numerical modelling

Production and recycling of Archean continental crust

Production and recycling of Archean continental crust

Continents are essential for the development and survival of life on Earth. However, as surprising as it may sound, there did not exist a planetary scale numerical model to show the formation of the oldest continents until the recent study ‘Growing primordial continental crust self-consistently in global mantle convection models‘ in Gondwana Research by Jain et al., 2019. Hot off the press, the first author of this study himself, Charitra Jain, Post Doctoral Research Associate in the Department of Earth Sciences at Durham University, shares the scoop in our News & Views!

Why do we care?

Uniquely positioned within the habitable zone [1], Earth is the sole planet within our solar system that sustains life. Understanding the factors that make a planet habitable [2,3] are becoming increasingly relevant with the rapidly expanding catalogue of extrasolar planets over the last decade [4,5]. The operation of plate tectonics and the formation and stability of continental landmasses have played a crucial role in the atmospheric evolution and development of life on Earth [6]. Plate tectonics is a theory where the outer surface of the Earth (lithosphere) is fragmented into a number of mobile plates that drift at a speed of few centimetres per year relative to each other, atop a convecting mantle. Mountains, volcanoes, and earthquakes are found at the boundaries of these plates. Continents cover about a third of the planet’s surface area and are made of thin crust overlying a thick and undeformable cratonic lithosphere [7,8]. Even after having assembled a reasonable model for its origins and internal workings, many fundamental questions pertaining to Earth sciences remain unresolved, for example:

  • How did the first continents form and what accounts for their stability over billions of years? Was their growth an episodic process [9] or a continuous process with a significant drop in crustal growth rate around 3 Ga (billion years ago) [10]? How much of the continental crust has recycled into the mantle [11]?
  • What was the global geodynamic regime exhibited by early Earth? When and how did the subduction-driven plate tectonics commence [12]? Did the presence of continents play a role in a regime transition from vertical tectonics to horizontal tectonics around 3Ga [13]?

Owing to the increasing paucity of natural observational data as we go back further in time [14], numerical modelling constrained by experimental and field data has thus become indispensable to uncover the secrets of Earth’s evolutionary history. Our recent study [15] is a step in the right direction where we have developed a new two-stage melting algorithm to create oceanic (basaltic/mafic) and continental (felsic) crust in self-consistent global mantle convection models for the first time.

What’s new in these models?

Generally, two stages of mantle differentiation are inferred to generate continental crust as shown in the schematic in Fig. 1A. First, basaltic magma is extracted from the mantle. Second, it is buried and partially melts to form felsic continental crust. During the much hotter Archean conditions [16,17], majority of continental crust was made of Tonalite-Trondhjemite-Granodiorite (TTG) [18,19] rocks. Experimental data suggests that TTGs are formed when hydrated basalt melts at garnet-amphibolite, granulite or eclogite facies conditions [20,21] and specific P-T conditions [22] have been employed as a criterion for generating TTGs by the authors in their models.

Interested in the long-term planetary evolution, we parametrised the processes of melt generation and melt extraction. If the melt is generated within the top 300 km of the mantle (Fig.1B1), it is instantaneously removed from the depth (Fig.1B2) [23,24] and transported both to the bottom of the crust (plutonism/intrusion) and to the top of the model domain (volcanism/eruption) (Fig. 1B3). The intruded melt stays molten while a temperature adjustment to account for adiabatic decompression is applied, and tends to result in a warm, weak lithosphere. The erupted melt is rapidly solidified by setting its temperature to the surface temperature (300K), resulting in a strong and cold lithosphere [25]. The mass ratio of erupted to intruded melt is controlled by a parameter called eruption efficiency, which is tested extensively in our simulations. Geological data suggests that the majority of mantle-derived melts intrude at a depth, corresponding to an eruption efficiency between 9% and 20% [26].


Figure 1: A, One-dimensional compositional variation with basalt-harzburgite continuum consisting of a mixture of olivine (ol) and pyroxene-garnet (px-gt) mineralogies in different proportions. Upon initialisa- tion, the whole mantle has a pyrolytic composition. B, Cartoon depicting a section of a mesh column (not to scale) in a stage: B1, where crustal production has already happened; B2, after melt removal but before compaction or opening gaps in lithosphere for magmatism; B3, with the eruption and intrusion of the melt with the white downgoing arrows representing compaction of tracers/markers.

