For example, such points can help to prevent the surface from plunging infinitely toward the periphery of the study area as minimum curvature surfaces may do in the absence of data constraint beyond the observation grid. Of the Please check your email for instructions on resetting your password.  are apparent, some less subtle than others, and these are highlighted by the contours in Figure 12 and evident on cross sections in Figure 13. Origin of magnetization in the Phosphoria Formation at Sheep Mountain, Wyoming: A possible relationship with hydrocarbons R. H. Benthien School of Geology and Geophysics, University of Oklahoma, Norman, Oklahoma We project points normal to bedding, based on the assumption that SMA is a flexural‐slip style, parallel fold [e.g., Ramsay, 1967]. Approximately half of the points extracted from the DEM (258,769) represent the top of the Tensleep Sandstone (mapped orange), while the fewest points (167) represent the surface in the Gypsum Springs Formation mapped in gold. The Sheep Mountain anticline, in the Bighorn Basin of Wyoming, formed during the Laramide orogeny. These differences must be considered critically to determine which model might be more appropriate. Therefore, our approach uses simpler biharmonic splines. User-contributed reviews Tags. google_ad_client = "pub-0036007678883152"; google_ad_format = "160x600_as"; Thickness measurements obtained from the ALSM data for several intervals in the Paleozoic section. Find this Pin and more on UM formations by Dennis Cox. These oscillations are characterized by a dominant fold‐parallel waviness, in the forelimb of the interpolated surface. The surface mapped in cyan is the oldest ridge‐forming unit in the Gypsum Springs Formation. If you do not receive an email within 10 minutes, your email address may not be registered, Summary not available for this title. . Outcrops are numerous in the backlimb, generally near the topographic crest of the fold, and are distributed more sparsely in the forelimb. locations may be determined with decimeter precision. In many subsequent methods for cross section construction, the interpolation of fold geometry between data points is dependent upon fault geometry [e.g., Dahlstrom, 1969; Suppe, 1983], which may be poorly constrained. This method fails at SMA because outcrops of any given surface generally occur only in relatively narrow bands along each limb of the fold. Geology Of the Bighorn Basin; 34th Annual Field Conference Guidebook, 1983 Pages 96-111. Geophysics, Mathematical Light gray triangles have high aspect ratio and are omitted from calculation. Second, absolute calibration was performed by nearest neighbor comparison of ALSM points with more than 800 check points acquired by vehicle‐mounted GPS along highway U.S. 310, several kilometers from the study area. Physics, Solar Overlying the Tensleep Sandstone is the Phosphoria Formation, in which four distinct beds were mapped. Shown above is a railroad cut that runs through this northwest-southeast trending anticline. Therefore, increasing northing measurements represent a progression in a northwestward direction. [Stevens, E. H.] on Amazon.com.  Three dimensional surface models of folded geologic strata, often portrayed as structure contour maps, are a fundamental tool for geologists and geophysicists. Any queries (other than missing content) should be directed to the corresponding author for the article.  Projection orientation, parallel to the local bedding‐normal vector, may be determined from strike and dip measurements or directly from the ALSM data (Figure 9). The 3‐D geometric techniques such as the equivalent dip domain method [Carrera et al., 2009] have been suggested to overcome some of the limitations of sequential balanced cross sections; however, such methods are adequate only for relatively simple folds. In some areas where the models differ significantly, the older model may be better, but in other areas, the new model may offer an improved representation of fold geometry. We show how paleo-principal stress magnitudes during the development of this fold can be estimated using the systematic Aerial view of the Sheep Mountain Anticline in Wyoming, USA. New Mapping—Create new large-scale bedrock and surficial geologic maps to further scientific investigations, answer geologic questions, and expand the public’s understanding of Wyoming geology. However, mapping was difficult because most outcrops are not accessible, making it difficult to identify whether exposed surfaces are indeed the top of the Madison Limestone, or if upper layers of the continuous and uniform limestone have been eroded. An Filtered and unfiltered digital elevation models with 1 m pixel resolution were generated from the raw point cloud with a kriging algorithm in Surfer® Version 8.04, from Golden Software, Inc. Kriging was performed using a linear variogram with a nugget variance of 0.07 m, microvariance of 0.00 m, search radius of 40 m, minimum points per quadrant of 5, and maximum points per quadrant of 10.  