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Geodynamics
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Enigmas at depth

Enigmas at depth
Dr. Marcel Thielmann

Dr. Marcel Thielmann.

The Geodynamics 101 series serves to showcase the diversity of research topics and/or methods in the geodynamics community in an understandable manner. In this week’s Geodynamics 101 post, Marcel Thielmann, Senior Researcher at the University of Bayreuth, discusses the possible mechanisms behind the ductile deformation at great depths that causes deep earthquakes. 

Earthquakes are one of the expressions of plate tectonics that everybody seems to be familiar with. When I started studying geophysics, people used to ask me what exactly I was studying. As soon as I mentioned earthquakes, I usually got a knowing nod and no further questions were asked (the same goes for volcanoes, but that’s a topic for another day).

Global hypocenter distribution over earthquakes with a magnitude of 5 or larger.

Figure 1: Global hypocentre distribution of earthquakes with a magnitude Mw>5 in the ISC catalogue for the interval 1960-2013. The x-axis has been truncated for better visibility.

 

Most earthquakes occur at the boundaries of tectonic plates, where rock breaks due to the forces originating from the plates’ relative movement. In 1928, Kiyoo Wadati discovered earthquakes that occurred at depths larger than 60 km, which were previously thought to be impossible. Today, we know that these earthquakes are not that extraordinary: about one out of four earthquakes observed on Earth occurs at depths larger than 60 km. At this depth, the pressure inside the Earth reaches values of about 3 GPa and more. Laboratory experiments have shown that at this pressure, rocks do not deform by breaking, but rather by ductile creep, like putty. This kind of deformation should not produce any earthquakes. So, 90 years after their discovery, the question still remains: What causes deep earthquakes?

How do rocks fail at these high pressures?

Proposed ductile failure mechanisms

Figure 2: Schematic view of the three proposed ductile failure mechanisms.

As rocks get transported to larger depths, the minerals making them up can experience phase transformations. Due to these transformations, two things may happen: (1) Previously stored water in the minerals is released. This release may trigger earthquakes due to the released water acting against the pressure of the surrounding rock in a mechanism called dehydration embrittlement (Green and Houston, 1995; Frohlich, 2006). (2) The phase transition renders a fine-grained rock that is easier to deform. If enough of this weak material is produced, rock failure occurs in a process called transformational faulting (Green and Houston,1995; Ferrand et al.,2017). Besides these two mechanisms, a third one called thermal runaway has been thrown into the ring (Hobbs et al., 1986; Ogawa, 1987). This mechanism is a result of shear heating, which describes the generation of heat inside a deforming rock. If heat generation is faster than its transport, temperatures inside the rock will continue to increase and ultimately result in its destabilization, thus causing an earthquake.

The Wind River earthquake

While most of the observed deep earthquakes occur in subduction zones, where one tectonic plate descends beneath another, there are some that occur far from them. One such earthquake hit the Wind River range in Wyoming with a magnitude of MW 4.7 in 2013 (Frohlich et al., 2015; Craig and Heyburn, 2015). This earthquake is not only enigmatic due to its depth of 75 km (making it the second deepest earthquake in such a stable continental region), but also because the Wind River area is considered to be “seismically quiet”. The location of the earthquake is far away from any plate boundary, with the closest tectonic feature being the Yellowstone supervolcano more than 200 km away. Since it occurred, the cause of this earthquake has been a matter of debate, with some scientists preferring a purely brittle origin (Craig and Heyburn, 2015), while others argue for a ductile mechanism (Prieto et al., 2017).

Dehydration embrittlement seems to be an unlikely candidate, since the earthquake is located far away from any subduction zone. How could fluids get down to those depths if not by subduction? Transformational faulting also seems to be unlikely, since this would require a phase transition to take place. The Wind River earthquake occurred in the continental mantle lithosphere, where we would not expect any major phase transitions. Thermal runaway may be a candidate, but studies have shown that very high stresses are required to make this mechanism work, stresses that are very hard to achieve in the Earth.

However, there may be a way out: grain size assisted thermal runaway. Oh no, yet another one you might think. But fear not, this mechanism is essentially the same as the “classical” thermal runaway, just with the effect of small grains included. The consequences of this effect are by no means small however, as it significantly reduces the stresses required for thermal runaway. Indeed, numerical models of this process at the conditions of the Wind River earthquake indicate that it may indeed be a viable mechanism to have generated this earthquake (Thielmann, 2018). However, these models also show that rock deformation has to be sufficiently fast (about 100 times faster than what is commonly assumed) in order to allow for earthquake generation.

Location and mantle structure of the 2013 Wind River earthquake.

