I First Steps Towards Modeling a Multi-Scale Earth System .... 1
Klaus Regenauer-Lieb, Thomas Poulet, Delphine Siret,
Florian Fusseis, Jie Liu, Klaus Gessner, Oliver Gaede,
Gabriele Morra, Bruce Hobbs, Alison Ord, Hans Muhlhaus,
David A. Yuen, Roberto Weinberg and Gideon Rosenbaum
1 Introduction ................................................. 2
2 Multiscale Non-Equilibrium Thermodynamics .................... 3
2.1 The Equilibrium Yardstick ............................... 3
2.2 Non Equilibrium Thermodynamics and Multiscaling ......... 5
2.3 Coupling Mechanics and Chemistry ........................ 6
2.4 Classical Brittle-Ductile Modeling ...................... 8
3 Mathematical Formulation .................................... 10
3.1 Classical Constitutive Approaches for the
Lithosphere ............................................ 10
3.2 Energy Approach ........................................ 12
3.3 Scale Dependence of Ductile Shear Zones ................ 15
3.4 Intrinsic Length Scales for Brittle Faults ............. 17
3.5 Scale Dependence for Brittle Faults .................... 19
4 Discussion .................................................. 20
References .................................................. 22
II 3D Mesh Generation in Geocomputing ........................ 27
Huilin Xing, Wenhui Yu and Ji Zhang
1 Introduction ................................................ 28
2 Geometrical Modeling ........................................ 32
3 Hexahedral Mesh Generation .................................. 33
3.1 Introduction ........................................... 33
3.2 Fracture Dominated Reservoir System .................... 35
3.3 Meshing Interacting Fault System of South Australia
with Mapped Block Method ............................... 39
3.4 All Hexahedron Mesh Generation for a Whole-Earth
Model .................................................. 43
3.4.1 The PREM whole-Earth model ...................... 43
3.4.2 The Whole-Earth Crust with Plate Boundaries ..... 44
4 Tetrahedral Mesh Generation ................................. 49
4.1 Introduction ........................................... 49
4.2 Automatic Tetrahedral Mesh Generation for the
Stratigraphy Point Set ................................. 50
4.3 Visualizing and Meshing with the Microseismicity
Data ................................................... 52
5 Conclusions ................................................. 59
References .................................................. 59
III Strategies for Preconditioning Methods of Parallel
Iterative Solvers for Finite-Element Applications in
Geophysics ................................................ 65
Kengo Nakajima
1 Background .................................................. 65
1.1 Why Preconditioned Iterative Solvers? .................. 65
1.2 Selective Blocking Preconditioning for Contact
Problems ............................................... 67
1.2.1 GeoFEM Project .................................. 67
1.2.2 Selective Blocking .............................. 69
1.3 Overview of this Work .................................. 70
2 Various Approaches for Parallel Preconditioning Methods
in Ш-Conditioned Problems ................................... 72
2.1 Selective Fill-Ins ..................................... 72
2.2 Selective Overlapping .................................. 76
2.3 Local Reordering in Distributed Data ................... 79
2.4 HID (Hierarchical Interface Decomposition) ............. 82
3 Examples: Contact Problems .................................. 86
3.1 Effect of Selective Fill-ins and Selective
Overlapping ............................................ 86
3.2 Effect of Local Reordering ............................. 88
3.3 Effect of HID .......................................... 90
4 Examples: Linear-Elastic Problems with Heterogeneous
Material Properties ......................................... 92
4.1 BILU(p+,ω)-(d+,α) ...................................... 92
4.2 Problem Description .................................... 93
4.3 Effect of Selective Fill-Ins and Selective
Overlapping ............................................ 96
4.4 Effect of Local Reordering ............................. 98
4.5 Effect of HID ......................................... 101
5 Concluding Remarks ......................................... 103
References ................................................. 105
6 Appendix 1: Parallel Iterative Solvers in GeoFEM ........... 107
6.1 Distributed Data Structure ............................ 107
6.2 Localized Preconditioning ............................. 109
7 Appendix 2: Selective Blocking ............................. 111
7.1 Robust Preconditioning Methods for Ill-Conditioned
Problems .............................................. 1ll
7.2 Strategy for Parallel Computations .................... 114
7.3 Large-Scale Computations .............................. 116
IV Algorithms for Optimizing Rheology and Loading Forces in
Finite Element Models of Lithospheric Deformation ........ 119
Youqing Yang and Mian Liu
1 Introduction ............................................... 119
