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Timetable (MIMW03)

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

Monday 6th June 2016 to Friday 10th June 2016

Monday 6th June 2016
09:00 to 09:50 Registration
09:50 to 10:00 Welcome from Christie Marr (INI Deputy Director) INI 1
10:00 to 11:00 Richard Katz (University of Oxford)
Workshop introduction, context, and review of previous workshops
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Douglas Wiens (Washington University in St. Louis)
Seismic imaging of mantle melting processes beneath volcanic arcs and backarc spreading centers
Co-author:  S. Shawn Wei  (Washington University in St Louis; now at Scripps Institition of Oceanography)

Seismological studies using land and ocean bottom seismographs can help constrain models of mantle melting by imaging velocity anomalies resulting from the presence of partial melt.   Arc-backarc systems are particularly interesting, as they involve both flux and decompression melting mechanisms, variable water input into the melting process, and various levels of interaction between arc and backarc.   In addition, an extensive dataset of petrological and geochemical measurements also provide important constraints.   Seismic tomographic results imaging arc-backarc systems show extensive upper mantle regions with velocities that are too slow to be explained without invoking partial melt.   In the Mariana arc, mantle seismic anomalies beneath the arc and backarc spreading center are separated by a high velocity, low attenuation region at shallow depths (< 80 km), implying distinct arc and backarc melting regions, with the anomalies coalescing at greater depths.   Large slow velocity anomalies delineate the regions with significant melt, extending from 10-50 km depth beneath the backarc and 40-80 km depth beneath the volcanic arc, consistent with final melt equilibrium depths estimated from basalt thermobarometry.  In the Lau basin, backarc spreading center basalts show a rapid transition from MORB-like chemistry in the north to back-arc basin basalts with strong water and slab-derived geochemical components in the south as the distance between the spreading center and the volcanic arc is reduced.   Slow seismic velocity anomalies beneath the spreading center extend deeper and farther west in the north, suggesting that partial melting occurs along an upwelling limb of mantle flow originating in the ambient mantle west of the backarc, but this feature is missing in the south, indicating that the southern ridge samples only mantle in the vicinity of the subducting slab, consistent with its high water content.  The amplitude of the observed Lau backarc seismic anomalies have an inverse relationship to inferred mantle water content, suggesting that water reduces the melt porosity.   Water may increase the efficiency of melt transport and reduce porosity by lowering the melt viscosity, increasing grain size through faster grain growth, or by causing a different topology of melt within the mantle rock.    A lower melt porosity for aqueous melts is also consistent with the smaller amplitude seismic anomaly seen for the water-rich volcanic arc melting regions compared to the backarc melt production zone.    Seismic attenuation studies show very high shear attenuation beneath the backarc spreading center consistent with high temperatures and partial melt.  Perhaps most surprisingly, we also observe strong bulk attenuation, suggesting that partially molten mantle absorbs seismic energy with some poorly understood dissipative process.

12:30 to 13:30 Lunch @ Wolfson Court
14:00 to 14:45 Garrett Ito (University of Hawaii)
Magma generation and extraction beneath mid-ocean ridges and oceanic hotspots
Much knowledge about the physics of melt generation and migration in the mantle has come from seismic imaging and geodynamic modelling studies of mid-ocean ridges (MORs) and oceanic hotspots.  Global-scale seismic studies show evidence for incipient, perhaps volatile rich, melting starting at depths of ~150 km beneath MORs.  Variations in the width of the seismically-imaged melting zone as well as asymmetries in this zone across MORs reveal important influences of mantle flow on melt generation.  Enhanced temperatures and mantle upwelling rates associated with mantle plumes are especially important in giving rise to local peaks in melt generation at hotspots.  The upper-mantle seismic structure of plumes can in some cases (Iceland) be explained by relatively simple models of thermal plume-lithosphere interaction, in other cases suggests more complex thermochemical convection (Hawaii), and in other cases (Galapagos) requires large variations in solid volatile content, temperature, and/or melt content not explained by current models.  The thermo-mechanical process by which melt is extract out of the asthenosphere and enters the lithosphere is poorly understood, but the process can evidently alter the isotropic as well as anisotropic seismic wave speeds over substantial volumes of this boundary beneath MORs and hotspots.  Other seismic studies show evidence that the amount of melt that is retained in the mantle increases as spreading rate decreases at slow spreading rates, thus explaining global trends of crustal thickness at MORs.  Studies also show that more melt is retained in the shallow-most mantle near offsets in ridge segments than near centers of ridge segments.  Together, these findings suggest that the ability of melt to penetrate the asthenosphere-lithosphere boundary is impeded by decreases in melt flux, strain rate, gradients in mantle temperature or a combination of the three.

