GD
Geodynamics

Archives / 2017 / November

Alaska: a gold rush of along strike variations

Alaska:  a gold rush of along strike variations

Every 8 weeks we turn our attention to a Remarkable Region that deserves a spot in the scientific limelight. After exploring the Mediterranean and the ancient Tethys realm, we now move further north and across the Pacific to the Aleutian-Alaska subduction zone. This post was contributed by Kirstie Haynie who is a PhD candidate at the department of geology at the University at Buffalo, State University of New York, in the United States of America.

Given that Alaska is a remarkable region, I decided to walk up to strangers and ask them what comes to mind when they hear the word “Alaska”. Indeed I received some confusing looks and laughs, but everyone I asked had something to say. Some people alluded to popular TV shows set in Alaska, such as Gold Rush, Bush People, and Alaska: the Last Frontier, while others spoke about the cold weather, dog mushing, Eskimos, fishing and hunting, and the Trans-Alaska pipeline. A few of the answers I received referenced the beauty and wilderness of the large snow capped mountains, glaciers, and the Northern Lights (Aurora Borealis): all emblematic of the largest state in America. But to me, Alaska is more than just a pretty landscape and a place to fish. It is a region riddled with geologic mysteries and rich in along strike variations.

The Aleutian-Alaska subducton zone marks a North American-Pacific plate boundary where subduction varies greatly along strike (Figure 1). At the western end of the subduction zone, the Aleutian volcanic islands are the result of oceanic-oceanic subduction while in the eastern part of the subduction zone there is oceanic-continental collision where the Pacific plate descends beneath the North American plate. The age of the subducting sea floor increases laterally from around 30 Ma in the eastern subduction corner to 80 Ma at the end of the Aleutian volcanic arc (Müller et al., 2008). Slab dip changes drastically from 50° to 60° in the west and central Aleutians to flat slab subduction under south-central Alaska (Ratchkovski and Hansen, 2002a; Lallemand et al., 2005; Jadamec and Billen, 2010). This leads to a variation in the slab pull force, which is a main driving force of subduction caused by the weight of dense slabs sinking into the mantle (Morra et al., 2006).

Figure 1: Tectonic map of Alaska modified from Haynie and Jadamec (2017). Topography/bathymetry is from Smith and Sandwell (1997) and Seafloor (SF) ages are from Müller et al. (2008). Blue lines are the slab contours of Jadamec and Billen (2010) in 40 km intervals; the thick black line is the plate boundary from Bird (2003); and the thinner black lines are faults from Plafker et al. (1994a). The location of Denali is marked by the orange hexagon. Holocene volcanoes are given by the pink triangles (Alaska Volcano Observatory). The purple polygon is the outline of the Yakutat oceanic plateau (Haynie and Jadamec, 2017). WB – Wrangell block fore-arc sliver; JdFR – Juan de Fuca Ridge.

There is also a distinct change in margin curvature from convex in the west to concave in the east. At the end of the eastern bend, the Alaska part of the subduction zone is truncated by a large transform boundary, the Fairweather-Queen Charolette fault, which gives rise to a corner-shaped subduction-transform plate boundary (Jadamec et al., 2013; Haynie and Jadamec, 2017). Here, convergence is oblique with an average velocity of 5.2 cm/year northwest (DeMets and Dixon, 1999). Seismic studies (Page et al., 1989; Ferris et al., 2003; Eberhart-Phillips et al., 2006; Fuis et al., 2008) show that thicker than normal oceanic crust lies off-shore in the subduction corner. This thick oceanic material has been identified as the Yakutat oceanic plateau (Plafker et al., 1994a; Brocher et al., 1994; Bruns, 1983; Worthington et al., 2008; Christeson et al., 2010; Worthington et al., 2012). Even though oceanic plateaus tend to resist subduction (Cloos, 1993; Kerr , 2003), the Yakutat plateau is currently subducting beneath the Central Alaska Range to depths of 150 km (Ferris et al., 2003; Eberhart-Phillips et al., 2006; Wang and Tape, 2014). It is also colliding into south-east Alaska (Mazzotti and Hyndman, 2002; Elliott et al., 2013; Marechal et al., 2015) where the largest coastal mountain range on Earth, the Saint Elias Mountains, are located (Enkelmann et al., 2015).