We acknowledge that data manipulation is not ideal because it introduces human subjectivity and limits model reproducibility. It too is exposed northeast of the forelimb syncline. We see that for both strike and dip, there are large differences between calculated and measured orientations for small outcrops. Contours of the difference between new and old models of the base Sundance Formation are presented in Figure 12. It was mapped, despite its limited extent, because the cyan surface is poorly exposed in this area. Previous studies [Forster et al., 1996; Hennier and Spang, 1983] suggest that SMA is a parallel fold, citing evidence such as relatively uniform bed thickness, even on the steeply dipping limbs. Field Conf. The lack of correlation between bed thickness variation and local bed dip (Figures 6b and 7b) is consistent with this conclusion. Thickness measurements between the cyan and red surfaces obtained in the forelimb have a mean value of 246 m, and thickness measurements obtained in the backlimb between the cyan and green surfaces have a mean value of 255 m. The green surface is uniformly about 8 m above the red surface everywhere on the fold, suggesting that in fact, the Chugwater Shale, which comprises most of the interval between the green and cyan surfaces, may be thinned in the steeply dipping forelimb by approximately 17 m (7%).  We implement a two‐dimensional minimum curvature (biharmonic) spline (MCS) interpolation method [Briggs, 1974; Sandwell, 1987; Wessel and Bercovici, 1998] constrained by ALSM data points and strike and dip measurements. In this region and beyond the forelimb syncline, the ALSM constrained MCS model could be improved by adding data points that estimate the surface geometry. These issues likely occur because of close neighboring noisy data points. Above the Madison Limestone is the Amsden Formation, followed by the Tensleep Sandstone. MATLAB fails to calculate the SVD of G for 5 m data resolution.  The complete technical report on acquisition and processing of ALSM data is available by contacting the authors or directly from NCALM (http://www.ncalm.org). Sheep Mountain. Geol. Geologic map of the Sheep Mountain--Little Sheep Mountain area, Big Horn County, Wyoming / U.S. Department of the Interior, U.S. Geological Survey ; by Robert L. Rioux. Down‐section projection paths of points in the forelimb and backlimb cross, which is geometrically inadmissible. Further decimation, for example, 50 m, eliminates too many data points, and important constraint on surface geometry is lost. The density of ALSM data provides more than three noncollinear points on many bedding surfaces, which theoretically provides a means for calculating local surface orientation. Regularization is critical to generate a smooth interpolated surface from noisy data. This extreme error occurs because the MCS method is not adequate for extrapolating fold geometry beyond the periphery of the data constraint. Faulting - brittle behavior in which a rock responds to stress by developing one or more fractures. Because most data points are projected down and in, toward the core of the fold, a surface model at this stratigraphic level does not leave much distance between forelimb and backlimb data points open to interpolation. Because the component of thickness calculation error resulting from dip measurement error scales with bed thickness, and the contribution from zab measurement error does not (equation (1)), dip provides a relatively greater contribution to error in the thicker units of the Mesozoic section and zab is the dominant contributor in the Paleozoic section. While the interpolated surface may in fact pass very close to the given data point in 3‐D space, because the interpolation scheme minimizes error in the vertical direction, rather than normal to the nearest surface point, excessive smoothing was required to prevent unrealistic oscillations. At the northwest end of the section where ALSM constraint from the