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14:45 to 15:30 Andrew Turner (University of Oxford)
Grain size and rheology as a control for melt transport beneath mid-ocean ridges
Authors: A. J. Turner, R. F. Katz, and M. D. Behn
Abstract: Grain size is a fundamental control on the rheology and permeability of the mantle. These properties, in turn, shape the transport and extraction of melt from the mantle source. It is therefore important to model the continuum grain-size field as a part of two-phase flow calculations that aim to capture the full spatial variability of melt transport in the upper mantle.
We first consider a two-dimensional, single-phase model to predict the steady-state grain size beneath a mid-ocean ridge.  The model employs a composite rheology of diffusion creep, dislocation creep, dislocation accommodated grain boundary sliding, and a brittle stress limiter. Grain size is calculated using the paleowattmeter model of Austin & Evans (2007). We investigate the sensitivity of the grain size model to parameter variations. Our model predicts that permeability varies by two orders of magnitude due to the spatial variability of grain size within the expected melt region of a mid-ocean ridge.
We then consider a two-phase model to test the influence of spatially varying grain size on melt transport. We find that the rheological coupling of grain size has a greater influence on melt transport than the coupling through permeability. The model predicts that a spatially variable grain-size field can promote focusing of melt towards the ridge axis. This focusing is distinct from the commonly discussed sub-lithospheric decompaction channel. Furthermore, our model predicts that the shape of the partially molten region is sensitive to rheological parameters associated with grain size. The comparison of this shape with observations may help to constrain the rheology of the upper mantle beneath mid-ocean ridges.
15:30 to 16:00 Afternoon Tea
16:15 to 17:00 Taras Gerya (ETH Zürich)
Melt-induced weakening of the lithosphere: theory, numerical implementation and geodynamic implications
Melt-induced weakening can play critical role for enabling lithospheric deformation in the areas of intense mantle-derived magmatism, such as mid-ocean ridges, rift zones and hot spots. It implies significant reduction in the long-term strength of the deforming lithosphere subjected to frequent rapid melt percolation episodes along planar, sharply localized zones (dykes). Mechanical energy dissipation balance shows that the long-term effective strength of the melt-weakened lithosphere is a strain-averaged rather than a time-averaged quantity. Its magnitude is mainly defined by the ratio between melt pressure and lithostatic pressure along rapidly propagating dykes, which control most of the visco-plastic lithospheric deformation. We implemented governing equations for melt-bearing deforming visco-elasto-plastic lithosphere based on staggered finite difference and marker in cell techniques. We then quantified the lithospheric strength by performing 2D numerical experiments on long-term lithospheric deformation assisted by frequent short-term dyke propagation episodes. The experiments showed that the lithospheric strength can be as low as few MPa and is critically dependent on the availability of mantle-derived melt for enabling frequent episodes of dyke propagation. Viscous-plastic deformation is localized along propagating weak dykes whereas bulk of the lithosphere only deforms elastically and is subjected to large deviatoric stresses. Thus, the low strength of the melt-weakened lithosphere is associated with high volume-averaged deviatoric stress. Possible geodynamic implications include (1) establishing of a global tectono-magmatic plume-lid tectonics regime in the Archean Earth and modern Venus as well as (2) enabling of plume-induced subduction initiation that triggered global modern-style plate tectonics on Earth.
17:00 to 18:00 Welcome Wine Reception
Tuesday 7th June 2016
09:00 to 11:00 Sander Rhebergen (University of Waterloo)
Preconditioners for models of coupled magma/mantle dynamics
Numerical techniques are essential in solving the equations governing magma dynamics. Discretizing these equations results in very large systems of (non)linear algebraic equations. For many simulations in two spatial dimensions one can easily use direct methods to solve these discrete systems. For simulations in three dimensions, however, iterative methods are vital since direct methods quickly become very inefficient.

