POPULATIONS OF FAULTS AND FAULT DISPLACEMENTS AND THEIR EFFECTS ON ESTIMATES OF FAULT-RELATED REGIONAL EXTENSION

Measured populations of fault displacements, derived from regional seismic, oilfield seismic, coalmine plans and outcrop data show a power law distribution with exponents (-S) of -0.45 to -0.95 for single-line samples across an array of faults. The more negative values indicate relatively larger numbers of smaller faults. An expression for a population of active faults, derived from the Gutenberg-Richter magnitude-frequency relation for earthquakes, is log N = a - b(D) log D, where D = maximum displacement of a fault, N = number of faults of maximum displacement D or greater, and b(D) is-approximately-equal-to 1.0 and has, the same value as b for the corresponding earthquake population. Populations of 'dead' faults existing at the end of a tectonic episode have been numerically derived, using a fault growth model, and satisfy the relation log N = a - E log D, where E has a value between 1.6 and 2.0. Numerically derived populations of fault displacements in a dead fault population have slopes of -S where S is-approximately=equal-to E - 1. The contribution of an individual fault to the regional strain varies with the lifetime seismic moment of thc fault and is proportional to D2. Estimation of fault-related extension by summing heaves on faults of a limited size range is valid only if the measured size range of faults accommodates most of the extension. Correction can be made if the S value of the fault displacement population is known.