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The Stability and Evolution of Triple Junctions

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The Stability and Evolution of Triple Junctions THE STABILITY AND EVOLUTION OF TRIPLE JUNCTIONS Theodore G. Apotria B.S., The University of Connecticut, 1982 A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science at The University of Connecticut 1985 APPROVAL PAGE Master of Science Thesis THE STABILITY AND EVOLUTION OP TRIPLE JUNCTIONS Presented by- Theodore G. Apotria, B.S. Major Adviser Associate Adviser | Peter Dehlrnger Associate Adviser 7 Peter Geiser Associate Adviser Thomas Moran The University of Connecticut 1985 ii DEDICATION This thesis is dedicated to my parents, George and Cleo Apotria, and to my "brother and best friend, John. Their support was essential in completing this work. iii ACKNOWLEDGEMENTS There are several individuals whose assistance and support contributed to this thesis, and to whom I am indebted: I am especially thankful to Dr. Norman Gray, who, as my major adviser, contributed many hours of stimulating discussion and attention. As the thesis topic evolved, his assistance in the theoretical development, computer programming, and critical commentary on the manuscript, all proved invaluable. Dr. Peter Dehlinger, Dr. Peter Geiser, and Dr. Thomas Moran, contributed their time reviewing the text and provided useful perspectives. Dr. Randolph Steinen contributed useful comments on the preliminary research proposal. I am also grateful to the Dept, of Geology and Geophysics for providing financial support in the form of a Teaching Assistantship, and an Amoco sponsored Master's Fellowship in Geophysics. I also thank Dr. Anthony Philpotts for providing a Research Assistantship from K.S.F. grant if EAR8017059* - iv ABSTRACT Triple junction stability, as introduced by McKenzie and Morgan (1969)> assumes constant relative velocities and can only be defined instantaneously. Factors that affect the stability of triple junctions as a function of time include changes in the boundary orientations and relative velocities. Changes in the velocity triangle can be induced by the effects of motion on a sphere, and the motion of the lithospheric plates with respect to the mantle. Each type of triple junction has been assigned a number of degrees of freedom, where a degree of freedom is an imparted change in boundary configurations or relative velocities without upsetting the stability condition. The number of degrees of freedom correlates positively with the junction's ability to maintain stability under imposed changes. The exact stability condition of any triple junction can be calculated by least squares analysis. An equation for the location of the triple junction with respect to each boundary is introduced with respect to any reference frame. - v - The equations are linear and of the form J = a + hh. A unique simultaneous solution results if the junction is stable. If the junction is unstable, the sum of the squares of the residuals is proposed as a measure of the degree of geometric instability. This analysis is particularly useful when several boundary types are consistent with a single velocity triangle. The type least affected by imposed changes can be regarded as the most geometrically stable, and can be considered in evolutionary schemes. The absolute motion of the Bouvet triple junction with respect to the mantle (mesosphere) plays a significant role in its evolution. Absolute poles of rotation from the AM1-2 model (Minster and Jordan, 1978) for the South American, African, and Antarctic plates were utilized to calculate an "isosceles line" in the South Atlantic. Along this locus (trending 91°)* the relative velocity triangle for the three plates is isosceles. The actual Bouvet triple junction lies about 5 degrees north of this line, presumably due to uncertainties in the AM1-2 poles. Assuming the Bouvet junction is actually isosceles, the absolute triple junction velocity vectors for the motion of the Ridge-Ridge-Ridge (RRR) and Ridge-Fault-Fault (RFF) configurations are respectively 14*7 km/yr, with an azimuth of 34j5> and 5*8 km/my with an azimuth of 157* A least squares analysis - vi - suggests the RFF configuration is geometrically more stable in the vicinity of the isosceles line and is the preferred mode. Consequently, a RRR triple junction located south of the present position of the Bouvet junction vould, relative to the mantle, migrate northwest until it intersects the isosceles line and spontaneously changes to a stable RFF configuration. As a RFF junction, its new velocity would take it southeast away from the isosceles line, rendering it increasingly unstable. As it migrates, the rotations of the relative velocities are such that both growing transform fault develop a small component of extension normal to the transform. Hence, the