Figure 3: Location and mantle structure of the 2013 Wind River earthquake. Inset: Location within the north-western US. Black points represent earthquakes larger than Mw 4.5 from the NEIC catalogue. The red circle indicates the location of the Wind River earthquake. The red box denotes the region of the main figure. Main Figure: Seismic velocity structure and hypocentre location. Tomographic data is taken from Shen et al. (2013). Colours denote seismic velocities, with blue colours indicating faster and red colours slower velocities. Fast seismic velocities are commonly associated with colder and denser material. The red spheres denote the location of the hypo- and epicentre. The grey isosurface at 4.4 km/s delineates the dense body extending to larger depths.

So now we have shifted the question from “How could fluids get down to those depths if not by subduction?” to “How could we deform that fast at those depths?” Here, seismology may come to the rescue: tomographic models of the north-western United States show that the Wind River earthquake lies directly at the transition between two regions with strongly varying seismic wave speeds (Shen et al., 2013; Wang et al., 2016). Fast wave speeds are commonly seen as an indicator for cold material, while slow wave speeds indicate warm material. 3D seismic tomographies such as the one from Shen et al. (2013) show that the 2013 Wind River earthquake occurred in a region where the continental lithosphere may be detaching in the form of a drip (Wang et al., 2016). In such tectonic environments, deformation rates may reach the values needed to initiate grain size assisted thermal runaway (Lorinczi and Houseman, 2009).

Does this now answer all questions we have on the Wind River earthquake and deep earthquakes in general? Certainly not. The example given above was just a single instance of where the combined information from seismology, laboratory experiments and numerical modelling may help us find an answer. We still have to keep in mind G.E.P. Box’s famous expression „Essentially, all models are wrong, but some are useful“. It is certain that deep earthquakes contain a wealth of information that remains to be unlocked. The following quote by Heidi Houston (2015) points the way:

Integration of seismological, laboratory, and modelling effort is needed to bridge the stubborn gap between source properties, which are extracted under strong assumptions and possess substantial intrinsic variability, and physical mechanisms of rupture generation, which are as yet neither well understood nor well constrained. (H. Houston)

 

References

Craig, T. J., and R. Heyburn (2015), An enigmatic earthquake in the continental mantle lithosphere of stable North America, Earth Plan. Sc. Lett., 425, 12–23, doi:10.1016/j.epsl.2015.05.048.

Ferrand, T., N. Hilairet, S. Incel, D. Deldicque, L. Labrousse, J. Gasc, J. Renner, Y. Wang, H. W. Green II, and A. Schubnel (2017), Dehydration-driven stress transfer triggers intermediate-depth earthquakes, Nat. Commun., 8, 15247, doi:10.1038/ncomms15247.

Frohlich, C. (2006), Deep Earthquakes, Cambridge University Press.

Frohlich, C., W. Gan, and R. B. Herrmann (2015), Two Deep Earthquakes in Wyoming, Seismological Research Letters, 86(3), 810–818, doi:10.1785/0220140197.

Green, H. W., and H. Houston (1995), The Mechanics of Deep Earthquakes, Annu. Rev. Earth. Planet. Sci., 23, 169–213.

Hobbs, B. E., A. Ord, and C. Teyssier (1986), Earthquakes in the Ductile Regime, Pure Appl. Geophys., 124(1-2), 309–336.

Houston, H. (2015), 4.13 - Deep Earthquakes, in Treatise on Geophysics (Second Edition), edited by G. Schubert, pp. 329–354, Elsevier, Oxford.

Lorinczi, P., and G. A. Houseman (2009), Lithospheric gravitational instability beneath the Southeast Carpathians, Tectonophysics, 474, 322–336, doi:10.1016/j.tecto.2008.05.024.

Ogawa, M. (1987), Shear instability in a viscoelastic material as the cause of deep focus earthquakes, J. Geophys. Res., 92, 13,801–13,810.

Prieto, G. A., B. Froment, C. Yu, P. Poli, and R. Abercrombie (2017), Earthquake rupture below the brittle-ductile transition in continental lithospheric mantle, Sci. Adv., 3(3), e1602642, doi:10.1126/sciadv.1602642.

Shen, W., M. H. Ritzwoller, and V. Schulte Pelkum (2013), A 3‐D model of the crust and uppermost mantle beneath the Central and Western US by joint inversion of receiver functions and surface wave dispersion, J. Geophys. Res., 118(1), 262–276, doi:10.1029/2012JB009602.

Thielmann, M. (2018), Grain size assisted thermal runaway as a nucleation mechanism for continental mantle earthquakes: Impact of complex rheologies, Tectonophysics, 746, 611–623, doi:10.1016/j.tecto.2017.08.038.

Wang, X., D. Zhao, and J. Li (2016), The 2013 Wyoming upper mantle earthquakes: Tomography and tectonic implications, J. Geophys. Res., 121(9), 6797–6808, doi:10.1002/2016JB013118.

