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 shown to provide insights on the sediments above the studied formation (Tensleep) was relationships between fault geometry, fault not eroded, and so based on the vertical separation of displacement, and stress perturbations in various cases the Tensleep and an early Laramide stratigraphic layer, (Bourne, 2001; Kattenhorn, 2000; Maerten, 2002). we set the overburden at 2200 m. We did not apply any The underlying fault at Sheep Mountain is stress or strain along the vertical axis, as gravity is interpreted as a SW-dipping basement fault that was taken into account, providing the overburden load. The active during the early Laramide compression and was Laramide orogeny is characterized by a NE later cut by a NE-dipping basement fault (Stanton and compression (Bird, 2002). We chose to apply a Erslev, 2004) (Fig. 5a). We consider only the SW- contraction in the NE direction of magnitude 0.1. The dipping fault as we investigate the early Laramide other horizontal boundary condition (perpendicular to compression stage. From seismic lines interpreted by the NE contraction) is the most difficult to set as we (Stanton and Erslev, 2004), the fault dips 50°. The fault have little information to constrain it. The only height is arbitrarily set to 5 km, as we have no information we have is that during the beginning of the constraints on its geometry at depth. Laramide orogeny vertical joints parallel to the compression direction formed. Thus, we postulate an effective tension striking perpendicular to the direction of compression, and apply an extension of magnitude 0.01 in that direction.
Results We describe the stress field perturbation across a 2D vertical grid (Fig. 5a) on which we plot the least compressive stress resulting from the remote strain boundary conditions and fault slip (Fig. 5c). At a depth of 2200 m, the maximum vertical displacement is in the fault hangingwall, above the fault tip (Fig. 5b). The displacement profile shows that this is an asymmetric fold with a short, rather steep forelimb and a long shallow backlimb. On the plot of least compressive principal stress, one can see the stress perturbation (Fig. 5c). This principal stress strikes perpendicular to the observation grid (parallel to the fault), and is horizontal due to the applied boundary conditions where an extension is applied in this direction. Globally, the stress becomes more compressive with depth due to gravity. The least compressive stress is positive (tensile, or slightly compressive) at the surface and compressive deeper. Because the magnitudes of our boundary conditions are poorly constrained, we interpret the results qualitatively, in terms of zones that are relatively Fig. 5: Elastic model. a) Model geometry. The fault more or less compressive than other zones, rather than dips at 50°. A vertical plane perpendicular to fault quantitatively. The least compressive principal stress strike and located at the center of the fault is controls the formation of joints that form perpendicular designated as an observation grid. b) Vertical to this principal stress. A zone of more compressive displacement at a depth of 2200 m. c) Least stress relative to another thus suggests that the compressive principal stress across the observation grid. A zone of enhanced compressive formation of joints in the former zone was inhibited. stress is located above the fault upper tip in the In the fault footwall, near the upper tip of the fault, hangingwall (compressive quadrant). fault slip creates a zone of tensile stress (in red) that correlates with the extensional quadrant of the fault. At similar depths in the hanging wall, a zone of We next consider the boundary conditions to apply compression is created. This compressive zone extends to the models. The vertical stress may be related to the about 1500 m from the upper fault tip, and is about weight of the overburden. We consider that, at the 1000 m wide at 2200 m depth. As mentioned above, the beginning of the Laramide orogeny, the pile of vertical displacement is asymmetric, defining an
Stanford Rock Fracture Project Vol. 16, 2005 H-4 asymmetric fold with a steep forelimb and a shallower Implications for the mode of folding backlimb. Relative to this uplift, the compressive zone Elastic modeling indicates that a zone where the is located within the forelimb (Fig. 5b and c). Above least compressive stress is more compressive than the that compressive zone, near the surface, a tensional surrounding area is located above the upper fault tip, zone can be observed due to the free surface and remote within the hanging wall. In this zone, the formation of extension. Also, the distribution of vertical joints striking parallel to the maximum compression displacement creates a concave upward bending with direction may be inhibited. In the field, we observed a tensile stress enhanced at the surface. similar zone in the forelimb, where joints parallel to the In Fig. 6, we show the results of models in which compression direction are sparse. Assuming that these different parameters are varied. The least compressive two zones correspond to each other, we conclude that stress is plotted at a depth of 2200 m along a profile the forelimb was located above the fault tip in the perpendicular to the fault (at its center). The hanging hangingwall of the thrust before significant folding wall is located on the left. Varying the depth (Fig. 6a) developed. and