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Virtual Tour of Multidimensional Orders of Scale University of Texas at El Paso DigitalCommons@UTEP Open Access Theses & Dissertations 2018-01-01 Grenvillian Tectonomagmatic Evolution Of Southwestern Laurentia; Virtual Tour Of Multidimensional Orders Of Scale; Two Methods To Describe The aV stness Of Time; Math Concepts Utilizing Google Earth; Systematic Approach To Motion Analyses; Mathematics And Earth Science-Based Knowledge And Learning Anthony M. Alvarez University of Texas at El Paso, [email protected] Follow this and additional works at: https://digitalcommons.utep.edu/open_etd Part of the Education Commons, Geology Commons, and the Oil, Gas, and Energy Commons Recommended Citation Alvarez, Anthony M., "Grenvillian Tectonomagmatic Evolution Of Southwestern Laurentia; Virtual Tour Of Multidimensional Orders Of Scale; Two Methods To Describe The asV tness Of Time; Math Concepts Utilizing Google Earth; Systematic Approach To Motion Analyses; Mathematics And Earth Science-Based Knowledge And Learning" (2018). Open Access Theses & Dissertations. 1395. https://digitalcommons.utep.edu/open_etd/1395 This is brought to you for free and open access by DigitalCommons@UTEP. It has been accepted for inclusion in Open Access Theses & Dissertations by an authorized administrator of DigitalCommons@UTEP. For more information, please contact [email protected]. GRENVILLIAN TECTONOMAGMATIC EVOLUTION OF SOUTHWESTERN LAURENTIA; VIRTUAL TOUR OF MULTIDIMENSIONAL ORDERS OF SCALE; TWO METHODS TO DESCRIBE THE VASTNESS OF TIME; MATH CONCEPTS UTILIZING GOOGLE EARTH; SYSTEMATIC APPROACH TO MOTION ANALYSES; MATHEMATICS AND EARTH SCIENCE-BASED KNOWLEDGE AND LEARNING TRENDS: A MULTI-TIERED INVESTIGATION AND RATIONALE ANTHONY M. ALVAREZ Doctoral Program in Geological Sciences APPROVED: Philip Goodell, Ph.D., Chair Eric Kappus, Ph.D. Munazzam Ali Mahar, Ph.D. Richard Jarvis, Ph.D. Mourat Tchoshanov, Ph.D. Charles Ambler, Ph.D. Dean of the Graduate School Copyright © by Anthony M. Alvarez 2018 Dedication This dissertation is dedicated to my children. I remember taking you to Earth Day at the Geology Department when you were young, now you are grown and even attending UTEP. You made me come to the realization that it was time to finish. GRENVILLIAN TECTONOMAGMATIC EVOLUTION OF SOUTHWESTERN LAURENTIA; VIRTUAL TOUR OF MULTIDIMENSIONAL ORDERS OF SCALE; TWO METHODS TO DESCRIBE THE VASTNESS OF TIME; MATH CONCEPTS UTILIZING GOOGLE EARTH; SYSTEMATIC APPROACH TO MOTION ANALYSES; MATHEMATICS AND EARTH SCIENCE-BASED KNOWLEDGE AND LEARNING TRENDS: A MULTI-TIERED INVESTIGATION AND RATIONALE ANTHONY M. ALVAREZ, M.A., B.S. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at El Paso in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department of Geological Sciences THE UNIVERSITY OF TEXAS AT EL PASO May 2018 Acknowledgements I would like to express my gratitude to my chair Philip Goodell. You have taught me more than any other individual on this planet, and for that I am grateful. I would also like to thank all the other members of my committee for their contributions. Richard Jarvis, you helped me maintain my sanity. Eric Kappus, you have been a vital mentor and my rock through the whole process. Munazzam Ali Mahar, you helped me learn new techniques and analyses relevant to my research, and Aaron Velasco, you made me realize the finish line was not too far away. Mourat Tchoshanov, you took me under your wing and served as my mentor. I would also like to thank Mercedes Guzman, Laura Serpa, Olga Kosheleva, and Kien Lim because each of you provided support and guidance in your own special way. I am a better individual because of every one of you. v Abstract This dissertation is the product of several individual multi-disciplinary investigations that cover a variety of topics in mathematics, physics, geology, and geoscience education. The first chapter formulates a better understanding of the timings, magma source, and relationships between dikes and associated magmatic bodies of the Red Bluff Granitic Complex to provide a clearer picture of the evolution of post-Grenville magmatism and tectonism of southwestern USA. The second chapter provides an improved method for representing spatial information in the form of a multidimensional virtual tour where the background map is used as a central object. The third chapter describes two methods to describe the vastness of time: the first a geo-spatial and chronologically organized virtual tour and the second calculates the date of the El Paso/Juarez regional formations proportionally to a 12-month calendar. The fourth chapter describes methods to utilize Google EarthTM to solve for the slope of a path frequently traveled and a new technique for manipulating polygons to calculate volume and surface area. The fifth chapter describes a methodological approach of incorporating motion analysis-based software within the classroom. The sixth chapter discusses the methods and outcomes for a two-year professional development grant for mathematics and Earth science teachers. The primary goal of the program was to encourage teachers to integrate these disciplines into their classrooms. vi Table of Contents Acknowledgements .........................................................................................................................v Abstract ......................................................................................................................................... vi Table of Contents ......................................................................................................................... vii List of Tables ............................................................................................................................... xii List of Figures .......................................................................................................................... xiiiiii Chapter 1: Grenvillian Tectonomagmatic Evolution of Southwestern Laurentia ...........................1 Abstract ..................................................................................................................................1 1. Introduction ........................................................................................................................2 2. North American Orogenies 1.7-1.0 Ga ...............................................................................4 3. Local Geologic Setting of the Franklin Mountains.............................................................6 4. Description of the RBGS Stages and Samples Description ..............................................11 5. Geochronological Studies of RBGS Magmatism .............................................................17 6. Grenvillian Magmatism of southwestern Laurentia .........................................................18 6.1 1125-1100 Ma .......................................................................................................18 6.2 1097-1082 Ma .......................................................................................................19 6.3 1081-1068 Ma .......................................................................................................20 7. Present Understanding for the Magmatic Evolution of Southwestern Laurentia .............22 7.1 Franklin, Llano, and and Little Hatchet Mountains ...............................................22 7.2 Pikes Peak Batholith and Wood Canyon Formation..............................................23 7.3 Grenville Related Magmatism from Northern Mexico ..........................................24 8. Analytical Methods ...........................................................................................................26 9. Results ...............................................................................................................................26 9.1 Whole Rock Geochemistry ....................................................................................26 9.2 Zircon Morphology ................................................................................................31 9.3 LA-ICP-MS U-Pb Geochronology .......................................................................33 9.4 LA-ICP-MS Hf Isotopic Data ................................................................................36 10. Discussion .......................................................................................................................38 10.1 Origin of Hf Compositions ..................................................................................38 10.2 Timing of Southwestern Laurentian Magmatism ...............................................41 10.3 Petrology of Red Bluff Granitic Suite ................................................................43 vii 10.4 Tectonic Implications...........................................................................................44 11. Conclusions .....................................................................................................................49 Chapter 2: Virtual Tour through Multidimensional Orders of Scale .............................................50 Abstract ................................................................................................................................50 1. Introduction ......................................................................................................................50 2. Background ......................................................................................................................51
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