Mantle dynamics following supercontinent formation by Philip J. Heron A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Physics University of Toronto c Copyright 2014 by Philip J. Heron Abstract Mantle dynamics following supercontinent formation Philip J. Heron Doctor of Philosophy Graduate Department of Physics University of Toronto 2014 This thesis presents mantle convection numerical simulations of supercontinent formation. Approxi- mately 300 million years ago, through the large-scale subduction of oceanic sea floor, continental mate- rial amalgamated to form the supercontinent Pangea. For 100 million years after its formation, Pangea remained relatively stationary, and subduction of oceanic material featured on its margins. The present- day location of the continents is due to the rifting apart of Pangea, with supercontinent dispersal being characterized by increased volcanic activity linked to the generation of deep mantle plumes. The work presented here investigates the thermal evolution of mantle dynamics (e.g., mantle temperatures and sub-continental plumes) following the formation of a supercontinent. Specifically, continental insulation and continental margin subduction are analyzed. Continental material, as compared to oceanic material, inhibits heat flow from the mantle. Previous numerical simulations have shown that the formation of a stationary supercontinent would elevate sub- continental mantle temperatures due to the effect of continental insulation, leading to the break-up of the continent. By modelling a vigorously convecting mantle that features thermally and mechanically distinct continental and oceanic plates, this study shows the effect of continental insulation on the mantle to be minimal. However, the formation of a supercontinent results in sub-continental plume formation due to the re-positioning of subduction zones to the margins of the continent. Accordingly, it is demonstrated that continental insulation is not a significant factor in producing sub-supercontinent plumes but that subduction patterns control the location and timing of upwelling formation. A theme throughout the thesis is an inquiry into why geodynamic studies would produce different results. Mantle viscosity, Rayleigh number, continental size, continental insulation, and oceanic plate boundary evolution are explored in over 600 2D and over 20 3D numerical simulations to better un- derstand how modelling method affects conclusions on mantle convection studies. The results from this thesis show that the failure to model tectonic plates, a high vigour of convection, and a (pseudo) temperature-dependent viscosity would distort the role of mantle plumes, continent insulation, and sub- duction in the thermal evolution of mantle dynamics. ii Dedication To my parents, Ann and Ray. iii Acknowledgements Thank you to Prof Julian Lowman for all the time and effort he has put into shaping my academic skill set. I’ve had the privilege of presenting work at conferences in Ottawa, San Francisco, Leeds, and in Massachusetts. For this, I am entirely grateful to Prof Lowman. Furthermore, my writing style has improved tremendously through Julian’s guidance (although I would now never use the word ‘tremendously’ (maybe ‘significantly’ instead?)). Through their honesty and thoughtfulness, my academic committee has made the PhD process very simple (although no less hard work). Thank you to Prof Stephen Morris and Prof Sabine Stanley. I am also grateful to Prof Stanley for the encouragement shown while I was her TA. Thanks to Prof Mathew Wells and Prof Dick Bailey who were part of my external committee. My external examiner, Prof Sam Butler, deserves credit for his excellent comments which helped improve the thesis. Keely O’Farrell and Sean Trim have always been on hand to offer help and encouragement (and to listen to a complaint about coding). I hope that one day we can publish our coffee table book, Numerical Modelling Mistakes. Robert Harrison and Ryan Vilim have helped with every presentation I have had to do. Thank you both for your excellent powerpoint skills and your 24/7 availability. A special thank you to the (past and present) Geophysics and Atmospheric graduates who have been great to be around (you know who you are). My graduate time in Toronto has been made a lot easier by the following people’s hard work and easy-going nature: Krystyna Biel, Crystal Liao, Teresa Baptista, Pierre Savaria, Jonathan Dursi, and all those at SciNet. I am also appreciative to Prof Tony Key for his excellent course on how to be an effective communicator, and to Becky Ghent, Adrian Lenardic, and Russ Pysklywec for taking an interest in my progress. This thesis is dedicated to my supportive parents. My family back home and my family in Ontario have been more caring and attentive to me than I have been to them over the past few years. Melissa has been a true collaborator with this work; she has heard every presentation and listened to every whinge. Thank you for your patience and encouragement. iv Contents List of Tables ix List of Figures x 1 Introduction 1 2 Method 17 2.1 Introduction.................................... ........ 