# Seminars (MIM)

Videos and presentation materials from other INI events are also available.

Search seminar archive

Event When Speaker Title Presentation Material
MIMW01 15th February 2016
10:00 to 11:00
Dan McKenzie Melt generation and extraction from the Mantle
In 1964 Paul Gast discovered that basalts from oceanic islands had quite different radiogenic isotope ratios from those of basalts from spreading ridges, and that these differences required their two source regions to have been separate for Ga. At the time he made this discovery almost all earth scientists believed that the continents had never moved. This belief changed completely over the following five years, to be replaced by a general acceptance that the Earth's mantle is a vigorously convecting fluid with a Rayleigh number of . Gast's discovery, which was quickly confirmed by many other measurements, then slowly became recognised as more and more unexpected. How can the source regions of ocean island basalts remain intact for long periods of time in a vigorously convecting fluid, and, if they are drawn out into thin sheets, as seems almost inevitable, how can melt be extracted preferentially from such a well stirred inhomogeneous material? Attempts to answer these questions have concerned igneous petrologists and geochemists ever since Gast's discovery, and are of central concern to this workshop. Though the resulting work has lead to considerable progress in understanding the process of melt generation, and some progress in understanding how it moves, it has not yet thrown much light on the original question.
MIMW01 15th February 2016
11:30 to 12:30
Paul Asimow Mantle Melting: the achievements, promise, and limits of thermodynamics
This workshop is an opportunity to consider the state of the art in application of thermodynamics to mantle melting. This approach constructs and calibrates Gibbs free energy models for relevant phases, enabling predictions of equilibrium states including phase proportions, compositions, and some physical properties. We will consider the achievements of this approach, its unfulfilled promise, and its theoretical limits.

Under achievements, a body of work has applied the MELTS and pMELTS models to upper mantle magmatism in ocean ridge, back-arc, intraplate, and subduction environments. From 0-3 GPa pressure, models of multicomponent minerals and silicate liquid appear good enough to recover most experimental results, to provide an internally-consistent forward model from source peridotite through melting to the observed volume and composition of magmas, to constrain the potential temperature of source regions, to elucidate the role of water, and more. There have been a few forays into integrating this approach with magma dynamics at various scales.

Under promise, we expect near-future, improved versions that incorporate carbon species, extend to substantially higher pressure, and account for variable speciation in the melt to achieve higher fidelity. Calibration strategies based on a flexible, evolving, community framework will liberate the enterprise from the slow progress of models based on fixed, internally-consistent datasets. Fully coupled, large-scale dynamical simulations incorporating MELTS thermodynamics are practical and close to implementation.

Under limits, we must recall the limitations of the equilibrium assumptions underlying thermodynamics. At some time and length scales these assumptions break down. In a heterogeneous mantle containing species with widely divergent mobility, there must be important roles for kinetics. Progress in incorporating kinetics in major element models has been nearly nil and must be a major focus of our efforts.

MIMW01 15th February 2016
14:30 to 15:30
John MacLennan Observational constraints on mantle melt transport
A number of models of melt extraction have been developed in order to understand the emergence of rapid channelized melt flow. One promising research direction is the study of the behaviour of mantle where fusible heterogeneities sit in a more refractory matrix.
MIMW01 15th February 2016
16:00 to 17:00
Neil Ribe Rothschild Lecture: The Hawaiian Plume: What do Surface Observables Tell Us?
Co-authors: Ulrich R. Christensen (MPI fuer Sonnensystemforschung, Göttingen, Germany), L. Cserepes (Eötvös University, Budapest, Hungary (deceased)), N. Asaadi (Institute for Advanced Studies in Basic Sciences, Zanjan, Iran), F. Sobouti (Institute for Advanced Studies in Basic Sciences, Zanjan, Iran)

The Hawaiian islands are the best known and most studied example of intraplate volcanoes generated by melting in an ascending mantle plume. Fluid mechanical models allow us to explore the link between the intrinsic physical properties of the plume and a variety of signatures that can be observed at the surface. We use two complementary models : a full three-dimensional (3-D) model with temperature- and pressure-dependent viscosity, and an isothermal “lubrication theory” model. The full 3-D model allows surface observables to be calculated directly, while the lubrication model reveals the dynamical scaling laws obeyed by those observables. Because evaluating the scaling laws is 10^9 times faster than running the 3-D model, we can invert them to determine the ranges of plume properties that are compatible with the observed values of the height of the Hawaiian swell, its width, and the total melting rate in the plume. Turning to the geoid anomaly, we discuss recent work showing that the geoid/topography ratio decreases steadily to the northwest, indicating that the plume thins the overriding lithosphere significantly . Finally, we study an extended lubrication model with a non-Newtonian rheology, which predicts a swell shape that agrees better with observations than a Newtonian model.
MIMW01 16th February 2016
09:00 to 10:00
John Rudge An overview of the two-phase-flow equations for magma dynamics
The equations of two-phase-flow arise from statements of conservation of mass, momentum, and energy. In addition to the conservation laws, a series of phenomenological laws must be prescribed to describe the interaction between the two phases. It is the choice of these phenomenological laws that makes two-phase-flow theory challenging.

In this presentation I will outline the choices of phenomenological laws that have been used thus far in magma dynamics, and their physical consequences. I will give an overview of the basic physics of compaction, and the important role of the compaction length, the natural length-scale in compaction problems. I will highlight which areas of the theory seem robust, and which are in need of further development.
MIMW01 16th February 2016
10:00 to 11:00
Marc Spiegelman The classics: Understanding the basic behavior of the "McKenzie" Equations
Given a set of consistent conservation equations for two-phase flow in deformable porous media, this presentation strives to develop a better physical intuition into their behavior through a series of classical model problems. These problems illustrate the basic behavior of the equations as well as highlighting some of the open questions and continuing mathematical/computational issues involved with their solution.

We begin by emphasizing that the solid velocity field can be usefully decomposed into incompressible and compressible components. Incompressible flow is governed by Stokes equation for porosity driven convection, while compressible flow is governed by a non-linear wave equation for the evolution of porosity. The driving force for non-linear waves is the non-linearity between porosity and permeability. However, the waveforms and propagation speed depend on the solid bulk rheology. Depending on choice of solid rheology, these waves can manifest as kinematic shocks, non-local dispersive solitary waves and wave-trains (poro-viscous) or diffusive porosity waves (poro-elastic). However, these waves all arise to accommodate variations in melt flux on scales much larger than the compaction length. We will also consider other localization phenomena that occur on scales smaller than the compaction length including the development of melt-bands due to shear of a solid with poro sity weakening shear viscosity, and channel formation due to simplified reactive flow.