Gypsum Springs Formation is available, the fold model returns to a more parallel form. The raw data were calibrated in a two step process. Above the Sundance are the Morrison and Cloverly formations. Because units above the Gypsum Springs Formation have been eroded throughout the steeply dipping forelimb and most of the hinge (except the plunging extremes), folding in these units cannot be characterized as parallel or otherwise. Reviews. Jennifer Beyer, W. Ashley Griffith, Influence of mechanical stratigraphy on clastic injectite growth at Sheep Mountain anticline, Wyoming: A case study of natural hydraulic fracture containment, Geosphere, 10.1130/GES01349.1, 12, 5, (1633-1655), (2016).  Thickness measurements obtained from the ALSM data are in agreement with field measurements using a Jacob's staff. Following this, ALSM constraints within the threshold distance of the remaining slope constraints are discarded and finally the decimation algorithm is applied to all remaining ALSM points. For example, Pearce et al. Auxiliary material files may require downloading to a local drive depending on platform, browser, configuration, and size. The greatest differences occur beyond the forelimb syncline in areas where ALSM data are unavailable (point C and beneath the scale bar in Figure 11b and cross sections B‐B′, E‐E′ and F‐F′ in Figure 13).  Extraneous low and high points (e.g., multipath and fog, respectively) were eliminated from the data set, and a filtered bare earth model (vegetation and buildings removed) was generated using Terrasolid's software TerraScan. Geologic map of the Sheep Mountain--Little Sheep Mountain area, Big Horn County, Wyoming / U.S. Department of the Interior, U.S. Geological Survey ; by Robert L. Rioux.  Sheep Mountain anticline is located on the eastern flank of the Bighorn Basin (Figure 1a), north central Wyoming, north of the town of Greybull. Semantic Scholar extracted view of "The geology of Sheep Canyon Quadrangle: Wyoming" by Robert Edward Ladd Fold geometry at Sheep Mountain anticline, Wyoming, constructed using airborne laser swath mapping data, outcrop‐scale geologic mapping, and As a take-home assignment worth 4% of your final mark, create a hand-drawn geological map of the northern part of Sheep Mountain in Wyoming. Where the pink and raspberry surfaces are difficult to identify, the younger magenta bed is the dominant ridge‐forming layer. This difference is substantiated by nearly continuous ALSM data coverage, and therefore is not an artifact of the MCS tendency to generate broad, smooth curves. Data points are decimated such that strike and dip measurements (slope constraints) are input first. The main area you’re looking out toward is the Sheep Mountain Wilderness. Rights Statement The University of Wyoming provides access to these public domain materials for educational and research/scholarly purposes. In addition to simply making geologic maps, stratigraphic sections and structural cross-sections, the students have to put the local geology into the broader contexts of the Big Horn Basin and sequences of western orogenies. While this may be an appropriate assumption for long, nearly cylindrical folds, SMA is a more complex, noncylindrical fold [Bellahsen et al., 2006a; Forster et al., 1996; Hennier and Spang, 1983; Savage and Cooke, 2004; Stanton and Erslev, 2004]. Earlier work [Forster et al., 1996; Hennier and Spang, 1983] suggests that the Sheep Mountain thrust is a third‐order structure, a back thrust off the northeast dipping Rio thrust, which itself is a back thrust of the southwest dipping, crustal‐scale Bighorn Mountains Eastern thrust. Small horizontal errors are prevalent among the projected data in this region, particularly for data points projected more than 200 m across the Chugwater Shale, because a large component of the projection vector for steeply dipping surfaces is in the horizontal plane. Also, short‐wavelength parasitic folding, which is relatively uncommon, though not absent, at SMA, may result in local perturbations to strike and dip measurements which are real but inappropriate for projection purposes.  suggest that a small, third‐order fault could not produce a structure as large as SMA.  The ALSM survey was carried out in two flights on 13 July 2007. Indeed, the interpolated representation of the base Sundance is somewhat higher (∼40 m) than the representation by projecting the top Tensleep Sandstone surface up section in the vicinity of the fold crest on sections C‐C′ and D‐D′, but considering the lack of data in the fold hinge and the uncertainty of any surface model at SMA, this difference is relatively small.  