Development of a package for modeling stress in the lithosphere

Spring AGU MeetingBaltimore, May, 2006

Development of a Package for Modeling Stress in the Lithosphere

Charles WilliamsRensselaer Polytechnic Institute


Other People Involved in Code Development

Matt Knepley (CIG/ANL)PETSc/Sieve development and implementation, parallelization.

Brad Aagaard (USGS)External packages, merging of LithoMop and EqSim into PyLith.

Leif Strand (CIG)Build system, SVN repository.

Michael Aivazis (CIG/CACR)Pyre/pythia.


What Types of Problems Would We Like To Solve?

Stress evolution over multiple earthquake cycles.Complex geometries, rheologies, and boundary conditions.

Realistic fault behavior on multiple time scales.

Large-scale models of inter/intra-plate stresses.Large spatial scales, spherical geometry.

Contributions from gravity and lithosphere/mantle coupling.

Volcanically-induced stresses (intrusion, emplacement, etc.).

Complex structure and plastic/viscoplastic rheology.


What Code Features Will Be Needed to Solve These Problems?

Need to represent a wide range of spatial and temporal scales.

Must allow complex structures and geometries.

Able to model faults and complex rheologies.

Different types of geometries (spherical, 2D, etc.).

Easily adaptable to different problem types, sometimes involving different physics.


SCEC Community Block Model

View of CBM for Mojave region fromhttp://structure.harvard.edu/cfm/blockmodel.jpg

Moderate-resolution mesh (56,472 nodes; 342, 998 elements)created by Carl Gable, LANL.

Forward/inverse models of elastic block interactions.

Models of multiple earthquake cycles.


Parallelization Using PETSc and SieveMesh represented in terms of hierarchical covering relations.

Sieves are inherently parallel, eliminating need for constructs such as “ghost nodes”.

Sieves make parallelization much easier.

PETSc/Sieve can import meshes from a variety of meshing packages, perform partitioning and refinement, and provide parallel data structures that may be used directly by PyLith.


Geometric Flexibility Through Multiple Element TypesMultiple element types provide compatibility with many meshing packages.

Different element types may be combined for greater flexibility.

We will use the FIAT (FInite element Automatic Tabulator) package to use arbitrary element types of any order.


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FIG. 3.7!Assembly of various interface elements with two solid elements. Notethat element trint12 can have curved edges.

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Presently:Kinematic case: ‘Split nodes’

‘Dynamic’ case: ‘Slippery nodes’

Soon - cohesive elements:

Kinematic case: Specified differential slip.

‘Dynamic’ case: Slip determined by element constitutive relationship.

Eventually - discontinuous elements:

Faults can cut through elements for kinematic or dynamic case.

From WARP3DManual


Stress Changes Due to Dynamic Rupture Propagation

Quasi-static solution is needed to provide realistic initial conditions for dynamic solution.

At end of dynamic solution, there are regions of high shear stress, which would likely be reduced by viscoelastic relaxation (quasi-static).

Movie of 2002 M 7.9 Denali earthquake provided by Brad Aagaard, USGS.


Code Coupling For Complex Problems

E. Choi, August, 2004

SNAC CitcomS

Pyre Modeling Framework

TECTON

Quasi-static

code

EqSim

Dynamic code

LithoMop

Quasi-static

codePyLith

Quasi-static/

dynamic code EqSim

Dynamic code

CitcomS

Convection

code

Other

Modeling

Codes

Merging of LithoMop and EqSim will facilitate simulation of problems involving interseismic and coseismic time scales.

Integration of both codes into Pyre framework will facilitate coupling with other codes in the framework.


Inversion SetupModular design allows one component (e.g., BC) to be replaced without altering anything else (e.g., mesh).

Computed values may be requested for specified locations and converted into cost functions by the driver application.

Image of Mojave portion of CBM from Carl Gable, LANL.

PyLith Package

Solver

Time stepping, BC,

etc.

FECore

Mesh, integration,

etc.

Faults

Kinematic BC,

Dynamic properties

Materials

Specification and

physics

Additional

Components

SpatialData Package

Generic Interface

Query

Query

Query

Driver Application

Python script to

control multiple

simulations

Pa

ram

ete

rs

ComputedValues


How Desired Features Are Being AddressedWide range of spatial and temporal scales.

Parallelization using PETSc/Sieve.

Merging LithoMop + EqSim -> PyLith.

Allowing code coupling using Pyre.

Complex structures and geometries.Multiple element types.

Use Sieve for interfacing with meshing packages.

Different types of geometries (e.g., spherical).Most components are independent of geometry.

Use of FIAT provides basis functions for any geometry.

Modular design will facilitate addition of new geometries.


How Desired Features Are Being Addressed (cont.)

Faults and complex rheologies.Modular design simplifies addition of new rheologies.

