EVALUATION OF TRANSTENSION AND TRANSPRESSION AT FAULT STEPS: COMPARING KINEMATIC AND MECHANICAL MODELS TO FIELD DATA Josie Nevitt, David Pollard, and Jessica Warren Department of GeoloGical and Environmental Sciences, Stanford University, Stanford, CA 94305 e-mail: [email protected] models. In addition, the mechanical model provides a Abstract means to investigate the underlying physics of the problem, including the governing constitutive laws, Deformation within fault steps contributes to many causative tectonic stress states, and frictional contact important geologic phenomena, including earthquakes, boundary conditions on the fault. In contrast, the mountain building, and basin development, and has kinematic model is constrained only by the geometry of previously been investigated using both kinematic and the structure in the final state and the assumption of mechanical models. This paper provides a direct constant volume. The comparison between kinematic comparison of these modeling techniques in the context and mechanical models presented here should compel of a meter-scale contractional fault step located in the future investigators to use the latter when considering Seven Gables outcrop (Bear Creek field area, Sierra deformation within fault steps. Nevada, CA). The Seven Gables fault step contains locally foliated granodiorite and a stretched and rotated dike, which serve as three-dimensional Keywords: deformation markers. Kinematic models in previous fault step, transtension/transpression, deformation studies have assumed one of two possible shear plane matrix, finite element model orientations: (i) shear plane parallel to the step- bounding faults; (ii) shear plane parallel to an internal Introduction fault, which is oblique to and connects the step- Faults can be discontinuous at many scales and bounding faults. This study presents kinematic models often exhibit en echelon Geometries, characterized by for the Seven Gables fault step using each of these sub-parallel fault segments that are either left- or right- geometries. Kinematic modeling is accomplished by use steppinG (Aydin and Schultz, 1990; SeGall and Pollard, of the deformation matrix, which is first formulated for 1980, 1983b; Wesnousky, 1988). Deformation within simple shear and then for transtension/transpression. fault steps plays a siGnificant role in both lonG- and The components of the deformation matrix are based on short-term fault processes, includinG fault coalescence outcrop measurements and the assumption of constant and lenGtheninG, and earthquake rupture nucleation and volume. Both models result in dike orientations with termination (CowGill et al., 2004; Harris et al., 1991; significant misfit (model 1: 28% total misfit; model 2: Harris and Day, 1993, 1999; Harris et al., 2002; Kase 44% total misfit) compared to the dike measured in and Kuge, 1998; KinG and Nabelek, 1985; Oglesby, outcrop. An interesting result of the kinematic analysis 2005; Sibson, 1985; Wesnousky, 2006; ZhanG et al., is that the contractional step may be classified as either 1991). Thus, an improved understandinG of deformation transtensional or transpressional, depending on which within fault steps will shed liGht on how fault structures model geometry is used, suggesting that these terms evolve throuGh time, with consequent benefits for may not be appropriate descriptors of deformation seismic hazard analysis. within fault steps. The ambiguity of the kinematic The nature of deformation within steps depends on results motivates the use of a mechanics-based finite the relationship between the step Geometry and the element model of deformation in the Seven Gables fault sense of slip (FiG. 1a). A step with the same sense as step. The results of this mechanical model indicate that that of the fault slip (e.G., left step alonG a left-lateral plastic strain localizes along a narrow zone that runs fault) results in extensional deformation, such as open diagonally through the step (consistent with the cracks at the meter scale (FiG. 1b) (Flodin and Aydin, orientation of the shear plane in the second kinematic 2004; Kim et al., 2000; Kim et al., 2003, 2004; Martel model). The mechanical model provides additional et al., 1988; SeGall and Pollard, 1980, 1983b) and the insights into the heterogeneous nature of deformation development of a pull-apart basin at the kilometer scale within the step, including the spatial variability of (FiG. 1c) (Aydin and Nur, 1985; Mann et al., 1983; plastic strain, slip gradient along the faults, and non- Westaway, 1995). In contrast, a step with an opposite uniform dike thinning. The ability to characterize sense to that of the fault slip (e.G., riGht step alonG a heterogeneous deformation represents a significant left-lateral fault) results