Models were investigated in which data was decimated to 5, 10, and 25 m resolution. Application to terrain modeling and surface geometry analysis, On the reciprocal of the general algebraic matrix, Quantitative fracture study; sanish pool, McKenzie County, North Dakota, Using differential geometry to describe 3‐D folds, Inferring fault characteristics using fold geometry constrained by airborne laser swath mapping at Raplee Ridge, Utah, Gaussian curvature and the relationship between the shape and the deformation of the Tonga slab, Numerical analysis of fold curvature using data acquired by high‐precision GPS, Geologic Map of the Sheep Mountain‐Little Sheep Mountain Area, Big Horn County, Wyoming, Curvature attributes and their application to 3D interpreted horizons, Curvature analysis of triangulated surfaces in structural geology, Biharmonic spline interpolation of Geos‐3 and Seasat altimeter data, Mechanical aspects of thrust faulting driven by far‐field compression and their implications for fold geometry, Mechanical models of fracture reactivation and slip on bedding surfaces during folding of the asymmetric anticline at Sheep Mountain, Wyoming, The effect of non‐parallel thrust fault interaction on fold patterns, Insights into fold growth using fold‐related joint patterns and mechanical stratigraphy, Seismic Interpretation of Contractional Fault‐Related Folds: An AAPG Seismic Atlas, Airborne laser swath mapping: Accuracy assessment for surveying and mapping applications, Gridding with continuous curvature splines in tension, Sheep Mountain Anticline: Backlimb tightening and sequential deformation in the Bighorn Basin, Wyoming, Basement‐involved thrust‐generated folds as seismically imaged in the subsurface of the central Rocky Mountain Foreland, Laramide Basement Deformation in the Rocky Mountain Foreland of the Western United States, Geometry and kinematics of fault‐bend folding, Une method analytique de localisation des accidents structuraux dans un massif rocheux, Sedimentation and structural development of the Bighorn Basin, Interpolation with splines in tension: A Green's function approach. The yellow mapped unit is underlain by a distinct red shale. However, field measurements may be influenced by cross‐bedding, weathering effects and measurement errors that do not reflect folding. Learn about our remote access options, Department of Geological and Environmental Science, Stanford University, Stanford, California, USA, Department of Geology and Geophysics, University of Minnesota‐Twin Cities, Minneapolis, Minnesota, USA. Anticlines form when deep seated, compressive forces within the earth’s crust, squeeze and shorten the crust. Several surfaces are less continuous, but were mapped because they are in a similar stratigraphic position to other mapped surfaces, and are exposed in areas where the adjacent surface does not provide good outcrops. Because the DEM consists of a 1 m × 1 m grid, triangles on the interior of any outcrop are, in map view, isosceles right triangles. Geologic setting and fracture data Sheep Mountain Anticline, located on the eastern edge of the Bighorn Basin, Wyoming, is a well known NW–SE trending, asymmetric Laramide fold (Fig. Oil and Gas Prospecting beneath Precambrian of Foreland Thrust Plates in Rocky Mountains, 3‐D Structural Geology: A Practical Guide to Quantitative Surface and Subsurface Map Interpretation, Relation of deformational fractures in sedimentary rocks to regional and local structures, Mechanisms for deformation of sedimentary strata at Sheep Mountain anticline, Big Horn Basin, Wyoming, Combining outcrop data and three‐dimensional structural models to characterize fractured reservoirs: An example from Wyoming, Structural geometry of Raplee Ridge monocline and thrust fault imaged using inverse boundary element modeling and ALSM data, Historical development of the structural theory of accumulation of oil and gas, A study of the structure and associated features of Sheep Mountain Anticline, Big Horn County, Wyoming, Constraining surface interpolations using elastic plate bending solutions with applications to geologic folding, The geology of Sheep Canyon Quadrangle: Wyoming, Reproducible research: Moving toward research the public can really trust, Constant bed‐length folding: Three‐dimensional geometrical implications, Detection of zones of abnormal strains in