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From the beginning of CIG, magma migration has been identified as a key scientific research area. The CIG Magma Migration Workshop, held August 18-19, 2006, was organized as the initial meeting for the magma migration community to understand the current state of magma modeling and determine what future software developments would most benefit this community.
Magmatism affects plate boundary dynamics and links geodynamics and geochemistry. However, it is seldom included in existing geodynamics models due to the lack of readily available software that includes consistent solid and fluid flow. Nevertheless, magmatism is a natural extension of both mantle convection and lithospheric deformation, which are central CIG initiatives. Thus CIG is presented with the opportunity, and challenge, to enable important scientific advances through the development of publicly-available magma modeling software that interoperates with other CIG-supported codes.
At the CIG Magma Migration Workshop, 44 scientists attended the meeting, including 10 students, 10 postdocs, representatives of the Ridge2000 and MARGINS programs and computational scientists (see participants list). Scientific interests were as varied as hydrogeology, petrology, magma-dynamics theory, mantle tomography, physics of grain-scale processes, and computational science. A list of modeling activities was identified (Table 1) that could greatly benefit from the coordinating efforts of CIG. The meeting also identified the core of a Magma Dynamics working group to work with CIG to develop new capabilities.
The clear long-term goal is to develop consistent models coupling melting, geochemical evolution, and melt transport in the mantle and crust. However, given the acknowledged complexity of this problem, the workshop identified the realistic and tractable short-term goal to incorporate magma migration into existing geodynamics software using well developed theory for magma migration in viscously deformable media (e.g., McKenzie, 1984). The workshop also proposed a systematic set of benchmark problems for testing such codes. Intermediate and long-term goals were also identified as coupling regional and global mantle flow models, coupling thermodynamics and geochemistry to magma migration, and modeling magma extraction through the lithosphere.
Principal Short-term Recommendations arising from the workshop are to
The meeting was organized principally as a discussion workshop with short presentations highlighting current work and challenges. The principal discussions included Major Scientific observations and questions (Kelemen, Toomey, Wiens, Buck), current theoretical formulations for magma dynamics (Bercovici, Hier-Majumder, Spiegelman, Katz, Hamiel), the current state of magma modeling (Katz, Baker, Cagnioncle, Yuen, Kaus) and computational issues involved in solving more complex coupled problems particularly in the context of frameworks (Appelbe, Quennette, Knepley, Yuen).
Principal Observations and Scientific questions: Peter Kelemen led the initial discussion highlighting geochemical and geological constraints on magma migration at mid-ocean ridges and subduction zones. Theory/models that can actually calculate magma flow and chemistry are essential for linking observations to dynamics. Doug Toomey presented recent seismic tomography from Ridges (9°N EPR) that demonstrated a clear need for high-resolution regional mantle flow models that are consistent with global plate-driven flow. There was unanimous agreement that such models, which fall in line with the goal of CIG to facilitate coupling, would greatly expand the utility of geodynamics modeling to the MG&G community. Doug Wiens discussed how partially molten regions may appear in seismic data and the related uncertainties. Coupling magma migration code and wave propagation codes in a CIG framework makes it possible to generate synthetic seismograms from dynamic models for direct comparison with seismic observations.
Model Formulations: David Bercovici and Saswata Hier-Majumder led a discussion on the current state of theory in magma dynamics. These theories divide into those for flow in viscously deformable media and fluid flow in an elastic/damaged media (Table 2). The viscous theories follow for the most part the formulation of McKenzie (1984), which is itself a straightforward extension of Stokes flow. Katz et al. recently validated this theory against laboratory experiments (Katz et al., 2006). More advanced viscous formulations (e.g., Connolly/Podlachikov; Bercovici, Hier-Majumder) can be expressed as extensions of the McKenzie equations. Magma migration in the brittle lithosphere requires better consideration of elasticity and damage. Constitutive relations are currently in development. Yariv Hamiel presented a novel formulation for damage and fluid flow in poroelastic medium. That theory has also been validated against laboratory experiments but has yet to be implemented in large scale geodynamics codes. Shemin Ge recommended looking into dual porosity models to capture fluid flow through cracks and dikes as well as porous fluid flow. Although a complete theory for magma migration through a general elastic-visco-plastic material is not yet available, existing formalisms can be organized as progressive extension of a compressible viscous flow theory. The McKenzie equations are a clear starting point for any magma flow software in geodynamics and should be implemented in priority in generally available software. Implementation of these equations is a tractable short term project that will enable new science through the integration of magma migration in mantle convection and lithosphere deformation projects.
Current Modeling activities: A wide range of current modeling activities were discussed throughout the workshop and are summarized in Table 1. These include purely solid flow models with estimated melting and geochemistry (e.g., Ito, Montesi/Behn, King, Yuen); Pure solid flow models coupled to pHMelts with approximated melt transport (e.g., Baker, Smith); full coupled fluid/solid flow without thermodynamics (Bercovici, Hier-Majumder), with simplified thermodynamics (e.g., Spiegelman, Katz), simplified melt/solid flow with parameterized thermodynamics (Parmentier, Cagnioncle, Sparks), and fully coupled melt/solid/thermodynamic approaches (Tirone, Sramek). All of these models are variations or simplifications of McKenzie (1984) for the melt and solid dynamics, suggesting that considerable progress could be made in this field by developing an extendable modeling toolkit based initially around the McKenzie formulation.
