Description:

_Journal of Structural Geology 32 (2010) 45–58 Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com locate jsg Structural geometry of Raplee Ridge monocline and thrust fault imaged using inverse Boundary Element Modeling and ALSM data G.E. Hilley*, I. Mynatt, D.D. Pollard Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305-2115, USA article info Article history: Received 16 September 2008 Received in revised form 30 April 2009 Accepted 29 June 2009 Available online 8 July 2009 Keywords: Monocline Boundary element model Airborne laser swath mapping Inversion methods abstract We model the Raplee Ridge monocline in southwest Utah, where Airborne Laser Swath Mapping (ALSM) topographic data define the geometry of exposed marker layers within this fold. The spatial extent of five surfaces were mapped using the ALSM data, elevations were extracted from the topography, and points on these surfaces were used to infer the underlying fault geometry and remote strain conditions. First, we compare elevations extracted from the ALSM data to the publicly available National Elevation Dataset 10-m DEM (Digital Elevation Model; NED-10) and 30-m DEM (NED-30). While the spatial resolution of the NED datasets was too coarse to locate the surfaces accurately, the elevations extracted at points spaced w50 m apart from each mapped surface yield similar values to the ALSM data. Next, we used a Boundary Element Model (BEM) to infer the geometry of the underlying fault and the remote strain tensor that is most consistent with the deformation recorded by strata exposed within the fold. Using a Bayesian sampling method, we assess the uncertainties within, and covariation between, the fault geometric parameters and remote strain tensor inferred using the model. We apply these methods to the Raplee Ridge monocline, and find that the resolution and precision of the ALSM data are unnecessary for inferring the fault geometry and remote strain tensor using our approach. However, the ALSM data were necessary for the mapping of the spatial distribution of surface outcrops. Our models considered two scenarios: one in which fault geometry and remote strains were inferred using a single deformed stratum, and another in which all mapped strata were used in the inversion. Modeled elevations match those observed to within a root-mean-squared error of 16–18 m, and show little bias with position along the fold. Both single-and multilayer inversions image a fault that is broadly constrained to be w4.5–14 km in down-dip height, 13–30 km in along-strike width, with a tip-line 2.0–9.5 km below the surface at the time of deformation. Poisson’s ratio was not well resolved by the inversion. The idealized elastic model is oversimplified when considering the complicated layered nature of this fold, however, it provides a good fit to the observations. Thus, comparable surface displacements may be produced with a variety of rheological models, so independent constraints on factors such as the fault geometry may be required to ascertain the appropriate rheology of the fold. ? 2009 Elsevier Ltd. All rights reserved. 1. Introduction The well-exposed Raplee Ridge monocline in southeastern Utah (Fig. 1) is a north-south oriented fold about 14 km long and 2 km wide (O’Sullivan, 1965; Ziony, 1966). The San Juan River has incised through the fold in the last several Ma (Wolkowinsky and Granger, 2004), exposing a thick sedimentary package (Jentgen, 1977; Ziony, 1966). Folding within the ridge likely occurred during the Laramide phase of deformation during latest Mesozoic and early Cenozoic time (Gregory and Moore, 1931). Many folds within the Colorado Plateau were formed due to reactivation of high-angle structures that likely date back as far as the Precambrian (Bump, 2003; Davis, 1978, 1999; Kelley, 1955). While no fault is exposed at the Raplee Ridge monocline and no subsurface information reveals the fault geometry, the presence of dipping beds along its west side, along with the fact that this fold is similar to many other Laramide folds in the Colorado Plateau for which faults are exposed (Tindall and Davis, 1999) or inferred (Bump, 2003; Bump et al., 1997; Davis, 1999; Kelley, 1955) implies that this fold was formed above a east-dipping high-angle reverse fault. As in the case of the Raplee Ridge monocline, faults that drive folding observed at the surface are often unexposed. As a result, both forward and inverse models have been used to relate fold form to the geometry of underlying faults. The simplest of these models 46 G.E. Hilley et al. Journal of Structural Geology 32 (2010) 45–58 Fig. 1. (A) Shaded relief map (color-coded for elevation), showing the location of Raplee monocline in southwestern Utah. Upper right inset shows Four Corners area; location of Fig. 2 noted in location map. (B) Arial photograph of Raplee Ridge showing displacement of strata. Photo looks to the north. Fold is w500 m in vertical relief. are kinematic models that assume no volume change of geologic units during folding-related fault slip in order to infer the subsurface geometry of unexposed faults and the fold evolution (Allmendinger and Shaw, 2000; Bump, 2003; Cardozo, 2008; Erslev, 1991; Jamison, 1987; Mitra, 1990; Suppe, 1985). While this geometric approach may violate the stress equilibrium equations, compatibility of stresses and strains within the crust, and the constitutive stress–strain relations of the rock, it nonetheless has the appeal that computational burden is low when calculating fault and fold geometry (e.g., Allmendinger, 1998; Cardozo, 2008), and that fold forms observed in the field can be coarsely reproduced. However, with the advent of high-speed computers, we now have the ability to create forward models that satisfy the constitutive stress–strain relations, stress–strain compatibility, and the equations of static equilibrium in the crust (e.g., Casey and Butler, 2004; Guiton et al., 2003). Such forward models have been developed for materials that are linear elastic (Bellahsen et al., 2006; Fiore et al., 2007; Shamir and Eyal, 1995), linear viscous (Johnson and Johnson, 2001, 2002), nonlinear elastoplastic with frictional faults (Sanz et al., 2007), and nonlinear viscous with frictional faults and bedding surfaces (Sanz et al., 2008). Each of these models assumes