The conundrum posed by data and models

The conundrum posed by data and models

A privilege of being an academic is the freedom to muse, staying faithful to the title of a PhD which is, after all, a doctor of philosophy. In his latest reflection on a topic of importance to all scientific disciplines, Dan Bower (CSH and Ambizione Fellow at the University of Bern) discusses the ambiguity that comes with the separation of data and models.  

Dan Bower is a CSH and Ambizione Fellow at the University of Bern, Switzerland

What are data? What are models? You are probably wondering how I can write a blog post about this—but bear with me—because these under-appreciated questions affect all scientific disciplines. The tug-of-war between models and data has been viscously fought since the enlightenment to the mutual benefit of both. Modelling has undergone a recent explosion due to the growth of computing power that enables numerical techniques to model physical systems that were beforehand intractable. But the notion of data and models extend beyond their immediate scientific applications; the preference of a scientist to lean towards data or models is often a defining aspect of their character. We’ve all heard (at least anecdotally) of the modeller that confidentially exclaims “the data is wrong, the model is right”. The passion with which this statement is made in a packed room at an international conference demonstrates that—for the individual at least—the vested interest in modelling can be perhaps a little too strong. Clearly, the battle between data and models as mechanisms to advance scientific knowledge is punctuated by the seemingly innate preference of a particular scientist to “believe” in the usefulness of models or data.

Battle for the heart of science

I define an “observer” as a scientist with a preference for data— either directly observed or experimentally collected—and a “modeller” as a scientist that formulates models. In the modern scientific landscape, it’s increasingly difficult to be a true end-member of either definition. Science is the endeavour to uncover the truth of the natural world. Establishing truth was purely observational in the early days; we observed the stars, planets, mountains, animals, plants, the list goes on. Observations by Charles Darwin led to the theory of natural selection – jump-starting modern biology. Observations of planets and stars established the Copernican model of the solar system, and geological observations led to the theory of plate tectonics. In this regard, the observer may always claim the closest affiliation to the heart of what science is, in the sense that a (good) observation is (in the best case scenario) an irrefutable truth about the natural world. What information this truth provides in the context of the bigger picture is not necessarily apparent—this is where modellers pick up the story. A truth of nature cannot be established by simply the outcome of a model or theory without observational proof; recall that Peter Higgs waited almost 50 years to be awarded the Nobel Prize following experimental verification of the Higg’s boson.

A classical observer makes an observation and reports the observation to the scientific community.  Following this approach led to the establishment of many scientific fields, including biology, astronomy, and geology.  The discovery and classification of a plant species in a rainforest by the pioneering botanists is a clear example of a scientific advancement made exclusively by observation. Essentially, there are no extra steps necessary to take the visual observation of a plant and realise that it is a truth of nature—I’m necessarily avoiding philosophical discussion of how we perceive and understand the natural world from the human perspective. Whilst observations akin to those of the botanist remain present in science, increasingly observers are necessarily dragged into the underworld of modelling—whether willingly or otherwise. This is because our scientific observations have gone beyond what our primitive senses can detect – technological developments in sensors and microchips have opened up a new space of sensory perception that we could never previously explore.

Increasingly observers are necessarily dragged into the underworld of modelling –
whether willingly or otherwise

The guts of the Earth

Seismic tomography provides imagery of Earth’s interior, and for someone interested in the interior dynamics of Earth, seismic tomography is often regarded as data.  Models of Earth’s dynamic interior are compared with seismic tomography to determine their validity. This is a perceived common interplay between models and data independent data can be used to test a model. However, this interplay hides over-simplifications that are important to appreciate.  The interior dynamics model is partly built on data.  For example, flow parameters such as viscosity are based on a secondary model devised from fits to experimental data.  Note that modellers refer to viscosity as a “parameter” rather than “data”.  There is no problem with this approach, as long as we don’t then use the primary model to infer the viscosity, as this would be circular reasoning. This demonstrates an important point that is often buried when feedbacks become more complicated in non-linear systems; it can become non-trivial to reason what is truly independent data with which to test our model. Are we analysing what we put in, or are we probing a new or interesting phenomenon?

Furthermore, seismic tomography images are not strictly data, because seismic images have been created by a model using input data; the input data is the observation of surface motions.  Furthermore, quantifying the accuracy and precision of these data are critical for determining their worth, yet error estimates are linked to an assumed noise model. Crucially, the input data itself is not “useful” information to non-seismologists, but visualising the 3-D wave speed of Earth’s interior is tremendously informative to fanatical geoscientists. Nowadays, tomographic models have converged to produce a coherent picture of the dominant features of Earth’s interior, such that we can argue that agreement between tomographic models has effectively established a truth of nature. This argument is bolstered by the fact that the interior is inaccessible, so there is not another approach to determine the interior wave speed structure. Nevertheless, we should not lose sight of the fact that any model outcome and any data is never immune from further scrutiny.