Cohesive elements with easily-defined constitutive relations.

Adaptable to different problems with different physics.

Integration into Pyre framework will eventually allow coupling with other codes in the framework.

Modular design allows easy extensibility.


Project Support and Further InformationSCECFault systems workshops, initial funding for code development.

GeoFramework projectDevelopment of Pyre/Pythia framework.

NSF ITR programFunding for code development.

CIGInfrastructure and code development assistance.

Further information: www.geodynamics.org.


component

bindings

library

services

services

services

services

component

bindings

engine

component

bindings

engine

solver (e.g., TECTON)

solver (e.g., EqSim)infrastructure

framework

package

python

C/C++

FORTRAN/C/C++

Pyre Architecture


Examples of Code Coupling Using Pyre

Mesher Lithomop3d Visualization

(e.g., DX)pyre pyre

Lithomop3dpyreRegional

Convection

(e.g., CitComS)

Rupture

Propagation

(e.g., EqSim)

pyre

Complete Quasi-static Modeling Package

Coupling Different Modeling Codes


TECTON 1.0 Material Property Specification

€

σ ij =Cijklεkl

€

˙ ε ijV =

′ σ ij ′ J 2n−1

2ηn

€

k e P( ) =αI1 + ′ J 2

Elastic

Power-lawviscous

Drucker-Pragerplastic


Lithomop Material Property Specification

Elastic

Viscoelastic

Elasto-plastic

Viscoelastic/plastic


Planned Material Models for LithoMop3d

Model TECTON 1.0 Lithomop3d

1. Isotropic Elastic Yes Yes

2. Transversely Isotropic Elastic No Planned

3. Orthotropic Elastic No Planned

4. Anisotropic Elastic No Planned

5. Maxwell Linear Viscoelastic Yes Yes

6. Maxwell Power-Law Viscoelastic Yes Planned

7. Drucker-Prager Elasto-Plastic Yes Planned

8. Model 5 + Model 7 Yes Planned

9. Model 6 + Model 7 Yes Planned


Automatic Computation of Prestresses

Application of gravity results in unrealistically large initial deformation.

Solution is to apply initial stresses to cancel gravity.

This is now done automatically in LithoMop.

Using this method, it is also possible to avoid the Poisson’s ratio problem with gravity.

Initial StateElastic SolutionGravity

‘turned on’


Code Usage - SCEC Benchmarks

BM5

Ux, m-0.6 0.6

Uy, m-0.6 0.6

Uz, m-0.6 0.6

BM7


Misfits for SCEC BM 5

0.01

-0.01

m

Ux

0.01

-0.01

m

Ux

0.01

-0.01

m

Uy0.01

-0.01

m

Uz

0.01

-0.01

m

Uz

Map View

Cross-Section


Code Usage - Multiple Earthquake Simulations for Taiwan

From Ya-Ju Hsu [2005]


Simple Spatial DatabasePoint

Constant material properties

Uniform boundary conditions

Line

Depth-varying material properties

Linearly-varying boundary conditions

Plane Volume

Fault slip distribution

BC on external boundary

Heterogeneous material properties


Mesh Creation

Meshing Package

LaGriT, CUBIT,

NetGen, etc.

CIG Package

Partitioning Uniform Refinement


Structure of PyLith Package

Pyre

low−level code inefficient, compiledlanguage

from Pythonbindings to call C++

high−level codein rich, expressiveinterpreted language

Bindings

Python scripts

C++ library

Solver

Bindings

Python scripts

C++ library

FECore

Bindings

Python scripts

C++ library

Faults

Bindings

Python scripts

C++ library

Materials

Python script

Application

C libraries

PETScC libraries

MPI

Bindings

Python scripts

C++ library

SpatialData

Bindings

Python scripts

C++ library


Future Data Import and Export Mechanisms

Lithomop3d

Data Import Facility

Import Ascii

Import AVS

UCD

Data Export Facility

Export

OpenDX

Export AVS

UCD

??? ???


Example Problem: SCEC BM5 Using Carl Gable’s Mesh

Similar procedure used when using package such as NETGEN.


Lithomop Surface Displacements Compared To Analytical Solution

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 4000 8000 1.2 104 1.6 104 2 104 2.4 104

Y = 0 mY = 8000 mY = 16000 mY = 24000 m

Y = 0 mY = 8000 mY = 16000 mY = 24000 m

X-Di

spla

cem

ent (

m)

X-Distance (m)

Lithomop Analytical

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 4000 8000 1.2 104 1.6 104 2 104 2.4 104

Y = 0 mY = 8000 mY = 16000 mY = 24000 m

Y = 0 mY = 8000 mY = 16000 mY = 24000 m

Z-Di

spla

cem

ent (

m)

X-Distance (m)

Lithomop Analytical

Documents

Development of a package for modeling stress in the lithosphere