Scaling of fault displacements and implications for the estimation of sub-seismic strain

Abstract

Abstract Fault displacement populations have been shown to follow a power-law scaling relationship characterized by an exponent D. This relationship can be used to make predictions of the sub-seismic fault population from data derived from seismic surveys. Although fault populations exist in three dimensions the use of section data is recommended. D -values derived from sections can be applied directly to several problems, and are also related to the D -value for the fault set in higher dimensions. Accurate determination of D requires proper consideration of the scale range and sample size limitations of available data. The most common technique of using a cumulative frequency graph often leads to an upwards bias. An iterative correction procedure is proposed. Discrete frequency methods avoid this bias, but as a standard linear interval graph has other associated problems, a log-interval graph method is preferred. Simulations of these methods, applied to random computer generated samples from power-law distributions, have been made to examine the accuracy of D-values derived from typical data. Equations to estimate the confidence intervals for these D-values have been derived from a synthesis of the results. The application of the techniques is shown using fault data measured on seismic sections from the Southern North Sea and the Inner Moray Firth. Where local differences in D are shown to be significant, there is usually a marked change in structural style. Fault data are used to make improved estimates of crustal extension (β) by extrapolating the derived power-law relationship. A value of β = 1.20 is calculated for the Inner Moray Firth. Applications predicting the intersection of horizontal wells with ‘large’ sub-seismic faults and quality control of fault interpretation on seismic sections are also described.