Efficiency of the numerical techniques used to solve the equations of coupled magma/mantle dynamics for a large part depends on the efficiency of the iterative method used to solve the system of algebraic equations. Preconditioners play a very important role in the efficiency of iterative methods as I will discuss in more detail in this talk.

This talk is will be divided into three parts. I will first give an introduction to preconditioners and the challenge of iterative methods for magma dynamics. Afterwards I will discuss the development and analysis of preconditioners designed especially for models of coupled magma/mantle dynamics. I will end this talk by discussing future directions of computational magma dynamics.
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Tobias Keller (University of Oxford)
Computational models of melt transport from source to surface
Melt transport from partial melt sources in the asthenosphere through the lithosphere and crust involves many complexities. Reactive and rheological instabilities lead to strongly localised flow of melt through a deforming and reacting host rock. The resulting regimes of magmatic activity involve a wide range of time and length scales. Numerical modelling offers promising avenues of quantitative research into these phenomena. Yet, the complex nature of melt transport processes poses challenging computational problems requiring robust and efficient numerical techniques. Here, I will present some recent developments in computational magma dynamics, in terms of physical model description, computational methods, and scientific applications. The latter include melt transport across the flow-to-fracture transition for intraplate magmatism in a continental lithosphere, as well as volatile flux-driven reactive melt transport beneath mid-ocean ridges. These examples illustrate both opportunities and challenges for computational modelling of melt transport from source to surface.
12:30 to 13:30 Lunch @ Wolfson Court
14:00 to 14:45 Chloe Michaut (Institut de Physique du Globe de Paris); (Université Paris 7 - Denis-Diderot)
Variability in melt extrusion at silicic volcanoes
Since the 80’s, the monitoring of silicic volcanoes using geophysical techniques has largely been developed around the world. This has allowed important advances on our understanding of magmatic and volcanic processes.
First, the concept of magma chamber has radically changed. Indeed, geophysical surveys do not find large liquid magma bodies below active volcanoes, but only large, diffuse, partial melt zones. Magma chambers are now described as large mush zones located at different levels in the crust and constructed by accumulation of small magma batches over hundreds of millions of years. The two-phase dynamics of a crystal and magma mixture thus controls melt extraction during periods of unrest.
Second, the activity of silicic volcanoes has appeared cyclic and marked by different periods of cyclicity going from tens of years to the second. Some of them are clearly linked to the very different physical properties and behaviors of the different phases present in magmatic systems: crystal, melt and gas.
In the end, at arc-volcanoes, melts extracted from the mantle face a complex and vertically stratified filter: the crust. Understanding the dynamics of a three-phase mixture in a vertically stratified environment is thus crucial for the assessment of eruptive risk, in particular to describe the transfer function characteristic of this crustal filter.
14:45 to 15:30 Boris Kaus (Johannes Gutenberg-Universität Mainz); (University of Southern California)
Modelling magma migration through the continental lithosphere: the importance of multiple pulses and channelized flow.
Oliver Jagoutz (MIT), Wenrong Cao (Rice University), Scott Paterson (University of Southern California), Tobias Keller (Oxford), Lisa Rummel (Mainz)

