some 40% of the extension would be recorded by map-scale faults. A corrected extension of 41% along the shear zone is estimated; which if typical for the entire 300 km zone represents some 87 km of along-strike extension. Thus, work suggests that significant displacement occurs on faults which are too small to be interpreted from conventional seismic profiles and geological maps.
