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Geodynamics

Conferences – so near and yet so far

Conferences – so near and yet so far

Attending conferences is expensive and time consuming, so going to all the conferences relevant for your research topic(s) is an impossible mission. One solution might be to attend (parts of) conferences remotely. Suzanne Atkins, postdoc at ETH Zürich, Switzerland, discusses the pros and cons of remote conferencing.

Last month the Geological Society of London live-streamed their celebration of 50 years of plate tectonics. Here at ETH we joined the love-in, camping out in the lecture theatre for two days. This follows the trend of many conferences to live-stream sessions or make them available on-line afterwards. But can video conferences replace the real thing? And would we want them too?

On paper, there are so many reasons to support video conferencing and replays. The most obvious one is financial. Many students are limited to local conferences and even professors have to watch their expenditure. The eye-watering cost of a large conference like EGU makes annual attendance unfeasible for many scientists, especially when extras like beer are factored in. If you’re only interested in one or two sessions, dropping in remotely makes far more sense than dragging yourself halfway across the continent for an afternoon.

But there are plenty of other reasons. Here at ETH, our flights make up around 60% of the department CO2 budget. Yes, I could take the train but I’m too lazy and impatient (I know, I know), especially if I’m only interested in half the conference. This doesn’t even take into account the vast carbon footprint of the hospitality industry, to which we are contributing every time we stay in a hotel or eat at a restaurant. Remote conference attendance is therefore the only really defensible environmental option.

The attraction of attending a conference where I can sleep in my own bed is high, but for academic parents, or even just academics with a life outside work, the benefits of cutting a few trips off the yearly circuit without missing out are obvious. Especially in the summer season, when we’re all trying to cram in holidays and a bit of teaching-free research time, the seemingly endless round of meetings and workshops can end up feeling more of a chore than a pleasure.

This brings me to my final point in favour. For a remote conference, etiquette is far more flexible than in person attendance. No one at the conference can see you checking your emails, or dipping in and out to talk to students. The university WiFi is nice and reliable. And the quality of the coffee is just so much more … predictable.

So, what are the drawbacks? Why don’t we all switch over immediately? Obviously attending conferences remotely can make it difficult to present your own work and get feedback, which is invaluable for us. We will never be able to fully replicate digitally the experience of a long poster discussion, chatting to someone after a talk, or the serendipitous meeting in the coffee queue.

But there may also be some subtler disadvantages. At cash-strapped institutes, remote conferencing will allow staff and students who otherwise couldn’t attend to see the talks. But it might also lead to pressure, particularly on students and junior researchers, to cut expenditure by never leaving the building. That deprives them of the networking and presentation opportunities that conferences offer. The flip-side of this is that conferences would get boring scientifically. The same few faces would attend every time, starving the community of new ideas and input. Both of these seem somewhat extreme endpoints, which could be guarded against by careful management within institutes and by conference organisers, and the availability of grants and scholarships for attendance.

So all in all, I think I have to conclude that live streaming conferences seems a sensible way to go. I can even head off to my post-conference Friday beer in the common room afterwards. Cheers!

On the influence of grain size in numerical modelling

On the influence of grain size in numerical modelling

The Geodynamics 101 series serves to showcase the diversity of research topics and methods in the geodynamics community in an understandable manner. We welcome all researchers – PhD students to Professors – to introduce their area of expertise in a lighthearted, entertaining manner and touch upon some of the outstanding questions and problems related to their fields. This month Juliane Dannberg from Colorado State University, discusses the influence of grain size and why it is important to consider it in numerical models. Do you want to talk about your research? Contact us!

Juliane Dannberg

When I started my PhD on geodynamic modelling, I was not aware that the size of mineral grains was something I might need to consider in my simulations. To me, grain size was something that sedimentologists need to describe rocks, and not something I had to deal with in my computations. In all the modelling papers I had read, if the mineral grain size was even mentioned, it was always assumed to be constant. However, it turns out that these tiny grains can have huge effects.

I first heard about the importance of grain size in a series of lectures given by Uli Faul when I participated in the CIDER summer program in 2014 (in case you’re interested, the lectures were recorded, and are available here and here). Primarily, I learned that for diffusion creep – the deformation mechanism people predominantly use in convection models – the viscosity does not only depend on temperature, but is also strongly controlled by the grain size, and that this grain size varies both in space and in time.

This made me think. If grain size in the mantle changes by several orders of magnitude, and the viscosity scales with the grain size to the power of 3, didn’t that mean that grain size variations could cause huge variations in viscosity that we do not account for in our models? Shouldn’t that have a major effect on mantle dynamics, and on the evolution of mantle plumes and subduction zones? How large are the errors we make by not including this effect? I was perplexed that there was such a major control on viscosity I had not thought about before, and wanted to look into this further myself.

