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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
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.
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.
Dynamic Evolution of Continents
Doin, Fleitout & Christensen, 1997
Shapiro, Hager & Jordan, 1999
2) Why do earthquakes and volcanic
eruptions occur?
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small time scales -- viscoelastic flow.
Post-seismic stress and strain evolution, GPS
and InSAR observations.
Modeling Post-seismic Surface Deformation –
Viscoelastic Effects
Pollitz et al., 2001
Modeling Post-seismic Stress Evolution –
Viscoelastic Effects
Freed & Lin, 2002
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.
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).
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.
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.
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.
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.
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
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].
Inclusion of Faults in Viscous Flow Models
Zhong and Gurnis, 1996
Dividing the Earth for Parallel
Computing
Zhong et al., 2000
Benchmarks on an Parallel Supercomputer
Intel Paragon with 512 processors
at Caltech’s CACR
Zhong et al., 1998
Accuracy of CitcomS
Thermal Convection with Temperaturedependent Viscosity and Plates
Zhong et al., 2000
Vertical Motion of Hawaiian Islands and
Plate-plume Interaction
Zhong & Watts, 2002
Modeling the Farallon Subduction
Billen and Gurnis, 2002
Modeling the Farallon subduction
Billen and Gurnis, 2002
Recent Developments to Citcom
-- Viscoelastic Analysis
•
Motivation: Post-glacial rebound problem.
 Most previous studies use a linearized theory that
ignores lateral structures.
Global Elastic Thickness Variations
North America
Modified from Watts [1999]
The Need for More Efficient Modeling for
Post-seismic Viscoelastic Deformation
Pollitz et al., 2001
Freed & Lin, 2002
3D Spherical Models of Viscoelastic
Deformation with Citcom
Zhong, 2001
Effect of Mantle Viscosity Anomalies on
Viscoelastic Stress Evolution
Colatitude (o)
Zhong, Paulson, & Wahr, 2002
Parallel Computing with BeowulfCluster 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).
The First Beowulf-cluster Computer
(GSFC)
Donald Becker, 1994
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.
So here we have: An Apparatus for
Geodynamic Modeling -- Citcoms
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Viscoelastic and viscous rheology (nonlinear).
3D Cartesian and spherical geometry.
Multi-physics in a single code.
Robust and accurate.
Parallel computing.
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.
Multiple-Scale Thermal Structure from
Mantle Convection
1025x1025x257 grid points
Dubuffet, Yuen & Murphy, 2001
Multiple-scale Structure in Thermo-chemical
Convection
Zhong & Hager, 2002
Van Keken et al., 1997
San Andreas Faults System
From USGS Website
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?
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.
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.
Adaptive Mesh Refinement
Wissink & Hornung, 2000
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.