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An industrial placement as a geodynamicist

An industrial placement as a geodynamicist

After years of trying to get a PhD, publishing papers, networking with professors, and trying to land that one, elusive, permanent job in science, it can be quite easy to forget that you actually do have career options outside of academia. To get a little taste of this, Nico Schliffke, PhD student in geodynamics at Durham University, tries out the industry life for a few weeks!

When coming close to the final stages of a PhD life, many students reconsider whether they want to stay in academia or prefer to step over to industry or other non-academic jobs. This is surely not a simple decision to take, as it could strongly shape your future. In this blog post, I would like to report my industrial placement experience during my PhD and share a few thoughts on the topic.

The taste of industry life was an opportunity I had within the frame of my PhD project. Split into two terms, I spent four weeks at a medium-sized company developing optical imaging techniques (both software and equipment) to measure flow fields and deformation. The branch I worked in was “digital image correlation” (DIC) which measures strain on given surfaces purely by comparing successive images on an object (see figure below). This technique is used in both industry (crash tests, quality assessments, etc.) as well as in academia (analogue experiments, wind tunnels, engineering..), and has the substantial advantage of measuring physical properties precisely, without using any materials or affecting dynamical processes. DIC is not directly related to or used in my PhD (I do numerical modelling of subduction zones and continental collision), but surprisingly enough I was able to contribute more than expected – but more on that later.

Basic principle of ‘digital image correlation’. A pattern on a digital image is traced through time on successive images to calculate displacements and strain rates.
Credit: LaVision

The specific project I worked on was inspired by the analogue tectonics lab at GFZ Potsdam, that uses DIC measuring systems to quantify and measure the deformation of their sandbox experiments. Typical earthquake experiments like the figure below span periods of a few minutes to several days during which individual earthquakes occur in a couple of milliseconds. The experiment is continuously recorded by cameras to both monitor deformation visually and quantify deformation by using the optical imaging technique developed by my host company. To resolve the deformation related to individual earthquakes, high imaging rates are required which in turn produce a vast amount of data (up to 2TB per experiment). However, only a small fraction (max. 5%) of the entire dataset is of interest, as there is hardly any deformation during interseismic periods. The project I was involved in tried to tackle the issue of unnecessarily cluttered hard discs: the recording frequency should be linked to a measurable characteristic within the experiment, e.g. displacement velocities in these specific experiments, and controlled by the DIC software.

Setup of the analogue experiment to model earthquakes in subduction zones (courtesy of Michael Rudolf). Cameras above the experiment measure deformation and strain rates by tracking patterns on the surface created by the contrast of black rubber and white sugar.

My general task during the internship was to develop this idea and the required software. We finally developed a ‘live-extensometer’ to calculate displacements between two given points of an image during recording and link its values to the camera’s recording frequency. Therefore, restricting high imaging rates to large (and fast) displacements of earthquakes should result in reducing the total amount of data acquired for a typical earthquake experiment by 95%. However, we needed an actual experiment to verify this. So, I met up with the team at GFZ to test the developed feature.

The main experiment the GFZ team had in mind is sketched in the figure above: a conveyor belt modelling a subducting slab continuously creates strain in the ‘orogenic wedge’ which is released by earthquakes leading to surface deformation. Cameras above the experiment monitor the surface while software computes strain rates and displacement (see figure below). The developed feature of changing frequencies during the experiment depending on slip rates was included and worked surprisingly well. Yet freshly programmed software is seldom perfect: minor issues and bugs crept up during the experiments. My final contribution during the internship was to report these problems back to the company to be fixed.

Displacement measured by ‘digital image correlation’ during an earthquake lasting ~5 ms (courtesy of Mathias Rosenau).

My geodynamical background allowed me to contribute to various fields within the company and resulted in various individual tasks throughout the internship: coding experience helped with discussing ideal software implementations and testing the latest implemented software on small (physical) experiments. My knowledge of various deformation mechanisms and geosciences in general, with its numerous subdisciplines and methods, provided a solid base for searching further applications for the developed software within academia, but also in industry. Last but not least, pursuing my own large project (my PhD) strongly facilitated discussing possible future development steps.

The atmosphere at the company in general was very pleasant and similar to what I experienced at the university: relaxed handling, pared with discussion how to improve products or use of new techniques that might be applicable to a problem. To stay competitive, the company needs to further develop their products which requires a large amount of research, developments and innovative ideas. Meetings to discuss further improvements of certain products were thus scheduled on a (nearly) daily basis. On the one hand this adds pressure to get work done as quickly as possible, but working on a project as a team with many numerous areas of expertise is also highly exciting.