These equations demonstrate a rich array of behavior, all arising from the rheological response of a deformable solid to variations in fluid flux. These solutions suggest that magma transport in the mantle is strongly localized and time-dependent. While considerable uncertainties in the formulations remain, the general framework is computationally tractable and provides a quantitative framework for investigating coupled fluid/solid mechanics in the Earth.
MIMW01 16th February 2016
11:30 to 12:30
Sash Hier-Majumder Partial Melting Above the Mantle Transition Zone
Recent seismic observations indicate the presence of a low velocity layer above the mantle transition zone. Marked by a reduction of shear wave speed, the top of this layer is generally detected around a depth of 350 km. In this talk, I will present an analysis of seismic data quantifying the amount of melt present in this region, stability of this partially molten layer over geologic time, and the possible origin of the layer in the context of crystallization of the Earth's mantle from a magma ocean.
MIMW01 16th February 2016
14:30 to 15:30
Ian Hewitt Two-phase-flow dynamics in ice sheets
Co-author: Christian Schoof (University of British Columbia)

The dynamics of large ice sheets have many similarities with mantle and magma dynamics. Polycrystalline material undergoes intense shear and creep deformation, slow evolution of grain structure, and dissipative heating that can cause partial melting. The presence of melt (water) can enhance creep and facilitates sliding past bedrock and sediments, leading to extreme patterns of ice flow, most clearly demonstrated in the Antarctic and Greenland ice streams.

In this talk I will review this related application of the two-phase flow equations often used to describe melt in the mantle. I will focus especially on polythermal ice, when the quantities of interest are the heat and water content together with their transport, and on the subglacial drainage system, which is thought to exhibit channelized flow similar (perhaps) to the mantle. Approximations used in the ice-sheet literature will be discussed, along with numerical solution methods for the resulting models. I will highlight analogies and difference with mantle models.
MIMW01 16th February 2016
16:00 to 17:00
S. Majid Hassanizadeh Advanced theories of two-phase flow in deformable porous media, including fluid-fluid interfaces
Two-phase flow in porous media is traditionally modeled using a modified form of Darcy’s law, two volume balance equations, and a so-called capillary pressure-saturation relationship. Darcy’s Law was proposed more than 150 years ago for the flow of a single fluid in soil. Since then, this equation, in almost original form, has been assumed to be applicable to more and more complicated porous media. But, there are many shortcomings of the so-called extended Darcy’s Law. The general understanding is that capillary pressure is equal to the difference in pressures of two fluids. It is assumed to be an algebraic empirical function of saturation. This empirical relationship for capillarity has been studied extensively in soil physics, subsurface hydrology, and petroleum engineering, because of its central role in multiphase-flow theory. Yet, the standard theory of capillarity has a mostly empirical character. The macroscale capillary pressure-saturation relationsh ip cannot be derived from basic physical principles or using averaging methods. Moreover, it is known to be hysteretic (i.e., it depends on the history of the fluids’ distribution) and rate-dependent (i.e., it depends on the rate of flow or rate of change of saturation). We present a new theory of two-phase flow, which comprises a truly extended Darcy’s law and a new capillarity theory, which has four main features: i) pressure gradient is not the only driving force, ii) capillary pressure is an intrinsic property of the porous medium and is not only a function of saturation but also fluid-fluid specific interfacial areas, iii) similarly, effective stress parameter is a function of fluid-fluid specific interfacial area as well as saturation, and iv) there is a dynamic (or non-equilibrium) capillarity effect. We provide experimental evidences for the validity of the new theory. Also, pore-scale and continuum-scale simulations are used to study the possible significance of the new theory at various scales.

MIMW01 17th February 2016
09:00 to 10:00
David Bercovici Interface effects in two-phase phase physics
Most theories of two-phase compaction theory converge to the same set of governing equations for geologically relevant limits.  However not many include the infuence of surface energyand thermodynamics on the interface between phases.  The effect of interface surface energyhas multiple effects in two-phase flows including capillary forces and wetting, self-separation, and is even at the heart of void-generating damage theories.  Moreover, surface energy effectsdrive coarsening in mixtures and grained media (e.g., Ostwald ripening or normal grain-growth), nucleation during phase changes, and blocking or Zener pinning of migrating grain boundaries.  Surface thermodynamics is, again, central to grain-damage theories, and the combined influence ofgrain-growth, interface coarsening, Zener pinning and damage in two phases allows a reasonable model for lithospheric localization and plate tectonic generation. Finally, a new theory for diffuse interface capillary effects might provide a means for band width selection in melt-shear band instabilities.
MIMW01 17th February 2016
10:00 to 11:00
Viktoriya Yarushina (De)compaction waves in porous viscoelastoplastic media and focused fluid flow
Co-authors: Yuri Podladchikov (Institut des Sciences de la Terre, University of Lausanne), Ludovic Raess (Institut des Sciences de la Terre, University of Lausanne), Nina Simon (Institute for Energy Technology)

Understanding of tectonic processes and melt transport in the deep Earth and management of commercially valuable hydrocarbon resources and engineering operations such as CCS in the shallow Earth are dependent on our knowledge about interaction between rocks and fluids. Rock-fluid interaction involves heat and mass transfer, deformation, hydrodynamic flow and chemical reactions, thereby necessitating its consideration as a complex process coupling several simultaneous mechanisms. Two most widely used models for coupled fluid flow and rock deformation are poroelastic theory of Biot and poroviscous model of McKenzie. Even though many extensions of these two theories were proposed in recent years, there is still a considerable effort directed towards formulation of new two-phase theories. Here, we present a simple mathematical model for nonlinear porous viscoelastoplastic materials. Our main motivation is to establish a simple unifying theory for porous fluid flow in a deformable matrix that is able to capture the range of rheological responses expected within the Earth. These responses can vary from elastic small strain consolidation to plastic porosity collapse from tenths to a few percents of porosity in near-surface sediments and up to high-temperature creep during extraction of melts and metamorphic fluids. Our model is thermodynamically consistent and can be generalized to the more complex multi-phase multi-component systems. Developed framework we apply to study focused fluid flow systems that are often evidenced as dikes, veins or volcanic diatremes in the deep Earth and fluid escape pipes, gas conducting chimneys, mud volcanoes, sand injectites or pockmarks in the shallow Earth. The particular attention is to porosity waves as a flow focusing mechanism.
MIMW01 17th February 2016
11:30 to 12:30
Peter Driscoll Influence of mantle melting on cooling and volatile cycling
Heat lost by melt eruption at the surface is a minor component of Earth’s internal heat budget and normally discarded from thermal history models. However, the strong temperature dependence of global melt production implies that an earlier, hotter Earth produced more melt, increasing internal heat loss via eruptive cooling. To address this we develop simple models for mantle melt production and eruptive cooling, and derive melt heat loss scaling laws. Including a melt heat sink in thermal history models results in more efficient mantle cooling, exacerbating the thermal catastrophe of the mantle, which can be overcome by adjustments to the present-day energy balance. In application to stagnant lid planets, cooling by melt eruption can compensate for slow conductive cooling but is dependent on the fraction of extrusive to intrusive melt. In the same vein, a generalized volatile cycling box-model illustrates how volatile reservoir size depends on melt eruption rates.
MIMW01 18th February 2016
09:00 to 10:00
Anne Davaille Thermal convection in an heterogeneous mantle: plumes, piles, domes, and LLSVPs.
Planetary long-term cooling, as well as surface phenomena such as plate tectonics, volcanoes and earthquakes, are mainly controlled by the existence and patterns of convective motions in the solid-state mantle. The morphology and characteristics of convective patterns strongly depends on the mantle physical properties and the existence of density heterogeneities.

