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numerical modelling

Don’t be a hero – unless you have to

Don’t be a hero – unless you have to

The Geodynamics 101 series serves to show the diversity of topics and methods in the geodynamics community in an understandable manner for every geodynamicist. PhD’s, postdocs, full professors, and everyone in between can introduce their field of expertise in a lighthearted, entertaining manner and touch on some of the outstanding questions and problems related to their method of choice.
This week Dr. Cedric Thieulot, assistant professor at the Mantle dynamics & theoretical geophysics group at Utrecht University in The Netherlands, discusses the advantages and disadvantages of writing your own numerical code. Do you want to talk about your research area? Contact us!

 
In December 2013, I was invited to give a talk about the ASPECT code [1] at the American Geological Union conference in San Francisco. Right after my talk, Prof. Louis Moresi took the stage and gave a talk entitled: Underworld: What we set out to do, How far did we get, What did we Learn?

The abstract went as follows:
 

Underworld was conceived as a tool for modelling 3D lithospheric deformation coupled with the underlying / surrounding mantle flow. The challenges involved were to find a method capable of representing the complicated, non-linear, history dependent rheology of the near surface as well as being able to model mantle convection, and, simultaneously, to be able to solve the numerical system efficiently. […] The elegance of the method is that it can be completely described in a couple of sentences. However, there are some limitations: it is not obvious how to retain this elegance for unstructured or adaptive meshes, arbitrary element types are not sufficiently well integrated by the simple quadrature approach, and swarms of particles representing volumes are usually an inefficient representation of surfaces.

Aside from the standard numerical modelling jargon, Louis used a term during his talk which I thought at the time had a nice ring to it: hero codes. In short, I believe he meant the codes written essentially by one or two people who at some point in time spent great effort into writing a code (usually choosing a range of applications, a geometry, a number of dimensions, a particular numerical method to solve the relevant PDEs(1), and a tracking method for the various fields of interest).

In the long list of Hero codes, one could cite (in alphabetical order) CITCOM [1], DOUAR [8], FANTOM [2], IELVIS [5], LaMEM [3], pTatin [4], SLIM3D [10], SOPALE [7], StaggYY [6], SULEC [11], Underworld [9], and I apologise to all other heroes out there whom I may have overlooked. And who does not want to be a hero? The Spiderman of geodynamics, the Superwoman of modelling?

Louis’ talk echoed my thoughts on two key choices we (computational geodynamicists) are facing: Hero or not, and if yes, what type?
 

Hero or not?

Speaking from experience, it is an intense source of satisfaction when peer-reviewed published results are obtained with the very code one has painstakingly put together over months, if not years. But is it worth it?

On the one hand, writing one own’s code is a source of deep learning, a way to ensure that one understands the tool and knows its limitations, and a way to ensure that the code has the appropriate combination of features which are necessary to answer the research question at hand. On the other hand, it is akin to a journey; a rather long term commitment; a sometimes frustrating endeavour, with no guarantee of success. Let us not deny it – many a student has started with one code only to switch to plan B sooner or later. Ultimately, this yiels a satisfactory tool with often little to no perennial survival over the 5 year mark, a scarce if at all existent documentation, and almost always not compliant with the growing trend of long term repeatability. Furthermore, the resulting code will probably bear the marks of its not-all-knowing creator in its DNA and is likely not to be optimal nor efficient by modern computational standards.

This brings me to the second choice: elegance & modularity or taylored code & raw performance? Should one develop a code in a very broad framework using as much external libraries as possible or is there still space for true heroism?

It is my opinion that the answer to this question is: both. The current form of heroism no more lies in writing one’s own FEM(2)/FDM(3) packages, meshers, or solvers from scratch, but in cleverly taking advantage of state-of-the-art packages such as for example p4est [15] for Adaptive Mesh Refinement, PetSc [13] or Trilinos [14] for solvers, Saint Germain [17] for particle tracking, deal.ii [12] or Fenics [16] for FEM, and sharing their codes through platforms such as svn, bitbucket or github.

In reality, the many different ways of approaching the development or usage of a (new) code is linked to the diversity of individual projects, but ultimately anyone who dares to touch a code (let alone write one) is a hero in his/her own right: although (super-)heroes can be awesome on their own, they often complete each other, team up and join forces for maximum efficiency. Let us all be heroes, then, and join efforts to serve Science to the best of our abilities.