This internship help reveal the variability of possible jobs that geodynamicists can have in industry besides the ‘classical’ companies linked to exploration, tunnel engineering or geological surveys. The skill set acquired in a geodynamical PhD (coding, modelling, combining numerics, physics, and geosciences) makes a very flexible and adaptive employee which is attractive to companies who are so specialised, that there is (nearly) no classical education at university level. Jobs at small to medium-sized companies are often harder to find, but it’s just as difficult for the companies to find suitable candidates for their open positions. Hence, it may be worth searching in-depth for a suitable job, if you are considering stepping out of academia and maybe even out of geoscience as well.

If PhD students are hesitant whether to stay in academia or change into industry, I would advise to do such a short internship with a company to get a taste of ‘the other side’. During a PhD, we get to know academic life thoroughly but industry mostly remains alien. Besides giving a good impression of daily life at a company and how you can contribute, an industry internship might also widen your perspective of which areas might be relevant to you, your methodology and your PhD topic. In total, this internship was definitely a valuable experience for me and will help when deciding: academia or industry?


Here are a few links for more information:
Host company
Digital Image Correlation
TecLab at GFZ Potsdam
Previous EGU blog post interviews of former geoscientists


Thoughts on geological modelling: an analogue perspective

Thoughts on geological modelling: an analogue perspective

In geodynamics we study the dynamics of the Earth (and other planets). We ground our studies in as much data as possible, however we are constrained by the fact that pretty much all direct information we can collect from the interior of the Earth only shows its present-day state. The surface rock record gives us a glimpse into the past dynamics and evolution of our planet, but this record gets sparser as we go back in time. This is why it is common to use modelling in geodynamics to fill this gap of knowledge. There are different types of modelling, and this week João Duarte writes about the importance of analogue modelling. 

João Duarte. Researcher at Instituto Dom Luiz and Invited Professor at the Geology Department, Faculty of Sciences of the University of Lisbon. Adjunct Researcher at Monash University.

The first time I went to EGU, in 2004, I presented a poster with some new marine geology data and a few sets of analogue models. I was doing accretionary wedges in sandboxes. At the time, I was in the third year of my bachelor’s degree and I was completely overwhelmed by the magnitude of the conference. It was incredible to see the faces of all those scientists that I used to read articles from. But one thing impressed me the most. Earth Sciences were consolidating as a modern, theoretical based science. The efforts in trying to develop an integrated dynamic theory of plate tectonics as part of mantle convection were obvious. The new emergent numerical models looked incredible, with all those colours, complex rheologies and stunning visualization that allowed us to “see” stresses, temperature gradients and non-linear viscosities. I was amazed.

Analogue modelling was at a relative peak in 2004, however it was also anticipated by some that it would quickly disappear (and indeed several analogue labs have closed since). It was with this mindset, that I later did the experiments for my PhD, which I finished in 2012 (Duarte et al., 2011). But I was fortunate. My supervisors, Filipe Rosas and Pedro Terrinha, took me to state-of-art labs, namely Toronto and Montpellier (lead at the time by Sandy Cruden and Jacques Malavieille, respectively), and I started to develop a passion for this kind of models. When I moved to Monash for a post-doc position, in 2011, this turned out to be a great advantage. There, modelers such as Wouter Schellart, Louis Moresi, Fabio Capitanio, David Boutelier and Sandy Cruden (yes, I met Sandy again at Monash) were using analogue models to benchmark numerical models. Why? Because many times, even though numerical models produce spectacular results, they might not be physically consistent. And there is only one way to get rid of this, which is to make sure that whatever numerical code we are using can reproduce simple experiments that we can run in a lab. The classical example is the sinking of a negatively buoyant sphere in a viscous medium.

Sandbox analogue model of an accretionary wedge. Part of the same experiment as shown in the header figure. Here, a sliced section cut after wetting, is shown. University of Lisbon, 2009. Experiments published in Duarte et al. (2011).

That was what we were doing at Monash. I worked with Wouter Schellart in the development of subduction experiments with an overriding plate, which were advancing step by step in both analogue and numerical schemes (see e.g., Duarte et al., 2013 and Chen et al., 2015, 2016 for the analogue models, and Schellart and Moresi, 2013 for numerical equivalents). The tricky bit was, we wanted to have self-consistent dynamic experiments in which we were ascribing the forces (negative buoyancy of the slab, the viscosity of the upper mantle, etc) and let the kinematics (i.e. the velocities) to be an emergent phenomenon. So, no lateral push or active kinematic boundaries were applied to the plates. This is because we now recognize that in general, it is the slab pull at subduction zones that majorly drives the plates and not the other way around. Therefore, if we want to investigate the fundamental physics and dynamics of subduction zones we need to use self-consistent models (both analogue and numerical). In order to carry out these models, we had to develop a new rheology for the subduction interface, which is a complex problem, both in the analogue and the numerical approaches (Duarte et al. 2013, 2014, 2015). But this is another very long story that would lead to a publication by itself.

Analogue models of subduction with an overriding plate and an interplate rheology. Monash University, 2012. Adapted from Duarte et al. (2013)

But what is analogue modelling all about? Basically, analogue models are scaled models that we can develop in the laboratory using analogue materials (such as sand), and that at the scale that we are doing our models have similar physical properties to those of natural materials (such as brittle rocks). But, as it is widely known, under certain circumstances (at large time and space scales), rocks behave like fluids, and for that we use analogue fluids, such as silicone putties, glucose and honey. We can also use fluids to simulate the interaction between subduction zones and mantle plumes in a fluid reservoir (see below figures and links to videos of scaled experiments using three different fluids to study slab-plume interaction; Meriaux et al., 2015a, 2015b, 2016). These are generally called geodynamic analogue models.

End of a slab-plume experiment in the upper mantle (see below). The tank is partially filled with glucose. The slab (laying at the analogue 660 discontinuity) is made of silicone mixed with iron powder. The plume is made of a water solution of glucose dyed with a red colorant. And that’s me on the left. Monash University, 2014.

I usually consider two main branches of analogue models. The first, which is the one mostly used by geologists, was started by Sir James Hall (1761 – 1832), that squeezed layers of clay to reproduce the patterns of folded rocks that he had observed in nature. This method was later improved by King Hubbert (1937), who laid the ground for the development of the field by developing a theory of scaling of analogue models applied to geological processes.

The other branch is probably as old as humans. It began when we started to manipulate objects and using them to understand basic empirical laws, such as the one that objects always fall. When Galileo was using small spheres in inclined surfaces to extract the physical laws that describe the movement of bodies, from rocks to planets, he was in a certain way using analogue models. He understood that many laws are scale invariant. Still today, these techniques are widely used by physicist and engineers when understanding for example the aerodynamics of airplanes, the stability of bridges, the dynamics of rivers or the resistance of dams. They use scaled models that reproduce at suitable laboratory scales the objects and processes that they are investigating.

What we did at Monash, was a mixture of both approaches. Though, we were less interested in exactly reproducing nature from a purely geometric and kinematic point of view, but we were more interested in understanding the physics of the object we were investigating: subduction zones. Therefore, we had to guarantee that we were using the correct dynamical approach in order to be able to extract generic physical empirical laws, hoping that these laws would provide us some insight on the dynamics of natural subduction zones. These empirical laws could readily be incorporated in numerical models, which would then help exploring more efficiently the space of the controlling parameters in the system.

Slab-Plume interaction in the upper mantle. Experiments published in Meriaux et al. (2015a, 2015b).

I want to finish with a question that I believe concerns all of us: are there still advantages in using analogue models? Yes, I believe so! One of the most important advantages is that analogue models are always three-dimensional and high-resolution. Furthermore, they allow a good tracking of the strain and to understand how it occurs in discontinuous mediums, for example when investigating the localization of deformation or the propagation of cracks. Numerical schemes still struggle with these problems. It is very difficult to have an efficient code that can deal simultaneously with very high resolution and large-scale three-dimensional problems, as it is required to investigate the process of subduction. Nevertheless, numerical models are of great help when it comes to track stresses, and model complex rheologies and temperature gradients. To sum up: nowadays, we recognize that certain problems can only be tackled using self-consistent dynamic models that model the whole system in three-dimensions, capturing different scales. For this, the combination of analogue and numerical models is still one of the most powerful tools we have. An interesting example of a field in which a combined approach is being used is the fascinating investigations on the seismic cycle (for example, see here).

