GD
Geodynamics

Grace Shephard

Grace is a postdoctoral researcher at the Centre for Earth Evolution and Dynamics (CEED) at the University of Oslo, Norway. She works on linking plate tectonic reconstructions and mantle structure, especially in the Arctic and Pacific regions. Grace is part of the GD blog team as an Editor. You can reach Grace via email.

Meeting, mentoring and awards at EGU18

Meeting, mentoring and awards at EGU18

Having just about recovered from the session-packed, networking-fest, coffee-filled, schnitzel-test that was EGU2018 (8-13th April, Vienna), it is now possible to reflect and look towards upcoming dates. Earlier posts in the blog have described some of the GD side event highlights. For this week’s post, I have summarised some key points from the GD Division meeting, the EGU Mentoring program, and the upcoming EGU award nominations.

Geodynamics (GD) Division Meeting

During the Friday lunchtime break GD President Paul Tackley (ETH Zürich) led the session about GD activities and statistics to an eager audience of around 50 attendees. Within the 19 GD-led sessions for EGU2018 there were 481 abstracts (adding co-organized sessions raised this to ~1450 abstracts). As in previous years, the structure of EGU, and meeting fun facts were delivered – this year there were over 15.000 attendees, 17.000 abstracts in the programme, 666 unique sessions and 68 short courses. New to this year’s conference, there was a Cartoonist and Poet-in-residence, re-usable water bottles, and CO2 emission offset initiative.

A portion of the lunchtime meeting was dedicated to discussing the time and space constraints associated with increasing attendance and presentations at the GA. Many rooms are already overcrowded and maximum poster capacity is expected to be reached within the next 2 years (this year 8% of GA presentations were PICOs, 64% posters and 28% orals). As extra space in the Austria Centre Vienna is not a possibility, several ideas were put forward by EGU including increasing the GA from 5 to 6 days, limiting to 1 abstract per person (2 if invited), increasing oral times from 6-8 hours per day, holding different posters in morning and afternoon, and shorter talks (12 minutes). Several audience members expressed opinions regarding the proposed changes, and the audience seemed in favour of more overall oral time-slots but not shorter talks, or moving to a 6 day conference. We shall see what is implemented but there are at least new set of rules for 2019:

Apart from the consumption of free sandwiches, audience arms were put to use when voting for Division Officers (van Hunen, Artemieva, Biggin, Bunge, Karato) and the Medal Committee (Houseman, Parmentier, Parsons, Phipps Morgan) – all approved.

For the GD ECS specifics, we will welcome the new GD Early Career Scientist (ECS) Representative Nicholas Schliffke (U. Durham), as Adina Pusok (UC San Diego) steps into a co-representative position for the next year. Our blog activities over the last year were also presented by our enthusiastic Editor-In-Chief Iris van Zelst (ETH, Zürich). As always, we encourage more ECR members to get in touch with us to be a guest writer.

Some important EGU2019 dates for your calendar:

25 June-13 September 2018
Public call-for-sessions
(the rolling over of sessions will not occur – join forces with your colleagues!)

15 October 2018 – 10 Jan 2019
Abstract submission

7-12 April 2019
EGU2019, Vienna

EGU GD Awards

The Meeting also highlighted the Division’s 2018 award recipients, Edgar Marc Parmentier and Thibault Duretz, which we here congratulate again:

The GD Outstanding Poster/PICO (OSPP) for 2017 was awarded to Ludovic Räss for his poster “M2Di: MATLAB 2D Stokes solvers using the finite difference method.”

In particular, please note the upcoming deadline for award nominations for 2019 on the 15th June.
We encourage you to put forward your colleagues for nominations for both categories! You can read more about the awards and nomination process here.

And with only a single female winner of the GD Outstanding Early Career Scientist Award (<7 years from highest degree; no age limitation), and none for the Augustus Love Medal, I am sure you do not have to look far for worthy candidate(s) to help improve the gender balance of these awards.

Mentoring program – we need you!

In its second year running, EGU organized a mentoring program during the conference. This year the program received double the number of registrations from 2017. The aim is to connect mentors – those who are EGU veterans in terms of multiple attendances – with mentees, prioritized to early-career participants (Masters and PhDs) who are first-time attendees. Matching was primarily based on division affiliations or research keywords, but as there are 22 divisions and over 50 identified research interests, interdisciplinary matches were commonplace.

This year from GD specifically there were 3 mentors and 2 mentees signing up – as EGU Media and Communications Officer Barbara Ferreira said “a rare (and positive) case of more mentors than mentees registering for the programme”. These 3 mentors were eventually matched with 6 mentees. However, across the board around 75 mentees had to be rejected because of insufficient mentors available.

So, if you have attended numerous EGU GAs and know the lay of the land, please do sign up next year! I can highly recommend being a mentor; to sit down for a coffee and a chat is really not taxing and is a good opportunity to meet new faces in your division and from further afield.

 

Tschüss – see you in Vienna next year.

Editorial thanks to GD President Paul Tackley and EGU Media and Communications Officer Bárbara Ferreira (@dinnerpartysci) for summary slides for the GD Meeting and Mentoring programs, respectively. Cheers again to the EGU organizers for a fantastic meeting.

