simulating solid-earth processes associated with viscous and viscoelastic deformation shijie zhong...

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?

• 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.

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.

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

FMG: Zhong et al. 2000MG: Moresi and Solomatov, 1995

t ~ N-1

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

Zhong et al., 1998

Intel Paragon with 512 processorsat Caltech’s CACR

Accuracy of CitcomS

Thermal Convection with Temperature-dependent 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

Zhong, Paulson, & Wahr, 2002

Colatitude (o)

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).

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

• 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

Dubuffet, Yuen & Murphy, 2001

1025x1025x257 grid points

Multiple-scale Structure in Thermo-chemical Convection

Van Keken et al., 1997

Zhong & Hager, 2002

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.