Links to videos:

VIDEO 1: https://www.youtube.com/watch?v=U1TXC2XPbFA&feature=youtu.be
(Subduction with an overriding plate and an interplate rheology. Duarte et al., 2013)

VIDEO 2: https://www.youtube.com/watch?v=n5P2TzS6h_0&feature=youtu.be
(Slab-plume interaction at mantle scale. Side-view of the experiment on the top, and top-view of the experiment on the bottom. Meriaux et al., 2016)
References:

Chen, Z., Schellart, W.P., Strak, V., Duarte, J.C., 2016. Does subduction-induced mantle flow drive backarc extension? Earth and Planetary Science Letters 441, 200-210. https://doi.org/10.1016/j.epsl.2016.02.027

Chen, Z., Schellart, W.P., Duarte, J.C., 2015. Overriding plate deformation and variability of forearc deformation during subduction: Insight from geodynamic models and application to the Calabria subduction zone. Geochemistry, Geophysics, Geosystems 16, 3697–3715. DOI: 10.1002/2015GC005958

Duarte, J.C., Schellart, W.P., Cruden, A.R., 2015. How weak is the subduction zone interface? Geophysical Research Letters 41, 1-10. DOI: 10.1002/2014GL062876

Duarte, J.C., Schellart, W.P., Cruden, A.R., 2014. Rheology of petrolatum – paraffin oil mixtures: applications to analogue modelling of geological processes. Journal of Structural Geology 63, 1-11. https://doi.org/10.1016/j.jsg.2014.02.004

Duarte, J.C., Schellart, W.P., Cruden, A.R., 2013. Three-dimensional dynamic laboratory models of subduction with an overriding plate and variable interplate rheology. Geophysical Journal International 195, 47-66. https://doi.org/10.1093/gji/ggt257

Duarte, J.C., F.M. Rosas P., Terrinha, M-A Gutscher, J. Malavieille, Sónia Silva, L. Matias, 2011. Thrust–wrench interference tectonics in the Gulf of Cadiz (Africa–Iberia plate boundary in the North-East Atlantic): Insights from analog models. Marine Geology 289, 135–149. https://doi.org/10.1016/j.margeo.2011.09.014

Hubbert, M.K., 1937. Theory of scale models as applied to the study of geologic structures. GSA Bulletin 48, 1459-1520. https://doi.org/10.1130/GSAB-48-1459

Meriaux, C., Meriaux, A-S., Schellart, W.P., Duarte, J.C., Duarte, S.S., Chen, Z., 2016. Mantle plumes in the vicinity of subduction zones. Earth and Planetary Science Letters 454, 166-177. https://doi.org/10.1016/j.epsl.2016.09.001

Mériaux, C.A., Duarte, J.C., Schellart, W.P., Mériaux, A-S., 2015. A two-way interaction between the Hainan plume and the Manila subduction zone. Geophysical Research Letters 42, 5796–5802. DOI: 10.1002/2015GL064313

Meriaux, C.A., Duarte, J.C., Duarte, S., Chen, Z., Rosas, F.M., Mata, J., Schellart, W.P., and Terrinha, P. 2015. Capture of the Canary mantle plume material by the Gibraltar arc mantle wedge during slab rollback. Geophysical Journal International 201, 1717-1721. https://doi.org/10.1093/gji/ggv120

Schellart, W.P., Moresi, L., 2013. A new driving mechanism for backarc extension and backarc shortening through slab sinking induced toroidal and poloidal mantle flow: Results from dynamic subduction models with an overriding plate. Journal of Geophysical Research: Solid Earth 118, 3221-3248. https://doi.org/10.1002/jgrb.50173

Let’s talk about disability in geosciences

Let’s talk about disability in geosciences

Climbing towards outcrops during fieldwork for your undergraduate studies simply isn’t doable for everyone. However, this doesn’t mean that there are adequate alternative solutions available. This week, Katy Willis, PhD student on strain-localisation in the continental lithosphere at the University of Leeds, UK, discusses disability in the geosciences, because regardless of who you are a career in geosciences should be available to you.

On June 4th, 2018 at The Geological Society in London, the UK branch of the International Association for Geodiversity (IAGD) was launched under the name DiG-UK (Diversity in Geosciences, UK), and I was one of those in attendance. The IAGD focuses on the inclusion of people with disabilities within the geosciences, and DiG-UK has incorporated this aim along with championing a better representation of black, Asian, and other ethnic minority groups. Here, I am going to focus on the disability inclusion.