the dip (Fig. 6b) of the fault does not affect the This conclusion places an important constraint on existence of the zone of enhanced compression, for fold kinematics. In the case of SMA, the basement represented by the minima in the plots. The presence or fault probably formed prior to the Laramide orogeny absence of gravity (Fig. 6c) does not affect that zone (Fig. 7a). With the onset of NE compression, the fault either. The boundary conditions do have an effect (Fig. became active before significant folding (Fig. 7b), 6d). A large extension parallel to the strike of the fault perturbing the stress field in its vicinity. Faulting prior or a low contraction perpendicular to the strike of the to folding is often invoked for basement fault-cored fault produces flatter curves that indicate that joints folding (Stone, 1993). The stress perturbation described would be present either everywhere or nowhere. above is based on a model of a basement that has the same material properties as the sedimentary cover, such that initial slip along the thrust fault is accompanied by deformation everywhere in the vicinity of the fault, including the basement. With ongoing compression, the fold developed above the fault, within the hangingwall. The subsurface fold geometry is not well defined at Sheep Mountain due to the lack of subsurface data below the fold. However, seismic lines (Stanton and Erslev, 2004; Stone, personal communication) in close proximity to the fold show that the fold is above the fault and not in front of the upper tip of the thrust fault, as in the forced fold model. Seismic lines of other basement fault-cored anticlines (Stone, 1993) indicate that this geometry is common. This geometric relationship between the fault and the fold is apparent in the numerical models, in which the vertical displacement fields indicate that the forelimb of the fold was located in the hanging wall of the thrust fault. Such a kinematics is possible if the basement were to undergo an internal deformation of similar magnitude to the cover (Fig. 7b, c, d). This deformation is apparent in seismic lines presented by (Stone, 1993). In most fold growth models that are applied to Wyoming Laramide folds, the basement is assumed to be rigid (Cosgrove, 2000; Stearns, 1978). With this assumption, if layer-parallel slip (Johnson and Johnson, 2002; Niño et al., 1998) is neglected, the only Fig. 6: Least compressive stress at a depth of 2200 way to generate backlimb rotation, is with a listric fault. m (depth of the black rectangle on Fig. 5c) across Conversely, in the model presented here, the backlimb the fault in models with varying parameters. rotation is due to basement deformation that results in a rotation of the basement-cover interface. This demonstrates that backlimb rotation can occur with a
Stanford Rock Fracture Project Vol. 16, 2005 H-5 planar fault. However, we do not exclude the fact that the thrust upper tip; Erslev, 1991), assumes that if the the thrust faults beneath Laramide folds may be listric. basement-cover interface is folded, the thrust fault has The fold grew with a fixed hinge (Fig. 7b, c, d), as propagated upward from a point below this interface. shown in Bellahsen et al. (submitted) for the specific According to this study, the only way to deform the case of Sheep Mountain and as generally described in basement is to nucleate a fault within it. Here, we the literature for basement fault-cored anticlines suggest that “folding” of the basement may accompany (Erslev, 1991; McConnell, 1994). displacement along the thrust fault, regardless of its propagation, if it is reactivated such that the fault tip was located at the basement-cover interface. The key assumption in trishear models is that no deformation occurs except in the triangular area above the tip of the fault. Johnson and Johnson (2002) and Cardozo, (2003) compared trishear folds with mechanical models. Cardozo (2003) used elasto-plastic rheologies and showed that a triangular zone, which resembles the trishear zone, is created along the propagation path of the fault. In their models, the layers are not significantly folded outside the zone of localized strain. It is important to note two specific characteristics of their models: no bedding-parallel slip is allowed and most of the deformation is dominated by plastic strain since yielding occurs at low stresses. Niño et al. (1998) show that with an elasto-plastic rheology, bedding- parallel slip is an important parameter and that it generates a wider distribution of folding than just within the zone of localized strain. Additionally, the models presented in this paper clearly show folding above the fault and not only in its prolongation path, a result also shown by (Johnson and Johnson, 2002). These studies indicate that trishear may be applicable only if there is no bedding-parallel slip and no significant elasticity in the layers. Johnson and Johnson (2002) also show that the trishear hypothesis may be acceptable only if the cover is perfectly welded to the basement. Furthermore, they show that trishear is not valid when the thrust fault is curved, which is the only phenomenon for explaining backlimb rotation, and thus the development of an anticline instead of a monocline in a trishear model (Erslev, 1986). If trishear is not applicable when there is bedding-parallel slip, a significant elasticity, and/or a curved basement thrust fault, we wonder when it can be acceptable.