Abbreviations
(1) PDE: Partial Differential Equation (2) FEM: Finite Element Method (3) FDM: Finite Difference Method

References
[1] Zhong et al., JGR 105, 2000; [2] Thieulot, PEPI 188, 2011; [3] Kaus et al., NIC Symposium proceedings, 2016; [4] May et al, CMAME 290, 2015 [5] Gerya and Yuen, PEPI 163, 2007 [6] Tackley, PEPI 171, 2008 [7] Fullsack, GJI 120, 1995 [8] Braun et al., PEPI 171, 2008 [9] http://www.underworldcode.org/ [10] Popov and Sobolev, PEPI 171, 2008 [11] http://www.geodynamics.no/buiter/sulec.html [12] Bangerth et al., J. Numer. Math., 2016; http://www.dealii.org/ [13] http://www.mcs.anl.gov/petsc/ [14] https://trilinos.org/ [15] Burstedde et al., SIAM journal on Scientific Computing, 2011; http://www.p4est.org/ [16] https://fenicsproject.org/ [17] Quenette et al., Proceedings 19th IEEE, 2007

 

Pre-plate-tectonics on early Earth: How to make primordial continental crust

Pre-plate-tectonics on early Earth: How to make primordial continental crust

The sequence of events before continental crust formation has long been contested. Numerical simulations performed by Rozel and colleagues imply that the key to the puzzle could lie in the intrusive magmatism.

Despite several decades of research on the topic, the trigger of proto-continental crust formation on early Earth remains an enigma. However, magmatic processes may hold the key to unravelling what controlled the pre-plate tectonic dynamics of Earth.

The hidden shreds of evidence narrating Earth’s geological history are located deep within the interiors of old and thick cratons or even deeper in the Earth’s mantle – there lies the answer to the non-trivial question: how does the Earth machine work? Synthesizing these clues requires gathering a vast array of data, and geodynamic simulations are required in an attempt to reproduce the processes that gave rise to continents on early Earth.

Writing in Nature, Antoine Rozel (ETH Zürich) and colleagues provide a first global picture of Archean geodynamics by exploring continental crust formation on the early Earth with numerical modelling. Attempting global simulations of the early Earth is challenging as the models must satisfy petrological constraints and must be able to explain field data in Archean (~4 to 2.5 billion years ago) provinces.

Rozel and colleagues use cutting-edge software (the global convection code StagYY) to investigate different magmatism scenarios. Eruptive or intrusive magmatism differs in the way in which magma is deposited, namely cold at the surface or warm at the bottom of the crust. This is important as the primordial continental crust can only be produced in small windows of pressure-temperature conditions.

Rozel and colleagues simulate the thermomechanical evolution of early Earth (0–1 billion years), and find that the tectonics model dominated by volcanism is not able to produce Earth-like primordial continental crust, because of a too low crustal temperature. In contrast, a tectonics regime dominated by intrusive magmatism results in a higher crustal temperature, resulting in a stable continental crust. Commenting on the research, Antoine Rozel said:

Our models explain how continental crust might have been formed.

This work illustrates that the sophistication of numerical models has now reached a level where crusts of various types as well as depleted mantle can form self-consistently. Such models have the potential to distil geological and geophysical knowledge into complex process models that allow geoscientists to investigate a very exotic, pre-plate tectonics Earth. However, the specific results of Rozel and colleagues depend on the details of the pre-defined hypothesis assumed in their model. Specifically, they assume two critical parameters: the eruption efficiency (as opposed to intrusion efficiency) and the strength of the lithosphere.

Via a systematic parameter study, they found that a volumetric melt eruption efficiency of <40% leads to the production of the primordial crustal, both in terms of quantity and composition. Despite inevitable uncertainties, co-author Charitra Jain (ETH Zürich) said:

The production of the expected amount of the main primordial crustal compositions is in agreement with data constrained from fieldwork.

The impact of the emplacement mechanism (eruption vs. intrusion) on the geotherm (modified from Rozel et al., 2017, Nature – doi: 10.1038/nature22042). (a) 100% eruption efficiency; (b) mix of eruption and intrusion and (c) intrusive emplacement only. The grey envelopes in the right-hand-side plots show the temporal evolution of the geotherm.

Whether or not the formation of primordial crust gave birth to plate tectonics will no doubt remain contested. Scientists have previously suggested numerous ways to understand when and how plate tectonics began. For instance, the apparently quiescent phase between the Paleo- and Meso-Archean (~3.2 billion years) seems to have been followed by a geological era of intense deformation. This has been interpreted as the onset of plate tectonics, although this question is beyond the scope of the work presented here.

Rozel and colleagues have thus provided a fresh perspective on the long-standing problem of understanding the sequence of events that led to the formation of continental crust on early Earth. However, whether these events have driven the initiation of plate tectonics is likely to remain controversial for some time. An important missing ingredient in this study is the formation of strong continental roots (cratons), which is now under investigation in the Geophysical Fluid Dynamics team at ETH Zürich.

 

REFERENCE:

Rozel, A. B., Golabek, G. J., Jain, C., Tackley, P. J., & Gerya, T. (2017). Continental crust formation on early Earth controlled by intrusive magmatism. Nature, doi: 10.1038/nature22042
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