EARTH ROTATION AND DEFORMATION SIGNALS CAUSED BY DEEP EARTH PROCESSES Andrew Watkins A Thesis Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE December 2017 Committee: Yuning Fu, Advisor Richard Gross Marco Nardone Margaret Yacobucci ii ABSTRACT Yuning Fu, Advisor The length of a day on Earth (abbreviated LOD) is not exactly 24 hours. There is a small excess LOD that varies on timescales ranging from a few days to thousands of years, generally on the order of milliseconds. One characteristic of LOD variations is a sinusoidal component with a period of ~6 years. The cause of the ~6-year signal is unknown, but is generally suspected to be exchanges of angular momentum between the mantle and the core. This study aimed to test the hypothesis that the ~6-year LOD signal is due to coupling between the mantle and fluid outer core. The flow of the core’s fluid deforms the base of the mantle, leading to redistribution of Earth’s mass (causing changes in the gravitational field) and deformation of the overlying crust. Surface deformation data from a global network of high-precision Global Positioning System (GPS) stations was analyzed, and the component that acts on the ~6-year timescale was isolated and inverted for the core’s flow. Resulting angular momentum changes were computed for the outer core and compared to the LOD signal to search for evidence of core-mantle coupling. Outer core angular momentum changes obtained from GPS deformation data exhibit evidence of the suspected core-mantle coupling, but this result is sensitive to inversion parameters. Changes in the gravitational field were also modeled and found to be smaller than the errors in the currently available data. iii ACKNOWLEDGEMENTS I would like to thank Yuning Fu, Richard Gross (JPL), Peg Yacobucci, and Marco Nardone for their support and guidance during this project, and for their willingness to serve as members of my thesis committee. I would also like to thank Mike Heflin (JPL), Mike Chin (JPL), and Ming Fang (MIT) for their helpful comments. Finally, this thesis would not be possible if not for the work of previous researchers in this field, and of those who have contributed to the production of datasets used in this project. iv TABLE OF CONTENTS Page 1. INTRODUCTION .…………………………………………………………………........ 1 2. BACKGROUND AND METHODS ................................................................................. 4 2.1. LOD Signal Isolation .......................................................................................... 4 2.2. Deformation Signal Isolation .............................................................................. 7 2.3. Inversion for the Outer Core’s Flow ................................................................... 10 2.3.1. Physical Model and Discretization ...................................................... 10 2.3.2. Staggered Inversion Approach ............................................................. 12 2.3.3. Geostrophic Flow Solutions ................................................................. 15 2.3.4. Angular Momentum Solutions ............................................................. 18 2.4. Gravitational Field Changes ............................................................................... 21 2.5. Error Estimation .................................................................................................. 24 2.6. Robustness Test .................................................................................................. 26 2.7. Values of Physical Parameters ............................................................................ 27 3. RESULTS .......................................................................................................................... 29 3.1. LOD Signal and Solid Earth Angular Momentum ............................................. 29 3.2. Deformation Signal ............................................................................................. 31 3.3. Outer Core Pressure and Flow ............................................................................ 36 3.4. Outer Core Angular Momentum ......................................................................... 37 3.5. Modeled Gravitational Field Changes ................................................................ 40 4. DISCUSSION AND CONCLUSION ............................................................................... 42 REFERENCES ...................................................................................................................... 47 v LIST OF FIGURES Figure Page 1.1 Decadal LOD Signals From the Outer Core .............................................................. 2 2.1. Spectral Properties of Loading Removal ................................................................... 10 2.2. Spatial Distribution of GPS Stations I ....................................................................... 13 2.3. Spatial Distribution of Grid Cells .............................................................................. 15 2.4. Geometry of the Direction Vector ............................................................................. 17 2.5. Geometry of Taylor’s Constraint ............................................................................... 18 2.6. Geometry of a Cylindrical Annulus ........................................................................... 21 3.1. Surface Fluid Effects on LOD ................................................................................... 29 3.2. Spectral Properties of LOD Signal Isolation ............................................................. 30 3.3. Rotation Signals of the Mantle and Crust .................................................................. 30 3.4. Spectral Properties of Deformation Signal Isolation I ............................................... 31 3.5. Spectral Properties of Deformation Signal Isolation II .............................................. 32 3.6. Spectral Properties of Deformation Signal Isolation III ............................................ 32 3.7. Spatial Distribution of GPS Stations II ...................................................................... 33 3.8. Spatial Distribution of GPS Stations III..................................................................... 34 3.9. Spatial Distribution of GPS Stations IV .................................................................... 34 3.10. Deformation Signal Size ............................................................................................ 35 3.11. Circulating Flow ........................................................................................................ 36 3.12. Latitudinal Flow ......................................................................................................... 37 3.13. Interannual Angular Momentum Signals I ................................................................ 38 3.14. Interannual Angular Momentum Signals II ............................................................... 39 vi 3.15. Interannual Angular Momentum Signals III .............................................................. 39 3.16. Modeled Gravitational Field Changes I ..................................................................... 40 3.17. Modeled Gravitational Field Changes II .................................................................... 41 4.1. Columnar Flow .......................................................................................................... 44 vii LIST OF TABLES Table Page 2.1. Inversion Acronyms ................................................................................................... 27 2.2. Values of Physical Parameters ................................................................................... 27 1 1. INTRODUCTION Earth is a complex system with many related components. One feature of this system is that components directly accessible at the surface are affected by inaccessible components deep below the crust. These effects are opportunities, as they provide a means to investigate deep Earth processes which are otherwise elusive. The fluid outer core is an illustrative example of such an inaccessible component. Clues about the core are available in the form of the geomagnetic field, gravitational field variations, surface deformation, and length of day (LOD) variations. This study made use of the latter three observations to investigate the outer core’s behavior on sub-decadal timescales. Measurements of LOD are made at Earth’s surface and are therefore related to the angular velocity of the solid Earth (crust and mantle). In general, the angular momentum L = Iω of a body rotating about a fixed axis is conserved, where ω is the body’s angular velocity and I, called the moment of inertia, is related to the body’s mass distribution (Barger and Olsson, 1994). The principle of conservation of angular momentum is therefore a valuable means of investigating Earth’s rotation, and requires either mass redistribution or some external torque to explain LOD variations. Previous investigations have established the outer core as one important source of torque on the solid Earth (Gross 2015). In these investigations, variations in the geomagnetic field were used to determine changes in the outer core’s flow and angular momentum L%&. Researchers found that a torque coupling the ∆L%& to the solid Earth would cause LOD changes that agree well with measured