2 Methodology ................................................ 120
3 A Plate Flexural Model ..................................... 123
4 A Three-Dimensional Viscous Model of Lithospheric
Deformation ................................................ 127
5 Discussions and Conclusions ................................ 136
References ................................................. 137
V Mantle Dynamics - A Case Study ........................... 139
Klaus-D. Gottschaldt, Uwe Walzer, Dave R. Stegman,
John R. Baumgardner and Hans B. Mühlhaus
1 Introduction ............................................... 140
1.1 Energy Budget of the Mantle ........................... 140
1.2 Physics of Mantle Convection in a Nutshell ............ 140
1.3 Surface Tectonics ..................................... 141
1.4 Volcanism ............................................. 141
1.5 Core and Magnetism .................................... 141
1.6 Composition ........................................... 142
2 Physics of Mantle Convection: Basic Equations .............. 142
2.1 Conservation of Mass .................................. 142
2.2 Conservation of Momentum .............................. 143
2.3 Conservation of Energy ................................ 143
2.4 Equation of State ..................................... 144
2.5 Constitutive Relations ................................ 144
3 Case Study: Stirring in Global Models of the Earth's
Mantle ..................................................... 145
3.1 Background ............................................ 146
3.1.1 Mantle Composition and Crustal Segregation ..... 146
3.1.2 Phase Transitions in the Mantle ................ 146
3.1.3 Geochemistry - a Primer ........................ 148
3.1.4 Geochemical Heterogeneities .................... 149
3.1.5 Mantle Degassing ............................... 150
3.1.6 Interpretation of Reservoirs ................... 150
3.1.7 Age of Reservoirs .............................. 151
3.1.8 Size of Reservoirs ............................. 151
3.1.9 Reconciliation of Geophysical and Geochemical
Constraints .................................... 152
3.2 Model Setup ........................................... 155
3.2.1 Rheology ....................................... 156
3.2.2 Boundary Conditions ............................ 157
3.2.3 Initial Conditions ............................. 158
3.3 Numerics .............................................. 159
3.3.1 Mantle Convection Code: TERRA .................. 159
3.3.2 Treatment of Compositional Fields .............. 160
3.3.3 Definition of Two Components ................... 160
3.4 Model Results ......................................... 161
3.5 Discussion ............................................ 166
3.5.1 Influence of Geometry .......................... 167
3.5.2 Influence of Rheology .......................... 167
3.5.3 Influence of Initial Conditions ................ 169
3.5.4 Minor Influences ............................... 170
3.6 Conclusions ........................................... 170
3.6.1 Relevance for the Earth ........................ 171
3.6.2 Other Hints for a Change of Convective Mode .... 173
3.6.3 Outlook ........................................ 174
References ................................................. 175
VI The ESyS_Particle: A New 3-D Discrete Element Model with
Single Particle Rotation ................................. 183
Yucang Wang and Peter Mora
1 Introduction: A Review of the Discrete Element Method ...... 183
1.1 Dimensionality: 2-D or 3-D ............................ 184
1.2 Contact Laws: Linear or Non-Linear .................... 185
1.3 Particle Shapes: Disks/Spheres or Polygons/
Polyhedrons ........................................... 185
1.4 Single Particle Rotation: With or Without ............. 185
1.5 Algorithm for Integrating the Equations of Motion ..... 186
1.6 Bonded or Not Bonded .................................. 186
1.7 Interactions Between Particles: Complete or
Simplified ............................................ 187
1.8 Criterion for Bond Breakage ........................... 187
1.9 Frictional Forces ..................................... 187
1.10 Parameter Calibration ................................. 188
2 The Model, Equations and Numerical Algorithms to
Integrate These Equations .................................. 189
2.1 A Brief Introduction to the ESyS_Particle ............. 189
2.2 Equations ............................................. 190
2.3 Algorithms to Integrate the Equations of Rotation ..... 191
3 Contact Laws, Particle Interactions and Calculation
of Forces and Torques ...................................... 193
3.1 Bonded Interaction .................................... 193
3.1.1 The Bonded Model ............................... 193
3.1.2 Calculation of Interactions due to Relative
Motion ......................................... 194
3.1.3 Criterion for Bond Breakage .................... 200
3.2 Solely Normal Repulsive Interaction ................... 201
3.3 Cohesionless Frictional Interaction ................... 201
4 Parameter Calibration ...................................... 204