17 2.2 Governingequations .............................. ......... 17 2.2.1 Approximations................................ ...... 18 2.2.2 Dimensionlessequations . ......... 21 2.3 Numericalmodelling .............................. ......... 23 2.3.1 Massandmomentumequations. ....... 23 2.3.2 Energyequation ................................ ..... 28 2.4 Mantleviscosity ................................. ........ 28 2.4.1 Isoviscous and depth-dependent viscosity . .............. 28 2.4.2 Temperature-dependentviscosity . ............ 28 2.5 Force-balancemethod . .. .. .. .. .. .. .. .. .. .. .. .. ......... 31 2.6 Time-dependentplatethickness . ............. 33 2.7 Mantle temperatures and Rayleigh number . ............. 33 2.8 Continentalinsulation . ........... 35 2.9 Supercontinentmodelling . ........... 38 2.10 Evolvingplategeometry . ........... 41 2.11Models......................................... ...... 43 v 3 The role of supercontinent thermal insulation and area in the formation of mantle plumes 44 3.1 Introduction.................................... ........ 44 3.2 2DResults ....................................... ..... 45 3.2.1 Initialcondition .............................. ....... 45 3.2.2 Continental coverage and mantle reversals . .............. 46 3.3 3DResults ....................................... ..... 48 3.3.1 Initialcondition .............................. ....... 48 3.3.2 Thermal response of the mantle after supercontinent formation . 50 3.3.3 Geothermsandmantletemperatures . .......... 50 3.3.4 Non-insulating supercontinent . ............ 53 3.3.5 Lower mantle viscosity and plume generation . ............. 55 3.4 Discussion...................................... ....... 55 3.4.1 Modelconsiderations. ........ 57 3.4.2 Mantlereversaltimeframe . ........ 58 3.4.3 Continentalgeotherm . ....... 59 3.5 Conclusion ...................................... ...... 59 4 Plate mobility regimes and a re-evaluation of plate reversals 61 4.1 Introduction.................................... ........ 61 4.2 Results......................................... ...... 62 4.2.1 Mantlereversalsandmantleviscosity . ............ 62 4.2.2 Parameter study: lithospheric cut-off temperature, TL ................ 64 4.2.3 Parameter study: thermal viscosity contrast, ∆ηT .................. 68 4.2.4 Parameter study: reference Rayleigh number, Ra0 .................. 71 4.2.5 Parameter study: aspect ratio and dimensionality study............... 74 4.3 Discussion...................................... ....... 77 4.3.1 Platethickness ................................ ...... 80 4.3.2 Limitations ................................... ..... 81 4.3.3 AspectRatio ................................... .... 82 4.3.4 Uniqueness .................................... .... 84 4.4 Conclusion ...................................... ...... 84 vi 5 The impact of Rayleigh number on the significance of supercontinent insulation 86 5.1 Introduction.................................... ........ 86 5.2 Comparing the vigour of mantle convection . .............. 88 5.3 2DSupercontinentresults . ........... 89 5.3.1 Initialcondition .............................. ....... 89 5.3.2 Isothermalcore-mantleboundary . ........... 90 5.3.3 Insulatingcore-mantleboundary . ........... 97 5.3.4 2D temperature increase due to insulation . ............. 99 5.3.5 Average mantle temperatures and continental insulation............... 100 5.4 3DSupercontinentModels. .......... 103 5.4.1 3DSetup ....................................... 105 5.4.2 3DResults ..................................... 105 5.5 Discussion...................................... ....... 107 5.5.1 Mantlepotentialtemperature . .......... 108 5.5.2 Mantleheatingmode.. .. .. .. .. .. .. .. .. .. .. .. ...... 108 5.5.3 Limitations ................................... ..... 110 5.6 Conclusion ...................................... ...... 110 6 Influences on the positioning of mantle plumes following supercontinent formation 112 6.1 Introduction.................................... ........ 112 6.2 Method .......................................... .... 113 6.3 2Dresults....................................... ...... 116 6.3.1 Initial condition and supercontinent modelling . ................ 116 6.3.2 Plume position as a function of subduction location . ............... 117 6.4 3Dresults......................................