THE GROWTH OF SHEEP MOUNTAIN ANTICLINE: COMPARISON OF FIELD DATA AND NUMERICAL MODELS Nicolas Bellahsen and Patricia E. Fiore Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305 e-mail: [email protected] be explained by this deformed basement cover interface Abstract and does not require that the underlying fault to be listric. In his kinematic model of a basement involved We study the vertical, compression parallel joint compressive structure, Narr (1994) assumes that the set that formed at Sheep Mountain Anticline during the basement can undergo significant deformations. Casas early Laramide orogeny, prior to the associated folding et al. (2003), in their analysis of field data, show that a event. Field data indicate that this joint set has a basement thrust sheet can undergo a significant heterogeneous distribution over the fold. It is much less penetrative deformation, as it passes over a flat-ramp numerous in the forelimb than in the hinge and geometry (fault-bend fold). Bump (2003) also discussed backlimb, and in fact is absent in many of the forelimb how, in several cases, the basement rocks must be field measurement sites. Using 3D elastic numerical deformed by the fault-propagation fold process. models, we show that early slip along an underlying It is noteworthy that basement deformation often is thrust fault would have locally perturbed the neglected in kinematic (Erslev, 1991; McConnell, surrounding stress field, inducing a compression that 1994), analogue (Sanford, 1959; Friedman et al., 1980), would inhibit joint formation above the fault tip. and numerical models. This can be attributed partially Relating the absence of joints in the forelimb to this to the fact that an understanding of how internal stress perturbation, we are able to constrain the deformation is delocalized in the basement is lacking. forelimb kinematics and, thus, the mode of folding. But it is also due to the persistence of the forced fold Accordingly, at Sheep Mountain, the forelimb was kinematic model as a simple yet incomplete model for originally located in the hanging wall, above the upper the basement involved fold. We say incomplete because tip of the thrust fault. We conclude that the fold there is abundant geophysical and rock mechanical data developed with a fixed hinge, rotating limbs, and an that demonstrate basement rocks are not rigid. For these internally deforming basement. reasons, we believe that field studies are important to illustrate the possible behavior of basement and cover Introduction rocks. The growth of basement fault-cored anticlines is In this study, we discuss the fold kinematics at often described using the classical forced fold model Sheep Mountain Anticline, Wyoming, to determine (Cosgrove, 2000; Stearns, 1978). In this model, an how fold development may have depended on a non- otherwise rigid basement is very locally deformed rigid basement. This fold is a well-known Laramide along a thrust fault that separates two blocks of anticline. Recently, both its subsurface geometry negligible internal deformation. The hanging wall (Stanton and Erslev, 2004) and its fracture patterns basement block is translated upward and deforms the (Bellahsen et al., submitted) have been studied. overlying sedimentary layers. When the thrust fault is planar, no rotation of the basement-cover interface occurs and the resulting geometry is a monocline (Reches, 1978a; Reches, 1978b). When the thrust fault is listric, rotation of this interface occurs and the result is an anticline with significant backlimb rotation (Erslev, 1986). These kinematic models are widely accepted and have been used for fracture prediction (Allmendinger, 1998). Few studies acknowledge that basement blocks may be significantly deformed internally. However, Stone (1993) showed, with fold shape interpretations derived from subsurface data, that the basement cover interface often is “folded” (meaning curved). In this case, the backlimb rotation that results in the Fig. 1: Sheep Mountain Anticline as viewed from the development of an anticline rather than a monocline can northern nose (photo by Steve Mabee). Stanford Rock Fracture Project Vol. 16, 2005 H-1 To rigorously discuss the fold kinematics, we use Stress perturbations around faults have been passive markers that define specific structural locations studied by analyzing the results of elastic models in of the fold and then determine where those markers light of available field data (Bourne, 2001; Kattenhorn, were before folding. In addition, we use the distribution 2000; Maerten, 2002). In this paper, we first use 3D of early Laramide pre-folding fractures as a constraint elastic models (Poly3D; Thomas, 1993) to study how on the folding process. These fractures