Making the most of the EGU General Assembly 2018 as a Geodynamicist and Early Career Scientist

Making the most of the EGU General Assembly 2018 as a Geodynamicist and Early Career Scientist

Are you still deciding on how to best fill your EGU General Assembly program next week in Vienna? Wondering what is on offer specifically for the Geodynamics (GD) early career community? Our EGU GD Early Career Scientist representative, Adina Pusok (Scripps, UC San Diego), shares some planning tips and event highlights for the big week ahead. We are looking forward to seeing you there!

The EGU General Assembly 2018 (popularly known as EGU2018, or the official hashtag of #EGU18) in Vienna is about to kick off this coming Sunday, and I am sure many geoscientists worldwide are making the last preparations, or even getting the last results in (good luck!). Hopefully, some of you have already had a chance to look on the EGU2018 meeting organizer available (also with a great mobile app) and “star” some of your favourite sessions and events in your personal programme. And probably soon enough, you have also realized that it is not humanly possible to attend everything that you find interesting (unless you are in possession of a time machine to be in multiple places at the same time).

A meeting the size of EGU2018 can be intimidating to most attendees, especially first timers, and being selective becomes a valuable skill. It is a place where you can check out the latest research across a wide range of fields within the geosciences, and within your own area of science. And of course, it is a place to catch up or make new friends and collaborations from all over the world.

Assuming that you’ve already marked in your personal programme your own presentation(s) and scientific sessions of interest, I want to draw your attention to the other side of the conference. The EGU2018 is not just a conference where the latest science is reported, but also one of the best places where you can develop your personal and career skills in a short amount of time. As I’ve written before, Early Career Scientists (ECS) have different needs compared to established scientists. And for that, the EGU2018 schedule comes with a wide range of sessions, short courses, great debates, union wide events, and division social events that complement the scientific agenda of the meeting.

I write this blog post primarily for Geodynamics ECS and first time attendees at the EGU2018 to help them navigate through this “hidden” schedule and make the most out of EGU2018. As an ECS myself, I’ve always liked to explore what every meeting has to offer, and try to learn some new things. So, here are some of my tips and highlights for this year’s EGU2018 meeting schedule:

  1. Short courses – learn a new skill or two in no time

    Learn a scientific skill:
  • Geodynamics 101 (Figure 1) – First short course on numerical geodynamics at the EGU General Assembly! So it’s a must whether you are a geodynamicist, or you just want to understand why all those pretty pictures also make sense scientifically (Wed, afternoon)
  • GPlates – Try this hands-on tutorial with a popular open-source software for plate tectonic reconstructions (Thu, morning) 
  • Seismology for non-seismologists – Learning how to correctly interpret seismic data is an important skill for every solid-earth geodynamicist (Mon, afternoon)

For first time attendees:

  • How to navigate EGU: tips and tricks – Dedicated to first time attendees! If you fit the bill, make sure you wake up early on Monday morning for this introductory short course (Mon, morning) 

Learn to polish these professional skills:

  • Academic presentations – Having last minute nerves about your presentation? Get some tips and tricks to ace that talk! (Mon, afternoon)
  • How to convene a session at EGU’s General Assembly – Convening a session is regarded as an important duty in the scientific community that also gets you a free ticket to the conveners’ party on the Friday evening (Tue, afternoon)
  • How do you peer-review? – Something that nobody during your graduate studies will actually tell you, but you’re expected to know how to do.
  • Applying for Marie Sklodowska-Curie grants – Info session on the highly competitive individual fellowships that are definitely worth applying for, and are aimed at Early Career Scientists (Wed, lunch) 
  • ERC grants – More funding opportunities from the European Research Council (ERC) at all career levels (Thu, evening) 

Explore outside your bubble:

  • Academia is not the only route – Are you finishing your degree and not overly excited by an academic future? Try this short course on exploring career alternatives both inside and outside academia (Thu, afternoon) 
  • Unconscious bias – Become aware of the obstacles that some of your colleagues face every day, and that might prevent them from doing the best science (Tue, morning)

Learn how new technology can help your research:

  • Writing reproducible science – You know you’ve complained at least once that it’s difficult to reproduce the results of a certain paper. Now you can learn ways to improve the conduction and dissemination of your work! (Thu, afternoon)
  • Learning git – This is a life-saver skill that every scientist should have! No more n-versions of your theses, manuscripts or projects (Wed, morning)

Fun skills:

  1. Great debates – teams argue opposite views on a particular topic. Let’s see some science-worthy arguments there!

Don’t worry if you cannot (really) make it to the great debates. You can follow and join in the debates using the web-streaming service.

