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mantle flow

Remarkable Regions – The Réunion Hotspot

Remarkable Regions – The Réunion Hotspot
Eva Bredow at Réunion caldera.

Eva Bredow in front of the caldera at Réunion Island. Credit: Simon Stähler.

This week we again turn our attention to a Remarkable Region that deserves a spot in the scientific limelight. Postdoctoral researcher Eva Bredow of Kiel University shares with us her long history with Réunion Island.

At first glance, Réunion is a relatively small tropical island, located between Madagascar and Mauritius, and from my personal experience, most Germans have never even heard of it. To be fair, it is much better known in France, because Réunion is officially a French overseas department, meaning that the eleven-hour flight from Paris is technically a domestic flight and that you can pay there with Euros (and I bet you did not know that a millimetre-sized outline of the island appears on every Euro banknote!). Besides, Réunion hosts one of the most active volcanoes in the world with one eruption per year on average. However, it rarely hits the headlines because the inhabitants live far enough away not to be overly threatened. And yet, for people interested in geodynamics, the name Réunion might actually have a familiar sound, since it regularly appears in hotspot catalogues and hotspot reference frames – a sure indication that there is more to discover.

For me, Réunion has been a very special place ever since I was a high school student lucky enough to visit the island in order to learn French. And who would have thought back then that hiking in this surreal volcanic landscape would be one of the first steps towards my decision to study geophysics? And what were the odds to stumble upon a PhD project years later, centred around the Réunion hotspot? Well, that is exactly what happened and in this article, it is my pleasure to give you at least a brief overview of why Réunion deserves to be called a remarkable spot indeed and how numerical modelling can help us to explore its geodynamic history.

NW Indian Ocean crustal thickness map.

Crustal thickness map of the north-western Indian Ocean with the entire hotspot track from Réunion Island to the Deccan Traps in India. Figure from Torsvik et al. (2013).

A deep root

The hypothesis that Réunion is an intraplate hotspot possibly fed by a hot, buoyant upwelling rooted deep in the mantle was already put forward by Jason Morgan (1971, 1972) in his famous papers outlining the classical mantle plume hypothesis. And as it happens, the Réunion plume has left a number of traces that fit the plume hypothesis extremely well and make it a kind of prototype for a deep plume and its surface manifestations. A brief look at a topographic map of the north-western Indian Ocean reveals not only the currently active hotspot at Réunion and the slightly older island of Mauritius, but also a clearly continuous (and age-progressive) hotspot track on the African and Indian plates, only split due to subsequent seafloor-spreading.

According to numerous laboratory and numerical studies that describe the mushroom-like geometry of a plume, the hotspot track is considered to be caused by the long-lived plume tail, whereas the voluminous plume head is supposed to create a huge flood basalt province in a relatively short geological time (Richards et al., 1989). In the case of the Réunion plume, the hotspot track starts at the Deccan Traps, a gigantic continental Large Igneous Province (LIP) in India. The LIP was created around 65 million years ago and the environmental changes triggered by the volcanic activities might have led to the extinction of the dinosaurs (an alternative theory to the Chicxulub impact in Mexico; Courtillot and Renne, 2003).

Further indications for a deep plume beneath Réunion include the broad topographic hotspot swell around the island, a geochemical signature of the volcanic rocks that clearly deviates from mid-ocean ridge basalts, and the present-day hotspot location above the plume generation zone at the margin of the African Large Low Shear Velocity Province (LLSVP).

Plume-ridge interaction

A more puzzling observation is the geochemical anomaly at the closest segments of the Central Indian Ridge, about 1000 km away from Réunion that implies a long-distance plume-ridge interaction. Already Morgan (1978) suggested that a sublithospheric flow channel connecting the upwelling plume and the ridge is responsible for the creation of the Rodrigues Ridge, a rather eye-catching feature not at all parallel to the hotspot track or recent plate motions.

And there is one more noteworthy hypothesis associated with Réunion, based on extremely old zircons found at Mauritius; it postulates that the hotspot track has (coincidentally) been created on top of a Precambrian microcontinent (Ashwal et al., 2017).

The RHUM-RUM experiment (completely alcohol-free…)

Concerning the (present-day) state of the Réunion plume at greater depths, seismic tomography is the most promising tool to answer the question if it is indeed fed by a deep plume or not. But given that the island is rather remotely located and a classical plume tail is expected to be quite narrow, there are plenty of technical obstacles, and it was not until 2006 that Montelli published the first seismic image of a continuous plume conduit reaching into the deep mantle. More recent global tomography models also image the Réunion plume as a clearly resolved, vertically continuous conduit at depths between 1,000 and 2,800 km (French and Romanowicz, 2015).

In 2012-2013, the French-German RHUM-RUM project (Réunion Hotspot and Upper Mantle – Réunions Unterer Mantel) aimed at an even higher resolved image of the plume. Therefore, 57 German and French ocean-bottom seismometers were deployed at the seafloor around Réunion for about a year (Stähler et al., 2016) – still the largest seismological experiment to image a deep oceanic mantle plume so far.

 

RHUM-RUM seismic stations

All seismic stations related to the RHUM-RUM project, with the 57 ocean-bottom seismometer stations shown in red. More information on the project can be found here.