How do these results stack up against data?

By varying initial core temperature, eruption efficiency, and limiting the mass of TTG that can be generated in our simulations to 10% and 50% of basalt mass, we present results from two sets of simulations. The crustal volumes have the same order of magnitude and the crustal composition follows similar trends as reported from geological and geochemical data [10,27,28]. Interestingly, we report two stages of TTG production without needing a significant change in convection regime: a period of continuous linear growth with time and intense recycling fuelled by strong plume activity and lasting for around 1 billion years, followed by a stage with reduced TTG growth and moderate recycling. The production of TTGs happen at the tip of deformation fronts driven by the lateral spreading of plumes (mantle upwellings) that rise to the surface (Fig. 2). These results indicate that the present-day slab- driven subduction was not required for the genesis of Archean TTGs [29,30] and early Earth exhibited a “plutonic squishy lid” or vertical-tectonics geodynamic regime [31–33].


Figure 2: Thermal (top) and compositional (bottom and zoom-in) evolution with time for a simulation with initial core temperature of 6000 K, mantle potential temperature of 1900 K, eruption efficiency of 40%, and TTG mass limited to 10% of basalt mass. The lighter shades of teal in the composition field represent progressive mantle depletion (higher harzburgite content) with time.

What’s coming next?

These results are parameter-dependent to some extent and they would change in a 3D domain as that would limit the impact of plumes on lithosphere dynamics. Future models will aim for forming the viscous cratonic roots and incorporating the effects of water [34,35] and grain-size [36–38] on mantle rheology. Going forward, modelling coupled core-mantle-atmosphere systems will shed more light on the role of different tectonic modes towards planetary habitability [39,40] and help solve these contentious aspects.

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The past is the key

The past is the key

Lorenzo Colli

“The present is the key to the past” is a oft-used phrase in the context of understanding our planet’s complex evolution. But this perspective can also be flipped, reflected, and reframed. In this Geodynamics 101 post, Lorenzo Colli, Research Assistant Professor at the University of Houston, USA, showcases some of the recent advances in modelling mantle convection.  


Mantle convection is the fundamental process that drives a large part of the geologic activity at the Earth’s surface. Indeed, mantle convection can be framed as a dynamical theory that complements and expands the kinematic theory of plate tectonics: on the one hand it aims to describe and quantify the forces that cause tectonic processes; on the other, it provides an explanation for features – such as hotspot volcanism, chains of seamounts, large igneous provinces and anomalous non-isostatic topography – that aren’t accounted for by plate tectonics.

Mantle convection is both very simple and very complicated. In its essence, it is simply thermal convection: hot (and lighter) material goes up, cold (and denser) material goes down. We can describe thermal convection using classical equations of fluid dynamics, which are based on well-founded physical principles: the continuity equation enforces conservation of mass; the Navier-Stokes equation deals with conservation of momentum; and the heat equation embodies conservation of energy. Moreover, given the extremely large viscosity of the Earth’s mantle and the low rates of deformation, inertia and turbulence are utterly negligible and the Navier-Stokes equation can be simplified accordingly. One incredible consequence is that the flow field only depends on an instantaneous force balance, not on its past states, and it is thus time reversible. And when I say incredible, I really mean it: it looks like a magic trick. Check it out yourself.

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk

This is as simple as it gets, in the sense that from here onward every additional aspect of mantle convection results in a more complex system: 3D variations in rheology and composition; phase transitions, melting and, more generally, the thermodynamics of mantle minerals; the feedbacks between deep Earth dynamics and surface processes. Each of these additional aspects results in a system that is harder and costlier to solve numerically, so much so that numerical models need to compromise, including some but excluding others, or giving up dimensionality, domain size or the ability to advance in time. More importantly, most of these aspects are so-called subgrid-scale processes: they deal with the macroscopic effect of some microscopic process that cannot be modelled at the same scale as the macroscopic flow and is too costly to model at the appropriate scale. Consequently, it needs to be parametrized. To make matters worse, some of these microscopic processes are not understood sufficiently well to begin with: the parametrizations are not formally derived from first-principle physics but are long-range extrapolations of semi-empirical laws. The end result is that it is possible to generate more complex – thus, in this regard, more Earth-like – models of mantle convection at the cost of an increase in tunable parameters. But what parameters give a truly better model? How can we test it?

