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Thoughts on geological modelling: an analogue perspective

Thoughts on geological modelling: an analogue perspective

In geodynamics we study the dynamics of the Earth (and other planets). We ground our studies in as much data as possible, however we are constrained by the fact that pretty much all direct information we can collect from the interior of the Earth only shows its present-day state. The surface rock record gives us a glimpse into the past dynamics and evolution of our planet, but this record gets sparser as we go back in time. This is why it is common to use modelling in geodynamics to fill this gap of knowledge. There are different types of modelling, and this week João Duarte writes about the importance of analogue modelling. 

João Duarte. Researcher at Instituto Dom Luiz and Invited Professor at the Geology Department, Faculty of Sciences of the University of Lisbon. Adjunct Researcher at Monash University.

The first time I went to EGU, in 2004, I presented a poster with some new marine geology data and a few sets of analogue models. I was doing accretionary wedges in sandboxes. At the time, I was in the third year of my bachelor’s degree and I was completely overwhelmed by the magnitude of the conference. It was incredible to see the faces of all those scientists that I used to read articles from. But one thing impressed me the most. Earth Sciences were consolidating as a modern, theoretical based science. The efforts in trying to develop an integrated dynamic theory of plate tectonics as part of mantle convection were obvious. The new emergent numerical models looked incredible, with all those colours, complex rheologies and stunning visualization that allowed us to “see” stresses, temperature gradients and non-linear viscosities. I was amazed.

Analogue modelling was at a relative peak in 2004, however it was also anticipated by some that it would quickly disappear (and indeed several analogue labs have closed since). It was with this mindset, that I later did the experiments for my PhD, which I finished in 2012 (Duarte et al., 2011). But I was fortunate. My supervisors, Filipe Rosas and Pedro Terrinha, took me to state-of-art labs, namely Toronto and Montpellier (lead at the time by Sandy Cruden and Jacques Malavieille, respectively), and I started to develop a passion for this kind of models. When I moved to Monash for a post-doc position, in 2011, this turned out to be a great advantage. There, modelers such as Wouter Schellart, Louis Moresi, Fabio Capitanio, David Boutelier and Sandy Cruden (yes, I met Sandy again at Monash) were using analogue models to benchmark numerical models. Why? Because many times, even though numerical models produce spectacular results, they might not be physically consistent. And there is only one way to get rid of this, which is to make sure that whatever numerical code we are using can reproduce simple experiments that we can run in a lab. The classical example is the sinking of a negatively buoyant sphere in a viscous medium.

Sandbox analogue model of an accretionary wedge. Part of the same experiment as shown in the header figure. Here, a sliced section cut after wetting, is shown. University of Lisbon, 2009. Experiments published in Duarte et al. (2011).

That was what we were doing at Monash. I worked with Wouter Schellart in the development of subduction experiments with an overriding plate, which were advancing step by step in both analogue and numerical schemes (see e.g., Duarte et al., 2013 and Chen et al., 2015, 2016 for the analogue models, and Schellart and Moresi, 2013 for numerical equivalents). The tricky bit was, we wanted to have self-consistent dynamic experiments in which we were ascribing the forces (negative buoyancy of the slab, the viscosity of the upper mantle, etc) and let the kinematics (i.e. the velocities) to be an emergent phenomenon. So, no lateral push or active kinematic boundaries were applied to the plates. This is because we now recognize that in general, it is the slab pull at subduction zones that majorly drives the plates and not the other way around. Therefore, if we want to investigate the fundamental physics and dynamics of subduction zones we need to use self-consistent models (both analogue and numerical). In order to carry out these models, we had to develop a new rheology for the subduction interface, which is a complex problem, both in the analogue and the numerical approaches (Duarte et al. 2013, 2014, 2015). But this is another very long story that would lead to a publication by itself.