 

An example of the “grey zone” between models and data in Earth sciences is seismic tomography. Here shown are whole-mantle cross-sections for models S40RTS and S20RTS, from Ritsema et al. (2011).

 

Cultural sensitivity

Despite the fact that models and data are nowadays intimately intertwined in all fields of modern science, there is still a perceived cultural difference between a scientist who is an observer versus one who is a modeller. The cost and technology necessary to make observations—whether a mass spectrometer in a laboratory, space telescope, or particle accelerator—requires a high level of expertise, time, and collaboration. An observer is understandably motivated to b-line to a truth of a nature through careful observation of a particular system, but this may be at the expense of a more general understanding (i.e., one observation is one data point). There can also be the perception that all data is “useful” after all, it’s a new truth of nature even though it may not provide any further information that influences our understanding. By contrast, a modeller is motivated to connect the dots to provide meaning to what may initially appear as disparate data. A modeller is typically driven to generate a holistic view of a complex system; ground-truthing the model against independent data is, of course, critical to the eventual success of a model, but a modeller is usually less beholden to any one particular data point. This is an acknowledgement of the modeller that the model cannot ever capture all the complexity of nature and thus reproduce all data; the goal is to capture the key components to provide understanding and predictive power.

But not all hope is lost for ardent modellers to stamp their signature on the annals of scientific discovery. This is because the best models those with unprecedented ability to explain observations and make predictions (which are later verified by more observations)  become scientific theories. And the most prominent scientific theories then establish new branches of science; natural selection is the tenet of modern biology and plate tectonics is the unifying framework of geology. Newton’s laws now permeate all branches of science, which at its core contains a beautifully elegant description of motion through a quantitative model, encapsulated in one of the most famous equations: F = ma. Now, of course, even the mighty Newton’s laws are only valid within a certain parameter space, but that parameter space is both extensive and relevant for scientific and engineering applications, such that the laws have stood the test of time. So modellers should remain optimistic that, at least in principle, they too can influence the course of science by effectively establishing new truths of nature (albeit with a little help from their observer colleagues). This is typically more likely for disciplines that are amiable to purely theory-based models, such as physics or astrophysics; by contrast, the lack of so-called “clean” physics in other disciplines renders an all-predictive quantitative model a formidable task (e.g., evolution in biology, plate tectonics in Earth science).

Life in the grey zone

So where does this leave us? Well, I think we must accept that we are in an era of data-dependent models and model-dependent data, and therefore the lines have been blurred between the classical notions of what are models and what are data. Remaining steadfast to what we perceive as either a “pure” model or “pure” data ignores the fact that one is increasingly inherent to the other. This point is emphasised by the growth of machine learning in all scientific disciplines, whereby a mathematical model is used to extract data from data, as it were. As we read and review papers and advance our own research projects, it is always a useful exercise to critically assess what is a model, and what are data. We must determine what is the truth of nature we are trying to probe, and how what we deem to be models or data affect our understanding of this truth. And whilst it is inevitable that there will be an increase of scientists equally apt to data collection as well as modelling, we should remember that history has ingrained the idea of being a modeller or an observer deep into an individual scientists psyche.

 

Ritsema, J., Deuss, A., van Heijst, H.J. and Woodhouse, J.H. (2011) S40RTS: a degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements. Geophysical Journal International, vol. 184(3), pp. 1223-1236,https://doi.org/10.1111/j.1365-246X.2010.04884.x

The geodynamics of planetary habitability

The geodynamics of planetary habitability

The Geodynamics 101 series serves to showcase the diversity of research topics and/or methods in the geodynamics community in an understandable manner. In this week’s Geodynamics 101 post, Brad Foley, Assistant Professor at the Department of Geosciences, Pennsylvania State University, talks about the geodynamics of planetary habitability and in particular the key role of CO2 cycling in the mantle. 

Figure 1: Assistant professor Brad Foley at the Department of Geosciences, Penn State University.

Earth’s mantle is the planet’s engine. The loss of heat from the interior to space drives Earth’s tectonic processes, mountain building and orogeny, volcanism, and the core dynamo generating Earth’s magnetic field. But perhaps less appreciated is that the mantle also plays a critical role in shaping the state of the atmosphere. This link between surface and interior evolution is not just important for studying the Earth, but also the other rocky planets in our solar system, and rocky exoplanets. Factors that make a planet, like Earth, a suitable home for life, such as the presence of liquid water oceans, weathering processes that provide critical nutrients to the oceans, and a temperate climate are all directly influenced by deep interior processes (Foley & Driscoll, 2016). Likewise, a complex interaction between life, atmospheric chemistry, weathering, volcanism, and sediment burial led to the rise of oxygen on Earth, which is both critical for some forms of life and a signature of the presence of life (Claire et al, 2006; Kump & Barley, 2007; Lyons et al, 2014). Thus, unravelling the factors that allowed Earth to develop into a planet teaming with life, whether those same factors are likely to be present on other rocky planets, and whether potential biosignatures, like atmospheric oxygen, are likely to arise on exoplanets if life is present, all require considering the role of the mantle.