Figure 1: The mantle convection model on the left runs in ten minutes on your laptop. It is not the Earth. The one on the right takes two days on a supercomputer. It is fancier, but it is still not the real Earth.

Meteorologists face similar issues with their models of atmospheric circulation. For example, processes related to turbulence, clouds and rainfall need to be parametrized. Early weather forecast models were… less than ideal. But meteorologists can compare every day their model predictions with what actually occurs, thus objectively and quantitatively assessing what works and what doesn’t. As a result, during the last 40 years weather predictions have improved steadily (Bauer et al., 2015). Current models are better at using available information (what is technically called data assimilation; more on this later) and have parametrizations that better represent the physics of the underlying processes.

If time travel is possible, where are the geophysicists from the future?

We could do the same, in theory. We can initialize a mantle convection model with some best estimate for the present-day state of the Earth’s mantle and let it run forward into the future, with the explicit aim of forecasting its future evolution. But mantle convection evolves over millions of years instead of days, thus making future predictions impractical. Another option would be to initialize a mantle convection model in the distant past and run it forward, thus making predictions-in-the-past. But in this case we really don’t know the state of the mantle in the past. And as mantle convection is a chaotic process, even a small error in the initial condition quickly grows into a completely different model trajectory (Bello et al., 2014). One can mitigate this chaotic divergence by using data assimilation and imposing surface velocities as reconstructed by a kinematic model of past plate motions (Bunge et al., 1998), which indeed tends to bring the modelled evolution closer to the true one (Colli et al., 2015). But it would take hundreds of millions of years of error-free plate motions to eliminate the influence of the unknown initial condition.

As I mentioned before, the flow field is time reversible, so one can try to start from the present-day state and integrate the governing equations backward in time. But while the flow field is time reversible, the temperature field is not. Heat diffusion is physically irreversible and mathematically unstable when solved back in time. Plainly said, the temperature field blows up. Heat diffusion needs to be turned off [1], thus keeping only heat advection. This approach, aptly called backward advection (Steinberger and O’Connell, 1997), is limited to only a few tens of millions of years in the past (Conrad and Gurnis, 2003; Moucha and Forte, 2011): the errors induced by neglecting heat diffusion add up and the recovered “initial condition”, when integrated forward in time (or should I say, back to the future), doesn’t land back at the desired present-day state, following instead a divergent trajectory.

Per aspera ad astra

As all the simple approaches turn out to be either unfeasible or unsatisfactory, we need to turn our attention to more sophisticated ones. One option is to be more clever about data assimilation, for example using a Kalman filter (Bocher et al., 2016; 2018). This methodology allow for the combining of the physics of the system, as embodied by the numerical model, with observational data, while at the same time taking into account their relative uncertainties. A different approach is given by posing a formal inverse problem aimed at finding the “optimal” initial condition that evolves into the known (best-estimate) present-day state of the mantle. This inverse problem can be solved using the adjoint method (Bunge et al., 2003; Liu and Gurnis, 2008), a rather elegant mathematical technique that exploits the physics of the system to compute the sensitivity of the final condition to variations in the initial condition. Both methodologies are computationally very expensive. Like, many millions of CPU-hours expensive. But they allow for explicit predictions of the past history of mantle flow (Spasojevic & Gurnis, 2012; Colli et al., 2018), which can then be compared with evidence of past flow states as preserved by the geologic record, for example in the form of regional- and continental-scale unconformities (Friedrich et al., 2018) and planation surfaces (Guillocheau et al., 2018). The past history of the Earth thus holds the key to significantly advance our understanding of mantle dynamics by allowing us to test and improve our models of mantle convection.

Figure 2: A schematic illustration of a reconstruction of past mantle flow obtained via the adjoint method. Symbols represent model states at discrete times. They are connected by lines representing model evolution over time. The procedure starts from a first guess of the state of the mantle in the distant past (orange circle). When evolved in time (red triangles) it will not reproduce the present-day state of the real Earth (purple cross). The adjoint method tells you in which direction the initial condition needs to be shifted in order to move the modeled present-day state closer to the real Earth. By iteratively correcting the first guess an optimized evolution (green stars) can be obtained, which matches the present-day state of the Earth.

