The upper Phosphoria Formation consists of a massive, carbonate‐rich quartz arenite [Bellahsen et al., 2006a], the top of which is mapped red. [58] A histogram of RMS error at each outcrop resulting from model smoothing (all decimated ALSM constraints are used but the numerical interpolation does not exactly honor all data, see section 5.2) is presented in Figure 14b. [64] The ALSM survey was carried out in two flights on 13 July 2007. On these same sections, similar magnitude deviation from perfectly parallel may be observed elsewhere on the fold. [47] Careful comparison of the difference in elevation of the two new surface models at the fold's crest presents another challenge to the parallel fold hypothesis. Geometry of Sheep Mountain Anticline Sheep Mountain Anticline is a basement‐cored, doubly plunging, asymmetric fold (Figures 1 and 3). [44] The top Tensleep Sandstone model should be very precise near the fold hinge, where the Tensleep Sandstone is exposed, but is subject to greater error around the periphery where outcrops high in the stratigraphic column (i.e., lime green) are projected nearly 1 km down section. Geometry of Sheep Mountain Anticline [14] Sheep Mountain Anticline is a basement‐cored, doubly plunging, asymmetric fold (Figures 1 and 3). [13] Mapping was performed in the manner of Mynatt et al. The fold at SMA is most nearly idealized as a parallel fold. 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. This occurs because the parallel fold hypothesis is necessarily violated if the down‐section projection distance exceeds the local radius of curvature in an anticline (or updip projection distance in a syncline). While these points are not sufficient to accurately constrain fold geometry in their immediate vicinity and their influence on surface geometry within the grid area is relatively small, we suggest that including additional data points outside the primary study area is more likely to improve than to detract from the final surface model. In the case of large outcrops, very accurate measurements, representative of the whole surface should be obtained from the ALSM data. [43] Models representing the top Tensleep Sandstone and the base Sundance Formation each have strengths and weaknesses. The rock in the foreground is the Cretaceous Mowry fm. This artificial, fold‐parallel waviness is prevented in the final surface models by omitting forelimb data points mapped in the Gypsum Springs, above the Chugwater Shale. Laramie, WY. Although some data manipulation, in the form of omitting selected problematic data points in a few locations, introduces a degree of subjectivity to our models, the numerical interpolation method for generating a continuous surface from raw data offers the distinct benefit of being entirely reproducible. Find this Pin and more on UM formations by Dennis Cox. Fold characteristics along cross sections may be omitted or misinterpreted if data points are not sufficiently dense or if the underlying assumptions of fold kinematics on which the cross section is based are incorrect [Woodward et al., 1989]. Sheep Mountain forms a 5-mile (8 km) long ridge in the Gros Ventre Range and is easily seen from Jackson Hole. The sandstone at the base of the Frontier Formation is the youngest ridge‐forming unit exposed in the extent of the ALSM survey. Stanton and Erslev [2004] suggest that the Sheep Mountain thrust is a deeply rooted structure that predates and has been crosscut by the younger Rio thrust; however, their model, like previous models, cannot be fully restored, and the geometry of the fault system underlying SMA remains obscure. Thickness measurements obtained from the ALSM data for several stratigraphic intervals in the Mesozoic section. Therefore, data points are omitted only when a specific, identifiable point or subset of points may be attributed to model behavior that is clearly and significantly unrealistic based on the known geology. [48] Fold profiles are parallel within reason (though not perfectly) everywhere that data are abundant; however, as might be expected, they tend to deviate from parallel where data are lacking. Composition and Structure, Atmospheric Uncertainty of the raw ALSM coordinates due to weathering and measurement imprecision is negligible relative to projection error. google_color_url = "663300"; An anticline is a geologic formation where the strata slope downward on either side of a crest, and this particular mountain is one of the more famous examples of this kind of formation. 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. [14] Strike and dip measurements taken at 282 sites across the study area (Figure 4) prove critical for projection and as slope constraints for interpolation because, while surface orientation may theoretically be derived from the DEM, errors are large when surface orientation is calculated from small outcrops. During Paleozoic and Mesozoic times, approximately 3 km of sediments were deposited in the Bighorn Basin and surrounding region [Ladd, 1979; Thomas, 1965]. Also, the cross sections rely on interpretation of the fault structure underlying the Thumb fold, which is poorly understood. [23] UTM northing coordinates are used as a proxy for position along the fold to investigate potential stratigraphic thickness gradients independent of folding and local dip. Cross sections B‐B′, E‐E′, and F‐F′ deviate from parallel significantly more. Balanced Geological Cross‐Sections: An Essential Technique in Geological Research and Exploration, Short Course Geol. A cross section of the fold in the Madison Limestone is exposed in Sheep Canyon, where the Bighorn River cuts through the anticline, nearly perpendicular to the axial surface trace. The manuscript has benefited greatly from thorough, constructive, detailed reviews by Ken McCaffrey and Richard Lisle and comments from Associate Editor W. P. Schellart. Statistical confidence in the new model is quite good where ALSM constraint is available. [Robert L Rioux; Geological Survey (U.S.)] Home WorldCat Home About WorldCat Help Search Search for … situated immediately west of the area of study, and Polecat Bench. 