are interpreted thrust faults perturb the surrounding stress field. This as early fractures that formed perpendicular to the least allows us to determine the location of a zone where compressive stress (Engelder, 1985) as joints, vertical joint formation is inhibited. Knowing, from collected and parallel to the direction of Laramide maximum field data, that this zone is presently located in the fold horizontal compression (NE-SW; Bird, 2002; forelimb, we can then deduce the fold kinematics. Engebretson et al., 1985). These fractures are usually homogeneously distributed spatially. Their presence is Geological setting controlled by the least compressive stress, whereby if Sheep Mountain Anticline (SMA) is a NW-SE trending this stress is a tensile effective principal stress, joints fold located in the northern part of Wyoming on the may initiate. In general, joints forming under these eastern edge of the Bighorn Basin (Fig. 1 and 2). The conditions are described as a regional set (Engelder and Laramide orogeny occurred at the end of the Geiser, 1980). Bellahsen et al. (submitted) show that, at Cretaceous, consisting of a NE-trending compression Sheep Mountain anticline, there is a zone where these (Bird, 2002; Engebretson et al., 1985) that generated joints are significantly less numerous (fold forelimb) SMA, a basement-fault cored asymmetric fold. The and suggested the possible influence of a stress underlying thrust fault (Fig. 3) dips 50° SW and is perturbation caused by the underlying basement thrust interpreted by some (see paper I in this volume) to be fault. cut by a younger NE-dipping thrust fault (Stanton and Fig. 2: Fracture data at Sheep Mountain Anticline. The fractures (joints) striking NE-SW comprise a major fracture set at all localities in the backlimb and the hinge. They are significantly less present or even absent at localities in the forelimb. Stanford Rock Fracture Project Vol. 16, 2005 H-2 Erslev, 2004). The steep northeastern limb of the fold (forelimb) dips between 40° and 90° northeast. The southwestern limb (backlimb) dips between 10° and 40° south. The SW-dipping basement thrust may represent an inherited fabric that was reactivated during the Laramide orogeny (Simmons, 1990; Ye et al., 1996).Fracture measurements were collected in Permian sandstone layers that are a few meters thick (Bellahsen et al., submitted). These sandstones are located within a competent assemblage that is both underlain and overlain by less competent shales. These sedimentary layers (about 3000m thick) lie above granitic basement rocks. A more complete description of Sheep Mountain stratigraphy and structure can be found in (Forster, 1996; Hennier, 1983; Rioux, 1994). Fig. 3: Cross-section from Stanton and Erslev (2004). The southwest dipping fault beneath Sheep Fig. 4: a) Sketch of set II joint distribution. These Mountain is interpreted as being cut and offset by fractures are less numerous in the forelimb. b) Pre- the younger northeast dipping fault. fold horizontal configuration of the layers. The absence of set II joints in the forelimb may be due to the stress perturbation related to slip along the underlying thrust fault. Several fracture sets can be observed at Sheep Mountain anticline (Bellahsen et al., submitted): ESE- trending pre-Laramide fractures, NE-trending early Laramide joints, SE-trending folding-related joints, and ESE-trending vertical late joints. The chronology Mechanical model among these fracture sets is based on abutting relationships observed in the field, mainly within the Model setup Tensleep Formation (Bellahsen et al., submitted). In We carried out our mechanical modeling using this paper, we attempt to constrain the formation of the Poly3D (Thomas, 1993), a 3D boundary element NE-trending joints. These joints were interpreted as program based on the displacement discontinuity early Laramide joints, forming while bedding was sub- method and the governing equations of linear elasticity. horizontal (i.e. pre-folding). Their heterogeneous The fault surface (boundary surface) is discretized into distribution over the anticline suggests the influence of triangular elements on which opening is not permitted. active faults during the time of their formation, the pre- The working space is a semi-infinite "half" space, to early-folding period. These joints are present in the composed of a homogeneous and isotropic linear-elastic backlimb, the hinge, and the northern nose, but are material. Single slip events or series of events, (with significantly absent or less numerous in the forelimb complete stress relaxation) are considered and fault (Fig. 2 and 4). friction is neglected. This approach has been widely Stanford Rock Fracture Project Vol. 16, 2005 H-3 used and is