 

Cycling of CO2: A key factor in planetary habitability

The abundance of atmospheric gases is determined by the balance between their sources and sinks, and the mantle acts as an important source and sink for many gases: volcanism releases volatiles locked in rocks to the surface, while subduction brings volatiles from the surface back into the interior. One of the most critical for habitability is CO2, which controls the climate state. On Earth, the cycling of CObetween surface, interior, and atmosphere involve a stabilizing feedback that acts to buffer climate (Kasting & Catling, 2003). COis drawn out of the atmosphere by weathering of silicate rocks and the formation of carbonate minerals on the seafloor, which are then subducted to return carbon to the mantle (Figure 2). Critically, the rate of silicate weathering increases with increasing surface temperature or atmospheric CO2. Thus when the climate warms the weathering rate increases, acting to cool the climate down, and when the climate is cool the weathering rate decreases, allowing outgassing of COby volcanism to warm the climate up (Walker et al, 1981).

 

Figure 2: Schematic cartoon of the carbonate-silicate cycle on Earth. Silicate weathering on land and seafloor weathering near mid-ocean ridges remove CO2 from the atmosphere and deposit it in the ocean crust. This carbon is then subducted, where some fraction is outgassed at arc volcanoes, with the rest returning the mantle. Outgassing from mid-ocean ridges and ocean islands returns mantle carbon to the atmosphere. From Foley & Driscoll, 2016.

 

However, this feedback can fail in two ways: first, rates of CO2outgassing must be high enough to keep the climate from plunging into a globally glaciated or snowball state (Kadoya & Tajika, 2014); second, there must be sufficiently high rates of physical erosion to remove weathered rock and bring fresh rock into the near-surface weathering zone (Foley, 2015). The mantle plays an important role in both CO2outgassing and surface erosion rates. The CO2outgassing rate is determined by the rate of volcanism, mantle carbon content, and oxidation state, while erosion rates are controlled by rates of tectonic uplift and mountain building over geologic timescales.

 

Role of the mantle in CO2 cycling: Future directions

However, there are many aspects of how the mantle influences COoutgassing and weathering rates that are still poorly understood, and exciting avenues of future research. First-order constraints on rates of volcanism and outgassing, and how they change over time, are straightforward to calculate from both simple box models of planetary thermal evolution or 2- and 3-D mantle convection calculations (Noack et al, 2017; Tosi et al, 2017). As planets cool over time, volcanic outgassing rates decline and eventually become low enough for frozen, snowball climates to develop. Factors that keep a planet’s mantle warmer for longer, such as higher rates of radiogenic heat production or tidal heating, will thus act to prolong the lifetime of habitable surface conditions (Foley & Smye, 2018; Valencia et al, 2018). Yet there are still important uncertainties, in particular on how carbon is carried into, and circulates within, the mantle that are key avenues for future research. Moreover, the connection between mantle dynamics, mountain building, erosion, and weathering rate is still poorly understood. Erosion rates are high when topographic gradients are large, as in mountainous regions. Mountain building is most likely connected to surface plate speed and the vigor of mantle convection, however just what form this connection takes is not known. How mantle convection and plate tectonics leads to the formation of topography, and hence influences weathering and erosion, is a critical area of research for understanding the controls on long-term climate evolution.

 

How Earth-like must a planet be to be habitable?

Ultimately one of the most important questions driving future research in planetary evolution and exoplanets, and which geodynamicists should be a central part of answering, is how Earth-like a planet needs to be in order to sustain volatile cycles that allow for the development of life and for biosignatures, such as oxygen, to accumulate in the atmosphere once life has developed (Tasker et al, 2017). Exoplanets come in a wide range of sizes (see Figure 3): planets up to about 4 Earth masses are found to be rocky, while beyond this limit planets are volatile-rich like Neptune (Rogers, 2015), and likely compositions as well (Hinkel & Unterborn, 2018). These planets could display a range of different surface tectonic modes, including plate tectonics, stagnant lids, or some intermediary style of tectonics. Oxidation states could be different, influencing the type of gases outgassed by volcanism. Instead of outgassing predominantly CO2, a planet with a more reduced mantle could outgas mostly CO or CH4. Likewise, different crustal compositions could alter weathering processes and the stability of volatiles as they are recycled into the interior at subduction zones or by crustal foundering. Exploring these issues will require interdisciplinary research including geochemists, mineral physicists, and geodynamicists, as well as biogeochemists, climate scientists, and astronomers. With future space telescopes poised to image exoplanet atmospheres, research on the role of the planetary interior in shaping the surface environment and atmosphere has never been so relevant.