structures using Gaussian curvature analysis, Predicting patterns of strain from three‐dimensional fold geometries: Neutral surface folds and forced folds, Structural analysis of seismically mapped horizons using the developable surface model, The Mohr circle for curvature and its application to fold description, Rapid static and kinematic Global Positioning System solutions using the ambiguity function technique, How to constrain 3‐D fault continuity and linkage using reflection seismic data: A geomechanical approach, Interpolation by regularized spline with tension. Average differences between the two calculated trajectories were 2.5 cm vertical and <1 cm horizontal. google_color_url = "663300"; This work has been supported by the National Science Foundation's Collaborations in Mathematical Geosciences grant CMG‐0417521, and P. Lovely has been supported by the Robert and Marvel Kirby Stanford Graduate Fellowship Fund. Both strengths and weaknesses of the new method are discussed in the context of comparison between the new surface model and an existing model constructed by traditional methods. Deformation of the rock concentrates along the fractures. This unit forms a consistent, identifiable ridge in the backlimb and most of the forelimb of the fold, and is exposed again beyond the syncline northeast of the forelimb. The manuscript has benefited greatly from thorough, constructive, detailed reviews by Ken McCaffrey and Richard Lisle and comments from Associate Editor W. P. Schellart. Intermediate (class 1c) and extreme (classes 1a and 3) fold types are characterized by more complicated relationships between bed thickness and dip isogon orientation, and therefore do not lend themselves to straightforward projection between folded surfaces. The bed mapped is 2–3 m thick and heavily cross‐bedded. Technical specifications for data acquisition and processing at SMA are summarized in the Appendix. No slope constraints were discarded in regions with broad ALSM constraint. Where such gaps exist in data coverage, it is generally difficult to determine the location or breadth of such zones of localized curvature, or even to determine if such zones exist; therefore, we suggest the MCS method is appropriate, particularly given the dense ALSM data coverage available across much of the fold.  One apparent limitation of the MCS approach is for chevron folds, in which deformation tends to concentrate within narrow zones of high curvature, which separate relatively planar dip domains [e.g., Carrera et al., 2009; Suppe, 1983]. Geophysics, Geomagnetism Composition and Structure, Atmospheric  The reproducible nature of the smoothed MCS interpolation enables a quantitative measure of model uncertainty in the form of cross validation. Color shaded polygons represent the extent of mapped bedding surface outcrops, and red dots represent locations of strike and dip measurements.  A clear advantage of the new method, based on geologic mapping, high‐resolution, precise geospatial data, and numerical interpolation, is the unique result and reproducible nature of the interpolation. In calculating the mean gradient, we disregard triangles with high aspect ratios, which are found only on the periphery of outcrops and are subject to error because peripheral points may easily be misidentified and therefore not represent the bedding surface. google_color_text = "000000"; Also, the cross sections rely on interpretation of the fault structure underlying the Thumb fold, which is poorly understood.  The new ALSM derived model and the Forster et al. Absolute value of the difference between (a) dip and (b) strike measured in the field with a compass and calculated from ALSM data points extracted from outcrops versus outcrop area. Additionally, we elect to model the base Sundance Formation because it is the surface modeled by Forster et al. These outcrops provide scattered data on the location and orientation of the folded surfaces. The Sheep Mountain area north of Greybull Wyoming has long been recognized as an excellent instructional area for field geology. Differential correction of the aircraft trajectory was performed using the KARS software [Mader, 1992] independently for each base station.  Constraints available at the Earth's surface on the geometry of geologic folds often are discontinuous, consisting of scattered bedding surface outcrops representing the position and orientation of different stratigraphic surfaces. The fold at SMA is most nearly idealized as a parallel fold.