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It doesn’t work! (Asking questions about scientific software)

It doesn’t work! (Asking questions about scientific software)

Numerical modelling is not always a walk in the park. In fact, many of us occasionally encounter problems that we cannot directly solve ourselves, and thus rely on help from others. In this month’s Wit & Wisdom post, Patrick Sanan, postdoctoral researcher at the Geophysical Fluid Dynamics group at ETH Zurich, will talk about asking the right questions about scientific software. As an experienced scientific software developer, Patrick has often been at the “receiving end” of questions regarding numerical modelling and hopes to guide you through some important points that could make life for you as well as your ‘helper’ a lot easier.

 

Patrick Sanan is a postdoctoral researcher at the Geophysical Fluid Dynamics group at ETH Zurich

Numerical modelling is essential for geodynamics; since we cannot directly measure relevant phenomena, we partake in the magic of making a set of reasonable assumptions, setting up a model, and letting a system evolve to produce insight. It’s beautiful. We gain an understanding of the subtle-yet-fundamental processes which shaped our apparently-so-special Earth. We turn our eye beyond, to other planets.

I’m not here to talk about that, though. I’m here to discuss an ugly part of the job, which can bring all the profundity to a screeching halt: what to do when the code doesn’t work.

You know the situation. You’re stuck. There’s no output. Segmentation fault. Error Code -123. You didn’t sign up for this…

You don’t know where to start looking. Is it your model parameters? Your physical assumptions? Are you using the code as intended? Is it your compiler? Can it be the cluster? Your .bashrc? Is your keyboard plugged in?

You’re frustrated. No one around you has a good suggestion. Why are these cruel computers doing this to you?

What to do? Ask for help, in the right way. In this blog, I’ll point out some facts about scientific software, try to use them to formulate an effective email in which you ask for help, and then try to extract some guiding principles.

Some Points on Scientific Software

First, I’ll list some observations I, as a developer, have made about scientific software:

  • Scientific software projects are usually short on maintainers and time.
  • Software designers are not psychic, but they are often experts at deductive problem-solving.
  • Reproducible, bisectable problems are surprisingly easy to solve. Other problems are surprisingly difficult.
  • Working reference cases are very valuable.
  • Sufficiently-complex computing tasks must be treated like lab experiments: one must document the setup and control as many factors as possible.
  • The solutions to most problems are obvious, once found.
  • Numerical software is harder to test than generic software, because floating point arithmetic and parallel computing lead to acceptable differences in numerical output. Higher-level understanding of physics or (parallel) numerical methods is often required to know if something is a “real problem”.

With these as a guide, let’s consider how one might try to resolve a confusing issue.

No pretty pictures here, just error messages (if you’re lucky).

Asking for Help: The Bad Way and the Good Way

Email is a common way to ask for help, as often the person who can best help you is across the world. Let’s say that I’m using a regional lithospheric dynamics code called Rifter3D. I’ve come across an error I have no explanation for. I can’t figure it out, so I write an email to developers of the code. You might also write to a dedicated help address.

Hello - I'm using Rifter3D but on our local cluster I get this error:

/cluster/shadow/.lsbatch/1559505025.92314771: line 8: 951 Segmentation fault (core dumped) ./rifter3d -options_file options.opts

Do you know what I'm doing wrong?

The person on the other end wants to help, but has no information to work with and doesn’t know how much of their time you’re asking for. There is a better way:

Hello - I'm having some trouble diagnosing a problem using Rifter3D and was hoping
you could give me some pointers.

I've been working with Prof. XYZ and have modified a rifting scenario from XYZ et al. 2017 to study the effects of varying A on B. When I run a small case on my laptop, the simulation finishes as expected. I use the attached options_small.opts and run mpiexec -np 4 ./rifter3d -options_file options_small.opts. I'd like to run a bigger case (512 x 256 x 64) for 300 million simulated years, on 64 cores on our cluster.
However, my job fails, producing a segmentation fault almost immediately. I attached the job submission script (job.sbatch), and output from my run (lsf.o92314771). I am using the cluster's existing PETSc 3.11 module, and version 1.0.3 of Rifter3D. I can successfully run a simple isoviscous setup on this cluster - see attached job_small.lsf, option2.opts, and lsf.o92314681

Do you have any insight as to how I might be able to run this simulation?

Best,
E. Scholar

Attachments: options_small.opts options.opts job.lsf job_small.lsf options2.opts lsf.o92314771 lsf.o92314681

The recipient will likely respond with more questions as you work towards resolving the issue. Perhaps they’ll ask you for more information about how you built Rifter3D, or point out some unusual settings in your options file.