junction may survive for an appreciable time in a geometrically unstable state. At the point of mechanical instability, the junction would change back to a stable RRR configuration and migrate northwest until it intersects the isosceles line once again. Each time the junction switched to RFF mode, paired transform faults would develop. The RFF configuration of the Bouvet junction was apparently able to migrate approximately 110 km (about 1 degree latitude) from the isosceles line before RRR mode intervened. vii A rigorous examination of the unstable Kendocino triple junction in velocity space reveals possible modes of evolution. If the requirement is relaxed that the trench is fixed with respect to the North American plate, trench rotation and subsequent back-arc spreading are possible. At specific orientations of the trench boundary, spreading at the North American-Pacific boundary allows the junction to regain stability. A third alternative is the migration of the San Andreas shear zone eastward, transferring part of the North American plate to the Pacific plate. - viii - CONTENTS APPROVAL PAGE ii DEDICATION iii ACKKOVLEDGEKENTS iv ABSTRACT v LIST OF FIGURES xi LIST OF TABLES xiii Chapter page I. INTRODUCTION 1 II. PREVIOUS WORK 5 Triple Junction Geometry 5 III. THE FRAMEWORK OF PLATE GEOMETRY 10 The Angular Displacement of a Plate 10 The Tectonic Character of Plate Boundaries 13 The Stability of Triple Junctions 14 Nomenclature 14 Defining Stability 16 IV. THE QUANTIFICATION OF GEOMETRIC INSTABILITY 22 Triple Junction Equations 23 The Best Fit Solution 26 least Squares Estimation 27 Relative Stability 29 V. THE PERTURBATION STABILITY OF TRIPLE JUNCTIONS 32 Analysis of Stability 33 The Problem on a Sphere Absolute Plate Motion 41 - ix - VI. GEOLOGIC APPLICATIONS 44 The Bouvet Triple Junction 44 Introduction 44 The Absolute Notion of the Eouvet Triple Junction 46 Eouvet Triple Junction Evolution 48 The Question of Relative Stability 51 Triple Junction Evolution in the Western United States 55 Introduction 55 Previous Work 55 Velocity Space Analysis 58 VII. CONCLUSIONS 61 BIBLIOGRAPHY 65 FIGURES 68 TABLES 132 Appendix page A. SINGULAR VALUE DECOMPOSITION 139 B. SUMMARY OF CONSTRAINT AND PERTURBATION STABILITY ANALYSIS 144 X -T LIST OP FIGURES Figure page 1. A stable configuration for the RRF triple junction. 68 2. An unstable RRR triple junction...................70 3* A stable TTT(b) triple junction....................72 4. A geometrically stable quadruple junction......... 74 5* Instantaneous displacement and angular velocity. 76 6. The vector circuit around a triple junction.......78 7. The possible types of plate boundaries............ 80 8. Nomenclature and labeling scheme.................. 82 9* An FRT triple junction defining the stable condition........................................ 84 10. Possible velocity diagrams for the RRR junction. 86 11. Direct space representation of Figure 10.......... 88 12. Four possible rff direct space configurations. ... 90 13» Development of vectors describing the location of (J).............................................. 92 14. Sum of square of the residuals.....................94 15* The effects of boundary rotation on stability. ... 96 16. The effects of triangle distortion on stability. 98 17. Constraints on the relative velocity............ 101 18. A description of perturbation stability.........103 - xi 19* Stability analysis of the RPP Junction............ 105 20. Stability analysis of the RRF and RRR junctions . 107 21. The location of the Bouvet triple junction. 109 22. The position and orientation of the isosceles line. 111 23. Velocity space representation of the Bouvet junction.........................................113 24* A model of evolution for the Eouvet triple junction.........................................115 25* The evolving velocity triangle for the RFF junction.........................................117 26. Relative geometric stability........................119 27* Location and tectonic map of the western United States...........................................121 28. The geometric evolution of the NE Pacific.......... 123 29. Stable and unstable FFT configurations............. 125 30. Cumulative deformation at an unstable FFT junction. 127 31. Tectonic consequences of the unstable Mendocino junction.........................................129 - xii - LIST OP TABLES Table page 1. The stability of triple junctions....................132 2. Stability involving oblique symmetrical spreading. 133 3« Topologically distinct varieties of triple junctions......................................... 134 4. Topologically distinct varieties of stable T- junctions.................. 136 5. Perturbation stability of some existing triple junctions.......................................137 6. AMI-2 absolute poles of
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