Fig 7: Conceptual model for basement fault-cored Conclusions anticlines. a) Pre-Laramide configuration. The thrust Previously published fracture data show that fault is inherited. b) Onset of Laramide faulting. The vertical joints parallel to the regional (Laramide) basement starts deforming, as does the cover. Both are affected by the stress field perturbation compression are rare in the forelimb at Sheep Mountain resulting from the superimposition of the slip Anticline. 3D elastic models mechanically constrain the related stresses and the shortening related location of an area where joints might be inhibited. We stresses. c) Fold initiation and d) fold amplification find that this area is located in the hanging wall of the with a fixed hinge and rotating limb. The basement thrust fault, above the upper fault tip. This implies that hangingwall block is significantly internally the forelimb was in this particular location before the deformed. folding event, which largely constrains the kinematics of folding. It is shown that the fold must have formed (Bump, 2003), using the trishear kinematic model above the thrust fault (and not flexed around its tip as in (rigid behavior outside the triangular zone attached to
Stanford Rock Fracture Project Vol. 16, 2005 H-6 forced fold models) with a fixed hinge and rotating Friedman, M., Hugman III, R.H.H., Handin, J., Experimental limbs, and that the basement was internally deformed in folding of rocks under confining pressure, part VIII - the thrust hangingwall. Mechanisms of deformation in forced folding of unconsolidated sand and lubricated the basement, including the condition for strain layers of limestone and sandstone, The Geological Society of America Bulletin, 19, 307-312,1980. delocalization that leads to the internal deformation of Hennier, J., and Spang, J., Mechanisms for deformation of the blocks, require further research. sedimentary strata at Sheep Mountain anticline, Big Horn Basin, Wyoming, WGA Guidebook, 34th annual Acknowledgements field conference, 97-111, 1983. Johnson, K.M., and A.M. Johnson, Mechanical models of We thank Dave Pollard for discussion and input. trishear-like folds, J. Structural Geology, 24, 277-287, This project is funded by the Stanford Rock Fracture 2002. Project, the National Science Foundation Tectonics Kattenhorn, S.A., Aydin, A., Pollard, D. D., Joints at high Program Grant No. EAR-012935, and the Collaboration angles to normal fault strike: an explanation using 3-D in Mathematical Geosciences Program Grant No. EAR- numerical models of fault-perturbed stress fields, J. 04177521. Structural Geology, 22, 1-23, 2000. Maerten, L., Gillespie, P., Pollard, D. D., Effects of local stress perturbation on secondary fault development, J. References Structural Geology, 24, 145-153, 2002. Allmendinger, R.W., Inverse and forward numerical modeling McConnell, D., David, Fixed-hinge, basement-involved fault- of trishear fault-propagation folds, Tectonics, 17, 640- propagation folds, Wyoming, Geological Society of 656, 1998. America bulletin, 106 (12), 1583-1593, 1994. 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