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Spatial Characterization of Western Interior Seaway Paleoceanography Using Foraminifera, Fuzzy Sets and Dempster-Shafer Theory

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Spatial Characterization of Western Interior Seaway Paleoceanography Using Foraminifera, Fuzzy Sets and Dempster-Shafer Theory SPATIAL CHARACTERIZATION OF WESTERN INTERIOR SEAWAY PALEOCEANOGRAPHY USING FORAMINIFERA, FUZZY SETS AND DEMPSTER-SHAFER THEORY Samuel N. Lockshin A Thesis Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE August 2016 Committee: Margaret Yacobucci, Advisor Peter Gorsevski Andrew Gregory © 2016 Sam Lockshin All Rights Reserved iii ABSTRACT Margaret Yacobucci, Advisor The spatial paleoceanography of the entire Western Interior Seaway (WIS) during the Cenomanian-Turonian Oceanic Anoxic Event has been reconstructed quantitatively for the first time using Geographic Information Systems. Models of foraminiferal occurrences—derived from Dempster-Shafer theory and driven by fuzzy sets of stratigraphic and spatial data—reflect water mass distributions during a brief period of rapid biotic turnover and oceanographic changes in a greenhouse world. Dempster-Shafer theory is a general framework for approximate reasoning based on combining information (evidence) to predict the probability (belief) that any phenomenon may occur. Because of the inherent imprecisions associated with paleontological data (e.g., preservational and sampling biases, missing time, reliance on expert knowledge), especially at fine-scale temporal resolutions, Dempster-Shafer theory is an appropriate technique because it factors uncertainty directly into its models. Locality data for four benthic and one planktic foraminiferal species and lithologic and geochemical data from sites distributed throughout the WIS were compiled from four ammonoid biozones of the Upper Cenomanian and Early Turonian stages. Of the 14 environmental parameters included in the dataset, percent silt, percent total carbonate, and depositional environment (essentially water depth) were associated with foraminiferal occurrences. The inductive Dempster-Shafer belief models for foraminiferal occurrences reveal the positions of northern and southern water masses consistent with the oceanographic gyre circulation pattern that dominated in the seaway during the Cenomanian- Turonian Boundary Event. The water-mixing interface in the southwestern part of the WIS was mostly restricted to the Four Corners region of the US, while the zone of overlap of northern and iv southern waters encompassed a much larger area along the eastern margin, where southern waters occasionally entered from the tropics. In addition to its paleospatial significance, this study introduces a rigorous, quantitative methodology with which to analyze paleontological occurrence data, assess the degree of uncertainty and prioritize regions for additional data collection. v This work is dedicated to Occam for showing scientists how to properly use a razor. vi ACKNOWLEDGMENTS I extend my sincerest thanks to Dr. Peg Yacobucci for her many hours of aid and guidance during the completion of this document. Her scientific knowledge, wisdom and good attitude have been imparted on this work and on the way by which I will conduct future research. I thank Dr. Peter Gorsevski for introducing new software and the power of Bayesian statistics to me and for spending lots of time going over the modeling process to ensure a firm grasp on the methods. I also sincerely appreciate the many conversations I had with Dr. Andy Gregory that helped to formulate the idea and analysis methods for this work and for always asking great (albeit hard to answer) questions. A special thanks goes to Dr. Cori Myers for her collaboration with the data collection process. To work with such bright people has been both an honor and humbling experience for which I am grateful. vii TABLE OF CONTENTS Page INTRODUCTION………………………………………………………………………........ 1 CHAPTER I. BACKGROUND…………………………………….……………………….. 4 1.1 Tectonic overview………………………………………………………………. 4 1.2 Paleoceanography and stratigraphy during the Cenomanian-Turonian Interval…………………...……………………………………………………… 5 1.3 Spatial modeling approach……………………………………………………... 11 1.3.1 Fuzzy set theory……………………………………………………............ 12 1.3.2 Dempster-Shafer theory……………………………………………............ 13 CHAPTER II. METHODS………………………………………………………………….. 19 2.1 Data collection and spatial analysis…...…………………………………………. 19 2.2 Spatial interpolation……………………………………………………………… 21 2.3 Choosing foraminifera to model….…...…………………………………………. 23 2.4 Implementing fuzzy..….........................…………………………………………. 25 2.5 Modeling species distributions with Dempster-Shafer theory................................ 29 2.5.1.1 Depositional Environment....…………………………………............ 30 2.5.1.2 Carbonate content...….…….…………………………………............ 31 2.5.1.3 Silt content.