Computational Science Issues: A fundamental question for the next generation of CIG codes is to understand how to handle more complex coupled systems such as mantle-convection with visco-plastic plates or coupled fluid/solid flow. Bill Appelbe led a discussion on the current state of frameworks in computational science, and Steve Quenette provided some details on the StGermain framework underlying GALE. In particular, Steve Quenette outlined a progressive series of more complex solids models afforded by StGermain and suggested that a similar hierarchy could be developed for coupled fluid/solid flow. An outstanding question, however, is at what level new coupling should occur, and Matt Knepley discussed general issues with coupled PDE’s and suggested that coupling needs to occur at the equation/weak form level. David Yuen discussed another approach for code generation and presented results from a Chinese company for FEM code generation from PDE’s.
The long-term vision for CIG software has been the development of interoperable/reusable codes to enable a wide range of solid-earth science. In the past year, CIG has made considerable strides to move away from stand-alone codes, with the latest generation of codes incorporating common reusable components (e.g., PyLith incorporates Sieve and PETSc, GALE is built entirely on StGermain). We feel that the magma-migration problem provides another opportunity to expand this approach and leverage the considerable effort CIG has already put into the solid mechanics codes (although the additional complexity of magma-migration may lead to new physics and new computational issues). We hope this will be a major topic at the October CIG workshop on Scientific Computation.
Table 1. Current modeling activities
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Table 2. Current formulations for magma migration
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The workshop demonstrated the interest of a wide community in seeing a magma migration modeling framework developed. Coordination with CIG is desired to facilitate interaction of this toolkit with other CIG software, both existing and in development. Accurate coupling between regional and global mantle flow models would be extremely beneficial to the magma migration and the general geodynamics communities. This workshop strongly encourages interaction between the magma dynamics and mantle convection working groups to ensure interoperability of codes. As an example, the ability to model high-resolution 3D mantle flow for specific ridge segments (such as 9°N of the East Pacific Rise) that were consistent with global mantle circulation would be beneficial for the entire Ridge community.
The inclusion of magma migration is seen as a natural extension of the existing solid flow modeling capacities. Four sequential tasks and a benchmark sequence (described in the next section) specific to magma migration were identified:
1. Populate the CIG Magma Migration working group (immediate development) Five volunteers were identified during the workshop: Garrett Ito (U. of Hawaii), Richard Katz (Cambridge University), Boris Kaus (U. South California), Laurent Montési (WHOI), Marc Spiegelman (Columbia University). A general call for volunteers should be issued to reach beyond workshop participants.
2. Implement the McKenzie poroviscous equations (short-term goal). These equations are an extension of Stokes viscous flow theory for solid mantle flow. As with other new CIG codes, they should be built using existing frameworks/libraries such as StGermain and PETSc. The magma migration working group will aim at building a demonstration project: 2D and 3D ridge models with forced adiabatic melting. Intermediate development stages that lead to this goal are defined as the realization of benchmark problems at Development Strategy. Several of these benchmarks have already been implemented as PETSc codes.
3. Develop a toolkit for chemical transport and thermodynamics (intermediate term goal). modeling geochemical tracers as they are carried by migrating melts enables the incorporation of new datasets in model evaluation. Chemical advection and full and simplified thermodynamic tables should be included as a separate toolkit to plug in on any CIG software. Given the essentially non-diffusive nature of chemical transport, highly accurate advection schemes for particles or fields will be necessary. These problems are common to thermo-chemical convection and advection of material properties during lithospheric deformation (e.g., GALE) and considerable progress could be made by coordinating between groups to develop more general software for Eulerian/Lagrangian methods. Coupling will enable the evaluation of feedback between chemistry and dynamics. Several preliminary benchmarks were identified that follow existing scientific applications
4. Model magma migration though the lithosphere (long-term goal). Elastic-visco-plastic rheologies are already implemented in CIG codes of long-term tectonics (e.g., GALE), and we should immediately evaluate the accuracy of the pressure fields (or more precisely pressure gradients) in existing models as they are an essential requirement for porous flow models. Porous migration through more complex solid media will be possible as soon as the initial magma migration toolkit is developed. While clearly desired, how to develop theory and computations for consistent magma migration through cracks and dikes remains an open question. The magma migration community needs to discuss in future workshops what is the best formalism to be followed for modeling cracks and dikes and what benchmarks to develop for porous flow through elastic-visco-plastic materials.
A preliminary sequence of benchmarks of increasing sophistication was identified. Benchmark details will be posted in a supplementary document. Benchmark specifics should be discussed in a future meeting of the CIG magma migration community, especially for benchmarks that address intermediate and long-term goals. Interest in such a meeting was expressed by the representative of the MARGINS community. We foresee additional coordination with MG&G and particularly the Ridge 2000 community.
1. Implement and test the McKenzie formulation (short term)
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2. Test geochemistry (intermediate term)
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3. Couple with other software (long term)
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The New York City workshop was the initial gathering of the magma migration modeling community. It revealed the desire of this community to see coordinated code development efforts, both to implement magma migration in generally available software, and to facilitate coupling with large-scale models, lithosphere deformation, and seismic wave migration. This community should gather again in the future, probably in the next 18 to 24 months. Such a meeting could be co-sponsored by CIG and the Margins community. The agenda of a future Magma Migration Workshop should include: