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Stress Modeling of the Nazca Plate: Advances in Modeling Ridge-Push and Slab-Pull Forces

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Stress Modeling of the Nazca Plate: Advances in Modeling Ridge-Push and Slab-Pull Forces Stress modeling of the Nazca plate: advances in modeling ridge-push and slab-pull forces Item Type text; Thesis-Reproduction (electronic) Authors Cox, Billie Lea 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 26/09/2021 01:05:53 Link to Item http://hdl.handle.net/10150/557971 STRESS MODELING OF THE NAZCA PLATE: ADVANCES IN MODELING RIDGE-PUSH AND SLAB-PULL FORCES by Billie Lea Cox A Thesis Submitted to the Faculty of the DEPARTMENT OF GEOSCIENCES In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE In the Graduate College THE UNIVERSITY OF ARIZONA STATEMENT BY AUTHOR This thesis has been submitted in partial ful­ fillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules . of the Library„ Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permis­ sion for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the mate­ rial is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below: R. M. RICHARDSON ' Date Assistant Professor of Geosciences ACKNOWLEDGMENTS I am very grateful to my thesis advisor, Professor Randall M. Richardson, for suggesting this thesis topic, convincing me that finite elements could be understandable given time and effort, and for patiently guiding my pro­ gress, supporting my work with a research assistantship and computer time. I want to thank Professors Spencer R. Titley and William R. Dickinson for reading my thesis, and for stimu­ lating my interest in plate tectonics through course lectures. The Department of Geosciences supported me with teaching assistantships in mineralogy, and I also received a research assistantship from Dr. Dennis K. Bird. Further Support for my graduate studies came from Amoco and Conoco scholarships awarded by the Geophysics Committee, and from earnings from summer employment with GeothermEx, Inc., and Sohio Petroleum Company. I appreciate all of this support. I want to express a special thanks to Murray C. Gardner for encouraging me to pursue graduate studies at the University of Arizona, and for sending flowers at the right times. And finally, I want to thank my mother, Marcilie G. Cox, for providing a coastal haven from desert heat and allergies, and for the moral support I needed to see my way through to the completion of this thesis. iii TABLE OF CONTENTS Page TABLE OF CONTENTS ......................... iv LIST OF ILLUSTRATIONS ................. vi LIST OF TABLES ......................... ix ABSTRACT x I. INTRODUCTION . ; ............ .... ... .1 II. DESCRIPTION OF THE NAZCA PLATE . .... 6 East Pacific Rise Ridge Boundary ...... 11 Galapagos Spreading Center Ridge Boundary . 13 Chile Ridge Spreading Center and Transforms .... ..... 15 South American Trench Boundary ........ 16 Intraplate Features ............ 20 III. STRESS DATA . » . 24 IV. DESCRIPTION OF MODELING METHOD 30 Elastic Modeling ............. 31 Viscous Modeling ............. 38 V. MODELING PLATE-DRIVING FORCES 40 Ridge-Push Forces ......................... 40 Distributed Ridge Forces Applied to the Nazca Plate .......... 48 Line Ridge Forces Applied to the Nazca Plate ........ ....... 48 Slab-Pull Forces . ..... 51 Drag Forces ................. 57 Transform Fault Shear Forces ....... 63 Hot Spot Forces .............. 63 Distant Forces From Other Plates . 64 iv V TABLE OF CONTENTS— Continued Page VI. STRESS MODELS . ....... 65 Distributed Ridge Models . 65 DR Models ............. 65 DRD Models . 68 Refined Grid Models .......... 71 Line Ridge Models ............. 74 LR Models . ■ 74 LRD Models .............. 78 Slab-Pull Models . 78 SD Models ............... 78 Angle Dependent Models . 80 Age Dependent Models . 83 Combined Ridge-Push and Slab-Pull Models . 87 DRSD Models . .. 87 LRSD Models .............. 90 Viscous Models ....... ...... 90 VII. CONCLUSIONS . v 97 REFERENCES 101 LIST OF ILLUSTRATIONS Figure Page 1. Location map of the Nazca plate . „ . 7 2. Nazca plate boundaries and intraplate f e a t U r e S oeeeoeoeooeepoooo IQ Topography along the East Pacific Rise Ridge Boundary . .■ „ . • . , . 12 4„ Segmentation of the South American Subduction Zone 17 5. Distribution of intraplate earthquakes in the Nazca plate recorded between 1901 and 1981 . 25 6. Location of the 1965 and 1944 intraplate earthquakes .............. .. 26 7. Triangular elements on a half-sphere . , . 