Analogue models of subduction with an overriding plate and an interplate rheology. Monash University, 2012. Adapted from Duarte et al. (2013)

But what is analogue modelling all about? Basically, analogue models are scaled models that we can develop in the laboratory using analogue materials (such as sand), and that at the scale that we are doing our models have similar physical properties to those of natural materials (such as brittle rocks). But, as it is widely known, under certain circumstances (at large time and space scales), rocks behave like fluids, and for that we use analogue fluids, such as silicone putties, glucose and honey. We can also use fluids to simulate the interaction between subduction zones and mantle plumes in a fluid reservoir (see below figures and links to videos of scaled experiments using three different fluids to study slab-plume interaction; Meriaux et al., 2015a, 2015b, 2016). These are generally called geodynamic analogue models.

End of a slab-plume experiment in the upper mantle (see below). The tank is partially filled with glucose. The slab (laying at the analogue 660 discontinuity) is made of silicone mixed with iron powder. The plume is made of a water solution of glucose dyed with a red colorant. And that’s me on the left. Monash University, 2014.

I usually consider two main branches of analogue models. The first, which is the one mostly used by geologists, was started by Sir James Hall (1761 – 1832), that squeezed layers of clay to reproduce the patterns of folded rocks that he had observed in nature. This method was later improved by King Hubbert (1937), who laid the ground for the development of the field by developing a theory of scaling of analogue models applied to geological processes.

The other branch is probably as old as humans. It began when we started to manipulate objects and using them to understand basic empirical laws, such as the one that objects always fall. When Galileo was using small spheres in inclined surfaces to extract the physical laws that describe the movement of bodies, from rocks to planets, he was in a certain way using analogue models. He understood that many laws are scale invariant. Still today, these techniques are widely used by physicist and engineers when understanding for example the aerodynamics of airplanes, the stability of bridges, the dynamics of rivers or the resistance of dams. They use scaled models that reproduce at suitable laboratory scales the objects and processes that they are investigating.

What we did at Monash, was a mixture of both approaches. Though, we were less interested in exactly reproducing nature from a purely geometric and kinematic point of view, but we were more interested in understanding the physics of the object we were investigating: subduction zones. Therefore, we had to guarantee that we were using the correct dynamical approach in order to be able to extract generic physical empirical laws, hoping that these laws would provide us some insight on the dynamics of natural subduction zones. These empirical laws could readily be incorporated in numerical models, which would then help exploring more efficiently the space of the controlling parameters in the system.

Slab-Plume interaction in the upper mantle. Experiments published in Meriaux et al. (2015a, 2015b).

I want to finish with a question that I believe concerns all of us: are there still advantages in using analogue models? Yes, I believe so! One of the most important advantages is that analogue models are always three-dimensional and high-resolution. Furthermore, they allow a good tracking of the strain and to understand how it occurs in discontinuous mediums, for example when investigating the localization of deformation or the propagation of cracks. Numerical schemes still struggle with these problems. It is very difficult to have an efficient code that can deal simultaneously with very high resolution and large-scale three-dimensional problems, as it is required to investigate the process of subduction. Nevertheless, numerical models are of great help when it comes to track stresses, and model complex rheologies and temperature gradients. To sum up: nowadays, we recognize that certain problems can only be tackled using self-consistent dynamic models that model the whole system in three-dimensions, capturing different scales. For this, the combination of analogue and numerical models is still one of the most powerful tools we have. An interesting example of a field in which a combined approach is being used is the fascinating investigations on the seismic cycle (for example, see here).

Links to videos:

VIDEO 1: https://www.youtube.com/watch?v=U1TXC2XPbFA&feature=youtu.be
(Subduction with an overriding plate and an interplate rheology. Duarte et al., 2013)

VIDEO 2: https://www.youtube.com/watch?v=n5P2TzS6h_0&feature=youtu.be
(Slab-plume interaction at mantle scale. Side-view of the experiment on the top, and top-view of the experiment on the bottom. Meriaux et al., 2016)
References:

Chen, Z., Schellart, W.P., Strak, V., Duarte, J.C., 2016. Does subduction-induced mantle flow drive backarc extension? Earth and Planetary Science Letters 441, 200-210. https://doi.org/10.1016/j.epsl.2016.02.027

