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Long-Term Rotational Effects on the Shape of the Earth and Its Oceans

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Long-Term Rotational Effects on the Shape of the Earth and Its Oceans LONG-TERM ROTATIONAL EFFECTS ON THE SHAPE OF THE EARTH AND ITS OCEANS Jonathan Edwin Mound A thesis submitted in cooforrnity with the reqnhents for the degree of Doctor of Philosophy Gradiiate Depart ment of P hysics University of Toront O @ Copyright by Jonathan E. Mound 2001 . .. ilbitionsand et 9-Bib iogrephic SeMces -Iiographiques 395 WeIlington Street 395, ni6 Wellington ûttawa ON K1AOW OtEaweON KtAW Canada Canada The author has granted a non- L'auteur a accorde une licence ncm exdusive licence allouing the exclusive permettant à la National Library of Cana& to Bibliotheque natiode du Canada de reproduce, Ioan, distriibute or seli reproduire, prêter, distniuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de reprociucbon sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. ttiesis nor substantial extracts &om it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. LONG-TERM RQTATLONAL E-FFECTS ON THE SHAPE OF THE EARTH AND ITS OCEANS Doctor of Philosophy, 2001. Jonathan E. Mound Department of Physics, University of Toronto Abstract The centrifuga1 potent ial associated with the Eart h's rotation influences the shape of both the solid Earth and the oceaos. Changes in rotation t hus deform both the ocean and solid surfaces. The equilibrium form of the rotating Earth is generally computed using hydrostatic theory that treats the planet as an inviscid body. 1 have found that a thin elastic shell acts to reduce the flattening of the equilibrium form relative to the value obtained from the tradi t ional hydrostat ic calcuiation. Futhermore, t his perturbation is large enough that the excess non-hydrostatic fl attening of the Eart h, defined as the difference between the observed and hydrostatic forms, may be a significant underestimate of the departure of the observed form from its equilibrium state. The ocean surface and the Earthk solid surface deform by different arnounts in re- sponse to an applied potential load and thus a relative sea-level change is produced. Due to the presence of the elastic lithosphere and slowly decaying modes of viscous relaxation within the mantle, even geologically long potential forcings can produce a non-negligible sea-level signal. Using the geologically constrained history of rotat ional variations over the past 130 million years (the Cretaceous-Tertiary) I have found that the sea-level sig- nal induced by truc polar wander may be as large as the sea-level change that has been observationally inferred for that the. True polar wander produces a long wavelength global pattern of sea-leuel trends that may be mistaken for a uoiforrn signal. The welC documented, and presumed global, Cretaceous-Tertiary sea-level cycle should therefore be reinterpreted as a combination of a globally uniform and a spatially varying true p* lar wander signal. Furt hermore, the distinct pattern of the induced sea-level variations enables the use of regional sea-level records as a test of, often contentious, true polar wan- der events proposed on the basis of paleomagnetic data. .4 prelirninary sea-Ievel test of a proposed Early Cambrian inert ial interchange t rue polar wander event found good gen- eral agreement bet ween predicted and observed sea-level t rends. O bservational sea-level constraints ivere not found to provide consistent support for a rapid true polar wander event proposed for the Late Cretaceous. Acknowledgements I'd like to thank a whole bunch of people, but I'd also like to keep the acknowledge- ments under one page so 1 won't be able to thank everyone by narne. 1'11 start by t hanking Jerry, for getting me into my studies and back out again, and Professors Bailey and Edwards for serving on rny committee over the years. 1 am also grateful to Professor Dunlop for serving on rny final examination committee, and Professor Sabadini for serving as my external examiner. Thanks to Russ. Glenn. Hamid and Xin for passing along the ever-evolving B'files used to produce this thesis, and Rad and Khader for their help with graphics both here and for various presentations. Thanks to my parents for so much for so long, my brother for (among other thiugs) 19 words, numerous faculty, post-docs, staff and fellow students from bot h physics and geology for being both helpful and/or diversionary as the case might be, roornmates and officernates for putting up with me, ultimate teammates for hammers thrown and received. patrons of the Foaming Boot for knowing where that is, and basically everybody who made my graduate life a little better. 1 received generous financial support from bot h the Ontario Graduate Scholarship and NS ERC Postgraduate Scholarshi p programmes. Contents Abstract Acknowledgements List of Tables vi List of Figures vii 1 Introduction 1 1.1 Sea-Level Change . 