I shall review how the interplay of the latter with thermal convection produces mantle instabilities of widely varying morphology and time-dependence, according to the magnitude of the density anomalies and the type of mantle rheology. They could therefore explain the diversity of hot spot volcanism observed on Earth, as well as the mantle structures revealed by seismic tomography.
MIMW01 18th February 2016
10:00 to 11:00
Andrea Tommasi Feedbacks between deformation and melts in the upper mantle
Co-authors: Katherine Higgie (CNRS & Universite Montpellier, France), Veronique Le Roux (WHOI, USA), Vincent Soustelle (University Wuhan, China), Virginie Baptiste (CNRS & Universite Montpellier, France), Alain Vauchez (CNRS & Universite Montpellier, France), Jean Louis Bodinier (CNRS & Universite Montpellier, France)

Experiments and theoretical considerations predict feedbacks between deformation and melts, namely strain localization controlled by the presence of melts and melt focusing controlled by deformation. Yet, peridotite massifs and mantle xenoliths, which record deformation and melt transport through the shallow mantle (lithosphere and lithosphere-asthenosphere boundary), feature a wide variety of relations between melts and deformation. These relations range from strong feedbacks between deformation and melt distribution to absence of any relation between the two processes. We will present an overview of the different types of relations between deformation and melts observed in the field (km to cm scale) and in thin sections (mm scale) and highlight the questions these observations bring.
MIMW01 18th February 2016
11:30 to 12:30
Christopher MacMinn Large deformations in soft porous materials: Squishing, swelling, and yielding
In an elastic solid, the state of stress depends on the displacement of material points from a relaxed reference state. In a poroelastic solid, the mechanics of the solid skeleton are additionally coupled to flow through the pore structure. The classical theory of linear poroelasticity captures this coupling by combining Darcy’s law with Terzaghi’s effective stress and linear elasticity in a linearized kinematic framework. This is a good model for very small deformations, but it becomes increasingly inappropriate for moderate to large deformations, which are common in the context of phenomena such as swelling and damage, and for soft materials such as gels and tissues. Here, we review the well-known theory of large-deformation poroelasticity and then consider the implications of large deformations in the context of two model problems: (1) Classical uniaxial consolidation and (2) the swelling and drying of a spherical gel.

MIMW01 18th February 2016
14:30 to 15:30
Christian Huber Multiphase transport, flirting with the limits of continuum models
Co-authors: Salah Faroughi (Georgia Tech), Hamid Karani (Georgia Tech), Andrea Parmigiani (ETH)

Multiphase flows can be found in a wide variety of Earth and Planetary Systems. Solving for mass, momentum and energy conservation becomes difficult because they are regulated by dynamic interfaces between the different components. Here, we will discuss the merits of continuum (spatially averaged) and discrete scale (granular where interfaces are explicitly treated) approaches in the light of different applications ranging from Planetary Sciences (water on Mars), to volcanology (bubble dynamics and rheology) and finally hydrology (heat transfer in porous media). The goal of the presentation is to discuss the necessity to develop a framework consistent with the granular scale (downscaling) as well as different elements of approaches for upscaling (effective medium theory, fractional derivatives).
MIMW01 18th February 2016
16:00 to 17:00
Joe Dufek Multiphase Flow in Crustal Magmatic Processes
Multiphase dynamics in crustal magmatic processes have analogy with many processes occurring in the mantle and span phenomena from slow, dense granular flows to rapidly shearing granular flows during volcanic eruptions. In this talk I will discuss these two end-members in the context of magma chamber dynamics and eruptive dynamics. In the magma dynamics case, the efficiency of the relative motion between melt and crystals produces distinct compositional trends that can be compared with the chemistry of melts and phase equilibria. This work will consider differentiation scenarios in both simplified magma reservoir geometries and those that are emergent with the successive input from intrusions in an open system. Evidence of open systems and assembly of magmatic systems incrementally are present in a range of plutonic and volcanic rocks. To evaluate the timescales of silicic magma production, a multiphase dynamics model will be discussed that includes heat transfer, phase equil ibria and relative motion between a melt and several crystal phases. A particular focus of this presentation is a comparison of dynamic processes to proxies used as chronometers. The other end-member considered are flows produced during explosive eruptions. During explosive eruptions the interstitial fluid is often a gas and the granular flow has significant inertia. I will compare and contrast granular stress concentration, entrainment, and fluid expulsion in this regime as well as discuss the prospects for integrating a range of laboratory experimental and numerical approaches.
MIMW01 19th February 2016
09:00 to 10:00
Marc Hesse Pore-scale controls on core formation in planetesimals
Co-authors: Soheil Ghanbarzadeh (University of Texas at Austin), Masa Prodanovic (University of Texas at Austin)