 

Figure 3: Exoplanet population as of August 2017. Image credit: NASA/Ames Research Center/Natalie Batalha/Wendy Stenzel

 

References

Claire, M. W., Catling, D. C., & Zahnle, K. J. (2006). Biogeochemical modelling of the rise in atmospheric oxygen. Geobiology4(4), 239-269.

Foley, B. J., & Driscoll, P. E. (2016). Whole planet coupling between climate, mantle, and core: Implications for rocky planet evolution. Geochemistry, Geophysics, Geosystems17(5), 1885-1914.

Foley, B. J., & Smye, A. J. (2018). Carbon Cycling and Habitability of Earth-Sized Stagnant Lid Planets. Astrobiology18(7), 873-896.

Hinkel, N. R., & Unterborn, C. T. (2018). The Star–Planet Connection. I. Using Stellar Composition to Observationally Constrain Planetary Mineralogy for the 10 Closest Stars. The Astrophysical Journal853(1), 83.

Kadoya, S., & Tajika, E. (2014). Conditions for oceans on Earth-like planets orbiting within the habitable zone: importance of volcanic CO2degassing. The Astrophysical Journal790(2), 107.

Kasting, J. F., & Catling, D. (2003). Evolution of a habitable planet. Annual Review of Astronomy and Astrophysics41(1), 429-463.

Kump, L. R., & Barley, M. E. (2007). Increased subaerial volcanism and the rise of atmospheric oxygen 2.5 billion years ago. Nature448(7157), 1033.

Lyons, T. W., Reinhard, C. T., & Planavsky, N. J. (2014). The rise of oxygen in Earth’s early ocean and atmosphere. Nature506(7488), 307.

Noack, L., Rivoldini, A., & Van Hoolst, T. (2017). Volcanism and outgassing of stagnant-lid planets: Implications for the habitable zone. Physics of the Earth and Planetary Interiors269, 40-57.

Rogers, L. A. (2015). Most 1.6 Earth-radius planets are not rocky. The Astrophysical Journal801(1), 41.

Tasker, E., Tan, J., Heng, K., Kane, S., Spiegel, D., Brasser, R., ... & Houser, C. (2017). The language of exoplanet ranking metrics needs to change. Nature astronomy1, 0042.

Tosi, Nicola, Mareike Godolt, Barbara Stracke, Thomas Ruedas, John Lee Grenfell, Dennis Höning, Athanasia Nikolaou, A-C. Plesa, Doris Breuer, and Tilman Spohn. "The habitability of a stagnant-lid Earth." Astronomy & Astrophysics 605 (2017): A71.

Valencia, D., Tan, V. Y. Y., & Zajac, Z. (2018). Habitability from Tidally Induced Tectonics. The Astrophysical Journal857(2), 106.

Walker, J. C., Hays, P. B., & Kasting, J. F. (1981). A negative feedback mechanism for the long‐term stabilization of Earth's surface temperature. Journal of Geophysical Research: Oceans86(C10), 9776-9782.

 

 

Magma dynamics

Magma dynamics
Assistant Professor Juliane Dannberg, University of Florida.

Assistant Professor Juliane Dannberg, University of Florida.

In this week’s Geodynamics 101 post, Juliane Dannberg, Assistant Professor at the University of Florida, outlines the role of mantle melt generation and transport in geodynamics.

Mantle melting and magma transport are important influences on the dynamics and chemical evolution of the Earth’s interior. All of Earth’s oceanic crust and depleted oceanic lithosphere is generated through melting at mid-ocean ridges, the main process to introduce chemical heterogeneity into the mantle. Mechanically, melt and fluids play an important role in the dynamics of plate boundaries like mid-ocean ridges and subduction zones, and in the formation of oceanic islands. Specifically, partially molten regions are weaker than solid rock, and because of that, mechanisms that localise melt often also localise deformation.

Many mantle convection models include the effects of melting and melt transport to a first order. They allow for the generation of oceanic crust and lithosphere when mantle material approaches the surface. This is typically done by using a thermodynamic model to determine where melting occurs, removing melt as soon as it it forms, and distributing it further up or at the surface of the model as basaltic crust. The residuum that is left behind becomes the depleted, harzburgitic lithosphere.

But considering the addition of melt, a low-viscosity fluid phase, in models of mantle dynamics is not only important for geochemical considerations. It also introduces new length and time scales and new dynamics. Rather than talking about numerical methods, my goal for this article is to give a short overview of the physics of magma dynamics, and to build intuition on how magma generation and transport can affect geodynamic processes.