32 8. Finite element grid of the Nazca plate (coarse) oopeppopppopeooao 35 9. Finite element grid of the Nazca plate (re fined) 9***99 99*90 * 9*9 37 10. Plate-driving forces acting on the Nazca plate * .............. .. 41 11. Test case for comparing distributed ridge and line ridge forces 46 12. Distributed ridge forces on the Nazca plate . 49 13. Line ridge forces applied to the Nazca plate . 52 14. Constant slab-pull forces on the Nazca plate . 56 15. a. Angle dependent slab-pull forces b. Age dependent slab-pull forces ........... 58 vi vii LIST OF ILLUSTRATIONS— Continued Figure Page 16. Drag forces balancing distributed ridge forces e o <» o -< <> • -•• « o o 62 17. a. Stress state for Model DR-a b. Stress state for Model DR-b . 67 18. Stress state for Model DRD--a • » • v ° o 69 19. a. Stress state for Model DRD-b be Stress state for Model DRD-C o • • • ° ° 70 20. a» Distributed ridge forces for refined grid be Stress state for Model *DR-a » •- • o o 73 - ' 21. ae Stress state for Model *DRD-a be Stress state for Model *DRD-b - • » • «, o 7 5 22. a. Stress state for Model LR-a be Stress state for Model LR-b » • * - o 76 23. Stress state for Model LR-(: » • > • • « < • e 77 24. a. Stress state for Model LRD-a b. Stress state for Model LRD-b • - e a o 79 25. a. Stress state for Model SD—a b. Stress state for Model SD—b a « • •• ° o o 81 26. a. Stress state for Model SD-c b. Stress state for Model SD—d e • • • « o 82 27. a. Stress state for Model SD-ang b. Stress state for Model SD-ang2 . a o o 84 28. Stress state for ModelModel SD-ageSD-age . 8528. 85 29. Composite of stress states for Models SD-c, SD-ang, SD-ang2, and SD-age . 86 30. a. Stress state for Model DRSD-1 b. Stress state for Model DRSD-2 . ..... .88 31. a. Stress state for Model DRSD-3 b. Stress state for Model DRSD-4 . , . 89 32. a. Stress state for Model LRSD-1 b. Stress state for Model LRSD-2 , . .... .91 viii LIST OF ILLUSTRATIONS— Continued Figure Page 33. Stress state for Model LRSD-3 Stress state for Model LRSD—4 . « . 92 34. fd Stress state for Model V-DR A Stress state for Model V-DRD . 94 35. ftirQ Velocities for Model V- -DR Velocities for Model V--DRD o o o e o o e o 96 LIST OF TABLES Table Page 1. Plate Motion Data Used in Nazca Plate Stress Modeling .............. 9 2. Description of Nazca Plate Models . 6 0 ix ABSTRACT The forces which drive the plates are evaluated by finite element stress modeling of the Nazca plate, where stresses resulting from various combinations of forces are compared with the record of intraplate earthquakes and other stress data. Both elastic and viscous rheologies are modeled. Advances in modeling both ridge-push and slab- pull forces are presented. Ridge forces are distributed over the entire plate, and then compared with line ridge force models. Angle and age-dependent slab-pull models are compared with constant slab-pull models. The distri­ buted ridge force models produce more realistic stresses and represent a significant improvement over line ridge forces. Age-dependent slab-pull models fit the data better than other slab-pull models. Angle-dependent slab-pull models do not fit the data in regions of shallow dipping slab segments. Both elastic and viscous models with drag forces are less correlatable with the stress data than models without drag forces. x I. INTRODUCTION The earth's lithosphere is made up of about a dozen plates, defined by seismicity, and although we can directly observe and measure the relative motion of the plates, we have no direct method for measuring the forces which drive the plates and must rely on theoretical modeling. The object of this thesis is to utilize one of these methods, stress modeling, to investigate the role and relative importance of possible forces in.driv­ ing and stressing a single plate, the Nazca plate. The forces considered are ridge-push, slab-pull and resistive drag at the base of the plate. The Nazca plate is modeled by the finite element method as in Richardson (1978) where combinations of the various plate-driving forces are applied and the resulting stress states compared with the stress data. Several advances to this earlier work are presented here. One improvement is a new, more realistic way of modeling ridge-push forces, by distributing the ridge-push over the entire plate. Distributed ridge forces are also modeled with a refined grid. Advances in modeling slab- pull forces include both age-dependent and angle-dependent slab-pull models. A fourth innovation is the use of an incompressible viscous rheology for two of the eight 1 distributed ridge models„ The viscous solution results in velocities and stresses rather than displacements and stresses obtained from elastic modeling.
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