Why is this second email better? It is not simply longer, but

  • It clearly describes the problem. Just trying to precisely describe a problem has an almost-magical clarifying effect, and the solution will often appear. Software engineers call this rubber ducking.
  • It explains the true objective and how the problem is to be resolved. This is important to avoid the XY problem, describing a problem with a method to achieve a goal, without mentioning the goal itself.
  • It gives concrete information to reproduce the problem: the version of the code, input files, and launch commands/scripts.
  • It provides enough output to allow deductive reasoning, more than just a copy-and-pasted error message.
  • It’s polite
  • It shows some effort has already been put into investigating.
  • It notes similar, working cases.
  • It’s not too long, but it is detailed enough to allow for quick, intelligent follow-up questions. Supporting data are included as attachments or links.
  • It doesn’t make too many assumptions about the cause of the problem.

Boiling it Down: 3 Questions to Ask Yourself

When asking for help, consider these three questions. They will help with the central objective: clearly describing the problem.

  • Why do you need it to work?
    What is the context? What is the goal?
  • How do you show that it doesn’t work?
    What are the steps to reproduce your problem?
    How will you know that the problem is resolved?
  • What does work?
    How far are you from a working state? What similar cases work?

Here is a 1-page pdf which you can print out, with some of this advice:

Pdf and LaTeX source on GitHub

The “Real” Answer

To conclude, I will try to avoid an “XY problem” of my own. The most efficient way to resolve bewildering problems is to avoid them. To make an alpine analogy, the most important topic in avalanche safety is not how to dig someone out, it’s how to avoid risky terrain.

Real-life debugging. Avoid if at all possible (from Wikimedia commons)

First, borrow techniques from software engineering. Version control (e.g. git) will encourage you to save working states, amongst many other benefits. Next, leverage your intuition and experience as a geodynamicist. Always be able to quickly run and verify small, quick, simple cases, and test and visualize often. Look out for simple cases where you “know the answer ahead of time”: established benchmarks and analytical solutions.

The points in this article can help everyone save time (and not just running geodynamical models!): problems will be resolved more quickly, bugs will get fixed faster, and more time can be spent exploring more interesting questions than “Why doesn’t it work?”.

 

Travel log – The Kenya rift

Travel log – The Kenya rift

Topographic map of the Kenya rift and surroundings. Dark red lines indicated faults from the GEM database. Dotted blue lines separate the northern, central and southern Kenya rift. In green circles the discussed locations.

A little over a year ago, I was lucky enough to join a field trip to the Kenya rift organized by Potsdam University and Roma III. This rift is part of the active East African Rift System, which I introduced in a previous blog post. With a group of 25 enthusiastic participants from Roma Tre, Potsdam University, Nairobi University and GFZ Potsdam (we somehow always managed to make the 20-person bus work), we set out to study the interaction between tectonics, magmatism and climate and their link to human and animal evolution. Based on several pictures, I’ll take you through the highlights.

 

 

 

 

Basement foliation and fault orientation

Two numerical modellers looking at rocks… Gneisses of the Mozambique belt with steeply dipping foliation – I think. Courtesy of Corinna Kallich, Potsdam University.

Although this first picture might not look so impressive (I promise, more impressive ones will come), this road outcrop shows the structure of the basement that is responsible for the orientation of the Kenya rift’s three western border faults. Here in particular, we are slightly west of the Elgeyo escarpment, the scarp of the major east-dipping Elgeyo fault. It reactivated the steep foliation of the Mozambique belt gneisses that formed during the Pan-African orogeny (550-500 Ma; Ring 2014). Changes in foliation orientation are mirrored by changes in fault orientation from NNE to NW upon going from the Northern to the Southern Kenya rift (see map). The Elgeyo fault itself displaced the 14.5 My old massive extrusion of phonolite lavas that can be seen throughout the Kenya rift area, marking the start of the current rift phase. From the differences in basement level between the western shoulder and the rift centre, the total offset along the fault is ~4 km!

Rift axis volcanism

Lunch overlooking the Menengai caldera that collapsed 36,000 yr ago. Courtesy of Corinna Kallich, Potsdam University.

With on-going rifting, the tectonic and magmatic activity localised in the centre of the Kenya rift. One massive central volcano is the Menengai volcano, whose view we enjoyed over lunch. This 12 km wide caldera collapsed 36,000 yr ago; the ash flows of the eruption can be found throughout the whole of Kenya. Within the caldera, diatomite layers alternating with trachyte lava flows indicate the presence of lakes 12 and 5 ky ago. These lakes were fed by the neighbouring Nakuru basin overflowing into the Menengai crater. The volcano itself was responsible for the earlier compartmentalization of the larger Nakuru-Elmentaita basin. At the moment, freshwater springs are being fed by the groundwater, and 40 geothermal wells are being constructed to benefit from the groundwater being heated by the magma chamber at 3-3.5 km depth.