With regards to surface deformation, in addition to Denali (the tallest mountain in North America), other notable along strike variations reside within the broad deformation zone of south-central Alaska. For example, a normal volcanic arc occurs over the Aleutian part of the subduction zone and above the Alaska Peninsula. However, above the flat slab there is a gap in volcanism followed by the presence of the enigmatic Wrangell volcanoes (Rondenay et al., 2010; Jadamec and Billen, 2012; Martin-Short et al., 2016; Chuang et al., 2017). These volcanoes are marked by a range of morphologies as well as adakitic geochemical signatures (Richter et al., 1990; Preece and Hart , 2004), which have a petrogenesis that may be attributed to slab melting (Defant and Drummond , 1990; Peacock et al., 1994; Castillo, 2006, 2012; Ribeiro et al., 2016). Analogue (Schellart , 2004; Strak and Schellart , 2014) and 3D numerical models (Stegman et al., 2006; Piromallo et al., 2006; Jadamec and Billen, 2010, 2012) predict that toroidal flow can produce upwellings around the edge of a slab that may have implications for melting of the slab and the formation of adakites. However, the formation of the Wrangell volcanoes is still debated.

Also located above the subducting plateau and flat slab is the Wrangell block fore-arc sliver, which exhibits northwest motion and counterclockwise rotation (Cross and Freymueller, 2008; Freymueller et al., 2008; Bemis et al., 2015; Waldien et al., 2015; Jadamec et al., 2013; Haynie and Jadamec, 2017). This sliver is bounded in the north by the arcuate shaped Denali fault, which illustrates a lateral change in slip rates that increases towards the center of the fault (Haynie and Jadamec, 2017; Haeussler et al., 2017). 3D high-resolution geodynamic models show that the flat slab drives motion of the Wrangell block fore-arc sliver (Jadamec et al., 2013; Haynie and Jadamec, 2017) and contributes to fault parallel motion along the eastern Denali fault and convergence along the apex of the fault (Haynie and Jadamec, 2017) (Figure 2). However, when model predictions of the Wrangell block motion and the difference in Denali fault parallel motion are compared with observations, model predictions are lower, suggesting that the flat slab alone is not sufficient enough to explain the broad deformation zone of Alaska (Haynie and Jadamec, 2017). Thus, it is thought that the neotectonics of south-central Alaska are predominantly driven by the subduction-collision of the buoyant Yakutat oceanic plateau (Bird , 1988; Plafker et al., 1994b; Fitzgerald et al., 1995; Ratchkovski and Hansen, 2002b; Bemis and Wallace, 2007; Chapman et al., 2008; Haeussler , 2008; Jadamec et al., 2013; Lease et al., 2016; Haynie and Jadamec, 2017). 4D numerical modelling of this process is currently underway.

Figure 2: Top: map of south-central Alaska (zoomed in from Figure 1) with model predicted velocities (blue arrows) from Haynie and Jadamec (2017) plotted on top. Bottom: percent of slab contribution from Haynie and Jadamec (2017) models to observed Denali fault slip rates (modified from Haynie and Jadamec (2017)). Results from Haynie and Jadamec (2017) show that the slab drives northwest and counter-clockwise motion of the Wrangell block fore-arc sliver and contributes to an average of 20-28% of motion along the Denali fault. The flat slab exerts the largest contribution to motion along the eastern segment of the fault, where surface motion parallels the fault, and also along the central segment of the fault, where the slab is driving the Wrangell block into the North American backstop and subducting obliquely to the fault.