Chen, Z., Schellart, W.P., Duarte, J.C., 2015. Overriding plate deformation and variability of forearc deformation during subduction: Insight from geodynamic models and application to the Calabria subduction zone. Geochemistry, Geophysics, Geosystems 16, 3697–3715. DOI: 10.1002/2015GC005958

Duarte, J.C., Schellart, W.P., Cruden, A.R., 2015. How weak is the subduction zone interface? Geophysical Research Letters 41, 1-10. DOI: 10.1002/2014GL062876

Duarte, J.C., Schellart, W.P., Cruden, A.R., 2014. Rheology of petrolatum – paraffin oil mixtures: applications to analogue modelling of geological processes. Journal of Structural Geology 63, 1-11. https://doi.org/10.1016/j.jsg.2014.02.004

Duarte, J.C., Schellart, W.P., Cruden, A.R., 2013. Three-dimensional dynamic laboratory models of subduction with an overriding plate and variable interplate rheology. Geophysical Journal International 195, 47-66. https://doi.org/10.1093/gji/ggt257

Duarte, J.C., F.M. Rosas P., Terrinha, M-A Gutscher, J. Malavieille, Sónia Silva, L. Matias, 2011. Thrust–wrench interference tectonics in the Gulf of Cadiz (Africa–Iberia plate boundary in the North-East Atlantic): Insights from analog models. Marine Geology 289, 135–149. https://doi.org/10.1016/j.margeo.2011.09.014

Hubbert, M.K., 1937. Theory of scale models as applied to the study of geologic structures. GSA Bulletin 48, 1459-1520. https://doi.org/10.1130/GSAB-48-1459

Meriaux, C., Meriaux, A-S., Schellart, W.P., Duarte, J.C., Duarte, S.S., Chen, Z., 2016. Mantle plumes in the vicinity of subduction zones. Earth and Planetary Science Letters 454, 166-177. https://doi.org/10.1016/j.epsl.2016.09.001

Mériaux, C.A., Duarte, J.C., Schellart, W.P., Mériaux, A-S., 2015. A two-way interaction between the Hainan plume and the Manila subduction zone. Geophysical Research Letters 42, 5796–5802. DOI: 10.1002/2015GL064313

Meriaux, C.A., Duarte, J.C., Duarte, S., Chen, Z., Rosas, F.M., Mata, J., Schellart, W.P., and Terrinha, P. 2015. Capture of the Canary mantle plume material by the Gibraltar arc mantle wedge during slab rollback. Geophysical Journal International 201, 1717-1721. https://doi.org/10.1093/gji/ggv120

Schellart, W.P., Moresi, L., 2013. A new driving mechanism for backarc extension and backarc shortening through slab sinking induced toroidal and poloidal mantle flow: Results from dynamic subduction models with an overriding plate. Journal of Geophysical Research: Solid Earth 118, 3221-3248. https://doi.org/10.1002/jgrb.50173

Reproducible Computational Science

Reproducible Computational Science

 

Krister with his bat-signal shirt for reproducibility.

We’ve all been there – you’re reading through a great new paper, keen to get to the Data Availability only to find nothing listed, or the uninspiring “data provided on request”. This week Krister Karlsen, PhD student from the Centre for Earth Evolution and Dynamics (CEED), University of Oslo shares some context and tips for increasing the reproducibility of your research from a computational science perspective. Spread the good word and reach for the “Gold Standard”!

Historically, computational methods and modelling have been considered the third avenue of the sciences, but they are now some of the most important, paralleling experimental and theoretical approaches. Thanks to the rapid development of electronics and theoretical advances in numerical methods, mathematical models combined with strong computing power provide an excellent tool to study what is not available for us to observe or sample (Fig. 1). In addition to being able to simulate complex physical phenomena on computer clusters, these advances have drastically improved our ability to gather and examine high-dimensional data. For these reasons, computational science is in fact the leading tool in many branches of physics, chemistry, biology, and geodynamics.

Figure 1: Time–depth diagram presenting availability of geodynamic data. Modified from (Gerya, 2014).