  1. Awards events – Come and celebrate the work of distinguished scientists! Tip: Medal lectures are particularly interesting across all geosciences fields! This year’s medal lectures specific to the GD division are:
  1. More events and sessions dedicated to professional and career development:
  • EarthArXiv – A general introduction to preprints and the new pre-print server for Earth Sciences, a concept that has been very successful across science disciplines (Mon, evening)
  • Industry career opportunities for early career scientists – The title is clear enough of what you can expect here: how to transition from academia to industry (Mon, evening) 
  • Promoting and supporting equality of opportunities in geosciences – If you care to promote an open, equal opportunities working environment (and you should!), this session promises some very interesting talks and posters on some common issues, solutions and initiatives (posters – Tue, morning, orals – Wed, afternoon) 
  • Meet the chief executive editor of Solid Earth – Thinking of submitting your next manuscript to an EGU journal, such as the Solid Earth? Learn tips and how the publishing process works by meeting the editor–in-chief of the journal (Mon, afternoon)
  • Games for Geoscience – Because it’s always more fun to work and play (orals and posters – Wed, afternoon) 
  1. Other ECS events – Get active and involved into the EGU ECS community with these events:
  • Meet the EGU ECS Representatives and EGU Communications Officer (Roelof Rietbroek, Stephanie Zihms, and Olivia Trani) – These are the people representing ECS at the union level and will be happy to chat with you about your EGU experience, or future plans for the ECS community! (Wed, afternoon)
  • EGU ECS Forum – Open-discussion session for all ECS. Lunch provided! (Thu, lunch)
  • Imaggeo photo competition – Announcing the winners of the photo competition. High-quality photos guaranteed! (Fri, lunch)
  1. Union wide events – Great events to network with medalists or other scientists over some food and drinks! Do not miss them!
  • Opening reception – Sun, 18:30–21:00
  • EGU Award Ceremony – Wed, 17:30–20:00
  • ECS Networking and Careers Reception – Mon, 19:00–20:30
  1. Geodynamics and ECS events
  • ECS GD informal lunch* – Meet in front of the conference center (look for “GD” stickers), to head to the food court in Kagran (2 subway stops away from the conference center). Looking forward to meeting many ECS and come up with more exciting projects for GD! (Note: this blog started taking shape at the ECS GD lunch last year) (Tue, 12:00-13:30)
  • ECS GD dinner* – Join us for a friendly dinner with fellow ECS Geodynamicists at Wieden Bräu – Waaggasse 5, 1040 Wien! (Wed, 19:30-22:00) If you would like to attend the ECS GD dinner on Wednesday, please fill out this form to keep track on the number of people: https://goo.gl/forms/v42iDyGHB0MvoBz13
  • GD/TS drinks* – No worries if you cannot make for the ECS GD dinner! We will continue with joint TS/GD drinks in Bermuda Bräu – Rabensteig 6, 1010 Wien! (Wed, after ECS GD dinner)
  • GD Division meeting – The division president, Paul Tackley, will show the latest updates regarding the GD division and will present the OSPP award winner from last year. Lunch provided! (Fri, lunch)

*All events are organized by the EGU GD ECS representative, and are open to GD division members and friends.

Just by writing this post, I’ve realized how many interesting events are going to happen next week! Hope you will be creative with your conference schedule and try some of these “hidden” events! Make sure you follow the EGU Blogs and social media, and the division specific events so that you make the most of your attendance at EGU General Assembly 2018. For GD division related news stay tuned for important updates on the EGU GD Facebook page and blog in the coming days. I wish you a great and productive EGU2018 week!

Finding the forces in continental rifting

Finding the forces in continental rifting

Luke Mondy

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. For our latest ‘Geodynamics 101’ post, PhD candidate Luke Mondy from the EarthByte Group at the University of Sydney blogs about some impressively high-resolution numerical models of ‘rotational rifting,’ and the role of gravity. Luke also shares a bit about the journey behind this work, which recently appeared in Geology.

 

In geodynamic modelling, we’re always thinking about forces. It’s a balancing act of plate driving forces potentially interacting with the upwelling mantle, or maybe sediment loading, or thermal relaxation… the list goes on.

Figure 1: A summary of the forces interacting during continental rifting, from Brune, 2018.

But the thing that underpins all of these forces, fundamentally, is our favourite but oft forgotten force: gravity. Here, I’ll tell the story of investigating a numerical model of continental rifting and discovering – or rather, rediscovering – the importance of gravity as a fundamental force in driving Earth dynamics.

How it started – a side project!

A few years ago, my colleagues and I were granted access to not just one, but two, big supercomputers in Australia: Raijin, and Magnus. Both were brand new and raring to go – but we needed something big to test them out on. At the time, 3D geodynamic models were typically limited to quite low resolution, since they can be so computationally demanding, but since we had access to this new power, we decided to see how far we could push the computers to address a fundamentally 3D problem.

2D vs 3D

Historically, subduction and rifting have been ideal settings to model as they can be constrained to two dimensions while still retaining most of their characteristic properties.

Figure 2. A 2D subduction model. Despite being ‘only’ two dimensions, the fundamental and interesting aspects of the problem are still captured by the model. Figure from Rey et al., 2014.

However, as tremendously useful as these models have been, many interesting problems in geodynamics are fundamentally three dimensional. The obvious example is global mantle convection, but we are starting to see more and more papers addressing both rifting and subduction problems that require 3D contexts, for example: continental accretion (Moresi et al., 2014), metamorphic core complex formation (Rey et al., 2017), or oblique rifting (Brune et al., 2012).

