GD
Geodynamics

modelling

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.

References
 Agrusta, R., J. van Hunen, and S. Goes (2014), The effect of metastable pyroxene on the slab dynamics, Geophys. Res. Lett., 41, 8800-8808.
 Agrusta, R., S. Goes, and J. van Hunen (2017), Subducting-slab transition-zone interaction: stagnation, penetration and mode switches, Earth Planet. Sci. Let., 464, 10-23.
 Capitanio, F. A., G. Morra, and S. Goes (2007), Dynamic models of downgoing plate buoyancy driven subduction: subduction motions and energy dissipation, Earth Planet. Sci. Lett., 262, 284-297.
 Čížková, H., J. van Hunen, A. P. van der Berg, and N. J. Vlaar (2002), The influence of rheological weakening and yield stress on the interaction of slabs with the 670 km discontinuity, Earth Plan. Sci. Let., 199(3-4), 447-457.
 Conrad, C. P., and B. H. Hager (1999), Effects of plate bending and fault strength at subduction zones on plate dynamics, J. Geophys. Res., 104(B8), 17551-17571.
 Forsyth, D. W., and S. Uyeda (1975), On the relative importance of driving forces of plate motion. , Geophys. J. R. Astron. Soc. , 43, 163-200.
 Garfunkel, Z., C. A. Anderson, and G. Schubert (1986), Mantle circulation and the lateral migration of subducted slab, J. Geophys. Res., 91(B7), 7205-7223.
 Goes, S., R. Agrusta, J. van Hunen, and F. Garel (2017), Subduction-transition zone interaction: a review, Geosphere, 13(3. Subduction Top to Bottom 2), 1-21.
 Karato, S. I., M. R. Riedel, and D. A. Yuen (2001), Rheological structure and deformation of subducted slabs in the mantle transition zone: implications for mantle circulation and deep earthquakes, Phys. Earth Plan. Int., 127, 83-108.
 Kincaid, C., and P. Olson (1987), An experimental study of subduction and slab migration, J. Geophys. Res., 92(B13), 13,832-813,840.
 King, S. D., D. J. Frost, and D. C. Rubie (2015), Why cold slabs stagnate in the transition zone, Geology, 43, 231-234.
 Van der Hilst, R. D., and T. Seno (1993), Effects of relative plate motion on the deep structure and penetration depth of slabs below the Izu-Bonin and Mariana island arcs, Earth Plan. Sci. Let., 120, 395-407.
 Van der Hilst, R. D., E. R. Engdahl, W. Spakman, and G. Nolet (1991), Tomographic imaging of subducted lithosphere below northwest Pacific island arcs, Nature, 353, 37-43.
 Zhou, H.-w., and R. W. Clayton (1990), P and S Wave Travel Time Inversions for Subducting Slab Under the Island Arcs of the Northwest Pacific, J. Geophys. Res., 95(B5), 6829-6851.

Being both strong and weak

Being both strong and weak

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, Postdoc Anthony Osei Tutu of GFZ Potsdam shares the outcomes of his PhD work, showing us that, like the lithosphere, it is OK to be weak sometimes!

Strength is not everything in achieving one’s goal. The lithospheric plate acts both strong and weak at times. This dual characteristic of the outermost part of the Earth, the crustal-lithospheric shell, is thought to have sustained plate tectonics throughout Earth’s history, in the presence of other controlling mechanisms such as the weak asthenospheric layer (Bercovici et al. 2000; Karato 2012). In the world of the lithospheric plates there is the saying “I might be strong and unbreakable, but sometimes and somewhere, I am very weak, soft and brittle” and this allows the plates to accommodate each other in their relative movements.

We all sometimes need to bring out the soft part in us to accommodate others such as friends, family or colleagues. For example, my graduate school, the Helmholtz-Kolleg GEOSIM, an experiment by the Helmholtz Association, GFZ-Potsdam, University of Potsdam and Free University of Berlin, brought together two or more experts in mathematics and geosciences to collaborate on and serve as PhD supervisors for answering some of Earth Sciences’ pressing questions. The many, many benefits of this multidisciplinary PhD supervising approach also came with challenges. Sometimes, the different supervisors would make opposing/contrasting suggestions to investigate a particular problem according to the experience of some students and myself. Then it falls on you as the student to stand firm (i.e. be strong) on what you believe works for your experiments and at the same time to be receptive (i.e. flexible or soft) to the different suggestions, while keeping in mind the limited time you have as a PhD student.