Pore-scale melt distribution is thought to evolve towards textural equilibrium. The topology of these pore-scale melt networks is controlled by the porosity and the dihedral angle at the contact line between two solid grains and the melt. I will present three-dimensional computations of texturally equilibrated melt networks in realistic poly-crystalline materials that have been obtained from x-ray diffraction contrast tomography. Our simulations show strong hysteresis in the topology of melt networks with large dihedral angles. A percolation threshold at dihedral angles above 60 degrees is generally thought to prevent rapid core formation in planetesimals by segregation of metallic melts. However, primitive achondrites show that the incipient melt fractions are between 25% and 35% and that metallic melt is connected despite dihedral angles of approximately 90 degrees. Our simulations show that hysteresis allows such a high porosity and high dihedral angle melt network to rem ain connected during drainage of the metallic melt. This provides a mechanism for rapid core formation in planetesimals by porous flow. Only a very small melt fraction, approximately 1%, is trapped and left behind in the silicate mantle after melt segregation. This may provide an explanation for the "excess siderophile problem" in the Earth.
MIMW01 19th February 2016
10:00 to 11:00
Richard Katz Treatment of energy and composition in models of magma/mantle dynamics and implications for reactive flow
Co-authors: Tobias Keller (University of Oxford), Andrew Turner (University of Oxford), Samuel Weatherley (Geological Survey of Denmark and Greenland)

There are relatively few theoretical studies of magma/mantle dynamics that incorporate conservation of energy and species mass in a consistent way. Doing so remains a challenge, both technically in terms of solving the equations, and scientifically in terms of formulating them in a way that is both physically reasonable and sufficiently simple. In this talk I review previous and current approaches to this problem. I highlight the importance of this treatment by discussing the question of reactive channelisation of magma. Reactive channelisation is thought to be an important process in melt transport, helping to explain some observed geochemical signals. It turns out that the behaviour of reactive-flow models depends in important ways on the way that energy and composition are treated. I discuss how mantle heterogeneity and the presence of volatile elements may be essential for channelised flow.

MIMW01 19th February 2016
11:30 to 12:30
Dave May Geodynamics and Two-Phase Flow: A Computational Perspective
The system of partial differential equations used in geodynamic contexts to study melt migration define the evolution of a two-phase system comprised of a highly viscous, porous crystalline mantle rock ("solid" phase) through which low viscosity magma ("fluid" phase) can flow. Typical geodynamic two-phase flow scenarios are characterized by rheological non-linearities, localization and flows possessing a range of characteristic length scales.

From a computational stand point, the inherently stiff and non-linear coupling between the fluid and solid phases, together with the typical flow characteristics associated with geodynamic processes represent a number of challenges with respect to: (i) the choice of primary variables; (ii) the choice of temporal and spatial discretisation scheme, and (iii) the development of efficient techniques for solving the discrete system of equations.

Within the context of these three themes, I will review the commonly adopted philosophies, computational methods and software used by the geodynamics community to study the dynamics two-phase flow systems. Trade-offs and compromises associated with the scope of the modelling software will be discussed, along with an identification of the numerical components which are presently lacking, or devoid of, rigorous mathematical analysis. Lastly, I will discuss recent algorithmic and software developments of highly efficient and scalable solver-discretisation components which will be crucial in enabling the simulation of high resolution, three-dimensional two-phase flow systems.
MIMW01 19th February 2016
14:30 to 15:30
Matthew Knepley Computational Considerations for Magma Dynamics Simulation
Co-author: Tobin Issac, University of Chicago

The optimal solver for a given problem depends not only on the equations being solved, but the boundary conditions, discretization, parameters, problem regime, and machine architecture. This interdependence means that \textit{a priori} selection of a solver is a fraught activity and should be avoided at all costs. While there are many packages which allow flexible selection and (some) combination of linear solvers, this understanding has not yet penetrated the world of nonlinear solvers. We will briefly discuss techniques for combining nonlinear solvers, theoretical underpinnings, and show concrete examples from magma dynamics.

The same considerations which are present for solver selection should also be taken into account when choosing a discretization. However, scientific software seems even less likely to allow the user freedom here than in the nonlinear solver regime. We will discuss tradeoffs involved in choosing a discretization of the magma dynamics problem, and demonstrate how a flexible mechanism might work using examples from the PETSc libraries from Argonne National Laboratory.
MIM 3rd March 2016
14:30 to 15:30
Jed Brown Building a community model for robustness and extensibility
MIM 10th March 2016
14:15 to 15:30
Takehiro Koyaguchi The diversity of eruption styles of silicic magmas
MIM 17th March 2016
14:15 to 15:30
David Rees Jones Solidification of 'mushy layers': the role of convection
MIM 17th March 2016
15:30 to 16:30
Meng Tian Compaction-driven fluid flow during metamorphism: its impacts on CO2 transfer, thermal advection and its competition with porous convection
MIM 21st March 2016
16:00 to 17:00
Jan Nordbotten Emerging fractal structure in freezing of brine
MIM 31st March 2016
14:15 to 15:30
Urmi Dutta Jets and plumes in Earth system: how they ascend
MIM 7th April 2016
14:15 to 15:30
Kundan Kumar Iterative methods for coupled flow and geomechanics problems
MIM 8th April 2016
16:00 to 17:00
Maarten de Hoop Inverse problems in seismology with a view to the mantle
MIMW02 11th April 2016
10:00 to 11:00
David Kohlstedt From stress-driven to reaction-driven melt segregation – the frog’s eye view (1)
Co-authors: Matej Pec (University of Minnesota), Ben Holtzman (Columbia University)

Separation of melt from residual solid and its migration from beneath a mid-ocean ridge to Earth’s surface require a transition from porous to channelized flow in order to preserve chemical and radiogenic disequilibrium. Chemically isolated, high-permeability melt conduits in Earth’s mantle develop as a consequence of instabilities in the deformable and dissolvable porous media. Models for the formation of such flow instabilities include stress-driven and reaction-driven melt channelization.

Melt rising from depth becomes under saturated in pyroxene with respect to the surrounding upper mantle; thus, pyroxene dissolves into the melt as it migrates toward the surface. Tabular rocks rich in olivine and depleted in pyroxene found in peridotite massifs serve as channels for rapid melt extraction from the mantle. Formation of such dunite channels involves dissolution-precipitation reactions between mantle rock and percolating reactive melt. Dunite channels also coincide with shear zones, indicating that deformation together with reaction plays an important role during melt channelization.