….……….…….…………………………………............ 31 2.5.1.4 Latitudinal extent…….…….…………………………………............ 31 2.5.1.5 Longitudinal extent.….…….…………………………………............ 32 CHAPTER III. RESULTS…………………………………………………………………... 42 3.1 M. mosbyense (Late Cenomanian) results...…………………………………...…. 42 viii 3.2 S. gracile (Late Cenomanian) results.………………………………...…………. 43 3.3 N. juddii (Uppermost Cenomanian) results……….……………………………... 45 3.4 W. devonense (Earliest Turonian) results...……….……………………………... 47 CHAPTER IV. DISCUSSION………………………………...……………………………. 65 4.1 Interpretation of results……………………….……………………………...…. 42 4.2 Dempster-Shafer theory: A befitting model that addresses potential uncertainties…………...……………………………………………….. 76 4.3 Fuzzy power………………………………………………………………………. 79 4.4 Future work…………………..……...…………………………………………… 80 CHAPTER V. CONCLUSIONS…………………………………………………………… 84 REFERENCES……………………………………………………………………………… 87 APPENDIX A. INTERPOLATION STATISTICS………………………………………… 99 APPENDIX B. ALL FUZZY CONTROL POINTS..……………………………………… 101 APPENDIX C. FORAMINIFERAL ABSENCE FIGURES….…………………………… 105 APPENDIX D. CODES……………………………………….…………………………… 112 APPENDIX E. DATA SOURCES…………………………….…………………………… 119 APPENDIX F. TIME-LAPSE VIDEO OF WATER MASS DISTRIBUTIONS........……. 120 ix LIST OF FIGURES Figure Page 1 Map of the Western Interior Seaway ......................................................................... 17 2 Stratigraphic column of the Rock Canyon, CO, section ........................................... 18 3 Map of the Western Interior Seaway with localities ................................................. 33 4 Semivariogram plot ................................................................................................... 34 5 Common fuzzy functions .......................................................................................... 34 6 Fuzzification process ................................................................................................. 35 7 Fuzzy layers for Rotalipora greenhornensis presence .............................................. 36 8 Fuzzy layers for Rotalipora greenhornensis absence ............................................... 37 9 Input interpolated surfaces for M. mosbyense zone ................................................... 48 10 Input interpolated surfaces for S. gracile zone .......................................................... 49 11 Input interpolated surfaces for N. juddii zone ........................................................... 50 12 Input interpolated surfaces for W. devonense zone ................................................... 51 13 Latitude and longitude rasters ................................................................................... 52 14 Interpolated surfaces for Late Cenomanian time zones ............................................ 53 15 Interpolated surfaces for Latest Cenomanian/Early Turonian ................................... 54 16 Benthic oxygenation trends over time ....................................................................... 55 17 Presence images for Rotalipora greenhornensis during M. mosbyense zone ........... 56 18 Presence images for Rotalipora greenhornensis during S. gracile zone ................... 57 19 Presence images for Valvulineria loetterlei during S. gracile zone .......................... 58 20 Presence images for Ammobaculites spp. during S. gracile zone ............................. 59 21 Belief images for Valvulineria loetterlei with varying levels of ignorance .............. 60 x 22 Interval images and histograms for Valvulineria loetterlei with varying levels of ignorance…………………………………………………………….…………….. 61 23 Presence images for Neobulimina albertensis during N. juddii zone ........................ 62 24 Presence images for Gavelinella dakotensis during N. juddii zone .......................... 63 25 Presence images for Neobulimina albertensis during W. devonense zone ................ 64 26 Presumable water mixing extent during OAE2 ......................................................... 82 27 Distribution of Heterohelix spp. across the CTB ...................................................... 83 xi LIST OF TABLES Table Page 1 Coding scheme for environmental parameters .......................................................... 38 2 Properties of modeled foraminifera ........................................................................... 40 3 Fuzzy control points .................................................................................................. 41 1 INTRODUCTION The paleoceanography of the Western Interior Seaway (WIS) of North America has been studied extensively to interpret the prevailing climatic and environmental conditions of this vast epicontinental seaway in the Late Cretaceous greenhouse world. Numerous works (e.g., Eicher and Worstell, 1970; Kauffman 1984; Elder, 1985; 1987; 1990; 1991;
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