Stress and the direction of slip on fault planes

The shear stress direction on a fault plane depends only on four of the six components of the stress tensor. Assuming only that the slip direction marks the shear stress direction on any fault plane (and that stress is homogeneous), it is possible to estimate these four stress parameters from populations of fault planes with known slip directions, as several workers have observed. Different formulations of the problem may yield varying best‐fitting stresses and estimates of uncertainty. In the simplest case, no assumptions are made regarding the orientations of fault planes relative to the stress tensor; thus the technique allows for the possibility that the fault planes may be very weak. Here we present simple analytical and graphical descriptions of the field of admissible fault geometries relative to any four‐parameter stress model, which can be used to illustrate the significance of various inverse strategies. In particular, this paper explores the effects of using two alternative measures of misfit between an observed fault datum and stress model: (1) the pole rotation (the angle between the observed and predicted slip direction on the observed fault plane), and (2) the minimum rotation (the smallest angle between the observed fault geometry and any fault geometry which is consistent with the model). By allowing for variation of the fault plane as well as the slip vector, the minimum rotation procedure generally achieves a more stable and (presumably) realistic estimate of the actual discrepancy between a fault observation and stress model than the pole rotation procedure. In a test case using 17 earthquake focal mechanisms from the YuIi region of eastern Taiwan, separate inversions based on the two misfit criteria yield different optimum stress models and uncertainty estimates. Additional constraints on the stress tensor, such as the effect of friction, can be superimposed on the ones used here.