Understanding stress-driven and reaction-driven melt segregation processes requires a close coupling of experiment with theory. My talk focuses on results from laboratory investigations of the formation and evolution of melt-enriched channels in mantle rocks. (i) The first part examines the formation of stress-driven, melt-enriched channels predicted by theory. Here, the experimentally observed alignment of channels motivated further development in theory. (ii) The second part considers experimental investigations of reaction infiltration instabilities in mantle rocks. In partially molten rock samples composed of olivine and pyroxene sandwiched between a source of reactive (pyroxene under-saturated) melt and a porous sink, finger-like melt-enriched channels composed of olivine + melt propagated into and often through the rock in response to a gradient in fluid pressure.
MIMW02 11th April 2016
11:30 to 12:30
David Kohlstedt From stress-driven to reaction-driven melt segregation – the frog’s eye view (2)
Co-authors: Matej Pec (University of Minnesota), Ben Holtzman (Columbia University)

Separation of melt from residual solid and its migration from beneath a mid-ocean ridge to Earth’s surface require a transition from porous to channelized flow in order to preserve chemical and radiogenic disequilibrium. Chemically isolated, high-permeability melt conduits in Earth’s mantle develop as a consequence of instabilities in the deformable and dissolvable porous media. Models for the formation of such flow instabilities include stress-driven and reaction-driven melt channelization.

Melt rising from depth becomes under saturated in pyroxene with respect to the surrounding upper mantle; thus, pyroxene dissolves into the melt as it migrates toward the surface. Tabular rocks rich in olivine and depleted in pyroxene found in peridotite massifs serve as channels for rapid melt extraction from the mantle. Formation of such dunite channels involves dissolution-precipitation reactions between mantle rock and percolating reactive melt. Dunite channels also coincide with shear zones, indicating that deformation together with reaction plays an important role during melt channelization.

Understanding stress-driven and reaction-driven melt segregation processes requires a close coupling of experiment with theory. My talk focuses on results from laboratory investigations of the formation and evolution of melt-enriched channels in mantle rocks. (i) The first part examines the formation of stress-driven, melt-enriched channels predicted by theory. Here, the experimentally observed alignment of channels motivated further development in theory. (ii) The second part considers experimental investigations of reaction infiltration instabilities in mantle rocks. In partially molten rock samples composed of olivine and pyroxene sandwiched between a source of reactive (pyroxene under-saturated) melt and a porous sink, finger-like melt-enriched channels composed of olivine + melt propagated into and often through the rock in response to a gradient in fluid pressure.
MIMW02 11th April 2016
13:30 to 14:30
Wenlu Zhu Physical Properties of Partially Molten Rocks from Microtomography Experiments and Digital Rock Physics
Co-authors: Kevin Miller (Stanford University), Laurent Montesi (University of Maryland), Glenn Gaetani (Woods Hole Oceanographic Institution)

Better constraints on rates of melt migration within the partially molten regions of the upper mantle are required to advance our current understanding of various dynamic processes at ocean ridges. In this study, we synthesized texturally equilibrated mono- and polymineralic aggregates containing various amounts of partial melt and characterized the 3-dimensional (3-D) distribution of melt using synchrotron-based x-ray microtomography. With the availability of the high-resolution 3D melt distribution, we developed digital rock physics models to calculate the physical properties of partially molten rocks. We focus on the characteristic change in melt geometry as a function of melt fraction and lithological variation, and how they affect the transport and elastic properties. Our results indicate that 1) the permeability and melt fraction are related by a power-law relation with an exponent of ~2.7 and geometric factor of 57±28 (Miller et al., 2014); 2) the bulk electrica l conductivity also follows a power-law relationship with melt fraction, with the exponent is ~1.3 and the geometric factor 0.66±0.06 (Miller et al., 2015); 3) in a partially molten rock, in general, the fluid pathways differ from, and are more tortuous than the electric current pathways; 4) lithological melt partitioning is observed: the presence of pyroxene causes melt focusing in olivine-rich regions of partially molten harzburgite. We quantified the effect of lithological partitioning on transport properties.
MIMW02 11th April 2016
14:30 to 15:30
Ken Golden Multiscale analysis of sea ice - a partially melted, polycrystalline composite material
Earth's sea ice packs are key players in the climate system and critical indicators of climate change, as evidenced by the recent precipitous losses of summer Arctic sea ice. As a material, frozen sea water is a polycrystalline composite of a pure ice matrix containing brine inclusions - the melt phase - whose volume fraction and connectivity depend strongly on temperature. The brine phase undergoes a percolation threshold at a critical temperature where the inclusions coalesce to form channels through which the melt phase can flow. Fluid transport through sea ice mediates key climatological and biological processes, and can enhance thermal transport via convection in the porous microstructure.

During the Arctic melt season, the sea ice surface is transformed from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is largely determined by melt pond evolution. As the ponds grow and coalesce, the melt phase undergoes a percolation threshold and the fractal dimension of the pond boundaries transitions from 1 to about 2 around a critical pond size.

In the two lectures, I will discuss mathematical models of composite materials and statistical physics that we have been using to describe the effective fluid, thermal, and electromagnetic transport properties of sea ice, and to address other problems in sea ice physics such as melt pond evolution. I will cover a range of mathematical techniques, some of which may possibly shed light on similar questions for partially molten rock. They include percolation theory, multiscale homogenization, integral representations for effective transport coefficients of composite media, spectral measures and random matrix theory, homogenization for advection diffusion processes, and Ising models. These models have been developed in conjunction with our field experiments in the Arctic and Antarctic. A short video on a recent Antarctic expedition will be shown.
MIMW02 11th April 2016
16:00 to 17:00
Ken Golden Multiscale analysis of sea ice - a partially melted, polycrystalline composite material
Earth's sea ice packs are key players in the climate system and critical indicators of climate change, as evidenced by the recent precipitous losses of summer Arctic sea ice. As a material, frozen sea water is a polycrystalline composite of a pure ice matrix containing brine inclusions - the melt phase - whose volume fraction and connectivity depend strongly on temperature. The brine phase undergoes a percolation threshold at a critical temperature where the inclusions coalesce to form channels through which the melt phase can flow. Fluid transport through sea ice mediates key climatological and biological processes, and can enhance thermal transport via convection in the porous microstructure.

During the Arctic melt season, the sea ice surface is transformed from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is largely determined by melt pond evolution. As the ponds grow and coalesce, the melt phase undergoes a percolation threshold and the fractal dimension of the pond boundaries transitions from 1 to about 2 around a critical pond size.