The forces at play

In mantle convection models, the driving force, buoyancy, is usually balanced by viscous stresses.
Consequently, the length scales of convective features are usually determined by how fast boundary layers can grow, by the density differences causing material to be buoyant, and by the mantle viscosity. When fluids are added to this system, new forces become important1:
(1) Darcy drag. Melt can segregate from where it forms by flowing through the pore spaces of the solid host rock. We can think of the system as a sponge-like solid rock matrix that can be squeezed and stretched, saturated with liquid melt. As melt starts to flow, the traction on the interface between the melt and the mineral grains opposes this motion. The more pore space there is, the better it is connected, and the lower the viscosity of the melt, the easier it becomes for the for the melt to flow through.
(2) Viscous compaction. When melt is generated, or when melt is about to flow into a space that had no melt before, the pore space of the solid rock has to dilate so that melt can flow in. In other words, magma is pushing the mineral grains of the rock apart. Conversely, when melt flows out of an existing pore space, it pulls the grains together and the solid rock needs to compact to fill this volume. This means that the forces that drive the flow of melt have to overcome the resistance of the solid rock to volumetric deformation, governed by the host rock’s compaction viscosity.

The equations

So instead of the Stokes equation used in mantle convection models, magma dynamics is described by a more complicated force balance with additional terms (McKenzie, 1984; Scott & Stevenson, 1984,1986; Bercovici, Ricard et al., 2001, 2003; Sramek et al, 2007):

This equation includes a number of material properties that control magma dynamics. The melt viscosity ηmelt and the permeability k express how easy it is for melt to flow through the pore space of the rock. The larger the pore space, and the better the connection between the pores, the larger the permeability. Because the rock is saturated with melt, the amount of pore space, or porosity ϕ, is equivalent to the fraction of melt. Consequently, the more melt is present, the larger the permeability. Δv is the difference between solid velocity and melt velocity and can be expressed using Darcy’s law:

In words, melt segregation relative to the motion of the solid is driven by differences in the melt or fluid pressure pf relative to the hydrostatic pressure in the melt, ρmelt g.

The viscous stresses are controlled by the shear viscosity η and the compaction viscosity ξ. Both properties depend on the melt fraction: The more melt is present (or, the larger the pore space of the rock), the easier it becomes to deform the solid rock matrix. This dependence is quite strong, and as soon as the porosity reaches 20–30% (the disaggregation threshold), the solid rock will break apart and will no longer form a connected matrix. Instead, the mineral grains will be suspended within the melt. Buoyancy is controlled by the density difference between solid and melt Δρ and the gravity g.

Depending on the importance of each of these forces in a given setting, the transport of melt can occur in different ways (Sramek et al., 2007). Buoyancy is caused by the lower density of the melt compared to the solid rock, so the more melt is present, the stronger the buoyancy forces. If viscous compaction forces are small (which corresponds to rocks that are easy to deform), buoyancy is balanced by Darcy drag (the so-called Darcy equilibrium; Sramek et al., 2007). In this case, melt ascends pervasively through the pores of the host rock, and its segregation velocity is limited by the rock’s permeability. Accordingly, the more melt is present, the faster it can ascend. This mode of melt transport may be representative of melting zones below mid-ocean ridges, where the amount of melt present in the pores of the host rock is small.

Numerical model of melt transport below MOR and in plume head.

Figure 1: Below mid-ocean ridges, melt can segregate from the solid and flow towards the ridge axis (top, modified from Dannberg et al., 2019). If there is a high-viscosity barrier to melt ascent, such as at the top of plumes, melt may circulate together with the solid in form of diapirs (bottom).

 

Conversely, if Darcy drag is small, then buoyancy is balanced by viscous compaction (the so-called viscogravitational equilibrium; Sramek et al., 2007). Melt can only flow if the solid rock deforms, and in this case the viscosity of the rock limits how fast melt can rise. If the compaction viscosity is comparable to or smaller than the shear viscosity, the host rock expands and melt can flow through the pores (Scott, 1988). But if the bulk viscosity is much larger than the shear viscosity, melt is forced to stay in the pocket of host rock it was created in over a long time scale. Instead of segregating, it will ascend together with the solid in form of a diapir (Scott, 1988). Because the Darcy drag becomes smaller the more melt is present (corresponding to a larger permeability), this mode of melt transport may occur near the top of plume heads (Fig. 1; Dannberg & Heister, 2016). Within the plume, high temperatures reduce the viscosity, but above the plume head, ambient mantle viscosities are larger and may limit melt segregation.

 

 

 

 

 

The equations also introduce a new length scale that controls the size of features that emerge in magma dynamics. This scale is controlled by the ratio of viscous forces and Darcy forces:

and is called the compaction length. It controls how far dynamic pressure differences between melt and solid, the compaction pressures, are transferred in partially molten rocks. This is important for the buoyant ascent of melt, which is hindered by the viscous resistance of the solid rock matrix to this compaction (Spiegelman 1993a, Spiegelman 1993b, Katz, 2015).