Whereas a considerable body of works exists on the physics of melt extraction from the hot mantle at mid-oceanic ridges, melt migration through the colder continental lithosphere is less well understood. As 500 million people live in the vicinity of active volcanoes and the most dangerous volcanoes are located on continental lithosphere, it however remains an important topic for the Earth Sciences.   High precision U-Pb dating of batholiths seems to suggest that many of them are formed by an amalgamation of smaller melt pulses. Since those pulses presumably rose at approximately the same location of the lithosphere, it is likely that this changed (and likely weakened) the mechanical state of the lithosphere with time. Here, I will discuss thermo-mechanical models of melt propagation through the cold mantle lithosphere to address the consequences of this mechanical weakening on melt transport. In addition, I will discuss (simple) models of granitic melt intrusion within the continental crust in which diking is incorporated in a parameterized manner and in which melt is emplaced in many pulses. The results of  these models suggests that that both pulses and localized mechanical weakening is of key importance for magma transport. They also show that in other to understand magmatic transport systems, it is insufficient to only focus on the batholiths itself or on the batholith-volcano connection. Instead, magmatic systems are lithospheric-scale systems, and should be modelled as such.  In this respect, many unresolved questions remain and I will discuss some of those.

15:30 to 16:00 Afternoon Tea
16:15 to 17:00 Jenny Suckale (Stanford University)
17:00 to 18:00 Posters & Discussion INI 1
Wednesday 8th June 2016
09:00 to 11:00 Todd Arbogast (University of Texas at Austin)
Mixed Methods for Two-Phase Darcy-Stokes Mixtures of Partially Melted Materials with Regions of Zero Porosity
Co-authors: Marc A. Hesse and Abraham L. Taicher

The Earth's mantle, or an ice sheet, involves a deformable solid matrix phase within which a second phase, a fluid, may form due to melting processes.  The mechanics of this system is modeled as a dual-continuum, with at each point of space the solid matrix being governed by a Stokes system and the fluid melt, if it exists, being governed by a Darcy law.  This system is mathematically degenerate when the porosity (volume fraction of fluid) vanishes.  We develop the variational framework needed for accurate approximation of this Darcy-Stokes system, even when there are regions of positive measure where only one phase exists.  We then develop an accurate mixed finite element method for solving the system and show some numerical results.
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Yasuko Takei (University of Tokyo)
Effect of partial melting on seismic velocity and attenuation: Polycrystal anelasticity at near-solidus temperatures
Co-author: Hatsuki Yamauchi (ERI, Univ. of Tokyo)

Seismic low velocity regions have been detected around the volcanic source regions in the upper mantle, where partial melting is expected to occur. However, temperature of these regions is, for the most part, below the solidus temperature of dry mantle peridotite. This suggests that seismic wave velocity is significantly reduced in the absence of melt or in the presence of a very small amount of melt stabilized by volatiles. Effects of partial melting on the seismic velocity and attenuation have long been studied within the framework of the direct effect of the melt phase, such as poroelastic effect. However, the direct effect is small for small melt fraction, and is difficult to explain the relatively large velocity reduction observed in these regions. Rock anelasticity, which can cause low velocity by grain boundary sliding even without the melt phase, has been considered as a key to solve this problem. However, due to the difficulty of high temperature experiment, we have had a limited understanding of rock anelasticity at the seismic frequencies. We therefore measured anelasticity by using a rock analogue (organic polycrystals). Elasticity, anelasticity, and viscosity were measured continuously from below to above the solidus temperature and the mechanical behavior at near solidus temperatures was clarified over a broad frequency range. The obtained data predict that a steep reduction of seismic shear wave velocity occurs just below the solidus temperature in the absence of melt. Our data also show that the seismic properties are not sensitive to the existence or nonexistence of a very small amount of melt, whereas more than 1 percent melt can cause additional velocity reduction depending on the melt fraction. 
12:30 to 13:30 Lunch @ Wolfson Court
14:00 to 14:45 Son-Young Yi (University of Texas at El Paso)
A four-field mixed finite element method for the Biot model and its solution algorithms
Co-author: Maranda L. Bean 

In this talk, I will present a four-field mixed finite element method for the 2D Biot’s consolidation model of poroelasticity. The method is based on coupling two mixed finite element methods for each subproblem: the standard mixed finite element method for the flow subproblem and the Hellinger-Reissner formulation for the mechanical subproblem. Optimal a-priori error estimates are proved for both semi-discrete and fully discrete problems.