 

References
Bemis, S. P., and W. K. Wallace (2007), Neotectonic framework of the north-central Alaska Range foothills, Geological Society of America Special Papers, 431, 549–572.
Bemis, S. P., R. J. Weldon, and G. A. Carver (2015), Slip partitioning along a continuously curved fault: Quaternary geologic controls on Denali fault system slip partitioning, growth of the Alaska Range, and the tectonics of south-central Alaska, Lithosphere, 7 (3), 235–246.
Bird, P. (1988), Formation of the Rocky Mountains, Western United States: A continuum computer model, Science, 239 (4847), 1501–1507.
Bird, P. (2003), An updated digital model of plate boundaries, Geochemistry, Geophysics, Geosystems, 4 (3).
Brocher, T. M., G. S. Fuis, M. A. Fisher, G. Plafker, Moses, M. J., J. J. Taber, and N. I. Christensen (1994), Mapping the megathrust beneath the northern gulf of alaska using wideangle seismic data, Journal of Geophysical Research: Solid Earth, 99 (B6), 11,663– 11,985.
Bruns, T. R. (1983), Model for the origin of the Yakutat block, an accreting terrane in the northern Gulf of Alaska, Geology, 11 (12), 718–721.
Castillo, P. R. (2006), An overview of adakite petrogenesis, Chinese Science Bulletin, 51 (3), 257–268.
Castillo, P. R. (2012), Adakite petrogenesis, Lithos, 134, 304–316.
Chapman, J. B., T. L. Pavlis, S. Gulick, A. Berger, L. Lowe, J. Spotila, R. Bruhn, M. Vorkink, P. Koons, A. Barker, et al. (2008), Neotectonics of the Yakutat collision: Changes in defor- mation driven by mass redistribution, Active Tectonics and Seismic Potential of Alaska, Geophys. Monogr. Ser, 179, 65–81.
Christeson, G. L., H. J. A. Gulick, P. S. ad Van Avendonk, L. L. Worthington, R. S. Reece, and T. L. Pavlis (2010), The Yakutat terrane: Dramatic change in crustal thickness across the Transition fault, Alaska, Geology, 38 (10), 895–898.
Chuang, L., M. Bostock, A. Wech, and A. Plourde (2017), Plateau subduction, intraslab seismicity, and the Denali (Alaska) volcanic gap, Geology, pp. G38,867–1.
Cloos, M. (1993), Lithospheric bouyancy and collisional orogenesis: Subduction of oceanic plateaus, continental margins, island arcs, spreading ridges, and seamounts, Geological Society of America Bulletin, 105 (715-737).
Cross, R. S., and J. T. Freymueller (2008), Plate coupling variation and block translation in the Andreanof segment of the Aleutian arc determined by subduction zone modeling using GPS data, Geophysical Research Letters, 34 (6).
Defant, M. J., and M. S. Drummond (1990), Derivation of some modern arc magmas by melting of young subducted lithosphere, Nature, 347 (6294), 662–665.
DeMets, C., and T. H. Dixon (1999), New kinematic models for Pacific-North America motion from 3 Ma to present, I: Evidence for steady motion and biases in the NUVEL-1A Model, Geophysical Research Letters, 26 (13), 1921–1924.
Eberhart-Phillips, D., D. H. Christensen, T. M. Brocher, R. Hansen, N. A. Ruppert, P. J. Haeussler, and G. A. Abers (2006), Imaging the transition from Aleutian subduction to Yakutat collision in central Alaska, with local earthquakes and active source data, Journal of Geophysical Research: Solid Earth, 111 (B11).
Elliott, J., J. T. Freymueller, and C. F. Larsen (2013), Active tectonics of the St. Elias orogen, Alaska, observed with GPS measurements, Journal of Geophysical Research: Solid Earth, 118 (10), 5625–5642.
Enkelmann, E., P. O. Koons, T. L. Pavlis, B. Hallet, A. Barker, J. Elliott, J. I. Garver, S. P. Gulick, R. M. Headley, G. L. Pavlis, et al. (2015), Cooperation among tectonic and surface processes in the St. Elias Range, Earth’s highest coastal mountains, Geophysical Research Letters, 42 (14), 5838–5846.