A side effect of the improvement of methods for simulation and data gathering is the availability of a vast variety of different software packages and huge data sets. This poses a challenge in terms of sufficient documentation that will allow the study to be reproduced. With great computing power, comes great responsibility.

“Non-reproducible single occurrences are of no significance to science.” – Popper (1959)

Reproducibility is the cornerstone of cumulative science; the ultimate standard by which scientific claims are judged. With replication, independent researchers address a scientific hypothesis and build up evidence for, or against, it. This methodology represents the self-correcting path that science should take to ensure robust discoveries; separating science from pseudoscience. Reports indicate increasing pressure to publish manuscripts whilst applying for competitive grants and positions (Baker, 2016). Furthermore, a growing burden of bureaucracy takes away precious time designing experiments and doing research. As the time available for actual research is decreasing, the number of articles that mention a “reproducibility crisis?” are rising towards the present day peak (Fig. 2). Does this mean we have become sloppy in terms of proper documentation?

Figure 2: Number of titles, abstracts, or keywords that contain one of the following phrases: “reproducibility crisis,” “scientific crisis,” “science in crisis,” “crisis in science,” “replication crisis,” “replicability crisis”, found in the Web of Science records. Modified from (Fanelli, 2018).

Are we facing a reproducibility crisis?

A survey conducted by Nature asked 1,576 researchers this exact question, and reported 52% responded with “Yes, a significant crisis,” and 38% with “Yes, a slight crisis” (Baker, 2016). Perhaps more alarming is that 70% report they have unsuccessfully tried to reproduce another scientist’s findings, and more than half have failed to reproduce their own results. To what degree these statistics apply to our own field of geodynamics is not clear, but it is nonetheless a timely remainder that reproducibility must remain at the forefront of our dissemination. Multiple journals have implemented policies on data and software sharing upon publication to ensure the replication and reproduction of computational science is maintained. But how well are they working? A recent empirical analysis of journal policy effectiveness for computational reproducibility sheds light on this issue (Stodden et al., 2018). The study randomly selected 204 papers published in Science after the implementation of their code and data sharing policy. Of these articles, 24 contained sufficient information, whereas for the remaining 180 publications the authors had to be contacted directly. Only 131 authors replied to the request, of these 36% provided some of the requested material and 7% simply refused to share code and data. Apparently the implementation of policies was not enough, and there is still a lot of confusion among researchers when it comes to obligations related to data and code sharing. Some of the anonymized responses highlighted by Stodden et al. (2018) underline the confusion regarding the data and code sharing policy:

Putting aside for the moment that you are, in many cases, obliged to share your code and data to enhance reproducibility; are there any additional motivating factors in making your computational research reproducible? Freire et al. (2012) lists a few simple benefits of reproducible research:

1. Reproducible research is well cited. A study (Vandewalle et al., 2009) found that published articles that reported reproducible results have higher impact and visibility.

2. Code and software comparisons. Well documented computational research allows software developed for similar purposes to be compared in terms of performance (e.g. efficiency and accuracy). This can potentially reveal interesting and publishable differences between seemingly identical programs.

3. Efficient communication of science between researchers. New-comers to a field of research can more efficiently understand how to modify and extend an existing program, allowing them to more easily build upon recently published discoveries (this is simply the positive counterpart to the argument made against software sharing earlier).

“Replicability is not reproducibility: nor is it good science.” – Drummond (2009)

I have discussed reproducibility over quite a few paragraphs already, without yet giving it a proper definition. What precisely is reproducibility? Drummond (2009) proposes a distinction between reproducibility and replicability. He argues that reproducibility requires, at the minimum, minor changes in experiment or model setup, while replication is an identical setup. In other words, reproducibility refers to a phenomenon that can be predicted to recur with slightly different experimental conditions, while replicability describes the ability to obtain an identical result when an experiment is performed under precisely the same conditions. I think this distinction makes the utmost sense in computational science, because if all software, data, post-processing scripts, random number seeds and so on, are shared and reported properly, the results should indeed be identical. However, replicability does not ensure the validity of the scientific discovery. A robust discovery made using computational methods should be reproducible with a different software (made for similar purposes, of course) and small perturbations to the input data such as initial conditions, physical parameters, etc. This is critical because we rarely, if ever, know the model inputs with zero error bars. A way for authors to address such issues is to include a sensitivity analysis of different parameters, initial conditions and boundary conditions in the publication or the supplementary material section.

