FLEXURE OF THE OCEANIC LITHOSPHERE IN THE VICINITY OF THE MARQUESAS ISLANDS by PAUL EDWARD FILMER B.Sc. with Honors, Geophysics California Institute of Technology (1985) SUBMITrED TO THE DEPARTMENT OF EARTH, ATMOSPHERIC AND PLANETARY SCIENCES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY November 1991 © Massachusetts Institute of Technology, 1991. All rights reserved. Signature of author .- - Department of Earth, Atmospheric and Planetary Sciences Certified by Marcia K. McNutt /- Department of Earth, Atmospheric and Planetary Sciences Accepted by Thomas H. Jordan Chairman, Department of Earth, Atmospheric and Planetary Sciences M RARaES DEDICATION 'Where shall I begin, please your Majesty?' he asked. 'Begin at the beginning,' the King said gravely, 'and go on till you come to the end: then stop.' Lewis Carroll Alice in Wonderland, ch. 11 This thesis is dedicated to the memory of my aunt, Agnes Waldron, who died six weeks before I defended. When I was young, I regarded her with fear: her unswerving wit and acerbic tongue were, for me and many others, like facing the Red Queen. Now that she is gone, I realize that she was really only Alice after all. iii TABLE OF CONTENTS DEDICATION........................................................................................ ii LIST OF FIGURES .................................................................................... vi LIST OF TABLES ................................................................................... ix ACKNOWLEDGEMENTS ........................................................................... x CURRICULUM VITAE............................................................................xiv PROLEGOMENON .................................................................................. xv ABSTRACT.......................................................................................xvi CHAPTER ONE The Marquesas Islands ................................................................... 1 1.1. Setting of the Survey Area ....................................................... 2. 1.2. Organization of the Thesis .......................................... ...... 7 1.3. Publication of Results .............................................................. 11 CHAPTER TWO The Alignment of Seafloor Features ................................................... 12 2.1. Introduction ....................................................................... 12 2.2. Data Collection .................................................... 15 2.3. Seafloor Features .................................................... 17 2.3.1. Feature type ............................................................ 23 2.3.1.1. Seamounts .................................................. 23 2.3.1.2. Ridges and lineations ...................................... 23 2.3.1.3. The Tuamotu Plateau ........................................25 2.3.1.4. The Marquesas Fracture Zone ............................25 2.3.2. Latitude and longitude of features ..................... 28 2.3.3. Depth and height of features ............................................ 28 2.3.4. Axial lengths and trends ................................................ 28 2.3.5. Dike and rift zone trends ................. 29 2.4. Feature Trends and Sizes......................................................... 41 2.4.1. Lineation statistics ...... ............................................ 45 2.4.2. Seamount and ridge major axis statistics...........................45 2.4.3. Dike trend statistics................... ................................52 2.4.4. Seamount dimensions............. ..................................52 2.5. Discussion ................................................................. 61 2.5.1. Fabric lineations and magnetic lineations ............................. 61 2.5.2. Seamount major axis alignment ........................................ 64 2.5.3. Dike alignments ........ ............................... 69 2.5.4. Other concerns ......................................................... 75 2.6. Conclusions..........................................................................75 CHAPTER THREE Island Volcanism and Archipelagic Aprons ............................................ 77 3.1. Introduction............................ ........................................... 77 3.1.1. Mass wasting............................................................ 78 3.1.2. Subsidence, mass wasting, and the sediments of the apron........80 3.2. Refraction Lines...................................................................82 3.2.1. Sonobuoy record interpretation....................... ..... 86 3.3. Reflection Profiles ................................................................ 90 3.3.1. Abyssal hills and pelagic sediment cover.......................... 90 3.3.2. Sediment ponds and apron turbidites ............................ 91 3.3.3. Inter-island sediments ................................................. 91 3.3.4. Volcanic carapace ........ .......... ................................ 97 3.4. Discussion....... .......................................................... 101 3.4.1. Volcanic stages and apron development............................ 104 3.4.2. Catastrophic collapses ................................................. 106 3.4.3. Areal extent of the apron ............................................. 107 3.4.4. Volume of apron sediments and building cycles ................ 109 3.5. Conclusions ....................................................................... 110 CHAPTER FOUR The Oceanic Lithosphere Under the Marquesas Islands ............................. 111 4.1. Introduction ................................................................................................ 111 4.2. Gravity Data....................................................................... 112 4.2.1. Adopted terminology ...................................... 116 4.2.2. Shipboard and satellite derived gravity ........................... 117 4.3. Revised Maps for the Marquesas ............................................. 117 4.4. Gravity Modelling ................................................................ 122 4.4.1. Local compensation..................................................... 124 4.4.2. Regional compensation ................................................ 124 4.4.2.1. Plate flexure .................................................. 125 4.4.3. Flexural effects on the gravity field ................................ 126 4.4.4. Initial estimates of Te and Ap.................................. 130 4.4.5. Two-dimensional models .......................................... 133 4.4.5.1. Admittance............................................... 134 4.4.5.2. Admittance results ........................................... 135 4.4.5.3. Forward modelling ...................................... 148 4.4.6. Three-dimensional models .......................................... 154 4.4.7. Convergence of the series................................. 155 4.5. D iscussion........................... ............................................ 161 4.5.1. Off-track bathymetry .................................................. 163 4.5.2. Locked versus unlocked fracture zones ............................ 164 4.5.3. Top and bottom loading .......................................... 168 4.5.4. Trends in Te ........................................................... 175 4.6. Conclusions ..................................................................... 183 CHAPTER FIVE The Thermal Power of the Marquesas Hotspot... ......................... 184 5.1. Erupted Volume and Average Thermal Power .............................. 184 5.1.1. Total volume of erupted volcanic material......................... 187 5.1.2. Average thermal power.............................................. 187 5.2. Perturbation of the Geotherm ................................................. 192 5.3. Present Location and Activity of the Marquesas Hotspot.................. 194 5.4. Conclusions......................................................................... 196 APPENDIX A Circular Error Analysis ....................................... ..................................... 198 A.1. Circular, or Periodic Variables ............................................... 198 A.2. The Mean Direction of a Circular Distribution .............................. 199 A.3. Binning Effects ................................................................... 201 A.4. The von Mises Distribution ..................................................... 202 A.4.1. Best estimates for K, 01, and ...................................... 204 V A.4.2. Confidence intervals for the estimates of 01 and K.................205 A.4.3. Higher order moments of distributions ............................... 205 A.5. Tests for Randomness ..................... ....................................206 A.5.1. The Rayleigh Test....................................................207 A.5.2. The V-test ............................................................ 207 A.6. Circular-Linear Correlation ...................... 208 A.6.1. 'Linearizing' the problem.............................................208 A.6.2. The Nr2 test ................ ........................ ...... 208 APPENDIX B Errors in estimations of Te .................. ........................................209 APPENDIX C "Xi-squared" ......................................... 214