Lunch at Hell’s Gate

Looking along Hell’s Gate Gorge – cut into the white diatomite and pyroclastic layers – towards feeder dikes of the remaining core of a volcano. Courtesy of Corinna Kallich, Potsdam University.

Watching the wildlife and beautiful scenery is usually the reason people visit Hell’s Gate National Park, but we studied the flow structures in a highly viscous, silica-rich lava flow. We then scrambled our way through Hell’s Gate Gorge that cut into mostly diatomite lake sediments (these algae are very helpful) alternated with pyroclastic layers. Most impressive however, were the crosscut basaltic intrusions that we could trace back to the centre of an otherwise eroded volcanic dome. The well-deserved lunch was a rather frustrating affair, as Vervet monkeys took every chance at stealing our food, not even shying away from distracting us with their adorable babies.

Monkey enjoying my lunch. Courtesy of Corinna Kallich, Potsdam University.

 

 

 

 

 

Wishing the lake was back

The white diatomites of the Olorgesailie Formation, indicating the presence of a lake. Courtesy of Corinna Kallich, Potsdam University.

The Olorgesailie basin is where paleoanthropologist Louis Leakey and his wife palaeontologist Mary Leakey (Wikipedia) unearthed a score of Acheulean hand axes in the 1940s. The 600-900 ky old tools were used to dig for roots, cleave, hammer and scrape meat and can be seen in the Kariandusi museum site. Besides the hand axes (made from all the trachyte found in the area), we marvelled at the Olorgesailie Formation that contains them, which was deposited between ~1.2-0.5 Ma. The formation consists of repetitions of wetland, river and lake sediments and paleosols (fossil soils, indicating dryer conditions). As we stand baking in the sun on top of the dusty, white diatomite, the vision of a lake sure is very alluring.

A not-so-fresh lake

On our way to a tiny hotspring along the edge of the slightly pink waters of Lake Magadi. In the foreground the white evaporates the lake is mined for. Courtesy of Corinna Kallich, Potsdam University.

While we mostly stayed in resorts, our only campsite (proper “glamping” with a shower and bathroom in the tent) was close to Lake Magadi, one of the lakes along the rift axis. This saline, alkaline lake gave its name to magadiite, a sodium hydro silicate, that when dehydrated forms chert (i.e. flint). The lake is also mined for its sodium carbonate, known as trona. During the African Humid Period (15,000-5,000 yr ago; Maslin et al. 2014), Lake Magadi was about 40 m higher, a lot fresher and connected to Lake Natron further south. Fun fact from Wikipedia: elephants visit the Magadi Basin to fill up on their own salts supplies as well. From my own experience, I can tell you, it does not taste very good.

 

 

My trusted companions for over a decade did not survive Kenya’s heat and volcanics… Serves me right for not taking them out often enough!

And then there were the hippos, neptunic dikes, dancing Maasai, a boat trip to the hydrothermal vents on Ol Kokwe Island, giraffes outside our cabin, midnight stargazing… too much to capture in one blog post. I had a wonderful time in Kenya exploring the geology, admiring the wildlife and getting to know its people. My only regret? Losing my shoes…

 

 

 

 

References:

Maslin, M. A., Brierly, C. M., Milner, A. M., Shultz, S., Trauth, M. H., Wilson, K. E. (2014). East African climate pulses and early human evolution, Quaternary Science Reviews 101, 1-17.

Ring, U. (2014). The East African Rift System, Austrian Journal of Earth Sciences, 107, 1.

Strecker, M. R., Faccenna, C., Wichura, H., Ballato, P., Olaka, L. A. and Riedl, S. (2018). Tectonics, seismicity, magmatic and sedimentary processes of the East African Rift Valley, Kenya, Kenya Field School Field Guide.

Personal communication with Strecker, M. R., Wichura, H., Olaka, L. A. and Riedl, S.

Remarkable Regions – The Kenya Rift

Remarkable Regions – The Kenya Rift

Every 8 weeks we turn our attention to a Remarkable Region that deserves a spot in the scientific limelight. After looking at several convergent plate boundaries, this week the focus lies on part of a nascent divergent plate boundary: the Kenya Rift. The post is by postdoctoral researcher Anne Glerum of GFZ Potsdam.