1.Or even to be reversed in sign, to make the time-reversed heat equation unconditionally stable.

The geodynamic processes behind the generation of the earliest continents

The geodynamic processes behind the generation of the earliest continents

The earliest continents played a fundamental role on Earth’s habitability. However, their generation is still not understood, and it requires an integrated approach between petrology and geodynamic modelling. In a new study, Piccolo and co-workers developed a method to handle the effects of chemical evolution on the geodynamic processes. They show that the production of the earliest felsic crust triggers a self-feeding chain of events that leads to the generation of the first proto-continents.

The Archean Eon (4.0-2.5) is the first act of the evolution of life and represent one of the first steps of Earth towards its present-state. Only few remnants have reached us representing different space-time windows that are difficult to reconcile in a unique interpretative framework. Many questions are still unsolved, and all the answers may be interconnected. One of them is related to the generation of the continental crust, which played a fundamental role on the developing of the biosphere as we know now. Although the present-day sites of production are all most understood, we still try to grasp the dominant process that were generating its constituents (e.g. granitoids) during the Archean. Herein the main “hot” topic is the felsic components of the continental crust,  (i.e. felsic crust/melts), and their generation during the Archean, following the recent results from Piccolo et al. (2019) [1].

Felsic melts cannot be directly produced from a partially molten mantle source; therefore, silica-rich magma generation must occur via a multistage process [2] that comprises at least two main steps: i) extraction of raw mafic materials; ii) differentiation via fractional crystallization or via partial melting of the hydrated basalts. Both processes come at costs, and, in fact the generation of felsic melts implies the production of large volume of complementary mafic/ultramafic dense residuum (the solid fraction of a partially melted rock), which is not observed in geological records. Such residual rocks have a different chemical composition with respect to the parental magma, being more mafic, and thus potentially producing denser minerals. During the Archean the most widely accepted recipe to produce felsic crust is to bake hydrated meta-basalts at high pressure until they partially melt [3]–[5].

Available Archean geological records are not enough to provide a coherent picture. Therefore, it is natural to assist the interpretation of available data with indirect means such as numerical and petrological modelling. Moreover, it is necessary to employ an integrated approach between geodynamic and petrology to study the effect of the chemical evolution on the overall dynamics of the lithosphere. In Piccolo et al. (2019), the authors accepted this challenge by conjugating petrological phase diagrams with geodynamic simulations to handle a simple — but petrologically robust — chemical evolution of the mafic protolith. They produce a set of genetically linked phase diagrams for both mantle and mafic crustal compositions — exploiting the recent advances on thermodynamic modelling for mafic/ultramafic systems (for further details, [5]–[8]) — to simulate the chemical evolution as a function of the melt extracted. Then, they modify their finite element code (MVEP2) to change the compositional phase as a function of the principal mineralogical transformation.

The base line scenario comprise a lithosphere (composed by hydrated effusive basalts, intrusive rocks and a residual lithospheric mantle) underlaid  by a fertile asthenosphere featuring high temperature and radiogenic heat production consistently with Archean conditions [9], [10]. During the initial stage of the experiments, asthenosphere self-heats above solidus, resulting in the genesis of more mafic melts that are readily extracted and converted into mafic hydrated basalts and dry intrusions. The latter are emplaced within the lower crust and heat the overlying hydrated units that start to partially melt. Such two-steps processes have two main consequences: the production of the first granitoids that are emplaced at middle-crust depths and the production of large amount of dense mafic residuum. Such rocks are not so common in the geological record, as stated above. Therefore, the inevitable question is: what are the processes that assists their disposal? The solution of this conundrum relies on the density contrast between the underlying mantle and complementary mafic residuum. If the density contrast is sufficient high, any geometrical and thermal perturbation between them can trigger Rayleigh-Taylor drip instabilities. The foundering of such drip into the mantle forces the weak asthenosphere to upwell causing more mafic melts and thus inducing more felsic crust production and consequent gravitational instabilities. After a few million years the mantle is quiescent because its temperature significantly drops because it mixes with the dripped mafic while the crust start being more enriched of felsic crustal components. Several parameters have been tested, and the main chains of events have been replicated in a plethora of conditions, especially at lower mantle temperature, suggesting that the generation of felsic crust is associated to mantle cooling events, that may buffer the upper mantle temperature.