Before I go on – and it’s a shame that I have to type this in the 21st century – let me point out that just because a person has a mental or physical handicap it in no way detracts from their ability to study geosciences or advance in a career in either academia or industry. What hinders them is the barriers that are erected by others before their careers even start. There are a range of disabilities. Anyone may experience a temporary one, like a broken leg restricting your mobility. Some people may experience longer term issues, for example depression triggered by the death of a parent. It may be a health issue that has intermittent effects, such as Crohn’s disease. Or it could be a lifelong issue, such as partial blindness or complex mental health issues.

Geosciences is a broad term for anything from geology to paleo-climate, right up to geodynamics. The one thing that unites such studies, especially at an undergraduate level, is fieldwork. In the UK, an accredited geology degree requires a component of fieldwork, and graduation above a certain level may demand an extended independent fieldwork experience lasting weeks. This is all well and good if you are physically and mentally capable of doing such work, but each year a small proportion of students find themselves unable to go on fieldwork. The old “solution” was to give them a desktop study while the rest of the year went off to Cyprus, Scotland, or Spain. The field group would form close friendships while away, so that those left searching dusty library shelves felt partially excluded from their year group. Hardly an acceptable solution.

The inaugural DiG-UK meeting brought together academia and industry to discuss disability inclusion. An open session looking at how different organisations have got people thinking about disability inclusion and how to practically implement it got us all chatting and sharing ideas. I was delighted to see the approach the Open University had taken regarding fieldwork. It acknowledges that not all field locations are accessible to those with physical disabilities, but there is no need to prevent such students attending field trips because there will remain a number of locations that can be readily visited. For the inaccessible locations they set up a local WiFi network and use iPads so an able bodied person can stream a live image to those who can’t reach that particular outcrop. Genius!

Manchester Metropolitan University has developed a “Diversity Dash” game to help groups understand the many barriers that all students and staff can face. Each team is allocated a character, and a range of scenarios are presented (lab work, unexpected meeting on the top floor, taking notes in lectures). The teams then have to find realistic ways in which their character can take part in the scenario. The characters cover a range of people, from someone who has a pregnant partner through to the rich student that seems to have everything but certain issues are causing increased complications.

If universities automatically allow for the provision of disabled people in their fieldwork plans, then it allows students to continue their studies should they suffer a mild injury such as a sprained ankle. During my undergraduate time, I saw two people fail to finish their course because the university was unable to accommodate their disability needs. They were intelligent people, who knew that beyond graduation lay geoscience careers that did not rely on fieldwork, but they could not pass that barrier of obtaining the appropriate degree. In both cases a few simple adjustments would have allowed them to finish.

It behoves any institute to set up a framework that encourages practical and workable disability inclusion in the geosciences. Organisations such as DiG-UK and the IAGD can provide valuable information on how to do this. Our area of study – geodynamics – sees many of us sat in front of a computer, but a lot of us were required to carry out field studies at some point in our education. It added to our knowledge and experience and in my case it inspired me into the direction of geodynamics and the desire to understand the broader picture.

In September I am taking part in a field trip to Anglesey UK. There will be a range of people going and we aim to discover which methods assist inclusion and accessibility in the field (and which don’t!). Then the findings will be shared so real and practical ways of being inclusive can be implemented for geoscience fieldwork across the UK (and hopefully internationally).

So, go on. What are you going to do this month to help people with disabilities become more involved in geosciences?

Follow DiG-UK on twitter: @DiG_UK_IAGD

Going with the toroidal mantle flow

Going with the toroidal mantle flow

Subduction zones host one of the most complex and fascinating tectonic systems on the planet. Numerical models by Király and colleagues recently published in Earth and Planetary Science Letters reveal that the strength of the toroidal flow depends on the mantle viscosity and the magnitude of the slab pull force while the characteristic size of the toroidal cells mainly depends on the size of the convecting mantle.

 

The motion of Earth’s tectonic plates—the lithosphere—is driven by the subduction of relatively cold and dense oceanic plates into the mantle. Subduction zones are some of the most striking features on Earth. They represent one of the two types of convergent plate boundaries, in which one tectonic plate sinks underneath another one into the Earth’s mantle. The resulting forces induce mantle flow around the subducting plate, but the manner in which this happens is still a matter of debate.

Below the tectonic plates, the mantle moves in a slow and unseen manner—as cold slabs sink, hot upwellings rise, and convection slowly rids the Earth’s interior of its primordial heat. Much of our knowledge of mantle flow patterns is indirect, inferred from geodynamical models or seismic tomography images.

