Structural Geology

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Basil Tikoff - One of the best experts on this subject based on the ideXlab platform.

  • The utility of statistical analysis in Structural Geology
    Journal of Structural Geology, 2019
    Co-Authors: Nicolas M. Roberts, Basil Tikoff, Joshua R. Davis, Tor Stetson-lee
    Abstract:

    Abstract Recent advances in statistical methods for Structural Geology make it possible to treat nearly all types of Structural Geology field data. These methods provide a way to objectively test hypotheses and to quantify uncertainty, and their adoption into standard practice is important for future quantitative analysis in Structural Geology. We outline an approach for Structural geologists seeking to incorporate statistics into their workflow using examples of statistical analyses from two locations within the western Idaho shear zone. In the West Mountain location, we test the published interpretation that there is a bend in the shear zone at the kilometer scale. Directional statistics on foliations corroborate this interpretation, while orientation statistics on foliation-lineation pairs do not. This discrepancy leads us to reconsider an assumption made in the earlier work. In the Orofino location, we present results from a full statistical analysis of foliation-lineation pairs, including data visualization, regressions, and inference. These results agree with thermochronological evidence that suggests that the Orofino area comprises two distinct, subparallel shear zones. The R programming language scripts that were used for both statistical analyses can be downloaded to reproduce the statistical analyses of this paper.

  • a perspective on the emergence of modern Structural Geology celebrating the feedbacks between historical based and process based approaches
    Geological Society of America Special Papers, 2013
    Co-Authors: Basil Tikoff, Thomas G Blenkinsop, Seth C Kruckenberg, Sven Morgan, Julie Newman, Steven Wojtal
    Abstract:

    Structural Geology has emerged as an integrative, synthetic science in the past 50 years, focused on deciphering the history preserved in the rock record and determining the processes of rock deformation. Owing to the nature of Structural Geology, studies focus on historical elements, such as Structural inheritance and tectonic history, and increasingly involve theoretical, process-based approaches. The strength of the field is that it uses these historical- and process-based approaches simultaneously in order to determine the three-dimensional architecture, kinematic evolution, and dynamic conditions of lithospheric deformation over a wide range of spatial and temporal scales. In this contribution we focus on significant progress made in understanding shear zones, fault zones, intrusions, and migmatites, both as individual features and as systems. Intrinsic to these advances are insights into the strain history, specifically through the temporal evolution of geologic structures. Increasingly sophisticated geochronological techniques have advanced the field of modern Structural Geology by allowing age determinations to be linked to rock microstructure and deformational fabrics, from which displacement rates and strain rates can be estimated in some settings. Structural studies involving new approaches (e.g., trenching), and integrated with geomorphology and geodesy, have been applied to study active geologic structures in near surface settings. Finally, significant progress has been made in constraining the rheology of naturally deformed rocks. These studies generally rely on results of experimental deformation, with microStructural analyses providing the connection between naturally deformed rocks and results of experiments. Integration of field-based observations, laboratory-derived rheological information, and numerical models provide significant opportunities for future work, and continues the tradition of simultaneously using historical- and process-based approaches.

  • Structural Geology practice and learning, from the perspective of cognitive science
    Journal of Structural Geology, 2013
    Co-Authors: Thomas F. Shipley, Basil Tikoff, Carol J. Ormand, Cathy Manduca
    Abstract:

    Abstract Spatial ability is required by practitioners and students of Structural Geology and so, considering spatial skills in the context of cognitive science has the potential to improve Structural Geology teaching and practice. Spatial thinking skills may be organized using three dichotomies, which can be linked to Structural Geology practice. First, a distinction is made between separating (attending to part of a whole) and combining (linking together aspects of the whole). While everyone has a basic ability to separate and combine, experts attend to differences guided by experiences of rock properties in context. Second, a distinction is made between seeing the relations among multiple objects as separate items or the relations within a single object with multiple parts. Experts can flexibly consider relations among or between objects to optimally reason about different types of spatial problems. Third, a distinction is made between reasoning about stationary and moving objects. Experts recognize static configurations that encode a movement history, and create mental models of the processes that led to the static state. The observations and inferences made by a geologist leading a field trip are compared with the corresponding observations and inferences made by a cognitive psychologist interested in spatial learning. The presented framework provides a vocabulary for discussing spatial skills both within and between the fields of Structural Geology and cognitive psychology.

John Wheeler - One of the best experts on this subject based on the ideXlab platform.

  • Structural Geology ALGORITHMS: VECTORS AND TENSORS
    American Mineralogist, 2013
    Co-Authors: John Wheeler
    Abstract:

    By Richard W. Allmendinger, Nestor Cardozo, and Donald M. Fisher (2012). Cambridge University Press, paperback 302 pages. ISBN: 978-1107401389. This book presents the mathematics behind Structural Geology and, by implication and example, tectonics—the difference being a matter of scale. The essence of Structural Geology is to understand the transition of an initial geometry (such as a layered sedimentary sequence) to a different final geometry (such as a fold and thrust belt). A huge part of that task involves characterizing the shape changes and their evolution, a prerequisite for understanding the driving forces behind such changes. That is a geometric and kinematic problem and the mathematical techniques of vector and tensor manipulation are ideally suited to the job. Some textbooks and lecture courses in Structural Geology tend to avoid or play down this mathematical framework, but this book does not: it puts the mathematics center stage and backs up the theoretical development with a suite of Matlab subroutines, which are given in the text and are available online. The book opens with a chapter on projections such as those used in constructing stereonets, then Chapters 2–5 introduce the …

Christie Peters - One of the best experts on this subject based on the ideXlab platform.

