Deformation fields around a fault embedded in a non-linear ductile medium

The geological record of deformation is often characterized by a combination of discontinuous deformation, in which strain is concentrated in faults, and continuous deformation, in which strain is distributed through the material. Where slip occurs on a fault that terminates, the surrounding material is deformed. In the lower crust and in cases where large strains occur over long geological time-scales, it is appropriate to model the deformation using a viscous (probably non-linear viscous) theology. We describe a method for practical finite-element solution of this problem using a dynamically self-consistent formulation for stress and displacement on a fault of arbitrary geometry; the accuracy of the method is tested by comparison with an analytical solution for the linear theology. We describe here the instantaneous deformation fields around a mode II fault under both plane-strain and plane-stress conditions, and a range of rheological exponents n (where strain rate is proportional to deviatoric stress to the nth power). The distributions of stress and strain rate around the fault tip are controlled primarily by the rheological exponent n. A localized zone of high strain rate projects beyond the end of the fault if n is about 3 or greater, and the degree of localization of deformation increases with the value of n. The zone of high shear-strain rate can be defined in practical terms by considering (1) the region in which the creep velocity differs by more than 20 per cent from the velocity on the nearby external boundary and (2) the region in which the maximum shear-strain rate is greater than about twice the externally imposed shear-strain rate. For n = 1, the volumes so defined differ considerably, but for large values of n, the two definitions both describe the same narrow zone of deformation beyond the end of the fault. Evaluation of the Navier-Coulomb criterion for brittle failure of the medium surrounding the fault tip shows first that brittle failure is much more likely on the extensional side of the fault than the compressional side. It also shows that the volume of material subject to brittle failure decreases rapidly with increasing n because of the relatively weaker stress singularity. We analyse previously published displacement versus distance data for faults terminating in sedimentary rocks at 0.1 to 100 m length-scales under different tectonic conditions, in order to determine the rheological exponent n. These analyses result in n values between approximately 0.85 and 5 for the different faults, with error bounds on n typically +/-1. The variation in n values may result from differences in pressure, temperature and fluid conditions at the time of faulting. More importantly, the analysis demonstrates a new method for the determination of the effective rheological exponent under in situ geological conditions.