Luckily, the multidisciplinary nature of CIDER meant that there were a number of people who could help me answer my questions. I teamed up with other participants1 interested in the topic, and from them I learned a lot about deformation in the Earth’s mantle.

How does the mantle deform?
For most of the mantle, the two important deformation mechanisms are diffusion and dislocation creep. In diffusion creep, single defects (or vacancies) – where an atom is missing in the lattice of the crystal – move through this lattice and the crystal deforms. For this type of deformation, the strain rate is generally proportional to the stress, which means that the viscosity does not depend on the strain rate. Many global mantle convection models use this kind of rheology, because it is thought to be dominant in the lower mantle, and also because it means that the problems described using this rheology are usually linear, which makes them easier to solve numerically. Furthermore, this is also the deformation mechanism that depends on the grain size. Usually, it is assumed that the viscosity scales with the grain size to the power of 3:

where ndiff is the diffusion creep viscosity, d is the grain size, m=3, T is the temperature, P is the pressure, and Adiff, E*diff, V*diff and R are constants.

However, if the stress is high (or the grain size is large, Figure 1), dislocation creep is the dominant deformation mechanism. In dislocation creep, linear defects – so-called dislocations – move through the crystal and cause deformation. In this regime, the viscosity depends on the strain rate, but not on grain size. Dislocation creep is generally assumed to be the dominant deformation mechanism in the upper mantle.

Figure 1: Deformation mechanisms in olivine

Why do grains grow or shrink?

In general, from an energy standpoint, larger crystals are more stable than smaller crystals, and so crystals tend to grow over time in a process called Ostwald ripening. The smaller the grains are, and the higher the temperature, the faster the grains grow. One the other hand, the propagation of dislocations through the grains causes so-called dynamic recrystallization, which reduces the grain size if the rock deforms due to dislocation creep. This means that there are always the competing mechanisms of grain growth and grain size reduction, and their balance depends on the dominance of either of the two deformation mechanisms described above – diffusion or dislocation creep:

The left-hand side of the equation describes the change of the grain size d over time, the first term on the right-hand side is grain growth (depending on grain size and temperature), the second term describes grain size reduction (depending the strain rate, the stress, and also on the grain size itself). The parameters Pg, kg, Eg, Vg, R, λ, c and γ are all constants.

If the flow field does not change, grains will evolve towards an equilibrium grain size, balancing grain growth and grain size reduction. In addition, the grain size may change when minerals cross a phase transition. If the mineral composition does not change upon crossing a phase transition (a polymorphic phase transition such as olivine–wadsleyite), there is almost no effect on grain size. But if the composition of the mineral that is stable after crossing the transition is different from the one before, the mineral breaks down, and the grain size is reduced, probably to the micrometer-scale [Solomatov and Reese, 2008].

And what does that mean for the dynamics of the Earth?

As there is a complex interaction between grain size evolution, mantle rheology and the deformation in the mantle, it is not straightforward to predict how an evolving grain size changes mantle dynamics. But it turned out that there had been a number of modelling studies investigating this effect. And they indeed found that grain size evolution may substantially influence the onset and dynamics of convection [Hall and Parmentier, 2003], the shape of mantle plumes [Korenaga, 2005], mixing of chemical heterogeneities [Solomatov and Reese, 2008], the seismic structure of the mantle [Behn et al., 2009], and the convection regime and thermal history of terrestrial planets [Rozel, 2012].

The long way to a working model…

But even knowing all of these things, it was still a long way to implement these mechanisms in a geodynamic modelling code, testing and debugging the implementation, and applying it to convection in the Earth. There were several reasons for that:

Firstly, large viscosity contrasts are already a problem for most solvers we use in our codes, and the strong dependence of viscosity on grain size means that viscosity varies by several orders of magnitude over a very small length scale in the model.

Secondly, considering an evolving grain size makes the problem we want to solve strongly nonlinear: Already in models with a diffusion–dislocation composite rheology and a constant grain size, the viscosity – which is needed to calculate the solution for the velocity – depends on the strain rate, making the momentum conservation equation nonlinear. But an evolving grain size introduces an additional nonlinearity: The viscosity now also depends (nonlinearly) on the grain size, whose evolution in turn depends on the velocity field. In terms of dynamics, this means that there is now another mechanism that can localize deformation. If the strain rate is large, the grain size is reduced due to dynamic recrystallization (as described above). A smaller grain size means a lower viscosity, which again enables a larger strain rate. Due to this feedback loop, velocities can become very high, up to several meters per year, which severely limits the time step size of a numerical model.

