Simulating Solid-Earth Processes Associated With Viscous and Viscoelastic Deformation

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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

• 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 (gt105 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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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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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
t N-1
FMG Zhong et al. 2000 MG Moresi and
Solomatov, 1995
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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
Intel Paragon with 512 processors at Caltechs
CACR
Zhong et al., 1998
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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
Colatitude (o)
Zhong, Paulson, Wahr, 2002
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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 CUs 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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Whats 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
1025x1025x257 grid points
Dubuffet, Yuen Murphy, 2001
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Multiple-scale Structure in Thermo-chemical
Convection
Zhong Hager, 2002
Van Keken et al., 1997
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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.