Figure 1: Schematic plot of the conditions in a subduction system (left) aiding or (right) hindering global plate motions.

The both strong and weak behavior of the lithospheric plates was one of the conclusions of my PhD study. Besides the strong plate interiors (Zhong and Watts 2013), weak regions along the plate boundaries, aided by sediment and water (see Fig. 1), are required to give the low friction between the subducting and overriding plates (Moresi and Solomatov 1998; Sobolev and Babeyko 2005), combined with a less viscous sublithospheric mantle. This combination was key to match the magnitude and direction of present-day global plate motions in the numerical modeling study (Osei Tutu et al. 2018). I used the global 3D lithosphere-asthenosphere numerical code SLIM3D (Popov and Sobolev 2008) with visco-elasto-plastic rheology coupled to a mantle flow code (Hager and O’Connell 1981) for the investigation. To understand the influence of intra-plate friction (brittle/plastic yielding) and asthenospheric viscosity on present-day plate motions, I tested a range of strengths of the plate boundary. Past numerical modeling studies (Moresi and Solomatov 1998; Crameri and Tackley 2015) have suggested that small friction coefficients (μ < 0.1, yield stress ~100 MPa) can lead to plate tectonics in models of mantle convection. This study shows that in order to match present-day plate motions and net rotation, the static frictional parameter must be less than 0.05 (15 MPa yield stress). I am able to obtain a good fit with the magnitude and orientation of observed plate velocities (NUVEL-1A) in a no-net-rotation reference frame with μ < 0.04 and a minimum asthenosphere viscosity of 5•1019 Pas to 1•1020 Pas (Fig. 2). The estimates of net-rotation (NR) of the lithosphere suggest that amplitudes of ~0.1– 0.2 °/My, similar to most observation-based estimates, can be obtained with asthenosphere viscosity cutoff values of ~1•1019 Pas to 5•1019 Pas and a friction coefficient μ < 0.05.

Figure 2: Set of predicted global plate motions for varying asthenosphere viscosity and plate boundary frictions, modified after Osei Tutu et al. (2018). Rectangular boxes show calculations with RMS velocities comparable to the observed RMS velocity of NUVEL-1A (DeMets et al. 2010).

The second part of my PhD study focused on the responses of the strong plate interiors to the convecting mantle below by evaluating the influence of shallow and deep mantle heterogeneities on the lithospheric stress field and topography. I explored the sensitivity of the considered surface observables to model parameters providing insights into the influence of the asthenosphere and plate boundary rheology on plate motion by testing various thermal-density structures to predict stresses and topography. Lithospheric stresses and dynamic topography were computed using the model setup and rheological parameters that gave the best fit to the observed plate motions (see rectangular boxes in Fig. 2). The modeled lithosphere stress field was compared the World Stress Map 2016 (Heidbach et al. 2016) and the modeled dynamic topography to models of observed residual topography (Hoggard et al. 2016; Steinberger 2016). I tested a number of upper mantle thermal-density structures. The thermal structure used to calculate the plate motions before is considered the reference thermal-density structure, see also Osei Tutu et al. (2017). This reference thermal-density structure is derived from a heat flow model combined with a sea floor age model. In addition I used three different thermal-density structures derived from global S-wave velocity models to show the influence of lateral density heterogeneities in the upper 300 km on model predictions. These different structures showed that a large portion of the total dynamic force generating stresses in the crust/lithosphere has its origin in the deep mantle, while topography is largely influenced by shallow heterogeneities. For example, there is hardly any difference between the stress orientation patterns predicted with and without consideration of the heterogeneities in the upper mantle density structure across North America, Australia and North Africa. However, inclusion of crustal thickness variations in the stress field simulations (as shown in Fig. 3a) resulted in crustal dominance in areas of high altitude in terms of stress orientation, for example in the Andes and Tibet, compared to the only-deep mantle contributions (as shown in Fig. 3b).

