Finite displacement gradients measured at fault tips appear to contradict the predictions of the post-yield fracture mechanics (PYFM) model for fault tip propagation proposed by Cowie, P. A. and Scholz, C. H. (1992) Journal of Structural Geology, 14, 1133–1148. The results of a high resolution survey of a 3.6 km long normal fault in SE Utah are presented as evidence that the contradiction is real and not simply due to problems of limited resolution. A theoretical explanation for finite tip gradients is then proposed which involves a positive stress feedback between sequential fault slip increments. According to this growth model, strength heterogeneities on a fault surface limit the size of individual ruptures so that only a patch of the fault moves at any one time. Each slipping patch produces a stress perturbation which raises the shear stress on adjacent healed portions of the fault as well as the surrounding rock volume. Healing takes place after each slip event, allowing local strength recovery. Using a simple two-dimensional planar fault model, we show that when the size of the slipping patch is much smaller than the dimensions of the fault plane, and strength recovery is geologically instantaneous, the displacement profile follows an approximately linear decrease towards the tip similar to natural examples. A bell-shaped displacement profile, with tip gradients that tend to zero, is predicted only in the special case where the size of each slip patch equals the fault plane dimensions. Our main modification of the earlier model is that the size of the process zone wake, or frictional breakdown zone, scales with the dimensions of the slipping patch as opposed to the entire fault length. Model results show that the stress field at the tips of faults formed by this mechanism decays rapidly, so the range of significant interaction is small compared to the fault dimensions.
- finite tip replacement gradients
- planar fault model
- slipping patches