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Challenges and Opportunities in Modeling Mantle Convection Shijie Zhong Department of Physics

Challenges and Opportunities in Modeling Mantle Convection Shijie Zhong Department of Physics University of Colorado at Boulder SDSC, 2006. Outline. Introduction. What is mantle convection and why it is interesting/important. 2) Unique challenges in mantle convection modeling.

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Challenges and Opportunities in Modeling Mantle Convection Shijie Zhong Department of Physics

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  1. Challenges and Opportunities in Modeling Mantle Convection Shijie Zhong Department of Physics University of Colorado at Boulder SDSC, 2006

  2. Outline • Introduction. • What is mantle convection and why it is interesting/important. 2) Unique challenges in mantle convection modeling. • Multi-scale physics and non-linear and highly variable rheology. 3) Current status and opportunities.

  3. What is mantle convection? • Objectives: Understand the long-term heat and mass transfer and structure formation in the mantle and its consequences to surface geological, geochemical and geophysical observables and evolution of the Earth and other planets. • Physical basis: Treat the mantle as viscous flow. Conservation of MASS, ENERGY, and MOMENTUM + VISCOUS rheological equation.

  4. The Earth’s Surface Motion and Plate Tectonics

  5. Surface Observations Controlled by Plate Tectonics Seafloor topography

  6. Tectonic Engine: Mantle Convection Powered by radiogenic heating & primordial heating

  7. Mantle Structure From Seismic Tomography Grand, van der Hilst, & Widiyantoro [1997]

  8. A Simple Picture of the Mantle: Boundary Layers Montelli et al. [2004] van der Hilst [1995]

  9. Vs Vc Compositionally Distinct Mantle Reservoirs at the Core-Mantle Boundary Region? A lot of geochemical evidences. Masters et al. [2000]. Ishii & Trump [1999] Important implications for the cooling of the core and geodynamo! Ni & Helmberger [2003], Wen et al. [2001]

  10. Mantle Convection Studies Seek Answers to: What controls the origin of plate tectonics? Why do not Venus and Mars have plate tectonics?

  11. Vs Vc Mantle Convection Studies Seek Answers to: formation and evolution of mantle thermal and compositional structures.

  12. Mantle Convection Studies Seek Answers to: thermal and tectonic evolution of the Earth and other terrestrial planets.

  13. Outline • Introduction. • What is mantle convection and why it is interesting/important. 2) Unique challenges in mantle convection modeling. • Multi-scale physics and non-linear and highly variable rheology. 3) Current status and opportunities.

  14. Van Keken et al., 1997 Multi-scale (from 100 km to 104 km) Physics • Plate margins and faults: • ~100- 102km. 2) Upwelling and downwellings: ~ 102km. 3) Chemical entrainment: ~ 10s-102km. 4) Plate scales: ~ 103-104km.

  15. Nonlinear and Highly Variable Rheology • Faulting and Plastic deformation: nonlinear 2) Highly temperature-dependent viscosity for silicate mantle (up to 3 orders of magnitude variations in plumes and downwellings).

  16. Outline • Introduction. • What is mantle convection and why it is interesting/important. 2) Unique challenges in mantle convection modeling. • Multi-scale physics and non-linear and highly variable rheology. 3) Current status and opportunities.

  17. Various Methods 1) Spectral methods [Glatzmaier et al., 1990; Zhang and Christensen, 1993]. 2) Finite volume methods [Ratcliff et al., 1997; Hansen, 2004]. 3) Finite elements [Baumgardner, 1985; Zhong et al., 2000].

  18. A Finite Element Code: CitcomS[Zhong, Zuber, Moresi & Gurnis, 2000] • Derived from Original Cartesian Citcom [Moresi & Gurnis, 1996]. • Quasi-uniform grid spacing on a spherical surface. • Uzawa algorithm with full multigrid solver (memory usage ~ N, # of flops ~ N). Suitable for parallel computing.

  19. Execution Time vs Grid Size N t ~ N

  20. Quasi-uniform Grids on A Spherical Surface Zhong, Zuber, Moresi, & Gurnis [2000]

  21. Benchmarks on Parallel Supercomputers Recently, favorable benchmark results were obtained for CitcomS on IBM BlueGene using ~ 10,000 processors [King, 2005]. Intel Paragon with 512 processors at Caltech’s CACR Zhong et al., 1995

  22. Thermal Convection with Temperature-dependent Viscosity and Plates Zhong, Zuber, Moresi, & Gurnis [2000]

  23. Mantle Convection with Distinct Mantle Reservoirs McNamara and Zhong [2005] (figure courtesy of Chuck Meertens, GEON)

  24. Hardware Requirement • Most of the current global mantle convection applications have 60-km horizontal and 40-km vertical resolution on ~50-100 processors (PC-clusters). • Hope to have ~10-20 km resolution (~109 grid points, 1 Tbytes RAM). • So far, only a test case was done on Earth Simulator with ~20 km resolution using Terra code for constant mantle viscosity [Yanagisawa & Yamagishi, 2005]. • Modeling nonlinear plate boundary processes is even more demanding.

  25. Computational Infrastructure for Geodynamics (CIG) • Funded by the NSF and participated by ~40 institutes and universities. • Lead the effort in developing more robust and efficient modeling software (reusable modules) in mantle convection and other areas in deep Earth Geophysics research. • Freely downloadable software packages. • At the moment, Petascale computing is not a priority, but should be our focus in the near future.

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