4.1 Elastic Parameters: Spring Stiffness .................. 204
4.1.1 2-D Triangular Lattice ......................... 204
4.1.2 3-D Lattices: HCP and FCC ...................... 205
4.2 Fracture Parameters ................................... 209
4.3 Other Parameters ...................................... 210
4.3.1 Time Step ...................................... 210
4.3.2 Artificial Damping ............................. 210
4.3.3 Loading Rate ................................... 211
5 Some Recent Simulation Results ............................. 211
5.1 2-D Tests ............................................. 211
5.1.1 Uni-Axial Tests ................................ 211
5.1.2 Wing Crack Extension ........................... 213
5.1.3 Shearing and Crushing of Aggregates ............ 214
5.1.4 Simulation of Brittle Fracture by Dynamic
Impact ......................................... 215
5.2 3-D Tests ............................................. 216
5.2.1 Uniaxial Test .................................. 216
5.2.2 Wing Crack ..................................... 217
6 Discussion: Major Differences of the ESyS_Particle
Compared with the Other Existing DEMs ...................... 219
7 Conclusions ................................................ 220
References ................................................. 222
VII The TeraShake Computational Platform for Large-Scale
Earthquake Simulations ................................... 229
Yifeng Cui, Kim Olsen, Amit Chourasia, Reagan Moore,
Philip Maechling and Thomas Jordan
1 Introduction ............................................... 230
2 The TeraShake Computational Platform ....................... 232
3 TeraShake Application: Anelastic Wave Model ................ 234
4 Enhancement and Optimization of the TeraShake
Application ................................................ 237
4.1 Porting and Optimizations ............................. 237
4.2 Optimization of Initialization ........................ 239
4.3 Optimization of I/O ................................... 240
4.4 Mapping TS-AWP to Different TeraGrid Architectures .... 242
4.5 Scaling the Code up to 40k Processors ................. 243
4.6 Preparing for TeraShake Executions .................... 245
4.7 Maintenance and Additional Techniques for the
TeraShake Platform .................................... 247
5 Data Archival and Management ............................... 248
5.1 SCEC Data Grid ........................................ 249
5.2 Wave Propagation Simulation Data Archival ............. 252
5.2.1 SCEC Data Management Challenges ................ 253
5.2.2 Comparison to Grid Technology .................. 255
5.3 SCEC Digital Library .................................. 256
6 TeraShake Visualization .................................... 257
6.1 Visualization Techniques .............................. 258
6.1.1 Surface Visualization .......................... 258
6.1.2 Topographic Visualization ...................... 259
6.1.3 Volumetric Visualization ....................... 261
6.1.4 Static Maps .................................... 262
6.1.5 Self Contoured Maps ............................ 262
6.1.6 Map Service Portal for Surface Data ............ 262
6.2 Visualization Tools and Results ....................... 264
6.3 Visualization Discussion .............................. 264
7 Scientific Results of TeraShake-1 and TeraShake-2 .......... 265
8 Lessons Learned from Enabling Very-Large Scale Earthquake
Simulations ................................................ 268
9 Summary .................................................... 273
References ................................................. 275
VIII Probabilistic Forecast of Tsunami Hazards along Chinese
Coast .................................................... 279
Yingchun Liu, Yaolin Shi, Erik O.D. Sevre, Huilin Xing
and David A. Yuen
1 Introduction ............................................... 280
2 Geological and Geophysical Analysis ........................ 283
3 Probabilistic Forecast of Tsunami Hazards .................. 288
3.1 Probabilistic Forecast of Tsunami and Seismic
Hazards ............................................... 288
3.2 Linear and Non-linear Modeling Potential Tsunami
Sources ............................................... 291
4 Probabilistic Forecast of Tsunami and Seismic Hazard
in China Sea Region ........................................ 296
4.1 Probabilistic Forecast of Seismic Hazard in South
China Sea Region ...................................... 296
4.2 Probabilistic Forecast of Seismic Hazard in Eastern
China Sea Region ...................................... 297
4.3 Tsunami Numerical Simulation in China Sea Region ...... 298
4.4 Probabilistic Forecast of Tsunami Hazard in China
Sea Region ............................................ 303
5 Discussions and Summary .................................... 310
6 Conclusion ................................................. 312
References .................................................... 314
Index ......................................................... 319
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