Typically when we model a rift in 2D, the dimensionality implies that we are looking at orthogonal rifting – that the plates move away from each other perpendicular to the rift axis. Since 2D models cannot account for forces in the third dimension, they are only suitable for when the applied tectonic forces pull within the plane of the model – that is, when the 2D model lies along a small circle of an Euler pole.

Euler poles have another interesting geometric property – the velocity of extension between two plates changes as we move closer or further away from the Euler pole: zero velocity at the pole itself, and fastest at the equator to the pole (Lundin et al., 2014).

Figure 3. Left: From Lundin et. al. (2014), the figure shows the geometric relationship of increasing rifting velocity as the distance from the pole increases. Right: the same relationship graphed out, showing the cosine curve (Kearey et.al. 2009).

This leads to differing extension velocities along the length of the rift axis. Extension velocities are a huge control on the resulting geodynamics (e.g., Buck et al., 1999). Employing a series of 2D models along a rift axis (Brune et al., 2014) has been used to show how these dynamics change, but misses out on the three-dimensionality of the problem – how do these differing and diachronous dynamics interact with each along other the rift margin as it forms?

Rotational Rifting

We decided to attempt to model this sort of rifting, as we termed it “rotational rifting”. Essentially we linked up the 2D slices along the rift axis into one big 3D model – so that we have slow extension towards the Euler pole, and fast extension away from it.

To do this, we ended up using the code Underworld (at the time version 1.8 – but their 2.0 version is the best place to start!), and a framework developed inside the EarthByte group at the University of Sydney called the ‘Lithospheric Modelling Recipe’, or LMR.

 

Figure 4. Map view of the two experiments. Arrows show the velocity boundary conditions applied. Note they are perpendicular to the model domain – we thought long and hard about this choice, and explain it fully in the Data Repository.

Using the LMR, we set up two 3D experiments: both are 1000 km by 500 km along the surface, and 180 km deep. The ‘orthogonal’ experiment is modelled at the equator to the pole – so the velocities along the walls are the same all the way along the rift axis. The ‘rotational’ experiment is very close to the Euler pole (where the rate of extension velocity change is greatest), from 89 degrees to 79 degrees (90 degrees being the Euler pole), which gives an imposed velocity at the slow end (89 degrees) of 0.5 cm/yr and at the fast end (79 degrees) 5.0 cm/yr.

 

Since we wanted to stress test the supercomputers, we ran these experiments at just under 2 km grid resolution (256 x 512 x 96). This meant each experiment ended up using about 2.5 billion particles to track the materials! The 2 km grid size is an important milestone – to properly resolve faulting, sub-2 km grid sizes are required (Gerya, 2009).

The results!

So we ran the experiments, and compared the results! To give a broad overview of what we found, here’s a nice animation:

Figure 5. Top: Animation showing the orthogonal experiment from a south-west perspective (with the Euler pole being the ‘north’ pole). The light grey layers show the upper crust, dark grey the lower crust. Half of the crust has been removed to show the lithospheric mantle topography. The blue to the white colours show the lithospheric mantle temperature, and from white to red shows the asthenospheric temperature. Bottom: As above but for the rotational experiment. Notice that the asthenospheric dome migrates along the rift towards the Euler pole.

What to do now?

Cool looking experiments, of course! The supercomputers had been able to handle the serious load we put on them (it took about 2 weeks per experiment, on ~800 cpus), so that part of the project was a success. But what about the experiments themselves – did switching to 3D actually tell us anything useful?

What we expected…

The things we expected were there. The orthogonal experiment behaved identically to a 2D model. For the rotational experiment, we found the style of faulting changed and evolved along the rift axis, and seemed to match up nicely with the 2D work about differing extension rates. We were able to identify phases of rifting via strain patterns, which were similar to those described by Lavier and Manatschal (2006), and seemed to match the outputs of the series of 2D models along a rift axis.

Figure 6. Map view of strain-rate of the rotational experiment through time. The phases (1 through 4, representing different modes of deformation) migrate along the rift towards the Euler pole.

What we didn’t expect…

Almost on a whim, we decided to start looking into the tectonic regime. Using the visualization program Paraview, we calculated the eigenvectors of the deviatoric stress and assigned a tectonic regime (blue for extension, red for compression, green for strike-slip, and white for undetermined), following a similar scheme to the World stress map (Zoback, 1992). Apologies to colour blind folk!

Here’s what a selected section of the orthogonal experiment surface looks like through time:

Figure 7. The stress regimes at the surface of the orthogonal experiment (clipped to y = ~400 to ~600 km).

Not really that surprising – we found mostly extension everywhere, with a bit of compression when the central graben sinks down and gets squeezed. However, it was a little bit surprising to see the compression come back on the rift flanks.

But when we applied the same technique to the rotational experiment, we found this on the surface:

Figure 8. The stress regimes at the surface of the rotational experiment. The three numbers at the top represent the total extension at y = 0 km, 500 km, and 1000 km respectively.

