Statistical tests of scaling relationships for geologic structures

Abstract

Displacement–length data from dilatant fractures (joints, veins, igneous dikes) and several varieties of deformation bands were analyzed statistically to investigate the applicability of mechanical models proposed for their formation. All 17 datasets are generally consistent with equilibrium or long-term power-law slopes on the displacement–length diagram of either 1.0 or 0.5. Similar to many faults, disaggregation deformation bands are consistent with a power-law scaling relation having a slope of approximately c = 1, implying a linear dependence of maximum displacement and discontinuity length (Dmax = γL). In contrast, dilatant fractures, cataclastic deformation bands, and shear-enhanced compaction bands are consistent with a power-law scaling relation with a slope of approximately c = 0.5, implying a dependence of maximum displacement on the square root of length (Dmax = αL1/2). The scaling relations represent an average, or long-term equilibrium outcome of deformation for conditions such as length-scale, time-scale, temperature, chemistry, and an effectively homogeneous far-field stress field, allowing for variations such as rapid and/or localized behaviors. The displacement–length scaling of these geologic structures follows systematic relationships that provide information on host-rock properties and the physics of fracture and deformation-band propagation.