Figure 3: Illustration of the “spectrum of reproducibility”, ranging from not reproducible to the gold standard that includes code, data and executable files that can directly replicate the reported results. Modified from (Peng, 2011).

However, the gold standard of reproducibility in computation-involved science, like geodynamics, is often described as what Drummond would classify as replication (Fig. 3). That is, making all data and code available to others to easily execute. Even though this does not ensure reproducibility (only replicability), it provides other researchers a level of detail regarding the work-flow and analysis that is beyond what can usually be achieved by using common language. And this deeper understanding can be crucial when trying to reproduce (and not replicate) the original results. Thus replication is a natural step towards reproduction. Open-source community codes for geodynamics, like eg. ASPECT (Heister et al., 2017), and more general FEM libraries like FEniCS (Logg et al., 2012), allows for friction-free replication of results. An input-file describing the model setup provides a 1-to-1 relation to the actual results1 (which in many cases is reasonable because the data are too large to be easily shared). Thus, sharing the post-processing scripts accompanied by the input file on eg. GitHub, will allow for complete replication of the results, at low cost in terms of data storage.

Light at the end of the tunnel?

In order to improve practices for reproducibility, contributions will need to come from multiple directions. The community needs to develop, encourage and maintain a culture of reproducibility. Journals and funding agencies can play an important role here. The American Geosciences Union (AGU) has shared a list of best practices regarding research data2 associated with a publication:

• Deposit the data in support of your publication in a leading domain repository that handles such data.

• If a domain repository is not available for some of all of your data, deposit your data in a general repository such as Zenodo, Dryad, or Figshare. All of these repositories can assign a DOI to deposited data, or use your institution’s archive.

• Data should not be listed as “available from authors.”

• Make sure that the data are available publicly at the time of publication and available to reviewers at submission—if you are unable to upload to a public repository before submission, you may provide access through an embargoed version in a repository or in datasets or tables uploaded with your submission (Zenodo, Dryad, Figshare, and some domain repositories provide embargoed access.) Questions about this should be sent to journal staff.

• Cite data or code sets used in your study as part of the reference list. Citations should follow the Joint Declaration of Data Citation Principles.

• Develop and deposit software in GitHub which can be cited, or include simple scripts in a supplement. Code in Github can be archived separately and assigned a DOI through Zenodo for submission.

In addition to best practice guidelines, wonderful initiatives from other communities include a research prize. The European College of Neuropsychopharmacology offers a (11,800 USD) award for negative results, more specifically for careful experiments that do not confirm an accepted hypothesis or previous result. Another example is the International Organization for Human Brain Mapping who awards 2,000 USD for the best replication study − successful or not. Whilst not a prize per se, at recent EGU General Assemblies in Vienna the GD community have held sessions around the theme of failed models. Hopefully, similar initiatives will lead by example so that others in the community will follow.

1To the exact same results, information about the software version, compilers, operating system etc. would also typically be needed.

2 AGU’s definition of data includes all code, software, data, methods and protocols used to produce the results here.

References

AGU, Best Practices. https://publications.agu.org/author-resource-center/publication-policies/datapolicy/data-policy-faq/ Accessed: 2018-08-31.

Baker, Monya. Reproducibility crisis? Nature, 533:26, 2016.

Drummond, Chris. Replicability is not reproducibility: nor is it good science. 2009.

Fanelli, Daniele. Opinion: Is science really facing a reproducibility crisis, and do we need it to?Proceedings of the National Academy of Sciences, 115(11):2628–2631, 2018.