Ferris, A., G. A. Abers, D. H. Christensen, and E. Veenstra (2003), High resolution image of the subducted Pacific (?) plate beneath central Alaska, 50–150 km depth, Earth and Planetary Science Letters, 214 (3), 575–588.
Fitzgerald, P. G., R. B. Sorkhabi, T. F. Redfield, and E. Stump (1995), Uplift and denuda- tion of the central Alaska Range: A case study in the use of apatite fission track ther- mochronology to determine absolute uplift parameters, Journal of Geophysical Research: Solid Earth, 100 (B10), 20,175–20,191.
Freymueller, J. T., H. Woodard, S. C. Cohen, R. Cross, J. Elliott, C. F. Larsen, S. Hreins- dottir, and C. Zweck (2008), Active deformation processes in Alaska, based on 15 years of GPS measurements, Active tectonics and seismic potential of Alaska, 179, 1–42.
Fuis, G. S., T. E. Moore, G. Plafker, T. M. Brocher, M. A. Fisher, W. D. Mooney, W. Nodle- berg, R. Page, B. Beaudoin, N. I. Christensen, A. Levander, W. Lutter, R. Saltus, and
N. A. Ruppert (2008), Trans-Alaska Crustal Transect and continental evolution involving subduction underplating and synchronous foreland thrusting, Geology, 36 (3), 267–270.
Haeussler, P. J. (2008), An Overview of the Neotectonics of Interior Alaska: Far-Field Defor- mation From the Yakutat Microplate Collision, American Geophysical Union, pp. 86–108.
Haeussler, P. J., A. Matmon, D. P. Schwartz, and G. G. Seitz (2017), Neotectonics of interior alaska and the late quaternary slip rate along the denali fault system, Geosphere.
Haynie, K., and M. A. Jadamec (2017), Tectonic drivers of the Wrangell block: Insights on forearc sliver processes from 3D geodynamic models of Alaska, Tectonics, 36 (7), 1180– 1206.
Jadamec, M., and M. Billen (2010), Reconciling surface plate motions with rapid three- dimensional mantle flow around a slab edge, Nature, 465 (7296), 338–341.
Jadamec, M. A., and M. I. Billen (2012), The role of rheology and slab shape on rapid mantle flow: Three-dimensional numerical models of the Alaska slab edge, Journal of Geophysical Research: Solid Earth, 117 (B2).
Jadamec, M. A., M. I. Billen, and S. M. Roeske (2013), Three-dimensional numerical models of flat slab subduction and the Denali fault driving deformation in south-central Alaska, Earth and Planetary Science Letters, 376, 29–42.
Kerr, A. C. (2003), Oceanic plateaus, The Crust, Treaste on Geochemistry, 3, 537–565. Lallemand, S., A. Heuret, and D. Boutelier (2005), On the relationships between slab dip, back-arc stress, upper plate absolute motion, and crustal nature in subduction zones, Geochemistry Geophysics Geosystems, 6 (9).
Lease, R. O., P. J. Haeussler, and P. O'Sullivan (2016), Changing exhumation patterns during Cenozoic growth and glaciation of the Alaska Range: Insight from detrital geo-and thermo-chronology, Tectonics.
Marechal, A., S. Mazzotti, J. L. Elliot, J. T. Freymueller, and M. Schmidt (2015), Indentor- corner tectonics in the Yakutat-St. Elias collision constrained by GPS, Journal of Geo- physical Research: Solid Earth.
Martin-Short, R., R. M. Allen, and I. D. Bastow (2016), Subduction geometry beneath south-central Alaska and its relationship to volcanism, Geophysical Research Letters, doi: 10.1002/2016GL070580, 2016GL070580.
Mazzotti, S., and R. Hyndman (2002), Yakutat collision and strain transfer across the north- ern Canadian Cordillera, Geology, 30 (6), 495–498.
Morra, G., K. Regenauer-Lieb, and D. Giardini (2006), Curvature of oceanic arcs, Geology, 34 (10), 877–880.
Müller, R. D., M. Sdrolias, C. Gaina, and W. R. Roest (2008), Age, spreading rates, and spreading asymmetry of the world’s ocean crust, Geochemistry, Geophysics, Geosystems, 9 (4).