Solitary waves

Variations in porosity in the direction of gravity cause disturbances in the compaction pressure (Fig. 2): For example, if the porosity decreases in the direction of flow, the corresponding decrease in permeability makes it more difficult for melt to flow through and causes a decreasing flux of melt upwards into the low-porosity region. This negative gradient in melt flux leads to melt pressures being larger than solid pressures (a positive compaction pressure) at the location of the porosity perturbation, pushing the grains of the solid rock apart. This means that more melt can flow into this region and porosity increases. At the upper end of this perturbation, this same process continues to act, drawing more melt in.

At the lower end of the high-porosity region, the opposite happens: Because permeability increases in the direction of flow, the melt flux increases in upwards direction, causing a negative compaction pressure. Mineral grains are pulled together, and melt is expelled. Because the process continues in upwards and downwards direction, variations in the amount of melt will develop into magmatic waves (or solitary waves). At the front of the wave, the positive compaction pressure draws in more melt, and at the back of the wave, the negative compaction pressure pulls the mineral grains together as melt flows out. The length scale of these waves is on the order of the compaction length. In one dimension, this process can also be illustrated by the flow of fluid through a viscously deformable pipe (Scott, 1988). Imagine a part of the pipe that locally has a larger radius than the rest of the pipe and that moves upwards. To accommodate the arrival of more liquid, the pipe has to expand in front of the perturbation. In the same way, the pipe contracts behind the perturbation, reverting to its original radius.

Formation of solitary waves.

Figure 2: [Updated] Formation of solitary waves. After Spiegelman 1993b.

In the Earth’s mantle, the compaction length is on the order of a few to a few tens of kilometres. So in geodynamic models on tectonic scales, these waves are so small that they may first look like pressure or porosity oscillations! But knowing where this behaviour comes from is important for understanding what these waves mean, and if pressure waves in a numerical model are numerical artefacts or part of the actual physical behaviour of the system.

There are many more mechanisms that can cause melt to localise. When partially molten rock is sheared, melt is drawn into thin, melt-rich bands in between larger melt-poor regions. Channels of high porosity can form when reactive melting is driven by the flux of magma along a solubility gradient. A good overview over these processes and sources of further information is given in the lectures notes by Katz, 2015.

The bigger picture

All of these processes may be important for the flow of melt in subduction zones, at mid-ocean ridges, and for hotspot volcanism. Therefore I believe it is essential to better understand magma dynamics if we want to answer questions such as: How much of the mantle melt reaches the surface? What is the reason for the location and spacing of volcanoes? How are plate boundaries generated and maintained? I hope this article helps to understand this topic better and inspires you to consider melt generation and transport in this bigger context.


1These are the two most important forces in the mantle, but there are other forces that may impact deformation of partially molten rock. I have made a number of assumptions here, for example that the melt viscosity is much smaller than the solid velocity, that surface tension is negligible, and that deformation of the solid rock is predominantly viscous.

References:

Bercovici, D. et al., 2001. A two‐phase model for compaction and damage: 1. General theory. J. Geophys. Res. Solid Earth, 106(B5), pp.8887-8906.

Bercovici, D. and Ricard, Y., 2003. Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation. Geophys. J. Int., 152(3), pp.581-596.

Dannberg, J. and Heister, T., 2016. Compressible magma/mantle dynamics: 3-D, adaptive simulations in ASPECT. Geophys. J. Int., 207(3), pp.1343-1366.

Dannberg, J. et al., 2019. A new formulation for coupled magma/mantle dynamics. Geophys. J. Int., 219(1), pp.94-107.

Katz, R.F., 2015. An introduction to coupled magma/mantle dynamics. http://foalab.earth.ox.ac.uk/files/IntroMagmaLectures.pdf

McKenzie, D., 1984. The generation and compaction of partially molten rock. J. Petrol., 25(3), pp.713-765.

Scott, D.R. and Stevenson, D.J., 1984. Magma solitons. Geophys. Res. Lett., 11(11), pp.1161-1164.

Scott, D.R. and Stevenson, D.J., 1986. Magma ascent by porous flow. J. Geophys. Res. Solid Earth, 91(B9), pp.9283-9296.

Scott, D.R., 1988. The competition between percolation and circulation in a deformable porous medium. J. Geophys. Res. Solid Earth, 93(B6), pp.6451-6462.

Spiegelman, M., 1993a. Flow in deformable porous media. Part 1 Simple analysis. J. Fluid Mech., 247, pp.17-38.

Spiegelman, M., 1993b. Flow in deformable porous media. Part 2 numerical analysis–the relationship between shock waves and solitary waves. J. Fluid Mech., 247, pp.39-63.

Šrámek, O. et al., 2007. Simultaneous melting and compaction in deformable two-phase media. Geophys. J. Int., 168(3), pp.964-982.