In the two lectures, I will discuss mathematical models of composite materials and statistical physics that we have been using to describe the effective fluid, thermal, and electromagnetic transport properties of sea ice, and to address other problems in sea ice physics such as melt pond evolution. I will cover a range of mathematical techniques, some of which may possibly shed light on similar questions for partially molten rock. They include percolation theory, multiscale homogenization, integral representations for effective transport coefficients of composite media, spectral measures and random matrix theory, homogenization for advection diffusion processes, and Ising models. These models have been developed in conjunction with our field experiments in the Arctic and Antarctic. A short video on a recent Antarctic expedition will be shown.
MIMW02 12th April 2016
09:00 to 10:00
Grigorios Pavliotis Homogenization methods (1)
MIMW02 12th April 2016
10:00 to 11:00
Grigorios Pavliotis Homogenization methods (2)
MIMW02 12th April 2016
11:30 to 12:30
Yasuko Takei Constitutive mechanical relations of a partially molten rock in terms of grain boundary contiguity: an approach with an internal state variable
Mechanical and transport properties of a partially molten rock strongly depend on the grain scale melt geometry. To quantify the microstructural effects, constitutive mechanical relations for elasticity (Takei, 1998) and diffusion creep viscosity (Takei and Holtzman, 2009) are derived theoretically by considering a realistic microstructural model. The essential geometrical factor which determines these properties was found to be the grain boundary contiguity’’ which represents the area of grain-to-grain contacts relative to the total surface area of each grain. One of the most striking results is that while contiguity affects both elasticity and viscosity, the effect on viscosity is about 100 times larger than that on elasticity. When partially molten rock is texturally equilibrated, contiguity is determined as a function of melt fraction and dihedral angle. However, when it is deformed under a deviatoric stress, contiguity deviates from the equilibrium value an d evolves, resulting in a significant change in the matrix viscosity. Possible consequences of these microstructural evolution on the macroscopic dynamics can be studied within the framework of continuum mechanics by solving the governing equations of two phase flow together with the viscous constitutive relation which includes contiguity as an internal state variable. By applying this approach to the formation of stress-driven, melt-enriched channels, I will demonstrate the important role of microstructural processes in the macroscopic dynamics.
MIMW02 12th April 2016
13:30 to 14:30
Ulrich Faul Experimental constraints on melt distribution and its effect on the rheology and seismic properties of polycrystalline olivine
Coauthors: Gordana Garapić (SUNY New Paltz), Ian Jackson (Australian National University)

Bulk properties of partially molten rocks are significantly affected by the melt distribution and geometry. Surface energy minimisation determines the melt geometry, both locally at the junction of two grains and melt (dihedral angle), and for the aggregate as whole, in the form of grain growth. Grain growth is a continuous process and partially molten rocks therefore constitute a dynamic system. This contrasts with the assumptions of the model melt distribution in a static system with isotropic grains of a single size that can be fully characterised by measuring dihedral angles. In the dynamic system the local melt geometry is not always in its minimum energy configuration, as grain growth continuously creates new neighbours that need to adjust their grain boundary plane orientations. In this dynamic system, the melt distribution can not be characterised by only measuring dihedral angles.
As a somewhat more comprehensive assessment of the melt distribution, we measure the proportion of grain boundaries wetted by melt (grain boundary wetness/contiguity). While deformation experiments in the diffusion creep regime by necessity need to be carried out on fine-grained samples, the melt distribution can be determined on significantly more coarse-grained samples, hot-pressed at high temperatures up to two weeks in a piston cylinder apparatus. The wetness data from these samples, obtained at suitably high resolution, allows augmentation of the experimentally measured diffusion creep rheology.
For the direct experimental determination of the effect of small amounts of melt on both large-strain rheology and seismic properties it is important to characterise genuinely melt-free materials for reference. For this reason we use synthetic Fo90 olivine aggregates that contain no melt or trace elements, unless deliberately added. Experiments with melt-bearing samples show that both the large strain rheology and seismic properties are substantially affected by small amounts of melt, consistent with the observations of the melt distribution described above. For seismic properties the presence of melt affects both the shear modulus and attenuation in the seismic frequency band. Important for the effect of melt on seismic properties are wetted grain boundaries with sufficiently low aspect ratio for local fluid flow to take place (i.e. on the scale of a single grain, ’melt squirt’).
Similar materials are also used to determine the effect of water (hydroxyl) on the rheology and seismic properties of olivine. This allows comparison of the relative effects of water and melt in the upper mantle.
MIMW02 12th April 2016
14:30 to 15:30
Sash Hier-Majumder Cross Scale Modeling of Melt Migration
The migration of melt over length scales of hundreds of kms takes place through grain edge tubules and films with typical dimensions of a few hundred nanometers to a few microns. The volume fraction, shape, and distribution of these tubules and films exert a strong influence on the effective physical properties, anisotropy, and the trajectory of melt migration in the mantle. In this talk, I will outline new techniques for modeling the microstructure in partially molten rocks,their influence on the effective physical properties, and the implications for large scale magma flow.
MIMW02 12th April 2016
16:00 to 17:00
Leila Hashim Reconciling macroscopic olivine grain growth with the microscopic physical properties of the intergranular medium
Co-authors: Gardés Emmanuel (CNRS - Université Caen), Sifré David (CNRS - Université d'Orléans), Morales Luiz F.G. (GFZ Potsdam), Précigout Jacques (CNRS - Université d'Orléans), Gaillard Fabrice (CNRS - Université d'Orléans)

Grain size is a critical parameter for the understanding of our planet’s mantle since it has considerable impact on seismological properties, on the permeability of mantle rocks and therefore on melt migration characteristics of Earth’s interior. Grain growth therefore becomes an important process that should be meticulously determined in order to better understand the dynamics of our planet’s interior.