Finally, the equation (2) that describes grain size evolution is an ordinary differential equation in itself, and the time scales of grain growth and grain size reduction can be much smaller than changes in the flow field in the mantle. So, in order to model grain size evolution and mantle convection together, one has to come up with a way to separate these scales, and use a different (and probably much smaller) time step to compute how the grain size evolves. I remember that at one point, our models generated mineral grains the size of kilometers (whereas the grain sizes we expect in the mantle are on the order of millimeters), because we had not chosen the time step size properly. And on countless occasions, the code would just crash, because the problem was so nonlinear that a small change in just one parameter or a solution variable had such a large impact that material properties, velocities and pressures went outside of the range of what was physically reasonable.

However, after a lot of debugging, we could finally investigate how an evolving grain size would influence mantle dynamics. But see for yourself below. In an example from our models, plumes become much thinner when reaching the upper mantle, and cause much more vigorous small-scale convection when they interact with the lithosphere. Slabs bend rather than thicken, and accumulate as piles at the core-mantle boundary.

Figure 2: Comparison of plumes and slabs in models with and without grain size evolution. Modified from Dannberg et al., 2017

Of course, there are also many other areas where grain size evolution is important, and many recent studies are concerned with the influence of grain size on the Earth’s dynamic evolution. Dave Bercovici and his collaborators found that grain evolution and damage mechanisms may be a key factor for the onset of plate tectonics [e.g. Bercovici and Ricard, 2014, 2016]: Grain size reduction in shear zones could make them weak enough to for subduction initiation. The evolution of grain size may also be a major factor for focusing of melt to mid-ocean ridges [Turner et al., 2017], as it influences how fast the solid matrix can dilate and compact to let melt flow in and out. And if the Large Low Shear Velocity Provinces at the core-mantle boundary are indeed piles of hot material that are stable on long time scales, mineral grains would have a long time to grow and may play a crucial role for pile stability [Schierjott et al., 2017].

So if you do not include grain size evolution in your geodynamic models – which in many cases is just not feasible to do – I hope that you now have a better feeling for how that may affect your model results.

1The other researchers in my CIDER group were Zach Eilon, Ulrich Faul, Rene Gassmöller, Raj Moulik and Bob Myhill. I learned a lot about grain size in the mantle in particular from Bob Myhill and Ulrich Faul; I developed the geodynamic models together with Rene Gassmöller, and Zach Eilon and Raj Moulik investigated how the evolving grain size predicted by our models would influence seismic observations.

References:

Solomatov, V. S., & Reese, C. C. (2008). Grain size variations in the Earth's mantle and the evolution of primordial chemical heterogeneities. Journal of Geophysical Research: Solid Earth, 113(B7).

Hall, C. E., & Parmentier, E. M. (2003). Influence of grain size evolution on convective instability. Geochemistry, Geophysics, Geosystems, 4(3).

Korenaga, J. (2005). Firm mantle plumes and the nature of the core–mantle boundary region. Earth and Planetary Science Letters, 232(1), 29-37.

Behn, M. D., Hirth, G., & Elsenbeck, J. R. (2009). Implications of grain size evolution on the seismic structure of the oceanic upper mantle. Earth and Planetary Science Letters, 282(1), 178-189.

Rozel, A. (2012). Impact of grain size on the convection of terrestrial planets. Geochemistry, Geophysics, Geosystems, 13(10).

Dannberg, J., Eilon, Z., Faul, U., Gassmöller, R., Moulik, P., & Myhill, R. (2017). The importance of grain size to mantle dynamics and seismological observations. Geochemistry, Geophysics, Geosystems.

Bercovici, D., & Ricard, Y. (2014). Plate tectonics, damage and inheritance. Nature, 508(7497), 513-516.

Bercovici, D., & Ricard, Y. (2016). Grain-damage hysteresis and plate tectonic states. Physics of the Earth and Planetary Interiors, 253, 31-47.

Turner, A. J., Katz, R. F., Behn, M. D., & Keller, T. (2017). Magmatic focusing to mid-ocean ridges: the role of grain size variability and non-Newtonian viscosity. arXiv preprint arXiv:1706.00609.

Schierjott, J., Rozel, A., & Tackley, P. (2017, April). Toward unraveling a secret of the lower mantle: Detecting and characterizing piles using a grain size-dependent, composite rheology. In EGU General Assembly Conference Abstracts (Vol. 19, p. 17433).