Freire, Juliana; Bonnet, Philippe, and Shasha, Dennis. Computational reproducibility: state-of-theart, challenges, and database research opportunities. In Proceedings of the 2012 ACM SIGMOD international conference on management of data, pages 593–596. ACM, 2012.

Gerya, Taras. Precambrian geodynamics: concepts and models. Gondwana Research, 25(2):442–463, 2014.

Heister, Timo; Dannberg, Juliane; Gassm"oller, Rene, and Bangerth, Wolfgang. High accuracy mantle convection simulation through modern numerical methods. II: Realistic models and problems. Geophysical Journal International, 210(2):833–851, 2017. doi: 10.1093/gji/ggx195. URL https://doi.org/10.1093/gji/ggx195.

Logg, Anders; Mardal, Kent-Andre; Wells, Garth N., and others, . Automated Solution of Differential Equations by the Finite Element Method. Springer, 2012. ISBN 978-3-642-23098-1. doi: 10.1007/978-3-642-23099-8.

Peng, Roger D. Reproducible research in computational science. Science, 334(6060):1226–1227, 2011.

Popper, Karl Raimund. The Logic of Scientific Discovery . University Press, 1959.

Stodden, Victoria; Seiler, Jennifer, and Ma, Zhaokun. An empirical analysis of journal policy effectiveness for computational reproducibility. Proceedings of the National Academy of Sciences , 115(11):2584–2589, 2018.

Vandewalle, Patrick; Kovacevic, Jelena, and Vetterli, Martin. Reproducible research in signal processing. IEEE Signal Processing Magazine , 26(3), 2009

EGU GD Whirlwind Wednesday: Geodynamics 101 & other events

EGU GD Whirlwind Wednesday: Geodynamics 101 & other events

Yesterday (Wednesday, April 12, 2018), the first ever Geodynamics 101 short course at EGU was held. It was inspired by our regular blog series of the same name. I can happily report that it was a success! With at least 60 people attending (admittedly, we didn’t count as we were trying to focus on explaining geodynamics) we had a nicely filled room. Surprisingly, quite some geodynamicists were in the audience. Hopefully, we inspired them with new, fun ways to communicate geodynamics to people from other disciplines.

The short course was organised by me (Iris van Zelst, ETH Zürich), Adina Pusok (ECS GD Representative; UCSD, Scripps Institution of Oceanography, IGPP), Antoine Rozel (ETH Zürich), Fabio Crameri (CEED, Oslo), Juliane Dannberg (UC Davis), and Anne Glerum (GFZ Potsdam). Unfortunately, Anne and Juliane were unable to attend EGU, so the presentation was given by Antoine, Adina, Fabio and me in the end.

The main goal of this short course was to provide an introduction into the basic concepts of numerical modelling of solid Earth processes in the Earth’s crust and mantle in a non-technical, fun manner. It was dedicated to everyone who is interested in, but not necessarily experienced with, understanding numerical models; in particular early career scientists (BSc, MSc, PhD students and postdocs) and people who are new to the field of geodynamic modelling. Emphasis was put on what numerical models are and how scientists can interpret, use, and work with them while taking into account the advantages and limitations of the different methods. We went through setting up a numerical model in a step-by-step process, with specific examples from key papers and problems in solid Earth geodynamics to showcase:

(1) The motivation behind using numerical methods,
(2) The basic equations used in geodynamic modelling studies, what they mean, and their assumptions,
(3) How to choose appropriate numerical methods,
(4) How to benchmark the resulting code,
(5) How to go from the geological problem to the model setup,
(6) How to set initial and boundary conditions,
(7) How to interpret the model results.

Armed with the knowledge of a typical modelling workflow, we hope that our participants will now be able to better assess geodynamical papers and maybe even start working with numerical methods themselves in the future.

Apart from the Geodynamics 101 course, the evening was packed with ECS events for geodynamicists. About 40 people attended the ECS GD dinner at Wieden Bräu that was organised by Adina and Nico (the ECS Co-representative for geodynamics; full introduction will follow soon). After the dinner, most people went onwards to Bermuda Bräu for drinks with the geodynamics, tectonics & structural geology, and seismology division. It featured lots of dancing and networking and should thus be also considered a great success. On to the last couple of days packed with science!