In solving the coupled system, the two subproblems can be solved either simultaneously in a fully coupled scheme or sequentially in a loosely coupled scheme.  I will present four iteratively coupled methods, known as drained, undrained, fixed-strain, and fixed-stress splits, in which the diffusion operator is separated from the elasticity operator and the two subproblems are solved in a staggered way while ensuring convergence of the solution.  A-priori convergence results for each iterative coupling scheme will be proved and confirmed numerically.

14:45 to 15:30 Shun-ichiro Karato (Yale University)
Melting in the deep mantle
Melting in the shallow mantle is well documented. It is caused by the adiabatic ascent of a material or by the addition of “flux” such as water and/or carbon dioxide that reduces the solidus. Melt density and melt morphology (i.e., the dihedral angle) are well known. Consequently, it is possible to interpret some geophysical observations in terms of the presence of melt: in most cases, geophysical anomalies are difficult to attribute to the presence of melt unless the melt geometry is unusual (e.g., zero dihedral angle).            
Melting can also occur in the deep mantle particularly across the mantle transition zone and in the D” layer. Recent experimental studies show that melting is ubiquitous in the deep mantle (deep upper mantle and the lower mantle), but the geochemical and geophysical consequence of melting in the deep mantle is largely unknown. In most cases, melting in the deep mantle is “flux melting” assisted by the volatiles. I will summarize the current status of studies on melting in the deep mantle with the focus on the conditions for melting, chemical composition of the melt and the melt density with the focus on the role of water. Water-induced melting in the lower mantle is extensive and in almost all areas in the lower mantle melting is difficult to avoid unless other materials that dissolve volatiles exists (e.g., metallic Fe). The composition of the melt produced in the lower mantle is (Mg,Fe)O-rich as opposed to the melt produced in the shallow mantle (SiO2-rich). Consequently, the deep mantle melting will affect the chemical evolution of Earth quite differently than the shallow mantle melting. However, two key parameters, namely the density and the dihedral angle, are poorly constrained. A review of current status and a discussion on the future directions will be provided.

19:30 to 22:00 Conference Dinner at Trinity College
Thursday 9th June 2016
09:00 to 11:00 Gabriel Wittum (Goethe-Universität Frankfurt)
An Approach to Large Scale Computing of Problems form Science and Technology
Numerical simulation has become one of the major topics in Computational Science. To promote modelling and simulation of complex problems new strategies are needed allowing for the solution of large, complex model systems. Crucial issues for such strategies are reliability, efficiency, robustness, usability, and versatility.
After discussing the needs of large-scale simulation we point out basic simulation strategies such as adaptivity, parallelism and multigrid solvers. To allow adaptive, parallel computations the load balancing problem for dynamically changing grids has to be solved efficiently by fast heuristics. These strategies are combined in the simulation system UG (“Unstructured Grids”) being presented in the following.
In the second part of the seminar we show the performance and efficiency of this strategy in various applications. In particular, large scale parallel computations of density-driven groundwater flow in heterogenous porous media are discussed in more detail. Load balancing and efficiency of parallel adaptive computations is discussed and the benefit of combining parallelism and adaptivity is shown.
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Samuel Butler (University of Saskatchewan)
Shear Induced Melt Bands: The Mechanics of their Formation and their Possible Role as Melt Conduits Beneath Mid-Ocean Ridges
The compaction equations predict that an instability will occur if the matrix viscosity decreases with porosity and the system is subjected to shear. The instability is manifest as a series of bands of high and low porosity. Porosity bands have been seen in experimental investigations of sheared partial melt systems and the bands are always oriented roughly 25° from the direction of maximum compression and occur on length scales similar to the compaction length and significantly larger than the grain size. Linear instability analysis of the compaction equations predicts that bands should grow fastest at the smallest possible length scale and, for purely porosity-dependent matrix viscosity, parallel to the direction of maximum compression. Various additions to the matrix rheology law have successfully been used to produce bands with orientations similar to those seen in experiments, including strain-rate dependent viscosity, anisotropic viscosity and grain-size and roughness dependent or damage rheology. Furthermore, melt bands have been proposed as high permeability conduits that could channel melt towards the mid-ocean ridge.  In order to be effective channels, the bands must be oriented towards the ridge and their amplitude must be sufficient to result in a significant permeability variation after evolving through a mid-ocean ridge corner flow. In this presentation, I will first present linearized theory and numerical modeling results for melt band formation in 2D in simple and pure shear geometries with the rheology laws listed above in order elucidate the process of melt band formation. I will then present an explanation for the growth of the width of melt bands to sizes greater than that of the initial heterogeneity. I will then present linear theory and numerical modeling results for bands formed when the background velocity field is that of a mid-ocean ridge corner flow in order to assess the efficacy of melt bands as a channeling mechanism for melt to mid-ocean ridges. I will show that the rotation of bands by the mid-ocean ridge flow field causes bands to be poorly oriented to channel melt to the mid-ocean ridge and that the amplitude of the bands is only likely to be sufficient to cause the significant permeability heterogeneity that is necessary to cause channelization if the matrix bulk viscosity is small.
12:30 to 13:30 Lunch @ Wolfson Court
14:00 to 14:45 Tim Schulze (University of Tennessee)
The rapid advance and slow retreat of a mushy zone
Co-author: Nick Gewecke (Dalton State College)

