Computational tools for magma dynamics of subduction zones: finite element models and efficient solvers

Lead Research Organisation: University of Oxford
Department Name: Earth Sciences


Plate tectonics describes three major plate-boundary types: convergent, divergent, and transform. A subduction zone is an example of a convergent boundary, in which an oceanic plate plunges back into the deep mantle. The subduction process is invariably associated with explosive volcanism; since subduction zones surround the Pacific ocean, this is also where many of the world's most dangerous volcanoes can be found. Why does subduction lead to volcanism? Scientists possess only the broad outlines of an answer to this question. We know that the subducting slab of oceanic sediments, crust, and lithosphere transports sea-water to 100+ kilometres depth in the mantle; we know that this water eventually is released from the slab, and that it percolates upward into the mantle and triggers melting. We know that the magma produced in this way feeds subduction-zone volcanoes. Beyond this, however, things become rather vague. The conditions of pressure and temperature under which magma is produced within the mantle, for example, are not known. This is largely due to the complexity of a system in which water, heat, and mantle rock are combined at inaccessible depths. The subduction zone is like a "black box"---we know the inputs and the outputs, but what happens inside remains a mystery. We are proposing to use supercomputers, and mathematical theory based on fundamental physics and chemistry, to discern the mechanical workings hidden within the black box of a subduction zone.

One available clue that may contain useful information about the magmatic processes that occur within a subduction zone comes from the position of the volcanoes themselves. In map view, the volcanoes are arrayed in arcs that sit above the subducting slab. Earthquakes within the slab have allowed scientists to determine the depth of the slab beneath the arc of volcanoes. Compiling this depth for all the world's volcanic arcs, and comparing it with the rate of descent of each slab into the mantle produces a striking trend: faster descent produces arc volcanoes over a shallower point on the slab, while slower descent leads to large slab-depths beneath the arc. A hypothesis to explain this trend was recently published; it states that the volcanoes form at a position determined by the temperature structure of the mantle beneath, and by the details of magmatic flow. In particular, it proposes that the hottest magmas that are produced in the subduction zone rise toward the surface, and create a hot conduit that other melts follow. The arc volcanoes are found on the surface, directly above the conduit.

Testing this hypothesis requires a physical/mathematical model of how magma moves through the mantle, and how it transports heat. Previous models of subduction zones have not included the flow of magma, mostly because it was too challenging to compute. To overcome this challenge, we have assembled a team of four scientists with complementary expertise in software engineering, mathematical modelling, fluid dynamics, and geophysics. Together we have the skills to create a new generation of computer model that will describe the flow of magma within a subduction zone. This model will allow us to test the hypothesis described above, as well as other, competing hypotheses. Developing the model will require a multi-stage assembly process, in which each component of the software is designed, written, and tested separately. In this proposal we detail a carefully planned series of tasks that culminate in our ultimate goal of a model of subduction zone magmatism and the position of volcanic arcs. Along the way, we intend to make our software available to other scientists for their use, with the hope that they might help us to improve it. After three years of work with help from two assistants, we'll have new knowledge about subduction, and new mathematical tools for research.

Planned Impact

One of the main research outputs of this project will be freely-available, open-source software tools for modelling multi-phase flows. These tools will be of clear benefit not only to a range of academic users, but also to a range of industrial users. The oil industry is particularly relevant, and the tools we develop could improve their modelling of the flow of oil through porous rock, to obvious economic benefit. Moreover, an understanding of the compaction of sediments is of clear concern if one wants to understand how oil is generated in the first place, and is closely related to the problem of compaction of partially molten mantle that we will study.

The flow of fluids through porous rock is also of key concern to the growing industry of carbon capture and storage (CCS). One of the leading suggestions for mitigating climate change is the storage of carbon dioxide deep underground in depleted oil reservoirs or saline aquifers. The carbon dioxide at these depths behaves as a supercritical fluid, and it is crucial that we understand how it will move through the reservoir if this technology is to be useful. Our tools will undoubtedly help in this task.

Volcanoes capture the public's imagination, particularly among children. They are an important natural hazard, and while we may think we are immune from the effects of volcanism living in the UK, the recent closure of UK air space by the Icelandic eruption demonstrates that this is not the case. Insurance companies would certainly like to know more about volcanism. Our main focus in this project is on understanding the origin of subduction zone volcanism by studying the processes occurring at great depths within the Earth's mantle, to understand how melting first begins and how that melt is transported to the Earth's surface. This fundamental research will lead to a better understanding of volcanism in general, and eventually to a better understanding of the natural hazard.


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Rhebergen S (2014) Analysis of Block Preconditioners for Models of Coupled Magma/Mantle Dynamics in SIAM Journal on Scientific Computing

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Rhebergen S (2015) Three-Field Block Preconditioners for Models of Coupled Magma/Mantle Dynamics in SIAM Journal on Scientific Computing

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Rees Jones D (2018) Thermal impact of magmatism in subduction zones in Earth and Planetary Science Letters

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Qi C (2015) Experimental test of the viscous anisotropy hypothesis for partially molten rocks. in Proceedings of the National Academy of Sciences of the United States of America

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Allwright J (2014) Pipe Poiseuille flow of viscously anisotropic, partially molten rock in Geophysical Journal International

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Alisic L (2014) Compaction around a rigid, circular inclusion in partially molten rock ALISIC ET AL. in Journal of Geophysical Research: Solid Earth

Description We have developed a high-performance preconditioner for simulating magma/mantle dynamics. This allows the governing equations to be solved efficiently on massively parallel supercomputers. By doing so, we are able to better model the dynamics of magmatism in the Earth.

We have analysed laboratory experiments on deformation of partially molten rock with embedded olivine spheres by simulating them in 3D. We have shown that the current theory and constitutive relations cannot simultaneously reproduce both the growth of porosity variations in pressure shadows and in high-porosity bands in the correct ratio. However, many aspects of these patterns can be matched for small total strains.
Exploitation Route The computational and mathematical methods may help in other areas where efficient simulation of mechanical processes is required. In particular, the algorithms are relevant for materials with elastic or viscous compressibility.
Sectors Aerospace, Defence and Marine

Description Kohlstedt group, University of Minnesota 
Organisation University of Minnesota
Country United States 
Sector Academic/University 
PI Contribution We develop models of their experiments
Collaborator Contribution They provide the experimental results
Impact publication: Alisic L., J.F. Rudge, R.F. Katz, G. Wells and S. Rhebergen (2014) Compaction around a rigid, circular inclusion in partially molten rock. Journal of Geophysical Research---Solid Earth. doi: 10.1002/2013JB010906.
Start Year 2013
Description Rudge and Wells at Cambridge 
Organisation University of Cambridge
Country United Kingdom 
Sector Academic/University 
PI Contribution We work on physical/numerical models
Collaborator Contribution They work on physical/numerical models
Impact Alisic L., J.F. Rudge, R.F. Katz, G. Wells and S. Rhebergen (2014) Compaction around a rigid, circular inclusion in partially molten rock. Journal of Geophysical Research---Solid Earth. doi: 10.1002/2013JB010906.
Start Year 2013
Title Computer code illustrating three-field preconditioner for magma/mantle dynamics 
Description Software to reproduce the computations performed in the manuscript and hence to adopt the preconditioner developed by the authors. 
Type Of Technology Software 
Year Produced 2015 
Impact This software/preconditioner is already in use by several groups who are developing and deploying open-source modelling software.