Olivine grain growth has therefore been experimentally determined by a wide number of grain growth studies where different effects have been considered (water, fO2, melt, secondary phases). However, no clear consensus on the values of the different material-dependent parameters in the empirical law has been reached. To increase the existing database on olivine grain growth, we experimentally investigated the effect of melt (from nominally melt-free to 12 wt.% melt) and water on San Carlos olivine under different pressure-temperature-duration conditions (0.3 GPa
By combining the existing database on olivine grain growth and our experimental data, we have succeeded in modeling (i) genuinely dry olivine grain growth aggregates, through grain boundary diffusion-controlled processes, (ii) H2O-oversaturated olivine aggregates and (iii) melt-bearing olivine aggregates, from nominally melt-free to ∼ 50 wt.% melt. Different important parameters have been constrained by using our model, namely the dry effective grain boundary thickness (δ ∼ 6 nm), melt contents in nominally melt-free samples (Φ ≤ 0.5 wt.%) as well as the wetting properties (Ψ) of melt as a function of melt content, pressure and temperature. We expect that our results will not only have considerable implications on the grain size-dependent deformation mechanisms of mantle rocks but also reconcile macroscopic observations to microscopic-scale key processes governing the mantle behavior, particularly in intergranular zones impregnated by low melt content s.
MIMW02 13th April 2016
09:00 to 10:00
Grigorios Pavliotis Homogenization methods (3)
MIMW02 13th April 2016
10:00 to 11:00
Grigorios Pavliotis Homogenization methods (4)
MIMW02 13th April 2016
11:30 to 12:30
Gideon Simpson Application to McKenzie model (1)
MIMW02 13th April 2016
13:30 to 14:30
Gideon Simpson Application to McKenzie model (2)
MIMW02 13th April 2016
14:30 to 15:30
Yann Capdeville Non-periodic homogenization for seismic forward and inverse problems
The modeling of seismic elastic wave full waveform in a limited frequency band is now well established with a set of efficient numerical methods like the spectral element, the discontinuous Galerking or the finite difference methods. The constant increase of computing power with time has now allow the use of seismic elastic wave full waveforms in a limited frequency band to image the elastic properties of the earth. Nevertheless, inhomogeneities of scale much smaller the minimum wavelength of the wavefield associated to the maximum frequency of the limited frequency band, are still a challenge for both forward and inverse problems. In this work, we tackle the problem of elastic properties and topography varying much faster than the minimum wavelength. Using a non periodic homogenization theory and a matching asymptotic technique, we show how to compute effective elastic properties and local correctors and how to remove the fast variation of the topography. The implications on the homogenization theory on the inverse problem will be presented.
MIMW02 14th April 2016
10:00 to 11:00
Harro Schmeling Physics of mantle melting: two-phase flow, variable matrix viscosity and density effects
In the introduction different partially molten regions within the earth's mantle will be identified. Then, the governing equations are introduced with emphasis on rheology, melt density, and solution strategies. The melt fraction and its geometrical distribution has an important influence on the shear and bulk viscosity of the matrix. A new semi-analytical model is introduced which may describe the geometrical distribution of the melt phase. Combined with a poro-elastic effective medium approach (Schmeling et al., 2012) effective shear and bulk viscosity can be estimated as a function of melt fraction. Models of 2D porosity waves are shown which use such effective viscosity laws. Another important quantity is the melt density which may be higher than the matrix density at transition zone depths. 1D models of a rising hot partially molten plume show that within a certain parameter regime standing porosity waves may develop. If there is time, I will briefly mention a simple mantle convection benchmark initiative with two-phase flow in its partially molten region. Schmeling, H., J.-P. Kruse, and G. Richard, 2012: Effective shear and bulk viscosity of partially molten rock based on elastic moduli theory of a fluid filled poroelastic medium. Geophys. J. Int., doi: 10.1111/j.1365-246X.2012.05596.x
MIMW02 14th April 2016
11:30 to 12:30
Ralph Showalter Multiscale Systems for Flow and Transport
An elliptic-parabolic system of partial differential equations describes the flow of a single-phase incompressible fluid and the transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium.  The objective is to develop an upscaled model of this system which represents the full range of scales observed.  After a review of homogenization results for the traditional low contrast and the $\epsilon^2$-scaled high contrast cases, the new discrete upscaled model based on local affine approximations is constructed. It reproduces the full range of scale contrasts observed in experiments.
MIMW02 14th April 2016
13:30 to 14:30
Claude le Bris Stochastic homogenization (1)
MIMW02 14th April 2016
14:30 to 15:30
Claude le Bris Stochastic homogenization (2)
MIMW02 14th April 2016
16:00 to 17:00
Stephen Morris The rippling instability of icicles
Co-authors: Jake Wells (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Alina Barnett (Dept. of Physics, McMaster University of Toronto, Hamilton ON Canada L8S 4M1), Josh Calafato (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Ken Liao (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7), Antony Szu-Han Chen (Southern Alberta Institute of Technology, Calgary AB Canada T2M 0L4), John Ladan (Dept. of Physics, University of Toronto, Toronto ON Canada M5S 1A7)

Icicles are a common ice formation, familiar to anyone who lives in a cold climate. The shape of an icicle emerges from a delicate dance between solidification, hydrodynamics and heat transport. Many, but not all, natural icicles are observed to be decorated around their circumference by ribs or ripples. These features are presumed to be the result of a morphological instability in the growth process of the ice. The sides of an icicle are covered by a thin supercooled water film which flows down their nearly vertical surface. The wavelength of the ripples, which is always found to be near 1~cm, is surprisingly constant, even under diverse growing conditions. A recent detailed study in which hundreds of icicles were grown in controlled laboratory experiments revealed that trace amounts of impurities are required for the formation of the ripples. Icicles grown from distilled water have no ripples. Ripples appear at a remarkably low concentration of impurity, becoming me asurable above a concentration of just 10−3 weight \% of salt. Thereafter, they grow at a rate which is roughly logarithmic in the concentration of the impurity. These effects are not explained by linear stability theory which does not account for impurities.

In this talk, we will discuss our recent experiments in which the concentration and molecular species of the impurity were varied, as well as our progress toward a generalized linear stability analysis of the growing ice surface, which includes the effects of impurities. The theory crucially depends on the boundary conditions on the ice-water interface and the possible presence of a mushy layer near this interface.