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. These issues likely occur because of close neighboring noisy data points. 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. google_ad_width = 160; Geol. The 25 m decimation is selected for the optimal model in preference to greater decimation because it maintains sufficient resolution to capture fold details resolvable above noise, and in preference to lesser decimation because it produces a model that is less sensitive to noisy data and because the increased decimation reduces computational time from hours to minutes. Rocks exposed in the study area range from Mississippian through Cretaceous in age, and span more than 1 km of the stratigraphic section (Figure 3). On each cross section, the interpolated surfaces representing the top Tensleep Sandstone and base Sundance Formation are plotted, as well as a representation of the base Sundance Formation calculated by up‐section projection of the top Tensleep Sandstone surface, assuming an ideal parallel fold. Therefore, only those slope constraints that are within the threshold distance of another slope constraint are discarded. The method for surface model construction presented here eliminates dependency on assumptions of the underlying fault structure, attempts to minimize model dependency upon fold kinematics, and takes advantage of the most precise and spatially extensive constraint on fold geometry available from surface outcrops. //-->. Finally, a scan cutoff angle of 4° was imposed to eliminate error‐prone data points at the edge of scan lines. Expected thinning in the more gently dipping backlimb would be generally less than 25%. 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. [21] Although significant heterogeneity among measurements is observed, none of the measured intervals suggest a strong correlation between thickness and local dip (Figures 6b and 7b). [32] Interpolation by splines in tension [Mitášová and Hofierka, 1993; Smith and Wessel, 1990; Wessel and Bercovici, 1998] is an extension of biharmonic splines, and has been suggested as a method to reduce the high‐frequency oscillations that may plague biharmonic splines. The decimation algorithm examines each data point sequentially in the order input, calculates its distance from all subsequent points input, and deletes subsequent points whose map (XY) coordinates are less than the threshold distance from the current observation point. Photographs of a selection of mapped bedding surface outcrops are presented in Figure 2. The northwestern extent of the fold is characterized by a very narrow hinge that becomes broader to the southeast. Shown above is a railroad cut that runs through this northwest-southeast trending anticline. It is 15 miles long and the involved rock formations, which were originally horizontal, have been bent and uplifted over 1000 feet. [38] We acknowledge that data manipulation is not ideal because it introduces human subjectivity and limits model reproducibility. The orange mapped unit corresponds to the top of the Tensleep Sandstone. In folds such as Raplee Ridge or SMA erosion results in the exposure of bedding surfaces at the top of weathering‐resistant strata. [37] Limitations of the 2‐D MCS method and instabilities of the numerical implementation, as well as limitations of computational power and numerical precision in MATLAB, prevent executing the interpolation with all 514,342 ALSM points representing bedding surface outcrops and 282 strike and dip measurements. Wyoming More information liesegangpoisoning: Sheep Mountain anticline - Wyoming All kindsa goodies up in there: Belemnites, pentacrinus, gastroliths, “devil’s toenails”… geologist/ paleontologist heaven. From the raw point cloud of processed laser returns, two digital elevation models with 1 m resolution were assembled. These data, supplemented by several hundred strike and dip measurements constraining local orientation of folded strata, are projected to the stratigraphic position of a single surface and used as constraint for a smoothed minimum curvature spline interpolation to generate a continuous representation of fold geometry. The Sheep Mountain anticline, in the Bighorn Basin of Wyoming, formed during the Laramide orogeny. [42] Two new surface models have been generated by MCS interpolation honoring projected ALSM data points that represent bedding surface outcrops and strike and dip measurements scattered across SMA. However, we use this approach because it provides relatively smooth interpolation with modest curvatures, and we do not pursue any physical interpretations. Sheep Mountain (11,244 feet (3,427 m)) is located in the U.S. state of Wyoming. After GPS processing, a Kalman filter algorithm, implemented in the Applanix™ software POSProc™, was used to integrate 1 Hz differential GPS data and 200 Hz IMU recordings to produce a smoothed and blended solution for aircraft position and orientation at 200 Hz. 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. If you do not receive an email within 10 minutes, your email address may not be registered, The yellow and blue mapped surfaces represent the tops of thin, carbonate‐rich, resistant units within the lower Phosphoria Formation. [8] Sheep Mountain anticline is located on the eastern flank of the Bighorn Basin (Figure 1a), north central Wyoming, north of the town of Greybull. We present a new method for modeling the geometry of kilometer‐scale folds using dense, precise topographic data available from airborne laser swath mapping (ALSM), outcrop‐scale geologic mapping, and a reproducible numerical interpolation method that is free of subjectivity. 