Page, R., C. Stephens, and J. Lahr (1989), Seismicity of the Wrangell and Aleutian Wadati- Benioff zones and the north American plate along the Trans-Alaska Crustal Transect, Chugach Mountains and Copper River Basin, Southern Alaska, Journal of Geophysical Research, 94 (B11), 16,059–16,082.
Peacock, S. M., T. Rushmer, and A. B. Thompson (1994), Partial melting of subducting oceanic crust, Earth and planetary science letters, 121 (1), 227–244.
Piromallo, C., T. Becker, F. Funiciello, and C. Faccenna (2006), Three-dimensional instan- taneous mantle flow induced by subduction, Geophysical Research Letters, 33 (8).
Plafker, G., J. C. Moore, and G. R. Winkler (1994a), Geology of the southern Alaska margin, The Geology of North America, The Geology of Alaska, G-1.
Plafker, G., L. M. Gilpin, and J. C. Lahr (1994b), Neotectonic map of Alaska, The Geology of North America, 1.
Preece, S. J., and W. K. Hart (2004), Geochemical variations in the <5 Ma Wrangell Volcanic Field, Alaska: implications for the magmatic and tectonic development of a complex continental arc system, Tectonophysics, 392 (1), 165–191.
Ratchkovski, N., and R. Hansen (2002a), New evidence for segmentation of the Alaska subduction zone, Bulletin Of The Seismological Society Of America, 92 (5), 1754–1765.
Ratchkovski, N. A., and R. A. Hansen (2002b), New Constraints on Tectonics of Interior Alaska: Earthquake Locations, Source Mechanisms, and Stress Regime, Bulletin Of The Seismological Society Of America, 92 (3), 998–1014.
Ribeiro, J. M., R. C. Maury, and M. Gr´egoire (2016), Are Adakites Slab Melts or High-pressure Fractionated Mantle Melts?, Journal of Petrology, 57 (5), 839, doi: 10.1093/petrology/egw023.
Richter, D., J. G. Smith, M. Lanphere, G. Dalrymple, B. Reed, and N. Shew (1990), Age and progression of volcanism, wrangell volcanic field, alaska, Bulletin of Volcanology, 53 (1), 29–44.
Rondenay, S., L. G. Mont´esi, and G. A. Abers (2010), New geophysical insight into the origin of the Denali volcanic gap, Geophysical Journal International, 182 (2), 613–630.
Schellart, W. (2004), Kinematics of subduction and subduction-induced flow in the upper mantle, Journal of Geophysical Research: Solid Earth, 109 (B7).
Smith, W. H., and D. T. Sandwell (1997), Global sea floor topography from satellite altimetry and ship depth soundings, Science, 277 (5334), 1956–1962.
Stegman, D., J. Freeman, W. Schellart, L. Moresi, and D. May (2006), Influence of trench width on subduction hinge retreat rates in 3-D models of slab rollback, Geochemistry, Geophysics, Geosystems, 7 (3).
Strak, V., and W. P. Schellart (2014), Evolution of 3-D subduction-induced mantle flow around lateral slab edges in analogue models of free subduction analysed by stereoscopic particle image velocimetry technique, Earth and Planetary Science Letters, 403, 368–379.
Waldien, T., S. M. Roeske, J. A. Benowitz, W. K. Allen, and K. D. Ridgway (2015), Neogene exhumation in the eastern Alaska Range and its relationship to splay fault activity in the Denali fault system, AGU Fall Meeting Abstracts.
Wang, Y., and C. Tape (2014), Seismic velocity structure and ansotropy of the Alaska subduction zone based on surface wave tomography, Journal of Geophysical Research: Solid Earth, 119, 8845–8865.
Worthington, L. L., S. P. Gulick, and T. L. Pavlis (2008), Identifying active structures in the Kayak Island and Pamplona zones: Implications for offshore tectonics of the Yakutat Microplate, Gulf of Alaska, Active tectonics and seismic potential of Alaska: American Geophysical Union Geophysical Monograph, 179, 257–268.
Worthington, L. L., H. Van Avendonk, S. Gulick, G. L. Christeson, and T. L. Pavlis (2012), Crustal structure of the Yakutat terrane and the evolution of subduction and collision in southern Alaska, Journal of Geophysical Research: Solid Earth, 117 (B1).