MIMW02 15th April 2016
10:00 to 11:00
Claude le Bris Stochastic homogenization (3)
MIMW02 15th April 2016
11:30 to 12:30
Claude le Bris Stochastic homogenization (4)
MIMW02 15th April 2016
13:30 to 14:30
Neil Ribe Evolution of Anisotropy in Olivine Polycrystals
Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystallographic preferred orientation or CPO) whose observable signatures include shear-wave splitting and azimuthal dependence of surface wave speeds. Comparison of these signatures with mantle flow models thus allows mantle dynamics to be unraveled on global and regional scales. However, existing self-consistent models of CPO evolution are computationally expensive when used in 3-D and/or time-dependent convection models. We propose a new method, called ANPAR, which is based on an analytical parameterization of the crystallographic spin predicted by the second-order (SO) self-consistent theory. Our parameterization runs ≈2–6\times 10^4 times faster than the SO model and fits its predictions for CPO and crystallographic spin with a variance reduction >99 per cent. We illustrate the ANPAR model predictions fo r the deformation of olivine with three dominant slip systems, (010)[100], (001)[100] and (010)[001], for three uniform deformations (uniaxial compression, pure shear and simple shear) and for a corner-flow model of a spreading mid-ocean ridge.
MIMW02 15th April 2016
14:30 to 15:30
Lars Hansen The development of seismic anisotropy in partially molten rocks: Laboratory observations
Co-authors: Chao Qi (University of Pennsylvania), David Wallis (University of Oxford), Benjamin Holtzman (Lamont-Doherty), David Kohlstedt (University of Minnesota)Seismic anisotropy is a key indicator of the kinematics of flow in the upper mantle. Much insight has been gained into seismic anisotropy that results from the crystallographic alignment of olivine during deformation. This anisotropy is primarily characterized by alignment of the seismically fast axis with the flow direction. This relationship between olivine anisotropy and the macroscopic kinematics allows detailed comparison between simulations of global mantle flow and seismic tomography. However, relatively little is known about the development of seismic anisotropy in partially molten rocks. Some experimental studies on partially molten rocks suggest that the seismically fast direction tends to lie at high angles to the flow direction, leading to a vastly different relationship between anisotropy and kinematics. Thus, the presence of a melt phase appears to fundamentally alter the grain-scale processes leading to crystallographic rotation of the solid phase.
Here we present a new experimental data set detailing the evolution of anisotropy during deformation of partially molten peridotite. Torsion experiments were conducted on samples composed of San Carlos olivine and basaltic melt at a temperature of 1473 K and a confining pressure of 300 MPa. Seismically fast axes of olivine tend to lie at a high angle to the flow direction in a manner similar to previous experiments. The anisotropy in these samples is weak compared to that in dry, melt-free olivine deformed to similar strains. The anisotropy also exhibits relatively little change in strength and orientation with progressive deformation. Detailed microstructural analyses allow us to distinguish between competeing models for the grain-scale deformation processes, favoring one in which intergranular processes control grain rotations. Based on our observations, we extrapolate our results to flow in the oceanic upper mantle, demonstrating good correlation between predicted and obse rved seismic anisotropy.
MIMW02 15th April 2016
16:00 to 17:00
Andrea Tommasi How do melts change texture and anisotropy of mantle rocks
In a melt-free mantle, development of crystal preferred orientations (CPO or texture) in response to deformation is the major source of anisotropy of physical properties. Measurement of seismic (elastic) anisotropy is indeed the best available tool to unravel flow patterns at various depths in the mantle. Though it cannot be easily measured in situ, anisotropy is even more marked for thermal diffusion and viscosity. These anisotropies probably induce a memory-effect on the thermo-mechanical evolution of the upper mantle. In this presentation, we will address how the presence of melts may change the anisotropy of physical properties in the upper mantle. The presence of melts may: (1) induce an additional (probably stronger) component of anisotropy if the melt is concentrated in aligned pockets or lenses, (2) change the olivine texture evolution and (3) the mineralogical composition. Anisotropy due to melt alignment, though strong, is only effective while melts are present in t he system. The two latter processes induce weaker, but long-term changes in the anisotropy, which remain effective even after melt extraction or crystallization. Observations in naturally deformed peridotites suggest all three processes occur in the upper mantle. Analysis of the spatial arrangement of products of melt-rock reactions in mantle peridotites provides evidence for melt organization in planar lenses or layers parallel to the shear plane at both the grain boundary and larger (cm to tens of meters) scales. Such an arrangement may induce significant decrease in the shear viscosity parallel to the shear plane. Comparison of olivine crystal preferred orientations within and outside melt-focusing domains records changes in the deformation processes and hence on the resulting CPO-induced anisotropy, which depend on the nature of the melt-rock reactions. The latter also controls the crystallization of new minerals, which most often dilutes the anisotropy.
MIM 18th April 2016
16:00 to 17:00
Peter Kelemen Melt transport in the mantle: constraints from field observations and ideas for future work
MIM 21st April 2016
14:15 to 15:30
Alex Song Probing transition zone seismic discontinuities: composition/mixing stratification near the stagnant slab
MIM 28th April 2016
14:15 to 15:30
Mikel Diez From melt in the pores to volcanic eruption: Links between tectonics and magmatism
MIM 5th May 2016
14:15 to 15:30
Paula Antoshechkina Silicate and Carbonatite Melts in the Mantle: Adding CO2 to the pMELTS Thermodynamic Model of Silicate Phase Equilibria
MIM 12th May 2016
14:15 to 15:30
Jacob Jordan Reactive transport in a partially molten system with binary solid solution
MIM 16th May 2016
16:00 to 17:00
Andrew Fowler Two-phase flow in strombolian volcanic conduits
MIM 19th May 2016
14:15 to 15:30
Timo Heister An Introduction to the Mantle Convection Community Project ASPECT
MIM 26th May 2016
14:15 to 15:30
Ryan Grove Discretizations and multigrid solver for problems related to fluid flow
MIMW03 6th June 2016
10:00 to 11:00
Richard Katz Workshop introduction, context, and review of previous workshops
MIMW03 6th June 2016
11:30 to 12:30
Douglas Wiens 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 (
MIMW03 6th June 2016
14:00 to 14:45
Garrett Ito 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.

MIMW03 6th June 2016
14:45 to 15:30
Andrew Turner 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.
MIMW03 6th June 2016
16:15 to 17:00
Taras Gerya 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.
MIMW03 7th June 2016
09:00 to 11:00
Sander Rhebergen 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.
MIMW03 7th June 2016
11:30 to 12:30
Tobias Keller 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.
MIMW03 7th June 2016
14:00 to 14:45
Chloe Michaut 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.
MIMW03 7th June 2016
14:45 to 15:30
Boris Kaus 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.

MIMW03 7th June 2016
16:15 to 17:00
Jenny Suckale tba
MIMW03 8th June 2016
09:00 to 11:00
Todd Arbogast 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.
MIMW03 8th June 2016
11:30 to 12:30
Yasuko Takei 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.
MIMW03 8th June 2016
14:00 to 14:45
Son-Young Yi 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.

MIMW03 8th June 2016
14:45 to 15:30
Shun-ichiro Karato 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.

MIMW03 9th June 2016
09:00 to 11:00
Gabriel Wittum 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.
MIMW03 9th June 2016
11:30 to 12:30
Samuel Butler 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.
MIMW03 9th June 2016
14:00 to 14:45
Tim Schulze 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.
MIMW03 9th June 2016
14:45 to 15:30
David Rees Jones 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.
MIMW03 9th June 2016
16:15 to 17:00
Ralph Showalter 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.

MIMW03 10th June 2016
09:00 to 11:00
Timo Heister, Juliane Dannberg 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.

MIMW03 10th June 2016
11:30 to 12:30
Michael Kendall 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.
MIMW03 10th June 2016
14:00 to 14:45
Jerome Neufeld 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.
MIM 16th June 2016
14:15 to 15:30
Laurent Montesi Melt migration at mid-ocean ridges: A tale in three acts