Alaska: a gold rush of along strike variations

Alaska:  a gold rush of along strike variations

Every 8 weeks we turn our attention to a Remarkable Region that deserves a spot in the scientific limelight. After exploring the Mediterranean and the ancient Tethys realm, we now move further north and across the Pacific to the Aleutian-Alaska subduction zone. This post was contributed by Kirstie Haynie who is a PhD candidate at the department of geology at the University at Buffalo, State University of New York, in the United States of America.

Given that Alaska is a remarkable region, I decided to walk up to strangers and ask them what comes to mind when they hear the word “Alaska”. Indeed I received some confusing looks and laughs, but everyone I asked had something to say. Some people alluded to popular TV shows set in Alaska, such as Gold Rush, Bush People, and Alaska: the Last Frontier, while others spoke about the cold weather, dog mushing, Eskimos, fishing and hunting, and the Trans-Alaska pipeline. A few of the answers I received referenced the beauty and wilderness of the large snow capped mountains, glaciers, and the Northern Lights (Aurora Borealis): all emblematic of the largest state in America. But to me, Alaska is more than just a pretty landscape and a place to fish. It is a region riddled with geologic mysteries and rich in along strike variations.

The Aleutian-Alaska subducton zone marks a North American-Pacific plate boundary where subduction varies greatly along strike (Figure 1). At the western end of the subduction zone, the Aleutian volcanic islands are the result of oceanic-oceanic subduction while in the eastern part of the subduction zone there is oceanic-continental collision where the Pacific plate descends beneath the North American plate. The age of the subducting sea floor increases laterally from around 30 Ma in the eastern subduction corner to 80 Ma at the end of the Aleutian volcanic arc (Müller et al., 2008). Slab dip changes drastically from 50° to 60° in the west and central Aleutians to flat slab subduction under south-central Alaska (Ratchkovski and Hansen, 2002a; Lallemand et al., 2005; Jadamec and Billen, 2010). This leads to a variation in the slab pull force, which is a main driving force of subduction caused by the weight of dense slabs sinking into the mantle (Morra et al., 2006).

Figure 1: Tectonic map of Alaska modified from Haynie and Jadamec (2017). Topography/bathymetry is from Smith and Sandwell (1997) and Seafloor (SF) ages are from Müller et al. (2008). Blue lines are the slab contours of Jadamec and Billen (2010) in 40 km intervals; the thick black line is the plate boundary from Bird (2003); and the thinner black lines are faults from Plafker et al. (1994a). The location of Denali is marked by the orange hexagon. Holocene volcanoes are given by the pink triangles (Alaska Volcano Observatory). The purple polygon is the outline of the Yakutat oceanic plateau (Haynie and Jadamec, 2017). WB – Wrangell block fore-arc sliver; JdFR – Juan de Fuca Ridge.

There is also a distinct change in margin curvature from convex in the west to concave in the east. At the end of the eastern bend, the Alaska part of the subduction zone is truncated by a large transform boundary, the Fairweather-Queen Charolette fault, which gives rise to a corner-shaped subduction-transform plate boundary (Jadamec et al., 2013; Haynie and Jadamec, 2017). Here, convergence is oblique with an average velocity of 5.2 cm/year northwest (DeMets and Dixon, 1999). Seismic studies (Page et al., 1989; Ferris et al., 2003; Eberhart-Phillips et al., 2006; Fuis et al., 2008) show that thicker than normal oceanic crust lies off-shore in the subduction corner. This thick oceanic material has been identified as the Yakutat oceanic plateau (Plafker et al., 1994a; Brocher et al., 1994; Bruns, 1983; Worthington et al., 2008; Christeson et al., 2010; Worthington et al., 2012). Even though oceanic plateaus tend to resist subduction (Cloos, 1993; Kerr , 2003), the Yakutat plateau is currently subducting beneath the Central Alaska Range to depths of 150 km (Ferris et al., 2003; Eberhart-Phillips et al., 2006; Wang and Tape, 2014). It is also colliding into south-east Alaska (Mazzotti and Hyndman, 2002; Elliott et al., 2013; Marechal et al., 2015) where the largest coastal mountain range on Earth, the Saint Elias Mountains, are located (Enkelmann et al., 2015).

