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The gravitational potential energy of the Earth's lithosphere. Item Type text; Dissertation-Reproduction (electronic) Authors Coblentz, David Dwight. Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 28/09/2021 14:08:53 Link to Item http://hdl.handle.net/10150/186601 INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. 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Contact UMI directly to order. U·M·I University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road. Ann Arbor. M148106-1346 USA 313/761-4700 800/521-0600 Order Number 9424935 The gravitational potential energy of the Earth's lithosphere Coblentz, David Dwight, Ph.D. The University of Arizona, 1994 V·M·I 300 N. Zeeb Rd. Ann Arbor, MI48106 ------------------------ --------------------------------------------- ------------- The Gravitational Potential Energy of the Earth's Lithosphere by David Dwight Coblentz A Dissertation Submitted to the Faculty of the DEPARTMENT OF GEOSCIENCES In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 1 994 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Final Examination Committee, we certify that we have read the dissertation prepared by ____~D~a~v~i~d~D~w~i~g~h~t~C~o~b~l~e~n~t~z ____________ ___ entitled The Gravitational Potential Energy of the Earth's Lithosphere and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy Anril 111 1994 Date April 11, 199LI Date April 11, 1994 Date Date Date Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation r.equirement. 7!c.~tct(~. ,2· /fc<-r~.L_~ Randall M. Richardson April 11, 1994 Dissertation Director Date I.' 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the Uni versity Library to be made available to borrowers under rules of the library. Brief quotations from this dissertation are allowable without special per mission, provided that accurate acknowledgment of SOUl'ce is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole 01' in part may be granted by the head of the major department or the Dean of the Graduate College when in his 01' her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED:L2~ ~ ACKNOWLEDGMENTS Many people have helped to make this project a reality. To my principal ad visor, Randall Richardson, I extend special thanks for providing motivation, tech nical expertise and guidance during my tenure at the University of Arizona. I should not neglect mentioning the fruitful time we spent discussing geodynamic problems at the ping-pong table. I also thank other members of my committee and faculty of the geophysics group for their advice and criticism, including Susan Beck, Roy Johnson, Clem Chase, and Terry Wallace. I am especially grateful for the help Steve Sorenson provided on computer-related problems and bugs. Many of my fellow students, including Steve Myers, Sterling Cook and Wolfram Schuh, made the path easier with their helpful distractions. My minor advisor Barbara Kosta provided me with inspiration, encouragement and introduced me to many wonderful "points of departure". Much of the research presented in this dissertation "vas completed during a short visit to the University of Adelaide in 1993. I thank Richard Hillis for the opportunity to work on the Indo-Australian stress project and Shaohua Zhou for all his assistance with LaTex and ANSYS. I am especially indebted to Kurt Stuewe, Karin Ehlers, and Martin a.nd Eva Kennedy who made our visit most enjoyable, both in the department and on the cliffs of Mount Arapiles. I reserve special thanks for Mike Sandiford who taught me the magic of Mathematica and LaTex. Without his motivation, help and guidance this dissertation would have been significantly less complete. I am particularly indebted to him for his help with the mathematical formulations presented