in contractional deformation advantage of the mechanical model over the kinematic structures, includinG ductile fabric (FiG. 1d) or pressure Stanford Rock Fracture Project Vol. 24, 2013 H-1 Figure 1. (a) Schematic diagram relating the geometry of extensional and contractional steps along left- lateral faults to block diagrams of transtension and transpression. (b) Photograph of a small-scale extensional step between left-lateral faults with opening-mode cracks surrounded by an alteration halo (pale yellow discoloration) in the Bear Creek field area. (c) Digital elevation model (DEM) of a large-scale extensional step between right-lateral faults in southern California. (d) Photograph of a small-scale contractional step containing mylonitic foliation between left-lateral faults in the Bear Creek field area. (e) DEM of a large-scale contractional step along the right-lateral Coyote Creek Fault, southern California, which resulted in the uplifted Ocotillo Badlands. solution seams at the meter scale (Bürgmann and extension in the vertical direction, such that Pollard, 1992, 1994; Peacock and Sanderson, 1995) and deformation is accommodated through other push-up ranges at the kilometer scale (Fig. 1e) (Aydin mechanisms (i.e., development of foliation or pressure and Nur, 1985; Westaway, 1995). Differences in solution seams). secondary structures for the small- and large-scale steps Extensional and contractional steps are sometimes may be related to the confinement during deformation. referred to as being sites of “transtension” and For example, kilometer-scale contractional steps at the “transpression,” respectively (De Paola et al., 2008; surface are unconfined in the vertical direction, which ; Elliott et al., 2009; Miller, facilitates the development of push-up ranges. For 1994). These terms were first introduced to describe meter-scale fault steps that form at depth, however, the deformation associated with oblique divergence and three-dimensional confinement discourages preferential convergence of tectonic plates (Harland, 1971). In Stanford Rock Fracture Project Vol. 24, 2013 H-2 or set of faults, linking the bounding faults. In the absence of a well-developed or well-exposed internal fault, Westaway (1995) suggests using the plane connecting the fault tips in the deformed state as the shear plane orientation. As fault steps are often examined from a kinematic perspective (Barnes et al., 2001; Cembrano et al., 2005; De Paola et al., 2008; Pluhar et al., 2006; Wakabayashi et al., 2004; Westaway, 1995), determining the appropriate shear plane orientation will benefit future studies of fault steps that rely on a correct understanding of the shear plane geometry for the interpretation of kinematic indicators (e.g., microstructures). In this study, we have identified and mapped a meter-scale contractional fault step that can be used to study the relationship between shear plane orientation and deformation. This fault step, located in the Lake Edison granodiorite in the Bear Creek field area (Sierra Nevada, CA), contains a leucocratic dike and ductile fabric that serve as deformation markers. The relatively small scale and excellent outcrop exposure allow a thorough kinematic analysis using the deformation matrix. We test the ability of simple shear Figure 2. (a) Photograph of a contractional fault and transtension/transpression to reproduce the rotation step located in Bear Creek with an internal fault; of the dike using the two models for shear plane (b) Outcrop map; (c) Zoomed-in view of internal orientation (step-bounding faults vs. internal fault). The fault; (d) Zoomed-in view of step-bounding fault. kinematic analysis is complemented with a mechanics- kinematic terms, transtension and transpression based finite element model of the deformation within describe strike-slip deformations that differ from simple the step, and the assumptions inherent to both the shear due to a component of extension or contraction kinematic and mechanical models are evaluated. orthogonal to the shear plane (Dewey et al., 1998; Fossen and Tikoff, 1998; Sanderson and Marchini, 1984). Thus, knowledge of the shear plane orientation is necessary to identify a region as transtensional or transpressional. Previous kinematic studies of fault steps can be classified into two groups, based on two different models for shear plane orientation. The shear plane orientation in the first model, which we interpret to have been used by Cembrano et al. (2005) and De Paola et al. (2008), is equivalent to the orientation of the step- bounding faults. This may be the most intuitive orientation, since faults are generally modeled as parallel to the shear planes in kinematic analyses (e.g., Cladouhos, 1999). Furthermore, block diagrams of transtension