Melt coming from the astenosphere percolates through the lithosphere, heating and both plastically and thermally weakening it. Part of the mafic melts are emplaced in the lower crust, while the remnants are erupted. As soon as a critical amount of residuum is reached, RTIs are triggered, and asthenosphere fills the space left by the delaminated lithosphere. This results in a feedback between mantle melting and new felsic crust production. From ref. [1].

The removal of the residuum implies production of more mafic melts, and thus more felsic crust that leads inevitably to again to gravitational instabilities yielding a self-feeding. Moreover, any vertical tectonic setting fuelled by mantle magmatic processes is suitable to produce proto-continents thank to these feedbacks. Such findings are consistent with many independent line of research (e.g., [11], [12], [13]) and the novelty of this study relies in a first attempt to conjugate realistic petrological constraint with the chemical evolution induced by melt extraction.


1. A. Piccolo, R. M. Palin, B. J. P. Kaus, and R. W. White, “Generation of Earth’s early continents from a relatively cool Archean mantle,” Geochemistry, Geophys. Geosystems, 2019.
2. R. L. Rudnick and S. Gao, “4.1 – Composition of the Continental Crust,” in Treatise on Geochemistry, 2014, pp. 1–51.
3. J.-F. Moyen and G. Stevens, “Experimental constraints on TTG petrogenesis: implications for Archean geodynamics,” Archean Geodyn. Environ., pp. 149–175, 2006.
4. R. P. Rapp, N. Shimizu, and M. D. Norman, “Growth of early continental crust by partial melting of eclogite,” Nature, vol. 425, pp. 605–609, Oct. 2003.
5. R. M. Palin, R. W. White, and E. C. R. Green, “Partial melting of metabasic rocks and the generation of tonalitic???trondhjemitic???granodioritic (TTG) crust in the Archaean: Constraints from phase equilibrium modelling,” Precambrian Res., vol. 287, pp. 73–90, 2016.
6. R. M. Palin, R. W. White, E. C. R. Green, J. F. A. Diener, R. Powell, and T. J. B. Holland, “High-grade metamorphism and partial melting of basic and intermediate rocks,” J. Metamorph. Geol., vol. 34, no. 9, pp. 871–892, 2016.
7. E. C. R. Green, R. W. White, J. F. A. Diener, R. Powell, T. J. B. Holland, and R. M. Palin, “Activity–composition relations for the calculation of partial melting equilibria in metabasic rocks,” J. Metamorph. Geol., vol. 34, no. 9, pp. 845–869, 2016.
8. R. W. White, R. M. Palin, and E. C. R. Green, “High-grade metamorphism and partial melting in Archean composite grey gneiss complexes,” J. Metamorph. Geol., vol. 35, no. 2, pp. 181–195, 2017.
9. C. T. Herzberg, K. C. Condie, and J. Korenaga, “Thermal history of the Earth and its petrological expression,” Earth Planet. Sci. Lett., vol. 292, no. 1–2, pp. 79–88, 2010.
10. J. Ganne and X. Feng, “Primary magmas and mantle temperatures through time,” Geochemistry, Geophys. Geosystems, vol. 18, no. 3, pp. 872–888, Feb. 2017.
11. J. H. Bédard, “A catalytic delamination-driven model for coupled genesis of Archaean crust and sub-continental lithospheric mantle,” Geochim. Cosmochim. Acta, vol. 70, no. 5, pp. 1188–1214, 2006. 12. T. E. Zegers and P. E. van Keken, “Middle Archean continent formation by crustal delamination,” Geology, vol. 29, no. 12, pp. 1083–1086, 2001. 13. E. Sizova, T. V. Gerya, K. Stüwe, and M. Brown, “Generation of felsic crust in the Archean: A geodynamic modeling perspective,” Precambrian Res., vol. 271, pp. 198–224, 2015.

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!