in Chapters 2 and 6. Chris Pigram of AGSO is thanked for input into the location and nature of the northern Indo-Australian plate boundary. I would like to thank my non-departmental friends Mike, Andrea, James and Beverly for helping me keep it all in perspective. Finally, and most importantly, Kristine is especially acknowledged for her help in overall "stress management". Parts of this study were funded by the Australian Cooperative Research Centre as part of a study of the factors controlling the stress field of the North West Shelf of Australia. Partial funding was also provided by NSF Grant No. EAR-921931 l1. 5 TABLE OF CONTENTS LIST OF FIGURES. 7 LIST OF TABLES. 9 ABSTRACT .... 10 CHAPTER 1 : INTRODUCTION 12 CHAPTER 2 : THE POTENTIAL ENERGY FORMULATION 18 2.1 Introduction .. 18 2.2 Theoretical Basis. 18 2.3 Lithospheric Density Models .. 20 2.:3.1 Young Oceanic Lithosphere. 22 2.3.2 Oceanic Basin . 22 2.3.3 Continental Lithosphere. 23 2.3.4 Constraint on the Density of the Continental Crust 25 2.4 Global and Plate Scale Lithospheric Potential Energy Estimates 27 2.5 Discussion ................. 32 2.5.1 Potential-Energy Torques. 33 2.5.2 The Tectonic Reference State. 37 2.5.3 The Ambient Stress State. 39 CHAPTER 3 : TRENDS IN THE INTRAPLATE STRESS FIELD 114 3.1 Introduction . ,14 3.2 Statistical Method . '15 3.3 Trends in the World Stress Map Da.tabase . 47 3.4 Discussion .................. .55 CHAPTER 4 : SOUTH AMERICAN INTRAPLATE-STRESS MAG- NITUDE. 60 '1.1 Introduction .. 60 ,1.2 Topography and Deformation Style. 63 4.3 Finite-Element Modeling .. 64 '1.3.1 Modeling Location. 65 L1.3.2 Description of the Finite-Element Grid 69 4.3.3 Modeling Results ........ 71 4.4 Discussion ...................... 76 CHAPTER 5 : INTRAPLATE STRESSES DUE TO POTENTIAL- ENERGY VARIATIONS: A FINITE-ELEMENT ANALYSIS 80 5.1 Introduction .. 80 5.2 Discussion of Tectonic Forces . 81 6 TABLE OF CONTENTS - Continued 5.2.1 Buoyancy Forces .... 81 5.2.2 Collisional Boundaries .. 83 5.2.3 Basal-Shear Tractions .. 85 5.3 Discussion of the Modeling Method 86 5A The African Plate . 87 5A.1 Description of the Plate. 89 5A.2 The Regional Intraplate Stress Field. 89 5.'1.3 Modeling Results 91 5AA Discussion . 95 5.5 The South American Pla.te ..... 97 5.5.1 Description of the Plate. 99 5.5.2 The Regional Intraplate Stress Field . 101 5.5.3 Modeling Results 104 5.5.'1 Discllssion ....... 118 5.6 The Indo-Australian Plate .... 121 5.6.1 Description of the Plate. 123 5.6.2 The Regional Intraplate Stress Field. 125 5.6.3 Modeling Results ......... 130 5.6,4 The North West Shelf Stress Field . 146 5.6.5 Discussion ............. 1<19 CHAPTER 6 : TIME-EVOLUTION OF PLATE-SCALE POTENTIAL- ENERGY DISTRIBUTIONS. 158 6.1 Introdudion . 158 6.2 Geoid Anomalies and Potential-Energy Variations 159 6.3 Circular Pla.te Model .............. 165 6.'1 The Aging of the African and Antardic Plates 173 6A.l The African Plate .. 173 6.'1.2 The Antarctic Plate . 180 6.5 Discllssion ........ 183 CHAPTER 7 : CONCLUSIONS 190 APPENDIX A: THE CLOSED-FORM SOLUTIONS FOR THE POTENTIAL ENERGY OF THE LITHOSPHERE. .. 196 APPENDIX B: THE DEPENDENCE OF THE POTENTIAL EN ERGY CALCULATION ON THE MECHANISM OF ISOSTATIC SUPPORT. 198 REFERENCES. 200 7 LIST OF FIGURES Figure 2.1 Schematic of the Lithospheric Depth-Density Distributions 24 Figure 2.2 Potential Energy as a Function of pc and Topography. 26 Figure 2.3 Topography and Potential-Energy Distributions . 28 Figure 2,4 Calculated Potential Energy Versus Topography . 31 Figure 2.5 U/ Torques vs Absolute Plate Velocities, Normalized 35 Figure 2.6 U/ Torques vs Absolute Plate Velocities, Absolute 36 Figure 3.1 Global Stress Indicators . 48 Figure 3.2 Average Stress Regime . L19 Figure 3.3 Average SH,l1H1X Orientations.

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