Report to CIG from the NSF Workshop on Tectonic Modeling

Report from the CIG Workshop on Tectonic Modeling (Long-term Tectonics) held on June 9-12, 2005, in Breckenridge, Colorado.


This meeting of 26 practitioners of tectonic modeling spent 2.5 days discussing current codes, and modeling needs and agreed on a number of recommendations for consideration by the CIG science steering committee.


The lithosphere geodynamics community is a diverse group of modelers working on a variety of tectonic problems from mantle-lithosphere coupling to surface-climate-tectonic interaction.  Spatial scales of interest range from the formation of rock fabric to lithosphere structure and temporal scales range from those of fault rupture processes to periods spanning the evolution of orogenic belts and rift systems.

Reflecting this diversity of problems, our community presently employs a diverse set of modeling tools. At this workshop, we identified classes of dynamic models in common use including (1) visco-elastic-plastic codes, usually solved with Lagrangian finite element methods; (2) viscous-plastic codes, solved as a non-linear Stokes flow problem with an Eulerian finite element method; (3) particle methods such as the Distinct Element Method or Smooth Particle Hydrodynamics used with elastic-viscous-plastic rheologies; (4) thin viscous sheet methods; (5) other, more specific, techniques including Boundary Element Methods. These methods, some existing codes and relative advantages and disadvantages are given in Table (1).

Codes implementing several of these methods are presently under development by CIG and collaborators and our community anticipates taking advantage of opportunities provided by this new availability and functionality.

In particular, we anticipate use of the visco-elastic-plastic codes, Pylith and Snac, and the Eulerian visco-plastic code, Snark, and a number of our community members would like to see training in their use and subsequent support by CIG.

Workshop participants noted than no code is currently available or being developed by CIG based on the Arbitrary Lagrangian Eulerian (ALE) method for solving visco-plastic tectonic problems within the CIG (see recommendation below).


In addition to Pylith, Snac, and Snark, the Arbitrary Lagrangian Eulerian (ALE) method is the other main modeling method in common use in our community. This method, which was developed primarily at Dalhousie University, solves a Stokes Flow problem on an Eulerian grid and uses a Lagrangian grid to track material properties and to integrate strain. This method has seen much use in lithosphere deformation problems such as orogenesis, rifting, subduction, and has been coupled to surface erosion models and has been employed for deeper mantle dynamics problems. Several versions of this code are presently in use internationally. We would like to see development of a code using this technique by the CIG.

We suggest a multistep process towards the goal of a supported ALE code. First, an existing code should be identified, tested, and benchmarked. This code should be incorporated into the CIG framework. The code should be studied for simple improvements such as replacement of the solver and made available to the community. Second, the code should be analyzed for modification using existing components from the framework. In particular, common components with Snark should be identified and incorporated into the code. Third, the possibility of full integration with Snark should be studied, and, if practical, implemented. ALE and the PIC method used in Snark share many common features and we expect that a single code containing strengths of each of these methods could eventually be developed and made available to the community.

As a long term goal, we would like to see a 3-D implementation of both the ALE/PIC method and the VEP implicit methods that include adaptive mesh refinement (AMR). AMR is desirable for efficiency and is a necessity for solving large-scale problems with high spatial resolution in regions of strain localization and fluid/rock interactions.

We recognize the need for greater benchmarking of existing codes and codes under development and would like to see CIG participate in, and support, the benchmarking exercise initiated at the GEOMOD 2004 conference (an international effort to compare numerical solutions obtained from various codes and compare them to analog model results) to test, validate and benchmark codes used in the community.

We would like to see the formation of a standing committee for long-term tectonics in the CIG.

We would like to see regular, perhaps annual, workshops of the tectonic modeling community for improved communication, code comparison and benchmarking. We would like to see sponsorship or partial support from the CIG for this effort.

Table 1:  Description of the methods and corresponding codes presently used in lithospheric Geodynamics.



Reference Frame




Visco Elastic Plastic (VEP)

Finite element based, implicit.

Existing codes: Tecton 3D, Pylith 3D (geoframework).


  • Elastic
  • Elastic-plastic
  • Visco-elastic, non linear (Maxwell)
  • Visco Elastic Plastic
  • Elastic stress predictor
  • Associative or non-associative plasticity
  • Discrete faults can be described by contact elements
  • Mesh distortion
  • Periodical remeshing causes diffusion.
  • Complex and numerous formulations for finite strain
  • Harder to include open flux boundaries

 Visco Elastic Plastic (VEP)

Discretization similar to finite element, explicit.

Existing codes: SNAC 3D (geoframework).


  • Elastic
  • Elastic-plastic
  • Visco-elastic, non linear (Maxwell)
  • Visco Elastic Plastic
  • Fast
  • Robust
  • Associative or non-associative plasticity
  • Parallelism built in through framework
  • Easy to test new rheologies
  • Deals naturally with free surface
  • Restrictive stability condition
  • AMR (Adaptive Mesh Refinement) inaccurate, inefficient
  • Periodical remeshing causes diffusion.
  • Harder to include open flux boundaries

ViscoPlastic (VP)

Stokes Flow Solver – Fluid dynamics based. Finite Element implicit method.



  • Viscous, non-linear viscous
  • Rigid-Plastic
  • Viscous Plastic
  • No grid distortion issues (material displacement tracked by lagrangian markers.
  • No large strain limitations
  • Free surface can handle flux at boundaries (i.e. erosion, deposition,  mantle processes)
  • Finite strain formulation is straightforward
  • Elasticity optional
  • Material tracking required by Lagrangian markers causes dispersion due to frequent interpolation between the Lagrangian and Eulerian mesh
  • Post yield flow treated as isotropic flow
  • Difficult to resolve localized deformation (faults)
  • Isotropic, associative plastic strains only
  • Parallelized using shared memory

Particle Methods

 Distinct Element Method, Smooth Particle Hydrodynamics (SPH), Meshless methods.


  • Elastic
  • Elastic-plastic
  • viscous
  • Accurate representation of discrete strain zones
  • Variable resolution
  • No grid distortion issues
  • Dynamic (momentum)
  • Rheology is an emergent property
  • Momentum can be a problem for long term problems.

Thin Sheets – 2D viscous sheet, solved with FEM


  • Viscous, non-linear
  • Reduced Dimensionality by vertical integration of stress and strain
  • Faults can be included as contact boundaries
  • No vertical partitioning or resolution of strain – neglect of components of strain rate
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