3- 1.2 True Polar Wander . 5 1.3 Rotational Variations and Sea-Level Change . 8 1.4 Contributions and Outline of Thesis . , . 12 2 Theoreticai Formulation of Rotation Induced Sea-Level Variations 14 2. Introduction . 14 2.2 The Sea-Level Equation . 15 2.2.1 Surface Slass Loads . 16 2.2.2 PotentiaI Loads . 18 2.2.3 Solving the Sea-Level Equation . 19 2.2.4 A Simplified Sea-Level Equation . 39-- 2.23 The Semi-Inviscid Approximation . 25 '2.3 Constant True Polar Wander: .4 Case Study . ZY 3 The Rotational Perturbation to the Shape of the Earth 37 3.1 Introduction . 37 3.2 The EKick of an Elde lithosphere on the Eqniiibriurrr Shape of the Earth 38 3.3 The Fossil Bulge ................................ 4% 4 True Polar Wander Induced Sea-Level Change: The Cretaceous-Tertiary Second-Order Cycle 46 4.1 Introduction ................................... 46 4.2 0bsermtional Constraints ........................... 47' 4'2.1 Sea Level ................................ 47 3.2.2 Earth Rotation ............................. 49 4.3 Mode1 Results and Discussion ......................... 53 5 nue Polar Wander Induced Sea-Level Change: A Test of Early Cam- brian Inertial Interchange True Polar Wander 58 5.1 Introduction ................................... 58 5.2 Modelling IITP W-induced Sea-level Trends .................. 59 5.3 A Preliminary Cornparison Wit h Cambrian Sea-level Records ........ 69 6 True Polar Wander Induced Sea-Level Change: A Test of Rapid Ttue Polar Wander During the Late Cretaceous 72 6.1 Introduction .................................... t2 6.2 Results of Sea-Level Modelling ......................... 73 6.3 Comparison With Observed Late Cretaceous Sea-Level Trends ....... 79 7 Discussion and Conclusions 83 7.1 Variations in Rotation .Variations by Rotation ............... S3 7.2 Speculations. Future CVork aod Final Remarks ................ 85 List of Tables 1.1 S t rat igraphic cycles and t heir causes ..................... 3 3.1 Geologic constraints on rotation rate ..................... 14 3.2 Magnitude of the fossil bulge .......................... 14 6.1 Predicted relative sea-level change at selected sites for the proposed Late Cretaceous TPtV event ............................. 76 6.2 Observational constraints on Late Cretaceous sea-level change . Y0 List of Figures Mid-ocean ridge volume and spreading rate . Geometry of potential perturbations associated with changes in rotation . Schernatic illustration of a restoring buoyant force . Dependence of the inviscid limit Earth response on effective thickness of the elastic lithosphere . Sensitivity of relative sea-Ievel predictions to TPW rate and Earth model structure for constant TPW events . Sensitivity of reiat ive sea-level predictions to TP W duration and Eart h model structure for constant TPW events . , . Semi tivity of relative sea-ievei predictions to TPW rate and duration for constant TPW events . Dependence of the flattening of t he geoid on effective t hickness of the elastic lithosphere . - . The Vail curve. True polar wander since the Early Cretaceous . Rotationalfy indnced sea-tevet change and site distribution . Relative sea-level predictions at four sites for Cretaceous-Tertiary TPW . Eart h model sensi t ivi t ies of relative sea-level predict ions for Cretaceous- Tertiary TPW . Early Cambrian paleogeography . Sea-level predictions at three sites for a 25 MwwIITPW event . Sea-level predictions for different initial positions of the site in Laurentia . Sea-level predictions for different initial positions of the site in Baltica . Sea-level predictions for different durations of the IITP W event . Sea-level predictions for different evolutions of the IITPW event . vii 5.7 Sensibivity of IWPW-i-indueedsea-levd pdictious to changes in the Earth mode1 parameters ................................ 68 6.1 Predicted sea-level response at t hree sites for the proposed Late Cretaceous RP TPWevent ................................... 13 6.2 Sensitivity of the predicted Late Cretaceous TPW-induced sea-level re- m- sponse tochanges iinlithospheric thickness .................. (4 6.3 Sensitivity of the predicted Late Cretaceous TPW-induced sea-level re- sponse to changes iii mantle viscosity ..................... 79 Chapter 1 Introduction As usual, and this should be obvious to anyone whose eyes have not been blinded by the false light of Western science, the pie that we see is not the real pole, for the real pole is the one that cannot be seen, ezcept by some adepts, whose lips are sealed. Urnberto Eco, Foucault's Pendulurn The planet Earth is a dynamic body which is constantly deformed by processes that act on a wide range of timescales. Tidal potentials deforrn not only the oceans, but also the solid Earth, wit h periodicities ranging from hours to years. Continental drift. driven by convection in the mantle, has led to the formation and break-up of supercontinents over timescales measured in the hundreds of millions of years.
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