Mechanical analysis of fault slip data: Implications for paleostress analysis

Abstract

Stress inversions are a useful and popular tool for structural geologist and seismologist alike. These methods were first introduced by Wallace (1951) and Bott (1959) and subsequent studies continue to be based on their assumptions: the remote stress tensor is spatially uniform for the rock mass containing the faults and temporally constant over the history of faulting in that region, and the slip on each fault surface has the same direction and sense as the maximum shear stress resolved on that surface from the remote stress tensor. Furthermore, successful implementation requires that slip accumulates on faults of diverse orientation. Many studies employ these methods on isolated faults or on fault systems with limited ranges of orientations, which can lead to erroneous results. We propose a new method that incorporates the effects of mechanical interaction of the entire fault or fault system, and solves the complete mechanical problem rather than employing empirical relationships between slip and stress or strain (or strain rate). The method requires knowledge of the fault geometry and information on at least one slip vector component along portions of the known fault geometry. For example, if throw is known, the strike-slip component can be solved for. We test the method using a single synthetic fault with anisotropic roughness similar to that measured at fault outcrops. While the orientation of remote stress may be determined precisely, the lack of diverse fault orientations introduces a systematic error in the remote stress ratio. We further test the effect of diversity of fault orientations and find that Wallace–Bott type inversions do not perform as well for limited ranges of orientations when compared to the proposed method. Finally, we use published data from the 1999 Chi-Chi, Taiwan, earthquake, and find that the method using surface data only, and surface data with subsurface focal mechanisms, produce similar results. The resulting stress orientations are in good agreement with results from Wallace–Bott inversions. Furthermore, the slip distribution is in general agreement with kinematic slip inversions using coseismic surface deformation. Stress inversion methods using fault slip data can thus be improved upon, significantly in some cases, by solving a mechanical boundary value problem that takes into account the geometry of faults or fault systems. As a bonus, the solution provides the stress, strain, and displacement fields throughout the region and the slip distributions on the faults.