Theory of slickenline patterns based on the velocity gradient tensor and microrotation

Abstract

Brittle fault zones commonly are characterized by a multitude of lineated shear planes having a wide distribution of orientations. In our model, we assume the faulted rock comprises an aggregate of rigid blocks whose surfaces are the shear planes. We define two independent scales of motion to distinguish the local rigid rotation of the blocks with their shear planes (the “micromotion”) from the average deformation of the material on a macroscopic scale (the “macromotion”). The macromotion is defined by the macrovelocity gradient tensor, which is separated into symmetric and antisymmetric parts, the deformation rate and the macrospin tensors respectively; the micromotion is defined by a microspin tensor. On any shear plane, slickenlines form parallel to the direction of the maximum rate of shear, which we assume is determined by the direction of the maximum component of the macrovelocity gradient tensor tangent to the shear plane and by a component of the microspin in the shear plane. For a restricted kinematic model, patterns of slickenline orientations are defined on a uniform distribution of shear plane orientations by the values of D and W. D is a ratio of differences in the principal values of the deformation rate tensor, and W is a ratio of the net spin to the maximum rate of macroshear. We distinguish between instantaneous slickenline patterns and finite-deformation patterns. The two are different if the shear planes rotate relative to the principal deformation rate axes, in which case finite-deformation slickenlines form curved or crossing lineations. If W = 0, the instantaneous slickenline patterns have orthorhombic symmetry (0 < D < 1), or higher symmetry ( D = 1 or 0). If W ≠ 0, the instantaneous slickenline patterns have monoclinic symmetry. For pure shear in an isotropic body, instantaneous slickenline patterns have orthorhombic symmetry ( W = 0, D = 0.5) whereas for pure shear accommodated by shear on a planar anisotropy ( W = −1, D = 0.5), the pattern is monoclinic. For simple shear with the rigid rotation of local shear planes defined by the shear-induced spin ( W = 0, D = 0.5), the instantaneous slickenline pattern is orthorhombic but the finite-deformation pattern is monoclinic. For simple shear with no shear plane rotation ( W = −1, D = 0.5), the instantaneous pattern is monoclinic. Special cases of our hypothesis are equivalent to the hypothesis that slickenlines are parallel to the direction of maximum resolved shear stress (e.g. Angelier, 1979, 1984). The slickenline patterns predicted for this case are always of orthorhombic or higher symmetry, and are equivalent to our instantaneous patterns for which W = 0 and to our finite-deformation patterns for which, in addition, there is no microspin.