Seismological and geochemical investigations suggest 3D subduction-induced mantle flow around lateral slab edges from the sub-slab zone towards the mantle wedge[1]. Such flow has also been observed in laboratory experiments[2] and numerical models of subduction[3]. In particular, geodynamic numerical models of subduction demonstrate that back-arc extension at narrow subduction zones is driven by rollback-induced mantle flow[4].

Observations of seismic anisotropy—the directional dependence of seismic wave speed—provide us with tantalizingly direct information about mantle flow direction. For example, crystals of olivine, which is the most common upper-mantle mineral, tend to become aligned by the mantle flow, and seismic anisotropy is an indicator of this alignment.

To apply the laboratory-derived viscosity laws to nature, they must be extrapolated over 10 orders of magnitude, which introduces uncertainty. Moreover, it is unclear to what extent experiments on centimeter-scale samples are representative of the crust and lithosphere.

The viscosity distribution of the lithosphere and the surrounding mantle is therefore one of the least certain parameters in geodynamics. Alternative ways to determine viscosity on geological time scales are thus needed.

Schematic diagram of a subduction zone, showing the dominance of 3D flow beneath the slab and the competing influence of 2D and 3D flow fields in the mantle wedge. Credit: Long and Silver, 2008, Science.

 

Writing in Earth and Planetary Science Letters, Király and colleagues[5] present a cutting-edge numerical model that shows how the strength and length scale of the toroidal flow vary with the mantle viscosity and the magnitude of the slab pull force. Király and co-workers highlight some remarkable implications of these effects: around subducting plates, the characteristic length, axis, and shape of the toroidal cell are almost independent of the slab’s properties and mainly depend on the thickness of the convecting mantle. The independence of the shape of the toroidal cell on the slab width can appear controversial with respect to previous studies[6–7] that showed that the overall mantle flow is dependent on the slab width. However, as Király et al. point out, these differences can be explained with the model setup adopted and the range of slab widths investigated.

In order to characterize the flow—in terms of its geometry and strength—Király and co-workers analysed the vertical component of the mantle vorticity as well as the ratio between the vertical and the trench parallel component of the vorticity vector. With a series of numerical experiments, they find that subduction-induced mantle flow is highly three-dimensional, and that the toroidal component is sub-horizontal with some vertical flow components. According to the authors, this vertical flow around the slab edges has significant implications, as it can be responsible for the presence of the off-arc volcanism around several laterally confined subduction zones.

The numerical experiments by Király et al. represent another step forward in our understanding of how mantle circulation plays a relevant role in the shaping of tectonic features around subduction zones, and they provide evidence that the slab properties only impact the vigour of the flow around subducting slabs. The extension of these numerical experiments to a range of different parameters will allow for a fuller characterization of the olivine fabric, which in turn will allow seismologists to relate their measurements of seismic anisotropy to flow directions and, ultimately, to mantle processes.

 

References:

1. Long, M. D., and P. G. Silver (2008), The subduction zone flow field from seismic anisotropy: A global view, Science, 319, 315-318.
2. Funiciello, F., C. Faccenna, and D. Giardini (2004), Role of lateral mantle flow in the evolution of subduction systems: insights from laboratory experiments, Geophy. J. Int., 157, 1393-1406.
3. Jadamec, M. A., and M. I. Billen (2010), Reconciling surface plate motions with rapid three-dimensional mantle flow around a slab edge, Nature, 465, 338-342.
4. Sternai, P., L. Jolivet, A. Menant, and T. Gerya (2014), Driving the upper plate surface deformation by slab rollback and mantle flow, Earth Planet. Sci. Lett., 405, 110-118.
5. Király, A. Capitanio, F.A., Funiciello, F., Faccenna, C. (2017). Subduction induced mantle flow: Length-scales and orientation of the toroidal cell. Earth Planet. Sci. Lett., 479, 284–297.
6. Funiciello, F., Moroni, M., Piromallo, C., Faccenna, C., Cenedese, A., Bui, H.A., 2006. Mapping mantle flow during retreating subduction: laboratory models analyzed by feature tracking. J. Geophys. Res., Solid Earth 111, 1–16.
7. Stegman, D.R., Freeman, J., Schellart, W.P., Moresi, L., May, D., 2006. Influence of trench width on subduction hinge retreat rates in 3-D models of slab rollback. Geochem. Geophys. Geosyst. 7.