We discuss a model for the evolution of a mushy zone which forms during the solidification of a binary alloy cooled from below in a finite domain. Our focus is on behavior of the system that does not appear when either a semi-infinite domain or negligible solute diffusion are assumed. The problem is simplified through an assumption of negligible latent heat, and we present a numerical scheme that will permit insights that are critical for developing a more general procedure. We demonstrate that a mushy zone will initially grow rapidly, then slows down and eventually retreats slowly. The mushy zone vanishes after a long time, due to being overtaken by a slowly-growing solid region at the base of the tank. Further results for mushy zones growing from boundaries cooled well below the eutectic temperature and for systems with partial solute rejection will also be discussed.
14:45 to 15:30 David Rees Jones (University of Oxford)
Salt fluxes from sea ice: simple models of reactively dissolved channels
Sea ice is a geophysically important material that bears some similarity to the partially molten mantle. Newly formed sea ice contains a significant amount of salt as liquid brine in the interstices of a permeable ice matrix through which the brine can flow. Compositional convection drives fluid motion within porous sea ice. The convective circulation leads to the development of so-called 'brine channels,' liquid channels formed by a dissolution reaction. I discuss the physical mechanisms that create and sustain these channels. Some aspects of these mechanisms may apply to reactive channelization of magmatic flow through the mantle beneath mid-ocean ridges, for example.

Salt fluxes through brine channels are an important buoyancy forcing for the polar oceans, with implications for ocean mixing and deep-water formation. I develop a simple, semi-analytical Chimney-Active-Passive (CAP) model of convection in sea ice. I investigate the physical controls on the convective velocities, brine channel size, and salt fluxes. I test my predictions by considering previous laboratory observations of the propagation of dye fronts within the ice and salt fluxes from it. Finally, I take a one-dimensional, thermodynamic sea-ice model of the kind currently used in coupled climate models and parameterize porous convection within a one-dimensional model. The parameterization allows dynamic determination of physical properties and salt fluxes from sea ice. I argue that existing models are likely to overestimate substantially the peak buoyancy forcing of the polar oceans.
15:30 to 16:00 Afternoon Tea
16:15 to 17:00 Ralph Showalter (Oregon State University)
Poro-Inelastic Filtration coupled to Stokes Flow
Models of flow of fluid through saturated inelastic porous media are described. The initial-boundary-value problem consists of a nonlinear diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto-visco-plastic type. Existence and uniqueness of a global strong solution follows from monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi-static momentum equation. The essential sufficient conditions for the well-posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid.