Now all of a sudden we’re seeing strike-slip stress regimes in different areas of the experiment!

The above figures displaying the stress in the experiments so far have been of the surface – where one of the principal stress axes must be vertical – but our colouring technique does not limit us to just the surface. We noticed when looking at cross-sections that the lithospheric mantle was also showing unexpected stress regimes!

Figure 9. Slices at y = 500 km across the rift axis (right in the middle). Coloured areas show where the plunge of one principal stress axis is >60 degrees. Both experiments have the same applied extension velocity at y = 500 km, and so total extension is equivalent between experiments.

In most of the lithosphere, the strain rate is still very small, not enough to notice much deformation (1e-16 to 1e-18 1/s). But a few puzzling questions were raised: why do we see compressional tectonic regimes in the orthogonal experiment; and why do we also see strike-slip regimes in the rotational experiment?

Gravitational Potential Energy (GPE)

It quickly became apparent that these stress changes were related to the upwelling asthenosphere, as the switch between regimes was well timed to when the asthenosphere would approach the Moho – about 40 km depth. This gave us the hint that perhaps buoyancy forces were at play. We used Paraview again to calculate the gravitational potential energy at each point on the surface (taking into account all the temperature dependent densities, detailed topography, and so on), and produced these maps:

Figure 10. A time series showing the gravitational potential energy (GPE) at each point on the surface of the rotational experiment. Only half the surface is shown because it is symmetrical. The small triangle notch is where we determined the rift tip to be located (where 1/(beta factor) < 0.2).

What we saw confirmed our suspicions – the rise of the asthenospheric dome induces a gravitational force that radiates outwards. The juxtaposition of the hot, yet still quite heavy, asthenospheric material, next to practically unthinned crust on both the rift flanks and ahead of the rift tip, produces a significant force.

But why the switch to compression or strike-slip tectonic regimes in an otherwise extensional setting? In the case of the orthogonal model, the force (aka the difference in GPE) is perpendicular to the rift axis, since the dome rises synchronously along the axis. When this force overcomes the far-field tectonic force (essentially the force required to drive our experiment boundary conditions), the stress regime changes from extension to compression.

However, in the rotational experiment, the dome is larger the further away from the Euler pole, and so instead the gravitational force radiates outwards from the dome. Now the stress in the lithospheric mantle has to deal with not only the force induced from the upwelling asthenosphere right next to it, but also from along the rift axis (have a look at the topography of the lithospheric mantle in Fig. 5). These combined forces end up rotating the principal stresses such that sigma_2 stands vertical and a strike-slip regime is generated.

We also see the gravitational force manifest in other ways. Looking at the along axis flow in the asthenosphere, the experiment initially predicts a suction force towards the rapidly opening end of the model (away from the Euler pole), similar to Koopmann et al. (2014). But once the dome is formed, we see a reversal of this flow, back towards the Euler pole, driven by gravitational collapse. This flow appears to apply a strong stress to the crust surrounding the dome, reaching upwards of 50 MPa in some places.

Figure 11. A: The direction of flow at the lithosphere-asthenosphere boundary in the centre of the rift. Early in the experiment, we see suction towards the fast end of the rift, while later in the experiment, we see a return flow. The dashed line shows the flow after the tectonic boundary conditions have been removed. B,C: cross-sections showing stress and velocity arrows from the experiment just after the tectonic boundary conditions have been removed.

How do we know it’s gravity?

To test this idea further, we ran some additional experiments. First, we let the rotational experiment run for about 3.6 Million years, and then ‘stopped’ the tectonics (changed the side velocity boundary conditions to 0 cm/yr) – leaving gravity as the only driving force. We saw that the return flow towards the Euler pole was still present (though reduced). By running some more rotational experiments with either doubled or halved Euler pole rotational rate, we saw that the initial suction magnitude correlates with the change in opening velocity, but the return flow to the Euler pole is almost identical, giving further evidence that this is gravity driven.

What about the real world?

We numerical modellers love to stay in the world of numbers – but alas sometime we must get our hands dirty and look at the real world – just to make sure our models actually tell us something useful!

Despite our slightly backwards methodology (model first, check nature second), it did give us an advantage: our experiments were producing predictions for us to go and test. We had our hypothesis – now to see if it could be validated.

So we went out and looked for examples of rifting near an Euler pole, and the two most notable we found were in the Woodlark Basin, Papua New Guinea, and the Galapagos Rise in the Pacific. Despite the ‘complications’ of the natural world (things like sediment loading, pre-existing weakness in the crust, etc. – things that get your hands dirty), we found a striking first order relationship between the earthquake focal mechanisms present in both areas, and what our experiments predicted:

Figure 12. Top: the Woodlark Basin, PNG. Bottom: the Galapagos Rise. Both show earthquake focal mechanisms, coloured the same way as our experiments: blue for extension, red for compression, and green for strike-slip.

Furthermore, much work has been done investigating the Hess deep, a depression that sits ahead of the rift tip in the Galapagos. We found in our rotational experiment a similar ‘deep’ that moves ahead of the rift tip through time, giving us greater confidence in our experimental predictions.

