Linking Surface Evolution with Mantle Dynamic Processes Using Adjoint Models with Data Assimilation

...............................................................................................................................iv Chapter 1: Introduction ................................................................................................1 Chapter 2: Adjoint Method in Mantle Convection .............................................5 2.1 Theoretical Basis of the Adjoint Method ....................................................................5 2.2 Numerical Implementation of the Adjoint Method...................................................11 2.2.1 Solving 1D Linear Problems ............................................................................11 2.2.2 Solving 3D Nonlinear Problems.......................................................................13 2.2.2.1 Models within a single layer ...................................................................14 2.2.2.2 Models with thermal boundary layers and depthand temperaturedependent mantle viscosities ................................................................20 2.2.3 Discussion.........................................................................................................25 Chapter 3: Constraining Uncertain Mantle Dynamic Properties with Time Dependent Observations ..................................................................................28 3.1 Need for Assimilation of Time-Dependent Data in Real Problems ........................28 3.2 Dynamic Topography Constrains Uncertain Mantle Properties...............................30 3.2.1 One-Layer Mantle ............................................................................................30 3.2.2 Two-Layer Mantle............................................................................................38 3.2.3 Discussion.........................................................................................................48 ix Chapter 4: Reconstructing the Farallon Plate Subduction beneath North America back to the Late Cretaceous.....................................................................53 4.1 Tectonics and Geology Background .........................................................................53 4.2 Data Constraints and Model Setup............................................................................56 4.3 Constraining Uncertain Mantle Properties................................................................65 4.3.1 Effective Slab Temperature Anomaly..............................................................73 4.3.2 Lower Mantle Viscosity ..................................................................................75 4.3.3 Upper Mantle Viscosity ...................................................................................77 4.3.4 Discussion.........................................................................................................80 4.4 Flat Subduction of Farallon Plate during the Late Cretaceous .................................83 Chapter 5: Farallon Subduction Affecting North American Tectonics ....93 5.1 The Enigmatic Laramide Orogeny ............................................................................93 5.2 The Role of Oceanic Plateau Subduction in the Laramide Orogeny........................96 5.2.1 Detection of Oceanic Plateaus with Plate Reconstruction...............................96 5.2.2 Mechanisms for the Laramide Orogeny ..........................................................99 5.2.3 Present-day Position of the Subducted Plateaus ............................................106 5.3 Dynamic Subsidence and Uplift of the Colorado Plateau (CP) .............................111 5.3.1 Background.....................................................................................................111 5.3.2 Subsidence and Uplift of CP due to Farallon Subduction .............................112 5.3.3 Plateau Uplift since the Oligocene due to Active Mantle Upwelling............119 5.3.4 Tilting of the Plateau during Uplift ................................................................121 5.3.5 Discussion ......................................................................................................122 x 5.4 Implications for the Evolution of the Western Interior Basins...............................127 5.4.1 Migrating Depocenter within the WIS Subsidence .......................................127 5.4.2 Implication for Oceanic Plateau Subduction..................................................130 5.5 Subsidence of the U.S. East Coast since the Eocene ..............................................135 Chapter 6: Broader Implications and Discussions ..........................................139 6.1 Subduction Evolution beyond North America........................................................139 6.2 Limitations of the Current Adjoint Models.............................................................146 6.2.1 Poorly Resolved Thermal Boundary Layers..................................................146 6.2.2 Uncertain Interpretation of Seismic Tomography .........................................147 6.2.3 Simplification in Physical Assumptions ........................................................150 6.2.4 Limited Applications with Forced Convection..............................................152 6.3 Some Thoughts on Future Model Development.....................................................154 6.3.1 Tomography: Push the Limit of Resolution...................................................154 6.3.2 Constraints: Multiple Datasets .......................................................................156 6.3.3 Constraints: Multiple Datasets .......................................................................157 Bibliography....................................................................................................................159