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. 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. Wyo. As discussed in the following paragraphs, it was necessary to discard selected, problematic data points from the constraint set and to significantly decimate the dense ALSM data in order to interpolate a realistic model of fold geometry at SMA. The Bighorn Basin is a structural low, with the Absaroka Range to the west, the Bighorn Mountains to the … Younger sandstone units within the Frontier Formation provide better orientation measurements but are not mapped because of discontinuous exposure and difficulty identifying a unique surface. [39] In regions of poor ALSM data constraint, slope constraints were liable to cause large, broad, geologically unrealistic vertical perturbations in the surface model, apparently due to limitations of the MCS interpolation technique and numerical instabilities inherent to the Green's function implementation. Additionally, balanced cross sections assume plane strain deformation. [49] Many differences between the new surface model and that of Forster et al. [1996] model, may be less accurate than an ALSM constrained MCS model. 16, 2005 I-2 Figure 1. google_ad_type = "text_image"; USGS US Topo 7.5-minute map for Big Sheep Mountain, WY 2015 Metadata Updated: August 31, 2018. Color shaded polygons represent the extent of mapped bedding surface outcrops, and red dots represent locations of strike and dip measurements. . Digitized polygons representing outcrop exposure enabled extraction of 514,342 DEM points, representing outcrops of the 14 exposed bedding surfaces. However, thickness measurements show significant variability (standard deviation is typically about 10% of the mean thickness for a given stratigraphic package) and error bars are relatively large. The studied outcrop is Sheep Mountain, an asymmetric basement cored anticline corresponding to a typical Laramide arch of the Bighorn Basin (Wyoming, USA). The Sheep Mountain area north of Greybull Wyoming has long been recognized as an excellent instructional area for field geology. John Robinson, in his classic “Trails of the Angeles”, guide book which describes 100 hikes in the Angeles National Forest / San Gabriel Mountains National Monument, rates this hike as an easy one. There is no doubt that cross sections are a valuable tool among geologists; however, they are not reproducible. It resulted from down cutting of the land surface by rivers and streams and the removal of much of the original basin fill sediment. [1996] model differ most dramatically around the periphery of the observation area, and in other areas where data constraint is limited. Points representing the extensive outcrops of the top of the Tensleep Sandstone (orange) are not projected, and therefore maintain the decimeter precision of the ALSM data, and points from other surfaces in the Paleozoic section are projected relatively small distances (<100 m). Thus, we would expect to observe forelimb thinning of at least 30%, and locally greater than 60%, relative to thicknesses observed in the backlimb. The town of Jackson, Wyoming is 13 miles (21 km) southwest of the peak. In regions of good data coverage, the difference is smaller, generally less than the 40 m contour interval. Nonetheless, having accounted for apparent thinning of the Chugwater Shale in the forelimb, and because local, appropriate thickness measurements are available for down‐section projection of data from younger Mesozoic surfaces in the backlimb, assuming constant bed‐perpendicular projection distances throughout this study seems appropriate. 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. [1996] model. 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. Other important sources of data to constrain fold geometry are geological mapping [e.g., Groshong, 2006; Woodward et al., 1989] and well logging [e.g., Serra, 1984]. To open auxiliary materials in a browser, click on the label. [2007b], by printing hill shade images generated from the 1 m DEM on a 42 inch plotter at a scale of roughly 4000:1, on which individual outcrops more than 2–3 m across may be identified. This method fails at SMA because outcrops of any given surface generally occur only in relatively narrow bands along each limb of the fold. Differences in excess of −400 m result (Figure 12). Barren or sparsely covered rock outcrops and magnificently developed folds and faults are characteristics of the northeastern Sheep Mountain is a textbook example of an anticline fold. [2009] use airborne laser swath mapping (ALSM), also known as airborne lidar, and numerical interpolation to constrain fold geometry at Raplee Ridge, Utah. The method uses data from a flight path perpendicular to the primary flight lines, and optimizes aircraft heading, roll, pitch, and scanner mirror scale to minimize the deviation between flight paths. This model is most precise near where Gypsum Springs Formation outcrops are exposed. Black letters show the locations of outcrops in Figures 2b–2e. 32, 53 p. Ninety‐five percent of outcrops are characterized by RMS error less than 25 m, 92% by error less than 20 m, and 83% by error less than 10 m. The maximum RMS error, however, is 1327 m, corresponding to omission of the most southeastern outcrop in the Gypsum Springs Formation, northeast of the forelimb syncline. Average differences between the two calculated trajectories were 2.5 cm vertical and <1 cm horizontal. For this reason, many strike and dip measurements are obtained from surfaces that are near to the mapped surfaces, and therefore have similar orientation, but they do not necessarily represent exactly the same surface. 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