Takeaways

There are a few things I’ve taken away from this experience. The first is that it’s important to remember the fundamentals. I’ve found that, generally, geodynamicists initially think about the force-balances going on in a particular setting, but gravity was staring me in the face for a while before I understood its critical role.

The second take-away was that exploratory modelling – playing around with experiments just for fun – is a great thing to do. Probably most of us do this anyway as part of the day-to-day activities, but putting aside some time to think about what sort of things to try out allowed us to find something really interesting. Furthermore, we then had a whole host of predictions we could go out and look for, rather than trying to tweak out experiment parameters to match something we already had found.

Finally, the 3D revolution we’re going through at the moment is exciting! Now that there are computers available to us that are able to run these enormous calculations, it gives us a chance to explore these fundamental problems in a new way and hopefully learn something about the world!

If you would like to checkout our paper, you can see it here. We made all of our input files open-source (and the code Underworld is already open-source), so please check them out too!

References

Brune, S., Popov, A. A., & Sobolev, S. V. (2012). Modeling suggests that oblique extension facilitates rifting and continental break‐up. Journal of Geophysical Research: Solid Earth, 117(B8).

Brune, S., Heine, C., Pérez-Gussinyé, M., & Sobolev, S. V. (2014). Rift migration explains continental margin asymmetry and crustal hyper-extension. Nature Communications, 5, 4014.

Brune, S. (2018). Forces within continental and oceanic rifts: Numerical modeling elucidates the impact of asthenospheric flow on surface stress. Geology, 46(2), 191-192.

Buck, W. R., Lavier, L. L., & Poliakov, A. N. (1999). How to make a rift wide. Philosophical Transactions - Royal Society of London Series A, Mathematical Physical and Engineering Sciences, 671-689.

Gerya, T. (2009). Introduction to numerical geodynamic modelling. Cambridge University Press.

Kearey, P. (Ed.). (2009). The Encyclopedia of the solid earth sciences. John Wiley & Sons.

Lundin, E. R., Redfield, T. F., Péron-Pindivic, G., & Pindell, J. (2014, January). Rifted continental margins: geometric influence on crustal architecture and melting. In Sedimentary Basins: Origin, Depositional Histories, and Petroleum Systems. 33rd Annual GCSSEPM Foundation Bob F. Perkins Conference. Gulf Coast Section SEPM (GCSSEPM), Houston, TX (pp. 18-53).

Koopmann, H., Brune, S., Franke, D., & Breuer, S. (2014). Linking rift propagation barriers to excess magmatism at volcanic rifted margins. Geology, 42(12), 1071-1074.

Lavier, L. L., & Manatschal, G. (2006). A mechanism to thin the continental lithosphere at magma-poor margins. Nature, 440(7082), 324.

Mondy, L. S., Rey, P. F., Duclaux, G., & Moresi, L. (2018). The role of asthenospheric flow during rift propagation and breakup. Geology.

Moresi, L., Betts, P. G., Miller, M. S., & Cayley, R. A. (2014). Dynamics of continental accretion. Nature, 508(7495), 245.

Rey, P. F., Coltice, N., & Flament, N. (2014). Spreading continents kick-started plate tectonics. Nature, 513(7518), 405.

Rey, P. F., Mondy, L., Duclaux, G., Teyssier, C., Whitney, D. L., Bocher, M., & Prigent, C. (2017). The origin of contractional structures in extensional gneiss domes. Geology, 45(3), 263-266.

Zoback, M. L. (1992). First‐and second‐order patterns of stress in the lithosphere: The World Stress Map Project. Journal of Geophysical Research: Solid Earth, 97(B8), 11703-11728.

Rheological Laws: Atoms on the Move

Rheological Laws: Atoms on the Move

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. For our first ‘101’ for 2018, we have an entry by postdoctoral researcher Elvira Mulyukova from Yale University about rheology and deformation occurring on atomic scales … it’s a fun and informative read indeed! Do you want to talk about your research? Contact us!

Elvira Mulyukova, Yale University

Most of us have an intuitive understanding that different materials resist being moved, or deformed, to different degrees. Splashing around in the mud is more energy-consuming (and fun, but never mind that) than in the water, and splashing around in the block of concrete is energy-intensive bordering on deadly. What are the physical reasons for these differences?

For Earth materials (rocks), the answer lies in the restless nature of their atoms: the little buggers constantly try to sneak out of their crystal lattice sites and relocate. Some are more successful at it than others, making those materials more easily deformable. A lattice site is really just other atoms surrounding the one that is trying to escape. You see, atoms are like a bunch of introverts: each is trying to escape from its neighbours, but doesn’t want to get near them. The ones that do escape have to overcome a temporary discomfort (or an increase in their potential energy, for those physically inclined) of getting close to their neighbours. This requires energy. The closer the neighbours – the more energy it takes to get past them. When you exert force on a material, you force some of the neighbours to be further away from our potential atomic fugitive, making it more likely for the atom to sneak in the direction of those neighbours. The fun part (well, fun for nerds like me) is that it doesn’t happen to just one atom, but to a whole bunch of them, wherever the stress field induced by the applied force is felt. A bunch of atoms escaping in some preferential direction is what we observe as material deformation. The more energy you need to supply to induce the mass migration of atoms – the stronger the material. But it’s really a question of how much energy the atom has to begin with, and how much energy is overall needed to barge through its detested neighbuors. For example, when you crank up the temperature, atoms wiggle more energetically and don’t need as much energy supplied from external forcing in order to escape – thus the material gets weaker.