Figure 3: Modeled lithosphere stress field in the Andes considering (a) crustal thickness variations from the CRUST 1.0 model as well as lithospheric variations and (b) uniform crustal and lithospheric thicknesses.

The outer shell of the solid Earth is complex, exhibiting different behaviors on different scales. In our quest to understand its dynamics, we can learn from the lithospheric plate’s life cycle how to live our lives and preserve our existence as scientist-humans by accommodating one another. After all, they have existed for billions of years.

 

References:

Bercovici, David, Yanick Ricard, and Mark A. Richards. 2000. “The Relation Between Mantle Dynamics and Plate Tectonics: A Primer.” 5–46.

Crameri, Fabio and Paul J. Tackley. 2015. “Parameters Controlling Dynamically Self-Consistent Plate Tectonics and Single-Sided Subduction in Global Models of Mantle Convection.” Journal of Geophysical Research: Solid Earth 120(5):3680–3706, 10.1002/2014JB011664.

DeMets, Charles, Richard G. Gordon, and Donald F. Argus. 2010. “Geologically Current Plate Motions.” Geophys. J. Int 181:1–80.

Hager, BH and RJ O’Connell. 1981. “A Simple Global Model of Plate Dynamics and Mantle Convection.” Journal of Geophysical Research: Solid Earth, 86(B6):4843–4867, 10.1029/JB086iB06p04843.

Heidbach, Oliver, Mojtaba Rajabi, Moritz Ziegler, Karsten Reiter, and Wsm Team. 2016. “The World Stress Map Database Release 2016 -Global Crustal Stress Pattern vs. Absolute Plate Motion.” Geophysical Research Abstracts EGU General Assembly 18:2016–4861.

Hoggard, M. J., N. White, and D. Al-Attar. 2016. “Global Dynamic Topography Observations Reveal Limited Influence of Large-Scale Mantle Flow.” Nature Geoscience 9(6):456–63, 10.1038/ngeo2709.

Karato, Shun-Ichiro. 2012. “On the Origin of the Asthenosphere.” Earth and Planetary Science Letters 321–322:95–103.

Moresi, Louis and Viatcheslav Solomatov. 1998. “Mantle Convection with a Brittle Lithosphere: Thoughts on the Global Tectonic Styles of the Earth and Venus.” Geophysical Journal International 133(3):669–82, 10.1046/j.1365-246X.1998.00521.x.

Osei Tutu, A., S. V Sobolev, B. Steinberger, A. A. Popov, and I. Rogozhina. 2018. “Evaluating the Influence of Plate Boundary Friction and Mantle Viscosity on Plate Velocities.” Geochemistry, Geophysics, Geosystems n/a-n/a, 10.1002/2017GC007112.

Popov, A. A. and S. V. Sobolev. 2008. “SLIM3D: A Tool for Three-Dimensional Thermomechanical Modeling of Lithospheric Deformation with Elasto-Visco-Plastic Rheology.” Physics of the Earth and Planetary Interiors 171(1–4):55–75.

Sobolev, S. V. and A. Y. Babeyko. 2005. “What Drives Orogeny in the Andes?” Geology 33(8).

Steinberger, Bernhard. 2016. “Topography Caused by Mantle Density Variations: Observation-Based Estimates and Models Derived from Tomography and Lithosphere Thickness.” Geophysical Journal International 205(1):604–21, 10.1093/gji/ggw040.

Osei Tutu, A., B. Steinberger, S. V Sobolev, I. Rogozhina, and A. Popov. 2017. "Effects of Upper Mantle Heterogeneities on Lithospheric Stress Field and Dynamic Topography." Solid Earth Discuss., https://doi.org/10.5194/se-2017-111, in review, 2017

Zhong, Shijie and A. B. Watts. 2013. “Lithospheric Deformation Induced by Loading of the Hawaiian Islands and Its Implications for Mantle Rheology.” Journal of Geophysical Research: Solid Earth 118(11):6025–48, 10.1002/2013JB010408.