The quest of a numerical modelling hero

The quest of a numerical modelling hero

Numerical modelling is not always a walk in the park. In fact, it resembles a heroic quest more often than not. In this month’s Wit & Wisdom post, Cedric Thieulot, assistant professor at the Mantle dynamics & theoretical geophysics group at Utrecht University in The Netherlands, tells the story of his heroic quest to save the princess from the dragon clear a code from bugs and shows that failed models can be the best models.

Heroes are also artists. I am a hero, therefore I am an artist. Sometimes against my will. In other words, sometimes the code works; most of the time it doesn’t.

A true hero embarks on his noble steed upon a long and perilous quest as the fire-breathing dragon who keeps the princess hostage awaits him in its lair.
“I am a hero too!” says my programmer ego although I spend most of my time sitting on ikea chairs looking for bugs. Yes, bugs. Bugs I have put there myself. Yup.

On my quest, I sometimes get lost in impossible mazes!

I have to cross mysterious mountain ranges

… but I am rewarded by a beautiful sunset on another planet.

I can’t believe what I C(++)

My quest can be dangerous.
Sometimes the enemy is tiny but viruses can be deadly too!

I sometimes feel like I am drowning in a petri dish.


Sometimes I encounter weird beings on my quest…



I even have to fight improbable gnu-snakes!

And the spirits of old viking warriors creep up in my models…

I need some candy to keep my spirits up.

And then… I find the bug and defeat the mighty bug! Fireworks!


Time to switch on the disco balls!

It’s party time!

One month to AGU!

One month to AGU!
As the leaves are falling; the sun is going down before you leave the office; and the stores are stacking up on Christmas decorations, it’s time to face the facts: it’s almost AGU! It shouldn’t come as a surprise, but just in case. Don’t worry, there is still time to reread your abstract to see what you’re supposed to be presenting, figure out how to do that in the several weeks that are left and wrap it all up in a convincing poster or talk.
But first, check out these tips on presenting your work: our EGU GD blogs on creating prize-winning posters and selecting proper color schemes, EGU resources on making posters and these Science magazine posts on creating and giving great oral presentations. And while you’re at it, research New Orleans  highlights, such as the French quarter and the excellent cuisine. There is still time to register for some of the AGU field trips too! And wait, did you book your hotel and flights? Then, get to work!

The jelly sandwich lithosphere: elastic bread, the jelly, and gummy bears

The jelly sandwich lithosphere: elastic bread, the jelly, and gummy bears

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. This month Vojtěch Patočka from the Charles University in Prague, Czech Republic, discusses the rheology of the lithosphere and its food analogies. Do you want to talk about your research? Contact us!

It is becoming increasingly obvious that geodynamics and cooking are closely related, especially to the participants of a recent workshop in the Netherlands. Food analogies are helping students to get a physical grasp of continuum mechanics and to forget their lunches at university canteens. Here we take a basic look at a field where talking about fine cuisine has long been established: the rheology of the lithosphere. But first we step back a little.

Elastic solids deform when a force is applied and return to their original shape when the force is removed. Viscous fluids eventually take the shape of a container that is applied to them: they spontaneously flow to a state of zero shear stress. One can hardly imagine more different materials than these two, and yet the Earth’s mantle is sometimes modelled as an elastic shell and sometimes considered to be a viscous fluid.

You may be thinking:

Sure, it is a matter of what time scale is relevant for the process at hand

– just as J.C. Maxwell already thought: “Hence, a block of pitch may be so hard that you cannot make a dent in it by striking it with your knuckles; and yet it will in the course of time flatten itself by its weight, and glide downhill like a stream of water.” To visualise Maxwell’s dreams, the University of Queensland has been continuously running a pitch drop experiment for the past 90 years.

