Distribution and scaling of extensional strain in sedimentary rocks

Abstract

For this study, spatial and size distributions of normal faults and associated tensile fractures were directly measured in deformed sedimentary rocks in three extensional regions: Kimmeridge Bay and Kilve in the UK and the Maltese Islands. The collected data allow i) quantifcation of regional extension at different scales, ii) determination of the relative importance of large and small structures, iii) quan- tifcation of the spatial heterogeneity of brittle extension, iv) comparison of scaling laws for veins and faults belonging to the same extension event, and v) analysis of the evolution of brittle damage in space and time. Multiple scan-lines of different length and resolution were collected in each study area to record the entire extension-related deformation. In order to quantify the heterogeneity of fracture and strain distributions, a new method of spatial analysis has been developed. The method is based on a non-parametric comparison of the cumulative frequency and extension with that for a uniform distribution and pro- vides a measure of heterogeneity based on both the position and the displacement of individual fractures sampled along a linear traverse. Seismically observable extension is found to scale with total extension in the three study areas, obeying a power-law relationship. The proportion of the total extension that is resolved in seismic refl ection data systematically increases with increasing strain. This means that seismic data signifcantly underestimate the total extension at low strains but record most of the total extension in higher strain regions. Heterogeneity analysis carried out for the three study areas shows that i) hetero- geneities of the distributions of fractures and strain in an area can differ signifcantly, ii) heterogeneities are strongly dependent on lithology and mechanical heterogeneity, and iii) heterogeneities evolve with increasing strain. At Kimmeridge Bay, both veins and faults display power-law scaling, but do not form part of the same distribution. Veins and faults along the Kilve-Lilstock section conform to a single power-law distribution. At the Maltese Islands fault-frequencies conform to power-law scaling, but yield a higher scaling exponent in lower-strain zones than in higher-strain (damage) zones. The platform carbonates at the Maltese Islands take up early extension by randomly distributed small-scale faulting. The layered and mudstone-rich rocks around Kim- meridge Bay respond to low strain by distributed ("ductile") deformation in the shales and by randomly distributed or anti-clustered veining in the stiffer carbonate beds. In inter-bedded carbonates and shales along the Kilve-Lilstock section, early extension is highly localised in narrow zones of faults and associated damage, pre- serving large portions of virtually unfractured rock in between. A tensor method has been developed which permits three-dimensional strain analy- sis from line-data. The results of this analysis show that one-dimensional estimates of extension generally are good approximations of the maximum principal strain and that deformation in most sampled sections conforms to pure-shear, plane-strain conditions. Fold-structures associated with normal faults are explained as due to superimposed "normal drag" within the process zone and slip-related "reverse drag" within the damage zone of a (propagating) normal fault.