Geometry and mechanics of three-dimensional faults [electronic resource] : implications for slip, aftershocks, and paleostress
Keywords: Geological and Environmental Sciences.

The geometry of faults and fault systems affects the source mechanics of earthquakes and the deformation associated with slip on faults. This dissertation investigates aspects of the geometry of fault surfaces, in particular those with non-planar topology. I quantify the surface geometry using the tools of differential geometry to evaluate the geometry in a spatially coherent way. The study finds that at cm-scale ([approximately equal to]2cm) fault surfaces have no clear pattern of basic shapes succession, while at larger scales (10cm-50cm) corrugations along the slip direction are predominant while small undulations parallel to the direction of sliding exist on the cm-scale. The changes in surface shape and orientation lead to changes in resolved traction on the order of a few MPa for crustal settings, which far exceed generally associated triggering stresses. The undulations significantly retard slip on heuristic faults when compared to those lacking undulations. Geometric fault surface complexity on a crustal scale faults is investigated using relocated seismicity from a catalog of events for the Joshua Tree - Landers earthquake sequence. The spatial density of seismicity is used to locate finite width fault zones and construct surfaces indicative of the centers of these fault zones. The method identifies ten separate faults that exhibit significant non-planar geometry. The mechanical effects of the geometrically complex fault surfaces are illustrated using solutions to the quasi-static boundary value problem. I investigate the resultant stresses and tractions induced by slip on the Joshua Tree fault before the rupture of the Landers earthquake. The propensity for slip on the Landers faults is increased in regions of initiation and largest slip during the subsequent event. The geometrically complex models predict greater propensity for slip along the northern faults involved in the Landers earthquake than the commonly used planar and vertical four-fault models. The stresses adjacent to the Joshua Tree fault are investigated by calculating the changes in Coulomb stresses on optimally oriented surfaces of weakness. The geometrically complex model for Joshua Tree fault predicts the aftershocks immediately following the Joshua Tree earthquake quite well, and better than the planar fault model. Stress inversions are a useful and popular tool for structural geologist and seismologist alike. Many studies employ these methods on isolated faults or on fault system with limited ranges of orientations, which can lead to erroneous results. I propose a new method that incorporates the effects of mechanical interaction of the entire fault or fault system, solves the complete mechanical boundary value problem problem rather than employing empirical relationships between slip and stress or strain (faultless inversion). The method is tested on synthetic faults with various orientations to evaluate the effects of non-planarity and I find that the lack of varying normal vector orientations can introduce significant errors even for simple idealized cases. The effect of diversity of fault orientations are tested and the results indicate that faultless inversions do not perform as well for limited ranges of orientations when compared to the proposed method. The 1999 Chi-Chi, Taiwan, earthquake is used to test the proposed method. The resulting stress orientations are in good agreement with results from faultless inversions. Furthermore, slip distribution results are in general agreement with kinematic slip inversions using co-seismic surface deformation. Stress inversion methods using fault slip data can thus be improved upon, significantly in many cases, by solving a mechanical boundary value problem that takes into account the geometry of faults or fault systems.