Donald M. Fisher - One of the best experts on this subject based on the ideXlab platform.

  • Structural Geology algorithms vectors and tensors
    2012
    Co-Authors: Richard W. Allmendinger, Nestor Cardozo, Donald M. Fisher
    Abstract:

    Preface 1. Problem solving in Structural Geology 2. Coordinate systems, scalars and vectors 3. Transformations of coordinate axes and vectors 4. Matrix operations and indicial notation 5. Tensors 6. Stress 7. Introduction to deformation 8. Infinitesimal strain 9. Finite strain 10. Progressive strain histories and kinematics 11. Velocity description of deformation 12. Error analysis References Index.

  • Structural Geology algorithms vectors and tensors
    2012
    Co-Authors: Richard W. Allmendinger, Nestor Cardozo, Donald M. Fisher
    Abstract:

    State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in Structural Geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own Structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also provide professional Structural geologists with a valuable reference and refresher for calculations.

  • Structural Geology Algorithms: Coordinate systems, scalars, and vectors
    Structural Geology Algorithms, 2011
    Co-Authors: Richard W. Allmendinger, Nestor Cardozo, Donald M. Fisher
    Abstract:

    Coordinate systems Virtually everything we do in Structural Geology explicitly or implicitly involves a coordinate system. When we plot data on a map each point has a latitude, longitude, and elevation. Strike and dip of bedding are given in azimuth or quadrant with respect to north, south, east, and west and with respect to the horizontal surface of the Earth. In the western United States, samples may be located with respect to township and range. We may not realize it, but more informal coordinate systems are used as well, particularly in the field. The location of an observation or a sample may be described as “1.2 km from the northwest corner fence post and 3.5 km from the peak with an elevation of 3150 m at an elevation of 1687 m.” A key aspect, but one that is commonly taken for granted, of all of these ways of reporting a location is that they are interchangeable. The sample that comes from near the fence post and the peak could just as easily be described by its latitude, longitude, and elevation or by its township, range, and elevation. Just because we change the way of reporting our coordinates (i.e., change our coordinate system), it does not mean that the physical location of the point in space has changed. This seems so simple as to be trivial, but we will see in Chapter 5 that this ability to change coordinate systems without changing the fundamental nature of what we are studying is essential to the concept of tensors.

  • Structural Geology Algorithms: Problem solving in Structural Geology
    Structural Geology Algorithms, 1
    Co-Authors: Richard W. Allmendinger, Nestor Cardozo, Donald M. Fisher
    Abstract:

    Objectives of Structural analysis In Structural analysis, a fundamental objective is to describe as accurately as possible the geological structures in which we are interested. Commonly, we want to quantify three types of observations. Orientations are the angles that describe how a line or plane is positioned in space. We commonly use either strike and true dip or true dip and dip direction to define planes, and trend and plunge for the orientations of lines (Fig. 1.1). The trend of the true dip is always at 90° to the strike, but the true dip is not the only angle that we can measure between the plane and the horizontal. An apparent dip is any angle between the plane and the horizontal that is not measured perpendicular to strike. For example, the angle labeled “plunge” in Figure 1.1 is also an apparent dip because line A lies in the gray plane. Strike, dip direction, and trend are all horizontal azimuths, usually measured with respect to the geographic north pole of the Earth. Dip and plunge are vertical angles measured downwards from the horizontal. Where a line lies in an inclined plane, we also use a measure known as the rake or the pitch , which is the angle between the strike direction and the line. There are few things more fundamental to Structural Geology than the accurate description of these quantities.

Tor Stetson-lee - One of the best experts on this subject based on the ideXlab platform.

  • The utility of statistical analysis in Structural Geology
    Journal of Structural Geology, 2019
    Co-Authors: Nicolas M. Roberts, Basil Tikoff, Joshua R. Davis, Tor Stetson-lee
    Abstract:

    Abstract Recent advances in statistical methods for Structural Geology make it possible to treat nearly all types of Structural Geology field data. These methods provide a way to objectively test hypotheses and to quantify uncertainty, and their adoption into standard practice is important for future quantitative analysis in Structural Geology. We outline an approach for Structural geologists seeking to incorporate statistics into their workflow using examples of statistical analyses from two locations within the western Idaho shear zone. In the West Mountain location, we test the published interpretation that there is a bend in the shear zone at the kilometer scale. Directional statistics on foliations corroborate this interpretation, while orientation statistics on foliation-lineation pairs do not. This discrepancy leads us to reconsider an assumption made in the earlier work. In the Orofino location, we present results from a full statistical analysis of foliation-lineation pairs, including data visualization, regressions, and inference. These results agree with thermochronological evidence that suggests that the Orofino area comprises two distinct, subparallel shear zones. The R programming language scripts that were used for both statistical analyses can be downloaded to reproduce the statistical analyses of this paper.