LIMITATIONS OF DIMENSION AND DISPLACEMENT DATA FROM SINGLE FAULTS AND THE CONSEQUENCES FOR DATA-ANALYSIS AND INTERPRETATION

The relationship between the maximum cumulative displacement on a fault (D) and the maximum linear dimension of the fault surface (W) is given by the expression D = c W(n), where the value of c is determined by rock properties; proposed values for n range from 1.0 to 2.0. Published datasets of D vs W measurements, together with new data, are presented in a common format. Most datasets are derived from maps and so the measurements of displacement and length do not represent maximum values for each fault. This factor, together with more than an order of magnitude range of c, causes regression on D vs W plots to be unsafe unless the range of W values plotted is ca 5 orders of magnitude. This restriction means that individual datasets must be combined to achieve the required range of fault size. Data analysis shows that the value of n must exceed 1.0 but discrimination between values of 1.5 and 2.0 cannot be made on the basis of data analysis alone. A modified fault growth model in which the increase in dimension of a fault with each slip event is proportional to W0.5 gives rise to a value for n of 1.5. As this model has a sound mechanical basis 1.5 is the preferred value for n. The value of n influences other aspects of fault geometry, including the displacement profile on a fault surface, the spacing of depth contours on faulted horizons and the displacement populations of single fault surfaces.