With all that in mind, and as part of the RHUM-RUM project, I set up a regional numerical model with some colleagues from the GFZ Potsdam in order to assemble Réunion’s entire dynamic history. We used time-dependent plate reconstructions and large-scale mantle flow as velocity boundary conditions as well as a laterally varying lithosphere thickness in order to specifically simulate the Réunion plume (for details, see Bredow et al., 2017). In short: altogether, we were able to reproduce a crustal thickness pattern that at first order fits the observed hotspot track (although the method is not suited to reproduce a continental LIP such as the Deccan Traps). Moreover, the interaction between the plume and the Central Indian Ridge explained both the genesis of the Rodrigues Ridge and the gap in crustal thickness between the Maldives and Chagos – both features that have not been dynamically modelled before.

After our models were published, the active long-distance plume-ridge interaction beneath the Rodrigues Ridge was additionally confirmed by seismological studies in the RHUM-RUM project: first in a three-dimensional anisotropic S-wave velocity model comprising the uppermost 300 km (Mazzullo et al., 2017), and second by SKS splitting measurements (Scholz et al., 2018). Overall, these interdisciplinary studies confirmed Morgan’s long-standing hypothesis – more than 30 years after its original publication.

 

Cross section geodynamic plume model of Bredow et al. 2017.

Cross section of the geodynamic plume model, showing the long-distance plume-ridge interaction as predicted by Morgan (1978). Figure after Bredow et al. (2017).

Surface wave tomography showing the Reunion plume.

Cross section of the surface wave tomography model, showing the low velocity signature of the plume rising toward the base of the lithosphere underneath Réunion and the sublithospheric flow toward the Central Indian Ridge (CIR). Figure after Mazzullo et al. (2017).

The whole-mantle P- and S-wave tomography models from the RHUM-RUM project have yet to be published, but the (almost final) results presented at this year’s EGU (Tsekhmistrenko et al., 2019) were quite intriguing: while the plume conduit can continuously be followed down to the LLSVP in the deep mantle, the conduit is not as narrow and not nearly as vertical as classically expected!

Therefore I think it is quite safe to say that we have not yet heard the last of the Réunion hotspot and I hope that the next time you hear this name, maybe you will remember it as a rather remarkable spot on our planet…

 

Ashwal et al. (2017), Archaean zircons in Miocene oceanic hotspot rocks establish ancient continental crust beneath Mauritius, Nat. Commun., 8, 14,086, doi: 10.1038/ncomms14086.

Bredow, E. et al. (2017), How plume-ridge interaction shapes the crustal thickness pattern of the Réunion hotspot track, Geochem. Geophys. Geosyst., 18, doi:10.1002/2017GC006875.

Courtillot, V. E. and P. R. Renne (2003), On the ages of flood basalt events, C. R. Geosci., 335(1), 113–140, doi: 10.1016/S1631-0713(03)00006-3.

French, S. W. and B. Romanowicz (2015), Broad plumes rooted at the base of the Earth’s mantle beneath major hotspots, Nature, 525, 95–99, doi: 10.1038/nature14876.

Mazzullo, A. et al. (2017), Anisotropic tomography around Réunion Island from Rayleigh waves Journal of Geophysical Research: Solid Earth, 122, doi: 10.1002/2017JB014354.

Montelli, R. et al. (2006), A catalogue of deep mantle plumes: New results from finite-frequency tomography, Geochem. Geophys. Geosyst., 7, Q11007, doi: 10.1029/2006GC001248.

Morgan, W. J. (1971), Convection plumes in the lower mantle, Nature, 230, 42–43, doi: 10.1038/230042a0.

Morgan, W. J. (1972), Deep mantle convection plumes and plate motions, AAPG bulletin, 56(2), 203–213.

Morgan, W. J. (1978), Rodriguez, Darwin, Amsterdam, ..., A second type of Hotspot Island, J. Geophys. Res., 83(B11), 5355–5360, doi: 10.1029/JB083iB11p05355.

Richards, M. A. et al. (1989), Flood Basalts and Hot-Spot Tracks: Plume Heads and Tails, Science, 246, 103–107, doi: 10.1126/science.246.4926.103.

Scholz, J.-R. et al. (2018), SKS splitting in the Western Indian Ocean from land and seafloor seismometers: Plume, plate and ridge signatures, Earth Planet. Sci. Lett., Volume 498, 169-184, doi: 10.1016/j.epsl.2018.06.033.

Stähler, S. C. et al. (2016), Performance report of the RHUM-RUM ocean bottom seismometer network around La Réunion, western Indian Ocean, Adv. Geosci., 41, 43-63, doi: 10.5194/adgeo-41-43-2016.

Torsvik, T. H. et al. (2013), A Precambrian microcontinent in the Indian Ocean, Nat. Geosci., 6(3), 223–227, doi: 10.1038/ngeo1736.

Tsekhmistrenko, M. et al. (2019), Deep mantle upwelling under Réunion hotspot and the western Indian Ocean from P- and S-wave tomography, Geophysical Research Abstracts, Vol. 21, EGU2019-9447, EGU GA 2019.

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.

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.