simulating solid-earth processes associated with viscous and viscoelastic deformation shijie zhong...
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Simulating Solid-Earth Processes Associated With Viscous and Viscoelastic
Deformation
Shijie Zhong
Dept. of Physics
University of Colorado
Boulder, Colorado
EarthScope CSIT Workshop
Snowbird, UT, 2002
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Outline
1) Introduction. Why is simulating viscous and viscoelastic
deformation relevant to the EarthScope? Definition of Geodynamic Modeling
• 2) Current status in geodynamic modeling. Where are we now in terms of modeling capability? How do we get where we are?
• 3) Future developments.
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Two questions asked in the EarthScope
1) How do continents form and evolve? • large time scales (>105 years) -- viscous flow.
Mantle convection and mantle-lithosphere interaction.
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Dynamic Evolution of Continents
Doin, Fleitout & Christensen, 1997 Shapiro, Hager & Jordan, 1999
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2) Why do earthquakes and volcanic eruptions occur?
• small time scales -- viscoelastic flow.Post-seismic stress and strain evolution,
GPS and InSAR observations.
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Modeling Post-seismic Surface Deformation – Viscoelastic Effects
Pollitz et al., 2001
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Modeling Post-seismic Stress Evolution – Viscoelastic Effects
Freed & Lin, 2002
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Definition of Geodynamic Modeling
1) Mantle convection• Physical basis: Conservation of MASS,
ENERGY, and MOMENTUM + VISCOUS rheological equation.
• Objectives: Understand the long-term heat and mass transfer in the mantle and its consequences to surface observables.
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2) Viscoelastic deformation
• Physical basis: Conservation of MASS and MOMENTUM + VISCOELASTIC
rheological equation.
• Objectives: Understand short-term evolution of surface deformation and lithospheric stress in response to certain forces (e.g., an earthquake).
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Why Numerical (Finite Element) Method?
A set of nonlinear equations.• Heterogeneous and nonlinear rheology. • Deformable mesh, critical for viscoelastic
stress analysis.• Tectonic faults, …
but spectral methods [Glatzmaier et al., 1990; Gable et al., 1991; Zhang and Christensen, 1993] and finite volume methods [Tackley, 1996; Ratcliff et al., 1997] work well for viscous flow problems.
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Outline1) Introduction.
Why is simulating viscous and viscoelastic deformation relevant to the EarthScope?
Definition of Geodynamic modeling.
• 2) Current status in geodynamic modeling. Where are we now in terms of modeling
capability? How do we get where we are?
3) Future developments.
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2-D F. E. models
• Tecton for viscoelastic stress analysis [Melosh & Raefsky, 1981].
• ConMan for mantle convection [King, Raefsky & Hager, 1990].
Director solver for matrix equations – robust but memory usage ~ N3/2, # of flops ~ N3, difficult for parallel computing.
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3-D F.E. models
• Citcom for mantle convection [e.g., Moresi & Gurnis, 1996; Moresi & Solomatov, 1995].
Iterative solver (multi-grid) for matrix equations
memory usage ~ N,# of flops ~ N,suitable for parallel computing.
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Execution Time vs Grid Size N for Multi-grid Solvers in Citcom
FMG: Zhong et al. 2000MG: Moresi and Solomatov, 1995
t ~ N-1
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Recent Developments to Citcom
1) tectonic faults [Zhong & Gurnis, 1996].
2) parallel computing [Zhong, Gurnis, & Moresi, 1998].
3) spherical geometry [Zhong et al., 2000, Billen & Gurnis, 2002].
4) viscoelastic rheology [Zhong, 2001].
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Inclusion of Faults in Viscous Flow Models
Zhong and Gurnis, 1996
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Dividing the Earth for Parallel Computing
Zhong et al., 2000
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Benchmarks on an Parallel Supercomputer
Zhong et al., 1998
Intel Paragon with 512 processorsat Caltech’s CACR
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Accuracy of CitcomS
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Thermal Convection with Temperature-dependent Viscosity and Plates
Zhong et al., 2000
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Vertical Motion of Hawaiian Islands and
Plate-plume Interaction
Zhong & Watts, 2002
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Modeling the Farallon Subduction
Billen and Gurnis, 2002
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Modeling the Farallon subduction
Billen and Gurnis, 2002
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Recent Developments to Citcom-- Viscoelastic Analysis
• Motivation: Post-glacial rebound problem.
Most previous studies use a linearized theory that ignores lateral structures.
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Global Elastic Thickness Variations
North America
Modified from Watts [1999]
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The Need for More Efficient Modeling for Post-seismic Viscoelastic Deformation
Pollitz et al., 2001
Freed & Lin, 2002
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3D Spherical Models of Viscoelastic Deformation with Citcom
Zhong, 2001
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Effect of Mantle Viscosity Anomalies on Viscoelastic Stress Evolution
Zhong, Paulson, & Wahr, 2002
Colatitude (o)
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Parallel Computing with Beowulf-Cluster Computers
• Clusters of commodity processors connected by commodity networks.
• Price-performance ratio: ~ $500/Gflops for best price systems (Aug. 2001).
• The first Beowulf cluster (16 nodes) was built in 1994 at the GSFC for the Earth and space sciences project (ESS).
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The First Beowulf-cluster Computer (GSFC)
Donald Becker, 1994
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A Beowulf-Cluster Computer for CU’s Geodynamics • 50 Processors (Pentium-III 1 GHz) • 50 Gbytes Memory.•100 Mbits/sec Ethernet Cards.• 100 Gflops theoretical peak speed.
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So here we have: An Apparatus for Geodynamic Modeling -- Citcoms
• Viscoelastic and viscous rheology (nonlinear).
• 3D Cartesian and spherical geometry.
• Multi-physics in a single code.
• Robust and accurate.
• Parallel computing.
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What’s next? -- Driving Forces for Future Developments in
Geodynamic Modeling
• Resolving multiple scale (both temporal and spatial) physics in mantle convection and lithospheric deformation.
• Better and faster modeling to understand the EarthScope observations.
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Multiple-Scale Thermal Structure from Mantle Convection
Dubuffet, Yuen & Murphy, 2001
1025x1025x257 grid points
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Multiple-scale Structure in Thermo-chemical Convection
Van Keken et al., 1997
Zhong & Hager, 2002
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San Andreas Faults System
From USGS Website
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Multiple Scale in Time
• Background stress in lithosphere from long-term tectonic processes.
Largely ignored in post-seismic stress analyses.
What is its role to the rheology?
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Computer Memory Requirement
• Mantle convection with uniform 20-km resolution: 1 Tbytes RAM for global models (190 million
elements). 120 Gbytes RAM for regional models like N.A.
• Viscoelastic deformation of lithosphere for a region of 400 km by 400 km with uniform 2-km resolution: 12 Gbytes RAM.
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Future Developments in Geodynamic Modeling Technologies
• Incorporation of multi-scale physics (from global to regional and from large time scale to small time scale).
• Incorporation of faults in modeling of viscoelastic deformation of lithosphere.
• Adaptive mesh refinement and its parallel computing and multi-grid scheme.
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Adaptive Mesh Refinement
Wissink & Hornung, 2000
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Future Developments in Geodynamic Modeling Technologies
More powerful PC clusters (faster networking with Gigabit ethernet and Myrinet, and faster processors).
Grid computing for resource sharing.