Subduction through the mantle transition zone: sink or stall?

Subduction through the mantle transition zone: sink or stall?

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, Saskia Goes, Reader at Imperial College London, UK, discusses the fate of subducting slabs at the mantle transition zone.

Saskia Goes

Subducting plates can follow quite different paths in their life times. While some sink straight through the upper into the lower mantle, others appear to stall in the mantle transition zone above 660 km depth. Geodynamicists have long puzzled about what controls these different styles of behaviour, especially because there appear to be correlations between sinking or stalling with faster or slower plate motions and mountain building or ocean basin formation, respectively. In the long run, how easily slabs sink through the transition zone controls how efficiently material and heat are circulated in the mantle.

The word subduction derives from the Latin verb subducere, which means pulled away from below, but metaphorically can mean to lose footing or remove secretly. Definitely, when Wegener first proposed continental drift, people were unaware that subduction is removing plates from the Earth’s surface. We now know this process is not quite so secret. The plates creak in earthquakes as they sink into the mantle, in some cases all the way through the mantle transition zone to about 700 km depth. Furthermore, where the subducting plate bends below the overriding plate, it creates deep-sea trenches with prominent gravity and geoid signals. This bending is a very important part of subduction dynamics, as I’ll explain below.

The seismic Wadati-Benioff zones and gravity expressions were sufficient clues of the location of the downwelling limbs of a mantle convection system to help acceptance of plate tectonics in the 1960s. However, it took another twenty odd years until seismology yielded images of cold plates sinking into the mantle, and it turned out that the plates extend beyond the seismic Wadati-Benioff zones [Van der Hilst et al., 1991; Zhou and Clayton, 1990]. These images showed that some subducting plates flatten in the mantle transition zone (e.g. below Japan and Izu-Bonin), while others continue with little to no deflection into the lower mantle (e.g., below the Northern Kuriles and Marianas) (Fig. 1). Soon after, it was realised that many of the places where the slabs are flat in the transition zone have a history of trench retreat [Van der Hilst and Seno, 1993]. Furthermore, mapping of seafloor ages revealed that flat slabs tend to form where plates older than about 50 Myr are subducted [Karato et al., 2001; King et al., 2015].

Figure 1: Variable modes of slab-transition zone interaction

Many mechanisms have been proposed for the variable slab transition-zone interaction. We recently reviewed the geodynamic and observational literature and combined these insights with those from our own set of mechanical and thermo-mechanical subduction models [Goes et al., 2017]. This effort shows that not one single mechanism, but an interplay of several mechanisms is the likely cause of the observed variable subduction behaviour.

It has long been realised that viscosity increases with depth into the mantle, quite possibly including jumps at the major phase transitions in the mantle transition zone. The ringwoodite-postspinel transition that is responsible for the global 660 km seismic discontinuity, usually taken as the base of the upper mantle, is an endothermic transition under most of the conditions prevailing in the mantle today. This means that the transition will take place at a higher pressure and thus depth in the subducting plate than the surrounding mantle, rendering the plate locally buoyant with respect to the mantle. Both these factors hamper the descent of the subducting plate through the transition zone. However, a viscosity increase within acceptable bounds (as derived from geoid and postglacial rebound modelling) can slow sinking, but does not lead to stalling material. By contrast, the phase transition can lead to stalling, as well as an alternation of periods of accumulation of material in the transition zone and periods where this material flushes rapidly into the lower mantle, at least in convection models without strong plates. But does this work with strong plates?

Making dynamic models of subduction with strong plates is challenging because the models need to capture strong strength gradients between the core of the plate and the underlying mantle, allow for some form of plate yielding, maintain a weak zone between the two plates and adequately represent the effect of plate bending (a free-surface effect). Most models prescribe at least part of the system by imposing velocities and/or plate geometries. This however needs to be done with great care and consideration for what forcing such imposed conditions imply.

