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1 Viscoelastic Relaxation Theory, Momentum and Poisson Equations |
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1 | (52) |
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1 | (2) |
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3 | (10) |
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1.2.1 The Linear Maxwell Solid |
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7 | (2) |
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1.2.2 Compressible and Incompressible Earth's Models |
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9 | (2) |
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1.2.3 The Correspondence Principle |
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11 | (2) |
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1.3 Expansion in Spherical Harmonics |
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13 | (5) |
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1.3.1 Volume Changes and Surface Forces |
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15 | (1) |
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1.3.2 Spheroidal and Toroidal Deformations |
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16 | (2) |
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1.4 Spheroidal Deformations |
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18 | (2) |
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1.5 Toroidal Deformations |
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20 | (1) |
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21 | (10) |
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1.6.1 The Earth's Surface |
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21 | (4) |
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1.6.2 Chemical Boundaries |
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25 | (1) |
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1.6.3 Core-Mantle Boundary |
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26 | (5) |
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1.7 Elastic and Viscoelastic Solutions |
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31 | (5) |
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1.7.1 Load and Tidal Love Numbers |
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33 | (1) |
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1.7.2 Application of the Correspondence Principle |
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34 | (2) |
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1.8 The Relaxation Spectrum |
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36 | (6) |
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1.8.1 Modal and Non-modal Contributions |
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41 | (1) |
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1.9 The Complex Contour Integration |
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42 | (1) |
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43 | (10) |
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43 | (2) |
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1.10.2 Fault Discontinuities |
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45 | (5) |
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50 | (3) |
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2 Incompressible and Compressible Analytical Viscoelastic Models |
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53 | (34) |
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53 | (1) |
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2.2 Green Functions for Incompressible and Compressible Stratified Viscoelastic Earth's Models |
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53 | (4) |
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2.2.1 Core-Mantle Boundary (CMB) Matrix |
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54 | (1) |
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2.2.2 Propagators and Fundamental Matrices |
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55 | (2) |
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2.3 Layered Incompressible Models |
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57 | (5) |
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2.4 Relaxation Times for Incompressible Earth's Models |
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62 | (6) |
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2.5 The Self-compressed, Compressible Sphere |
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68 | (11) |
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2.5.1 The Analytical Solution |
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70 | (4) |
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2.5.2 The Relaxation Spectrum of the Self-compressed Compressible Sphere |
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74 | (2) |
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2.5.3 The Compositional Modes |
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76 | (3) |
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2.6 Viscoelastic Perturbations Due to Surface Loading |
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79 | (2) |
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81 | (1) |
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2.8 Time Dependent Loading Love Numbers |
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82 | (5) |
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84 | (3) |
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3 Rotational Dynamics of Viscoelastic Planets: Linear Theory |
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87 | (62) |
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3.1 Introduction to Earth's Rotation |
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87 | (4) |
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3.1.1 Liouville Equations |
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90 | (1) |
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91 | (6) |
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3.2.1 Inertia Perturbations Due to Changes in the Centrifugal Potential |
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94 | (3) |
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3.3 Linearized Liouville Equations |
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97 | (2) |
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3.4 The Concept of True Polar Wander (TPW) |
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99 | (4) |
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101 | (1) |
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3.4.2 Adjustment of the Equatorial Bulge |
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102 | (1) |
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3.5 Developments of Linearized Rotation Theories |
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103 | (12) |
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3.5.1 Comparison Between Different Rotation Theories |
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108 | (1) |
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3.5.2 Omission of the M0 Rotation Mode |
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109 | (3) |
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3.5.3 Analytical Formula for the M0 Rotation Mode |
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112 | (2) |
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3.5.4 Unification of the Different Approaches |
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114 | (1) |
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3.6 Non-hydrostatic Bulge Contribution |
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115 | (3) |
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3.7 Readjustment of the Rotational Bulge |
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118 | (3) |
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3.8 Compressible and Incompressible Readjustment of the Equatorial Bulge |
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121 | (4) |
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3.9 Long-Term Behavior of the Rotation Equation |
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125 | (7) |
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3.9.1 Theory for Rotation Changes Due to Mantle Convection |
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127 | (5) |
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3.10 Time-Dependent Inertia Due to Mantle Convection |
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132 | (6) |
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134 | (4) |
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3.11 Polar Wander on the Earth, Moon, Mars and Venus |
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138 | (11) |
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144 | (5) |
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4 TPW and J2 Induced by Ice-Sheet Loading |
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149 | (40) |
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149 | (2) |