Related Links
17:00 to 18:00 Posters & Discussion INI 1
Friday 10th June 2016
09:00 to 11:00 Timo Heister ; Juliane Dannberg (Texas A&M University)
3D Numerical Modelling of Compressible Coupled Magma/Mantle Dynamics With Adaptive Mesh Refinement
Juliane Dannberg (dannberg[at]math.tamu[dot]edu), Ryan Grove, Timo Heister (heister[at]clemson[dot]edu)

Melt generation and migration are important processes for the evolution of the Earth's interior and impact the global convection of the mantle.
While they have been the subject of numerous investigations, the typical time and length-scales of melt transport are vastly different from global mantle convection, which determines where melt is generated. This makes it difficult to study mantle convection and melt migration in a unified framework. In addition, modelling magma dynamics poses the challenge of highly non-linear and spatially variable material properties, in particular the viscosity.

Here, we present our extension of the community mantle convection code ASPECT, which adds the equations of two-phase flow of melt and solid, as an example for how these challenges can be addressed. First, We will analyse well-posedness, existence, and uniqueness of the problem. Then we will discuss the correct way to do a stable higher order finite element discretization. Finally, the resulting linear system is solved with an iterated solver preconditioned by a Schur complement-based block preconditioner. We demonstrate that applying adaptive mesh refinement to this type of problem is particularly advantageous, as the resolution can be increased in mesh cells where melt is present and viscosity gradients are high, whereas a lower resolution is sufficient in regions without melt. Together with a high-performance, massively parallel implementation, this allows for high resolution, 3d, compressible, global mantle convection simulations coupled with melt migration.

We present benchmarks of our solver to confirm the theoretical results, and apply our software to large-scale 3d simulations of melting and melt transport in mantle plumes interacting with the lithosphere to show robustness and parallel scalability of the linear solver. Our model incorporates the individual compressibilities of the solid and the fluid phase in addition to compaction, and we demonstrate that including these effects can change melt volumes by more than 20%. Moreover, we show how including melting, melt migration and freezing of melt in global convection models can influence convection patterns and the distribution of chemical heterogeneities in the mantle.

Our model of magma dynamics provides a framework for modelling processes on different scales and investigating links between processes occurring in the deep mantle and melt generation and migration.

11:00 to 11:30 Morning Coffee
11:30 to 12:30 Michael Kendall (University of Bristol)
Seismic evidence for melt in the upper mantle
Michael Kendall, School of Earth Sciences, University of Bristol, UK.   
(Co-author) James Hammond, Department of Earth and Planetary Sciences, Birkbeck, University of London, UK.  
A range of seismic measurements can be used to map melt distribution in the deep Earth. These include seismic P- and S-wave velocities derived from tomography, Vp/Vs ratios obtained from receiver functions, and estimates of seismic anisotropy and attenuation. The most obvious melt parameter that seismic data might be sensitive to is volume fraction. However, in many cases such data are more sensitive to the aspect ratio of melt inclusions, which is controlled by the wetting angle. In many active regions these observations are readily explained by silicate melt in the upper 100 km of the mantle. While low wavespeeds may be attributed to thermal effects in tectonically young or actively volcanic regions, in older, tectonically stable regions low velocity anomalies apparently persist even past the decay time of any thermal perturbation, rendering such a mechanism implausible. Low volume melts can also reduce wavespeeds, but their buoyancy should drain them upward away from source regions, preventing significant accumulation if they are able to segregate. Sulfide, ubiquitous as inclusions in lithospheric mantle xenoliths, forms dense, non‐segregating melts at temperatures and volatile fugacities characteristic of even old lithospheric mantle. Modest amounts of sulfide melt can lead to long-term reductions in seismic wavespeeds in areas of the lithosphere and the asthenosphere disturbed by prior melting events that carry and concentrate sulfide.      
12:30 to 13:30 Lunch @ Wolfson Court
14:00 to 14:45 Jerome Neufeld (University of Cambridge)
The permeability of deformable and reactive porous media
Fluid flow in deformable porous media imparts and viscous drag on the solid matrix, causing deformation.  Likewise, flow through reactive porous media may cause dissolution, precipitation, freezing and melting.  Here we will review the theoretical framework for compaction and dissolution in porous media, and introduce a new method for measuring the permeability and bulk modulus of complex porous media.
14:45 to 15:00 Closing Remarks by Organisers INI 1
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons