From the continuum to the tectonic: the magma/mantle dynamics of planet earth

Workshop theme

Plate-tectonic boundaries are the predominant (but not the only!) geological context for mantle melting. Global-scale tectonic forces acting on plates give rise to mantle flows. At divergent and convergent plate boundaries, these flows carry with them the energy required for partial melting, leading to extensive volcanism. The nature of the boundary imposes geometric and material aspects of the problem: in subduction zones, for example, melting takes place in a wedge of mantle rock that lies above the foundering tectonic plate and below the surface tectonic plate. This wedge is permeated with water, CO2, and other chemicals that are released from the foundering plate and that chemically react to trigger melting. Furthermore, the tectonic context shapes the observations that can be made, and which models should aim to reproduce: mid-ocean ridges, for example, are found beneath several kilometres of ocean, creating some challenges (and some advantages) for observationalists.

Models of magma/mantle dynamics that seek to match observations must respect the geometric and material influences of the tectonic context. For understanding the Earth, modelling the geological context may be as important as capturing the fundamental conservation principles and the material properties of a two-phase continuum. However, putting magma/mantle dynamics into the plate-tectonic context creates challenges including

• Broad range of length scales from the plate (~100 km) to the compaction scale (~1 km).
• Broad range of time scales from plate motion (~1 Ma) to melt transport (~10 ka).
• Thermo-chemical complexity and spatial heterogeneity (at a range of intermediate length-scales).
• Adjacent regions of unmolten, partially molten, and (almost) fully molten rock.

These features impose the multi-scale nature of the phenomena and present significant challenges for numerical modelling. They are, however, crucial aspects of the system that should not be neglected in an attempt to explain observations.

One important class of observation that could constrain such models comes from measurements of seismic waves. When seismic waves have passed through the partially molten region and arrived at the surface, they carry some information about the properties of the medium. However, interpretation of such measurements in terms of those properties is not straightforward. Their analysis requires models of poro-(an)elasticity based-on grain scale physics, represented in terms of continuum theory, and informed by the meso-scale patterns that emerge from magma/mantle dynamics. There are many challenges in the development and use of such theory.

The aim of this workshop is therefore to bring together mathematicians and scientists working on multi-scale problems in numerical analysis, software, and modelling. In particular, the workshop will focus on measuring (seismically) and modelling magma transport through a porous medium, albeit one that is deforming viscously. And it will focus on the challenges that arise in simulations that capture the geological context: plate-imposed domain/flow geometry, melting and freezing of thermo-chemically heterogeneous material, and the multi-scale features that emerge as a consequence. Finally, the workshop will consider cutting-edge topics in modelling more exotic systems: solidification of a magma ocean that was present very early in Earth history and modern production (and detection) of melt at much greater depths in the mantle.