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4.2 The Inference of Mantle Viscosity from TPW and J2 Data |
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151 | (2) |
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153 | (3) |
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156 | (15) |
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4.4.1 Variations in Depth of the Two-Layer Mantle Viscosity Profile |
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167 | (1) |
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4.4.2 Upper Mantle Viscosities Lower Than 10 21 Pa s |
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168 | (3) |
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4.5 Ice Age Cycles and the Polar Wander Path: Lithospheric and Mantle Rheology |
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171 | (4) |
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4.6 Ice Age True Polar Wander in a Compressible and Non-hydrostatic Earth |
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175 | (14) |
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4.6.1 The Role of Mantle Heterogeneities |
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178 | (7) |
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185 | (4) |
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5 Detection of the Time-Dependent Gravity Field and Global Change |
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189 | (36) |
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5.1 Changes in the Long-Wavelength Geoid Components from Satellite Laser Ranging Techniques |
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189 | (6) |
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5.2 Trade-Off Between Lower Mantle Viscosity and Present-Day Mass Imbalance in Antarctica and Greenland |
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195 | (7) |
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5.3 Time Dependent Gravity Field from the GRACE Space Mission: The Importance of PGR Models |
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202 | (8) |
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5.3.1 Global Vertical and Horizontal Displacements from PGR |
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206 | (4) |
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5.4 The 2004 Sumatran and 2011 Tohoku-Oki Giant Earthquakes |
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210 | (15) |
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5.4.1 Modeling the 2004 Sumatran Earthquake |
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211 | (3) |
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214 | (1) |
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5.4.3 Constraining the 2004 Sumatran Earthquake |
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215 | (3) |
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5.4.4 The 2011 Tohoku-Oki Earthquake: Gravitational Seismology |
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218 | (3) |
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221 | (4) |
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225 | (32) |
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6.1 The Issue of Sea-Level Change, a Present-Day Concern |
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225 | (2) |
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6.2 Sea-Level Variations, Geoid and Gravity Anomalies Due To Pleistocene Deglaciation |
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227 | (8) |
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6.2.1 Mathematical Formulation |
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228 | (3) |
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6.2.2 Sea-Level Variations, the Geoid and Free-Air Gravity Anomalies |
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231 | (4) |
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6.3 Glacial Isostatic Adjustment (GIA) Versus Tectonic Processes: The Example of the Mediterranean Sea |
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235 | (7) |
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6.4 Sea-Level Fluctuations Induced by Polar Wander |
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242 | (4) |
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6.5 Sea-Level Changes Induced by Subduction |
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246 | (11) |
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6.5.1 Sea-Level Variations, Geoid Anomalies and The Long-Wavelength Dynamic Topography |
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247 | (2) |
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6.5.2 A Single Sinking Slab |
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249 | (2) |
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6.5.3 A Distribution of Slabs |
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251 | (3) |
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254 | (3) |
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7 TPW Driven by Subduction: Non-linear Rotation Theory |
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257 | (12) |
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7.1 Formulation of the Non-linear Rotation Problem |
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257 | (8) |
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7.2 Polar Wander Velocity for a Distribution of Slabs |
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265 | (4) |
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267 | (2) |
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8 Post-seismic Deformation |
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269 | (24) |
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8.1 Global Post-seismic Deformation |
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269 | (8) |
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8.2 Post-seismic Deformation for Shallow Earthquakes |
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277 | (16) |
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8.2.1 The Umbria-Marche (1997) Earthquake |
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277 | (7) |
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8.2.2 The Irpinia (1980) Earthquake |
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284 | (5) |
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289 | (4) |
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293 | (44) |
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9.1 Diurnal and Non-synchronous Rotation (NSR) Stresses Acting on Europa's Surface |
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293 | (3) |
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296 | (5) |
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9.3 The Interior of Europa |
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301 | (1) |
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9.4 The Impulse Tidal Response of Europa |
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302 | (8) |
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9.4.1 The Impulse Response of Interior Models with a Global Subsurface Ocean |
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302 | (3) |
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9.4.2 Boundary Conditions |
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305 | (2) |
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9.4.3 Application to Icy Moons I: Normal Modes |
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307 | (1) |
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9.4.4 Application to Icy Moons II: Impulse Response to Tidal Forces |
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307 | (3) |
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9.5 Radial Deformation at the Surface |
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310 | (3) |
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9.6 Stresses at the Surface of Europa |
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313 | (9) |
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9.6.1 Diurnal Stresses at the Surface |
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313 | (5) |
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9.6.2 NSR Stresses at the Surface |
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318 | (4) |
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9.7 Stress Patterns on Europa's Surface |
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322 | (7) |
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9.8 Morphology of the Europa Icy Moon |
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329 | (8) |
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332 | (5) |
Appendix A Dyads and Vector Identities |
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337 | (4) |
Appendix B Analytical Functions |
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341 | (6) |
Appendix C Icy Moons |
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347 | (8) |
Index |
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355 | |