that the crust is in a state of static stress equilibrium, and so the component of the momentum budget that arises from accelerations (e.g., individual earthquake rupture dynamics) is small. Some of these models have been used to infer the kinematics of slip on prescribed faults (Burgmann et al., 2005; Maerten et al., 2005), or loading and fault geometry in two dimensions (Johnson and Johnson, 2002). Thus, the ability to use a fully mechanical approach that infers fault geometry and loading conditions from surface observations now exists (Mynatt et al., 2007). The National Center for Airborne Laser Mapping (NCALM) collected ALSM topographic data funded by the National Science Foundation Collaborations in Mathematics and Geosciences (NSFCMG) program that images the deformed strata at Raplee Ridge (Fig. 2a). These data provide a high precision, dense array of points on patches of marker bedding surfaces that we use to infer the subsurface geometry of the fault that may be responsible for the monocline. Our previous work at Raplee Ridge (Mynatt et al., 2007) combined the ALSM data with an elastic boundary element model to infer the geometry of the fault. The present study builds on this previous work by jointly estimating Poisson’s ratio of the modeled fold, and implementing a scheme that uses multiple layers and observations of bedding-plane rotations to constrain the fold geometry. In this contribution, we compare the ALSM data to other more commonly available topographic data (Fig. 2b and c) to determine what spatial resolution is required to infer the subsurface geometry of faults based on the displacements of exposed folded strata. In addition, we expand the previously described method to use a series of layers within the fold in order to better constrain the geometry of the underlying structure. We use a Markov–Chain Monte Carlo method to provide an estimate of the variation within, and covariation between, model estimates of fault geometry parameters that produce deformation similar to that recorded within the fold. 2. Study area Raplee Ridge monocline (Fig. 1) is located in southeast Utah, east of the town of Mexican Hat Mynatt et al., 2009. This structure lies west of the laterally continuous Comb Ridge monocline, which strikes N-S to NNE-SSW in this area (Kelley, 1955; Fig. 1, Ziony, 1966). The orientation of folded strata exposed within the Comb Ridge monocline is consistent with slip along an underlying W- to WNW-dipping fault that strikes parallel to the trend of the monocline. Unlike this more extensive structure, which can be traced for 10s of kilometers along its strike, Raplee Ridge is spatially restricted to w15 km along its N-S strike. No subsurface data in this area image the relationship between the Raplee Ridge monocline and structures that accommodate the displacement along the Comb Ridge monocline in the subsurface; however, it is plausible that a fault that drives folding seen in Raplee Ridge serves as a backthrust to the larger Comb Ridge fault. If this were the case, the thrust fault geometry may shoal as the deeper basement backthrust advances into the mechanically weak strata above, as has been seen in other reactivated basement-involved structures (e.g., Narr and Suppe, 1994). The strata exposed within Raplee Ridge include the Pennsylvanian Paradox Formation to Permian Halgaito Tongue, Ключевые слова: pollard, simplifying assumption, hilley journal, estimate, loading, sample, structural geology, depth, geological, along-strike width, strain, ned datasets, parameter space, parenthesis represents, time, mapping, mapped surface, mckim limestone, structure, fault underlying, surface outcrop, modeled, underlying distribution, square meter, ridge monocline, predicted elevation, point, best-tting set, wa, fault geometry, datasets, colorado, surface displacement, ridge, extent, alsm, mckim surface, southeastern utah, italic represent, elevation measurement, bayes, range, ratio, arizona, deformed, best-tting model, distribution, america memoirs, extracted, deected stratum, geometry, alsm measurement, laramide, davis, data, stratum exposed, suppe, lett, single-layer model, probability density, ?tting, elevation, utah, high accuracy, basement, probability, rotation, poissons ratio, predicted, elevation observed, unnamed surface, struct, elastic, marker, bedding surface, paleoseismic data, loading parameter, colorado plateau, stratum, initial choice, allmendinger, posterior density, applied, mechanical model, inversion, parameter, monocline, stratigraphic thickness, residual, surface, joint pdf, best-?tting, loading condition, raplee ridge, elsevier, posterior, condition, random number, ziony, model, fault, ned, mckim, folding, strike, underlying fault, university, journal structural, down-dip extent, reches, vector consisting, slip, geometry loading, sci, boundary, maerten, at-lying portion, deected surface, bull, bem idealizes, journal, area, bedding rotation, raplee, starting point, previous set, selection process, elevation extracted, displacement discontinuity, elevation estimate, problem, spatial resolution, produced, exposed, previous work, approach, raplee monocline, huntoon, underlying, western united, down-dip height, addition, model parameter, structural, density, soc, map-view scale, study, element, laramide contraction, spatial distribution, folded material, national center, observed geometry, aapg bull, dip, method, shafer surface, fold, layer, italic number, model estimate, mapped, mynatt, observed rotation, standard deviation, erslev, geology, displacement, mapped stratum, metropolis, observation, deformation, broadly constrained, observed, idealized model, uncertainty, mckim goodrich, stratigraphic level, at-depth geometry, folds geometry, north, geol, rheology, mapped layer, seismol, geological society, regular grid, elevation data, rock, mechanical, laramide folding, analysis, aapg, kelley, bedding, prior density, rheological model, geophys, earth, bump, alsm data, result, stratigraphic, subsurface, inferred, mechanical analysis, study build, johnson, subsurface geometry, current study, trishear, multiple layer, location, hilley, computing, infer, root-mean-squared error, remote strain, deformed surface, remote, mjx, observed elevation, number, set, united, bem, dem, study assumed, average mist