Properties of fault populations in the Gullfaks Field, northern North Sea

Abstract

There are many published examples of the size-frequency distributions of natural fault populations that have been interpreted as showing scale-invariant power-law scaling. In this paper we present the statistics of the fault throw population in the Gullfaks Field and show that the distribution can not be described by a single power law. Instead, the throw population, when plotted in log-log space, displays two distinct slopes with different exponents at scales well above the limit of seismic resolution. At scales ranging from 10 to 90 m we obtained a slope of approximately 0.3, while at scales ranging from 90 to 165 m the slope is approximately 1.0. A systematic variation in fault orientation with fault size does not appear to be the cause of this break in slope, and a simple explanation has yet to be found. However, the documentation of such a change in scaling above seismic resolution implies that similar breaks may occur equally well below the resolution limit. This suggests that extrapolation of the straight line segments of population curves to sub-seismic scales may give incorrect estimates of small-scale faults and fractures. Separation of the Gullfaks fault data set into subareas and sub-populations, based on geometric criteria, revealed several sub-populations of faults that do exhibit simpler power-law relationships. However, the wide range of values found for the scaling exponent (varying from 0.73 to 2.05) suggests that the choice of such subdivisions is an important step in the analysis procedure. We argue here that a more thorough understanding of fault populations can be achieved by documenting this sub-population variability as well as by characterizing the combined data set.