With regards to surface deformation, in addition to Denali (the tallest mountain in North America), other notable along strike variations reside within the broad deformation zone of south-central Alaska. For example, a normal volcanic arc occurs over the Aleutian part of the subduction zone and above the Alaska Peninsula. However, above the flat slab there is a gap in volcanism followed by the presence of the enigmatic Wrangell volcanoes (Rondenay et al., 2010; Jadamec and Billen, 2012; Martin-Short et al., 2016; Chuang et al., 2017). These volcanoes are marked by a range of morphologies as well as adakitic geochemical signatures (Richter et al., 1990; Preece and Hart , 2004), which have a petrogenesis that may be attributed to slab melting (Defant and Drummond , 1990; Peacock et al., 1994; Castillo, 2006, 2012; Ribeiro et al., 2016). Analogue (Schellart , 2004; Strak and Schellart , 2014) and 3D numerical models (Stegman et al., 2006; Piromallo et al., 2006; Jadamec and Billen, 2010, 2012) predict that toroidal flow can produce upwellings around the edge of a slab that may have implications for melting of the slab and the formation of adakites. However, the formation of the Wrangell volcanoes is still debated.

Also located above the subducting plateau and flat slab is the Wrangell block fore-arc sliver, which exhibits northwest motion and counterclockwise rotation (Cross and Freymueller, 2008; Freymueller et al., 2008; Bemis et al., 2015; Waldien et al., 2015; Jadamec et al., 2013; Haynie and Jadamec, 2017). This sliver is bounded in the north by the arcuate shaped Denali fault, which illustrates a lateral change in slip rates that increases towards the center of the fault (Haynie and Jadamec, 2017; Haeussler et al., 2017). 3D high-resolution geodynamic models show that the flat slab drives motion of the Wrangell block fore-arc sliver (Jadamec et al., 2013; Haynie and Jadamec, 2017) and contributes to fault parallel motion along the eastern Denali fault and convergence along the apex of the fault (Haynie and Jadamec, 2017) (Figure 2). However, when model predictions of the Wrangell block motion and the difference in Denali fault parallel motion are compared with observations, model predictions are lower, suggesting that the flat slab alone is not sufficient enough to explain the broad deformation zone of Alaska (Haynie and Jadamec, 2017). Thus, it is thought that the neotectonics of south-central Alaska are predominantly driven by the subduction-collision of the buoyant Yakutat oceanic plateau (Bird , 1988; Plafker et al., 1994b; Fitzgerald et al., 1995; Ratchkovski and Hansen, 2002b; Bemis and Wallace, 2007; Chapman et al., 2008; Haeussler , 2008; Jadamec et al., 2013; Lease et al., 2016; Haynie and Jadamec, 2017). 4D numerical modelling of this process is currently underway.

Figure 2: Top: map of south-central Alaska (zoomed in from Figure 1) with model predicted velocities (blue arrows) from Haynie and Jadamec (2017) plotted on top. Bottom: percent of slab contribution from Haynie and Jadamec (2017) models to observed Denali fault slip rates (modified from Haynie and Jadamec (2017)). Results from Haynie and Jadamec (2017) show that the slab drives northwest and counter-clockwise motion of the Wrangell block fore-arc sliver and contributes to an average of 20-28% of motion along the Denali fault. The flat slab exerts the largest contribution to motion along the eastern segment of the fault, where surface motion parallels the fault, and also along the central segment of the fault, where the slab is driving the Wrangell block into the North American backstop and subducting obliquely to the fault.

 

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The quest of a numerical modelling hero

The quest of a numerical modelling hero

Numerical modelling is not always a walk in the park. In fact, it resembles a heroic quest more often than not. In this month’s Wit & Wisdom post, Cedric Thieulot, assistant professor at the Mantle dynamics & theoretical geophysics group at Utrecht University in The Netherlands, tells the story of his heroic quest to save the princess from the dragon clear a code from bugs and shows that failed models can be the best models.

Heroes are also artists. I am a hero, therefore I am an artist. Sometimes against my will. In other words, sometimes the code works; most of the time it doesn’t.

A true hero embarks on his noble steed upon a long and perilous quest as the fire-breathing dragon who keeps the princess hostage awaits him in its lair.
“I am a hero too!” says my programmer ego although I spend most of my time sitting on ikea chairs looking for bugs. Yes, bugs. Bugs I have put there myself. Yup.

On my quest, I sometimes get lost in impossible mazes!

I have to cross mysterious mountain ranges

… but I am rewarded by a beautiful sunset on another planet.

I can’t believe what I C(++)

My quest can be dangerous.
Sometimes the enemy is tiny but viruses can be deadly too!

I sometimes feel like I am drowning in a petri dish.


Sometimes I encounter weird beings on my quest…



I even have to fight improbable gnu-snakes!

And the spirits of old viking warriors creep up in my models…

I need some candy to keep my spirits up.

And then… I find the bug and defeat the mighty bug! Fireworks!


Time to switch on the disco balls!

It’s party time!