Of course an active continental rift is worthy of the title “Remarkable Region”. And naturally I consider my own research area highly interesting. But after seeing it up-close and personal on a recent 10-day trip organized by the University of Potsdam, Roma Tre and the University of Nairobi (stay tuned for the travel log, or read that of the University of Potsdam), I must say, the Kenya Rift is a truly beautiful and fascinating region.

Figure 1. Topography (Amante and Eakins 2009) and kinematic plate boundaries (Sarah D. Stamps based on Bird 2003) of the East African Rift System (EARS). Plate boundary colors schematically indicate the western and eastern branches of the EARS.

Constituting one segment of the 5000 km long East African Rift System (EARS, Fig. 1), the Kenya Rift is host to an amazing landscape, wildlife and people, all of which somehow tie back to continental rifting processes. Although the youngest rifting phase in Kenya commenced in the Miocene, the east African region as a whole has been shaped by rifting episodes since Permian times (Bosworth and Morley 1994). The present active rift system runs from the Afar region in the north all the way south to Mozambique and is split into a western and an eastern branch that run around the Archean Tanzanian Craton (Chorowitz 2005, see Fig. 1). Generally speaking, the western branch is more seismically active, but deprived of magmatism, compared to the eastern branch, of which the Kenya Rift is part (Chorowitz 2005). Three processes characterize the EARS (Burke 1996) as well as the Kenya Rift specifically: normal faulting, volcanism and uplift.

Uplift

The Tanzanian Craton together with the enveloping western and eastern EARS branches constitutes the broad, uplifted area coined the East African Plateau (~1200 m elevation, Strecker 1991; Simiyu and Keller 1997, Fig. 2). The onset of uplift of this plateau can be constrained to the Early Miocene with the help of one of the longest phonolitic lava flows on Earth (> 300 km, Wichura et al. 2010; 2011) and a whale that stranded inland 17 Ma (and was only recently found again after going missing for 30 years, Wichura et al. 2015). Plume-lithosphere interaction is thought responsible for the uplift (e.g. Wichura et al. 2010), although there is disagreement about the continuity of the low seismic velocity anomalies seen in the east African upper mantle and whether they are connected to the lower mantle. For example Ebinger and Sleep (1998), Hansen et al. (2012), Sun et al. (2017) and Torres Acosta et al. (2015) advocate for one East African superplume, while Pik et al. (2006) distinguish separate lower and upper mantle plumes and Davis and Sack (2002) and Halldórsson et al. (2014) consider a lower mantle plume splitting in the upper mantle.

Figure 2. Topography (Amante and Eakins 2009) and fault traces (GEM) of the central EARS. Triangles indicate off-rift volcanoes, dotted grey lines the three segments of the Kenya Rift.

Magmatism and volcanism

The northward motion of Africa over this hot mantle anomaly has been thought the cause of a north-to-south younging trend in the age of the ensuing EARS volcanism and rifting (e.g. Ebinger and Sleep 1998; George et al. 1998; Nyblade and Brazier 2002), although more recent studies arrive at a more spatially disparate and diachronous rifting evolution (Torres Acosta et al. 2015 and references therein). In general, massive emplacement of flood-phonolites preceded the onset of rifting in Kenya around 15 Ma (Torres Acosta et al. 2015). With ongoing rifting, and localization of faulting towards the rift axis, volcanism also migrated towards the center of the rift. Since the Miocene, massive amounts of volcanics have thus been emplaced (144,000-230,000 km3, MacDonald 1994; Wichura et al. 2011). Moreover, dyking also accommodated a significant part of the extension, with 22 to 26 % of the crust in the rift valley being composed of dykes (MacDonald 2012). Not surprisingly, the highlands directly around the rift valley, the Kenya Dome (Fig. 2) formed through a combination of volcanism and uplift (Davis and Slack 2002) with elevations of up to 1900 m.

The composition of rift magmatism is bimodal, showing phonolites and trachytes on the one side and nephelinites and basalt on the other, predominantly resulting from fractional crystallization of a basaltic source. The low viscosity of these magmas allows the young volcanoes in the volcano-tectonic axis to reach significant heights (see Fig. 3; MacDonald 2012). The most impressive volcanoes are to be found outside of the rift however (Fig. 2), with Mnt. Elgon reaching 4321 m and Africa’s highest mountains Mnt. Kenya and Mnt. Kilimanjaro reaching up to 5200 m and 5964 m, respectively (Chorowitz 2005).

Figure 3. View on the crater rim of the 400 ky old Mnt. Longonot volcano in the tectono-magmatic rift axis, at 2560 m asl. Courtesy of Corinna Kallich, GFZ Potsdam.