“A lattice site is really just other atoms surrounding the one that is trying to escape. You see, atoms are like a bunch of introverts: each is trying to escape from its neighbours, but doesn’t want to get near them.” cartoon by Elvira Mulyukova

One more thing. Where are the atoms escaping to? Well, there happen to be sanctuaries within the crystal lattice – namely, crystalline defects such as vacancies (aka point defects, where an atom is missing from the otherwise ordered lattice), dislocations (where a whole row of atoms is missing), grain boundaries (where one crystal lattice borders another, which is tilted relative to it) and other crystalline imperfections. These regions are sanctuaries because the lattice is more disordered there, which allows for larger distances in-between the neighbors. When occupying a regular lattice site – the atom is sort of trapped by the crystalline order. Think of the lattice as an oppressive regime, and the crystalline defects as liberal countries that are welcoming refugees. I don’t know, is this not the place for political metaphors? *…whistling and looking away…*

Ok, enough anthropomorphisms, let’s get to the physics. If this is the last sentence you’ll read in this blog entry, let it be this: rocks are made up of atoms that are arranged into crystal lattices (i.e., ordered rows and columns of atoms), which are further organized into crystal grains (adjacent crystals tilted relative to each other); applying force to a material encourages atoms to move in a preferential direction of the largest atomic spacing, as determined by the direction of the applied force; the ability of the lattice sites to keep their atoms in place (call it a potential energy barrier) determines how easily a material deforms. Ok, so it was more like three sentences, but now you know why we need to get to the atomic intricacies of the matter to understand materials macroscopic behaviour.

Alright, so we’re applying a force (or stress, which is simply force per area) to a material and watch it deform (a zen-inducing activity in its own right). We say that a material behaves like a fluid when its response to the applied stress (and not just any stress, but differential stress) is to acquire a strain rate (i.e., to progressively shorten or elongate in one direction or the other at some rate). On geological time scales, rocks behave like fluids, and their continuous deformation (mass migration of atoms within a crystal lattice) under stress is called creep.

The resistance to deformation is termed viscosity (let’s denote it µ), which basically tells you how much strain rate (˙e) you get for a given applied differential stress (τ). Buckle up, here comes the math. For a given dimension (say x, and for the record – I’ll only be dealing with one dimension here to keep the math symbols simple, but bear in mind that µ, ˙e and τ are all tensors, so you’d normally either have a separate set of equations for each dimension, or some cleverly indexed symbols in a single set of equations), you have:

So if I’m holding a chunk of peridotite with a viscosity of 1020 Pa s (that’s units of Pascal-seconds, and that’s a typical upper mantle viscosity) and squeezing it in horizontal direction with a stress of 108 Pa (typical tectonic stress), it’ll shorten at a rate of 5 · 10-13 s-1 (typical tectonic rates). A lower viscosity would give me a higher strain rate, or, equivalently, with a lower viscosity I could obtain the same strain rate by applying a smaller stress. If at this point you’re not thinking “oh, cool, so what determines the viscosity then?,” I failed massively at motivating the subject of this blog entry. So I’m just gonna go ahead and assume that you are thinking that. Right, so what controls the viscosity? We already mentioned temperature (let’s call it T), and this one is a beast of an effect. Viscosity depends on temperature exponentially, which is another way of saying that viscosity depends on temperature hellavulot. To throw more math at you, here is what this dependence looks like:

where R = 8.3144598 J/K/mol (that’s Joule per Kelvin per mol) is the gas constant and E is the activation energy. Activation energy is the amount of energy that an atom needs to have in order to even start thinking about escaping from its lattice site, which of course depends on the potential energy barrier set up by its neighbours. Let’s say your activation energy is E = 530·103 J mol-1 . If I raised your temperature from 900 to 1000 K (that’s Kelvin, and those are typical mid-lithospheric temperatures), your viscosity would drop by a factor of ∼ 1000. That’s a three orders of magnitude drop.

Like I said, helluvalot. If instead you had a lower activation energy, say E = 300 · 103 J mol-1 , the same temperature experiment would bring your viscosity down by a factor of ∼ 50, which is less dramatic, but still significant. It’s like running through peanut butter versus running through chocolate syrup (running through peanut butter is a little harder… I clearly need to work on my intuition-enhancing examples). Notice, however, that while the temperature dependence is stronger for materials with higher activation energies, it is more energy-consuming to get the creep going in those materials in the first place, since atoms have to overcome higher energy barriers. There’s more to the story. Viscosity also depends on pressure (call it P), which has a say in both the energy barrier the atoms have to overcome in order to escape their neighbours, as well as how many lattice defects (called sanctuaries earlier) the atoms have available to escape to. The higher the pressure, the higher the energy barrier and the fewer lattice sanctuaries to resort to, thus the higher the viscosity. Throwing in the pressure effect, viscosity goes as:

The exact dependence of viscosity on pressure is determined by V – the activation volume.