“Pulled away from below” is a good description of the dynamics of subduction. Subduction is primarily driven by slab pull, the gravitational force on the dense subducting plate [Forsyth and Uyeda, 1975]. And to “lose footing” reminds us that gravity is the main driving force. Gravity tries to pull the plate straight down (Fig. 2), so the easiest way for a plate to subduct is to fall into the mantle, a process that leads to trench retreat [Garfunkel et al., 1986; Kincaid and Olson, 1987]. Besides letting the plate follow the path of gravity, subduction by trench retreat has the other advantage that the plate does not need to bend too much. Bending a high-strength plate takes significant energy. Some studies have shown that if plates are assigned laboratory-based rheologies, such bending can easily take up all of the gravitational potential energy of the subducting plate [Conrad and Hager, 1999], so if plates are to sink into the mantle, they have to do this by minimising the amount of energy used for bending into the trench. As a consequence, strong and dense plates prefer to subduct at smaller dip angles while weaker and lighter plates can be bent to subduct more vertically [Capitanio et al., 2007].

Figure 2: If subduction occurs freely, i.e., driven by the pull of gravity on the dense slab with sinking resisted by the viscous mantle, it is usually energetically most favourable to subduct by trench retreat.

The angle at which plates subduct strongly affects how they subsequently interact with viscosity or phase interfaces (Fig. 3). Steeply dipping plates will buckle and thicken when they encounter resistance to sinking. This deformation facilitates further sinking, as a bigger mass. But plates that reach the interface at a lower dip may be deflected. Such deflected plates have a harder time sinking onwards, both because the high viscosity resistance is now distributed over a wider section of the plate and due to the spread-out additional buoyancy from the depressed endothermic phase boundary.

Figure 3: The subduction angle largely determines how the slab interacts with viscosity and phase changes.

So, variable plate density and strength can lead to variable behaviour of subduction in the transition zone. And we know plates have variable density and strength. Older plates are denser and if strength is thermally controlled, as most lab experiments predict, also stronger than younger plates. This implies that older plates can drive trench retreat more easily than young plates. And indeed this matches observations that significant trench retreat has only taken places where old plates subduct. Furthermore, significant trench retreat will facilitate plate flattening in the transition zone, consistent with the observation that flat plates tends to underlie regions with a history of trench retreat (even if that does not always mean trench motions are high at the present day). This mechanism can also explain why flat slabs tend to be associated with old plate subduction.

So what about the role of other proposed mechanisms? Our models with strong slabs show that only when slabs encounter both an increase in viscosity (which forces the slabs to deform or flatten) and an endothermic phase transition (which can lead to stalling of material in the transition zone) do we find the different modes of slab dynamics. Neither a viscosity increase alone, nor an endothermic phase transition alone leads to mixed slab dynamics.

Other factors likely contribute to the regional variability. In the cold cores of the slabs, some phases may persist metastably, thus delaying the transformations to higher density phases to a larger depth. Metastability will be more pervasive in colder old plates thus making older plates more buoyant and hence resistant to sinking than young ones. In combination with trench retreat facilitated by a strong slab at the trench, this can further encourage slab flattening [Agrusta et al., 2014; King et al., 2015]. Phase transformations may also lead to slab weakening in the transition zone because they can cause grain size reduction. Such weakening can aid slab deflection [Čížková et al., 2002; Karato et al., 2001]. However, several studies have shown that transition zone slab strength is less important than slab strength at the trench, which governs how a slab starts sinking through the transition zone.

The Earth is clearly more complex than the models discussed. For example, present-day plate dip angles display various trends with plate age at the trench. Lateral variations in plate strength and buoyancy can complicate subduction behaviour. Furthermore, forces on the upper plate and large-scale mantle flow may also impede or assist trench motions and may thus affect or trigger changes in how slabs interact with the transition zone [Agrusta et al., 2017]. All these factors remain to be fully investigated. However, the first order trends of subduction-transition zone interaction can be understood as a consequence of plates of various ages interacting with a viscosity increase and endothermic phase change.

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