Normal faulting

The Kenya rift itself is composed of 3 asymmetric segments, distinguished by sharp changes in their orientation (Chorowitz 2005, Fig. 2). The 2300-3000 m high Elgeyo, Mau and Nguruman escarpments result from the steep Miocene east-dipping border faults in the west, while the antithetic border faults on the eastern side formed later during the Pliocene (Strecker et al. 1990). The older border faults formed along preexisting foliation generated by the Mozambique Belt orogeny in the late Proterozoic (Shackleton 1993; Hetzel and Strecker 1994). A change in strike of this foliation from NNE in the northern and southern Kenya rifts to NW determined the change in orientation in the central Kenya rift (Strecker et al. 1990). Consequently, different generations of faults in the northern and southern rift segments run parallel, while in the central segment, the Pleistocene change in extension direction from ENE-WSW/E-W to the present-day WNW-ESE/NW-SE directed extension results in obliquely reactivated border faults and younger, en echelon arranged left-stepping NNE-striking fault zones along the rift axis (Strecker et al. 1990). Extension is transferred between the different zones by coeval normal and strike-slip faulting or dense sets of normal faults.

Figure 4. View of lake Magadi and the Nguruman escarpment. Lake Magadi is a saline, alkaline lake, commercially mined for trona. Courtesy of Corinna Kallich, GFZ Potsdam.

Human evolution

The uplift, volcanism and normal faulting together have set the stage for human and animal evolution. For example, the shift in hoofed mammals from eating predominantly woods to grazing species evidences that the large-scale uplift modified air circulation patterns resulting in aridification and savannah-expansion at the expense of forested areas (Sepulchre et al. 2006; Wichura et al. 2015). The rift basins enabled the formation of large lakes, which were subsequently compartmentalized by tectonic and volcanic morphological barriers (Fig. 4). On the short-term, lake coverage varied due to tectonically induced changes in catchment areas, drainage networks and outlets. Maslin et al. (2014) actually found a correlation between this ephemeral lake coverage and hominin diversity and dispersal. Lake highstands link with the emergence of new species and allowed the spread of hominins north and southward out of east Africa. Remarkable, or what!

References:
Amante, C. and Eakins B. W., 2009. NOAA Technical Memorandum NESDIS NGDC-24. National Geophysical Data Center, NOAA.
Bosworth, W. and Morley, C.K., 1994.  Tectonophysics 236, 93–115.
Burke, K., 1996. S. Afr. J. Geol. 99 (4), 339–409.
Chorowitz, J., 2005. J. Afr. Earth Sci. 43, 379-410.
Davis, P. M. and Slack, P. D. 2002. Geophys. Res. Lett. 29 (7), 1117.
Ebinger, C.J. and Sleep, N.H., 1998. Nature 395, 788-791.
George, R. et al., 1998.  Geology 26, 923–926.
Halldórsson, S. A. et al., 2014. Geophys. Res. Lett. 41, 2304–2311,
Hansen, S. E. et al., 2012.  Earth Planet. Sc. Lett. 319-320, 23-34.
Hetzel, R., Strecker, M.R., 1994. J. Struct. Geol. 16, 189–201.
Macdonald, R. et al., 1994a. J. Volcanol. Geoth. Res. 60, 301–325.
Macdonald, R., et al., 1994b. J. Geol. Soc. London 151, 879–888.
MacDonald, R., 2012. Lithos 152, 11-22.
Maslin, M. A. et al., 2014. Quaternary Sci. Rev. 101, 1-17.
Nyblade, A. A. and Brazier, R. A., 2002. Geology 30 (8), 755-758.
Pik, R. et al., 2006. Chem. Geol. 266, 100-114.
Sepulchre, P. et al., 2006. Science, 1419-1423.
Shackleton, R.M., 1993. Geological Society, London, Special Publications 76, 345–362.
Simiyu, S.M., Keller, G.R., 1997. Tectonophysics 278, 291–313.
Strecker, M., 1991. Das zentrale und südliche Kenia-rift unter besonderer berücksichtigung der neotektonischen entwicklung, habilitation, Universität Fridericiana.
Sun, M. et al., 2017.  Geophys. Res. Lett. 44, 12,116–12,124.
Torres Acosta, V. et al., 2015. Tectonics 34, 2367–2386.
Wichura, H. et al., 2010. Geology 38 (6), 543–546.
Wichura, H. et al , 2011. The Formation and Evolution of Africa: A Synopsis of 3.8 Ga of Earth History, eds. D. J. J. Van Hinsbergen, S. J. H. Buiter, T. H. Torsvik, C. and Gaina, S. J.
Wichura, H. et al., 2015. P. Natl. Acad. Sci. USA 112 (13), 3910-3915.

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.

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