Alright, we’re finally getting to my favourite part – the atoms’ choice of sanctuary sites. If the atomic mass migration happens mainly via point defects, i.e., by atoms hopping from one single lattice vacancy to another, the deformation regime is called diffusion creep. As atoms hop away, vacancies accumulate in regions of compressive stress, and fewer vacancies remain in regions of tensional stress. Such redistribution of vacancies can come about by atoms migrating through the bulk of a crystal (i.e., the interior of a grain, which is really just a crystal that is tilted relative to its surrounding crystals), or atoms migrating along the boundary of a crystal (i.e., a grain boundary). In both cases, the rate at which atoms and vacancies get redistributed depends on grain size (let’s denote it r). The larger the grains – the more distance an atom has to cover to get from the part of the grain that is being compressed to the part that is under tension. More math is due. Here is what the viscosity of a material deforming by diffusion creep looks like:

Exponent m depends on whether the atoms are barging through the bulk of a grain (m = 2), or along the grain boundaries (m = 3). What’s that new symbol B in the denominator, you ask? That’s creep compliance (in this case – diffusion creep compliance), and you two have already met, sort of. Creep compliance specifies how a given creep mechanism depends on pressure and temperature:

For diffusion creep of upper mantle rocks, I typically use m = 3, B0 ∼ 13 µmm MPa-1 s-1 (which is just a material-specific prefactor), Ediff = 300 · 103 J mol-1 and Vdiff = 5 cm3 mol-1 from Karato and Wu (1993). Sometimes I go bananas and set Vdiff = 0 cm3 mol-1 , blatantly ignoring pressure dependence of viscosity, which is ok as long as I’m looking at relatively modest depth-ranges, like a few tens of kilometers.

At sufficiently high stresses, a whole row of atoms can become mobilized and move through the crystal, instead of the meagre one-by-one atomic hopping between the vacancies. This mode of deformation is called dislocation creep. Dislocations are really just a larger scale glitch in the structure of atoms (compared to vacancies). They are linear lattice defects, where a whole row of atoms can be out of order, displaced or missing. It requires more energy to displace a dislocation, because you are displacing more than one atom, but once it’s on the move, it accommodates strain much more efficiently than in the each-atom-for-itself diffusion creep regime. As the material creeps, dislocations get born (nucleated), get displaced and get dead (annihilated). Dislocations don’t care about grain size. What they do care about is stress. Stress determines the rate at which dislocations appear, move and disappear. I know you saw it coming, more math, here is the dislocation creep viscosity:

Exponent n dictates the stress dependence of viscosity. Stress dependence of dislocation creep viscosity is a real pain, making the whole thing nonlinear and difficult to use in a geodynamical model. Not impossible, but rage-inducingly difficult. Say you’re trying to increase the strain rate by some amount, so you increase the stress, but then the viscosity drops, and suddenly you have a monster of a strain rate you never asked for. Ok, maybe it’s not quite this bad, but it’s not as good as if the viscosity just stayed constant. You wouldn’t be able to have strain localization, form tectonic plate boundaries and develop life on Earth then, but maaaan would you be cracking geodynamic problems like they were peanuts! I’m derailing. Just like all the other creeps, dislocation creep has its own compliance, A, that governs its dependence on pressure and temperature:

For dislocation creep of upper mantle rocks, I typically use n = 3, A0 = 1.1 · 105 MPa-n s -1 (which is just a material-specific prefactor), Edisl = 530 · 103 J mol -1 and Vdiff = 20 cm3 mol-1 , similar to Karato and Wu (1993). Just like for diffusion creep, I sometimes just set Vdisl = 0 cm3 mol-1 to keep things simple.

We’re almost done. Allow me one last remark. A rock has an insane amount of atoms, crystal grains and defects, all subject to local and far-field conditions (stress, temperature, pressure, deformation history, etc). A typical rock is therefore heterogeneous on the atomic (nano), granular (micro) and outcrop (meter) scales. Thus, within one and the same rock, deformation will likely be accommodated by more than just one mechanism. With that in mind, and sticking to just two deformation mechanisms described above, we can mix it all together to get:

This is known as composite rheology, where we assumed that the strain rates accommodated by diffusion and dislocation creep can be simply summed up, like so:

Alright. If you got down to here, I salute you! Next time you’re squeezing a peridotite, or splashing in the mud, or running through peanut butter – give a shout out to those little atoms that enable you to do such madness. And if you want to get to the physics of it all, you can find some good introductory texts in Karato (2008); Turcotte and Schubert (2002).

References 

S. Karato. Deformation of earth materials: an introduction to the rheology of solid earth. Cambridge Univ Pr, 2008. 

S. Karato and P. Wu. Rheology of the upper mantle: a synthesis. Science, 260(5109):771–778, 1993. 

D.L. Turcotte and G. Schubert. Geodynamics. Cambridge Univ Pr, 2002.