It is for the reason above that seismologists vibrate a Hookean Earth in their computers and geodynamicists play with viscous fluids. Are both of them right? Surprisingly, only the seismologists are. There is direct evidence that the outer parts of planetary mantles have an important elastic component even on geological time scales, which implies that treating the entire mantle as viscous is wrong. A textbook example can be found near the deepest part of the world’s oceans. Fig. 1, adopted from the bible by Turcotte & Schubert, shows how one can fit the bathymetric profile across the Mariana trench to the shape of a bent elastic plate. Note that the slab is subducting at the rate of a few centimeters per year, meaning that each segment of the slab is loaded for tens of millions of years before it disappears into the mantle and it still retains the elastic strain.

Figure 1: Comparison of a bathymetric profile across the Mariana trench (solid line) with the deflection of a thin elastic plate subject to end loading (dashed line). Distance xbx0 is the half-width of the forebulge from which the thickness of the plate can be inferred. Adopted from section 3 of Turcotte & Schubert, 2002.

Flexure studies and effective elastic thickness

Other similar examples, referred to as flexure studies, are summarised nicely by Watts et al., 2013. They include deflections under seamounts that litter oceanic floors and also some much longer lasting structures, such as continental foreland basins with the Ganges basin representing a particularly popular case. The free parameter that plays first fiddle in flexure studies is the thickness of elastic plate that matches observation. What does the resulting value, known as the effective elastic thickness, actually tell us?

I will use a dirty trick of bad journalism and quote an innocent geology blog slightly out of context:

The Indian crust is cold and rigid. Clever folk can do the maths on the shape of the crust as it bends down. This confirms that the pattern matches the model for rigid, elastic deformation. It also allows us to calculate the plate’s flexural rigidity, which is a measure of its strength. This means quantifying the rheology of real bits of the earth, which is a very useful trick

The math referred to involves purely elastic deformation and the flexural rigidity in its definition depends only on Young’s modulus, thickness, and Poisson ratio of the plate. Are the clever folk trying to fool us into believing that the lithosphere is an elastic plate? From lab measurements and geology we know for sure that it is not. Brittle failures are an abundant feature in both the crust and upper mantle, and various solid state creep mechanisms must be active in the deeper parts of the lithosphere.

The best fit for the Indo-Australian plate subducted below the Ganges basin is obtained with an elastic plate of circa 90 km thickness and for the Pacific plate at the Mariana trench it is circa 30 km. In both cases the plates are actually much thicker. What the computed values of 90 and 30 km tell us, is how much of elastic energy is present within the plate over the process of subduction, despite the brittle failures and despite the ductile creep activated in response to shear stresses within the plate.

To move away from sinking slabs, think about the story of a seamount that popped out on an ocean floor. Imagine a fresh, unstressed segment of oceanic plate that gets suddenly loaded by the uninvited underwater volcano. Small intra-plate fractures may immediately form, depending on the size of the load, and ductile creep will begin to continuously deform the plate’s deeper parts. The elastic energy present in the material upon loading gets partially released, either immediately through cracking or gradually via ductile creep. Measuring effective (or equivalent) elastic thickness merely tells us the amount of elastic energy left at the time of measurement.

This is all well known to the authors of flexure studies. In fact, they often re-draw the Christmas trees (see Fig. 2) and provide constraints on rheological zonation of the Earth. Pioneers in the field are E.B. Burov and A.B. Watts, whose papers are often accidentaly googled by chefs searching for latest trends in the dessert industry due to the extensive use of the words jelly sandwich and crème brûlée ([4] and [5], for breakfast see also [6]). The main point of the discussion is to determine the brittle/ductile transition and the active creep mechanism in a realistic, compositionally stratified lithosphere. This is usually complicated by the fact that lithologies measured in lab experiments strongly depend on composition, water content and temperature – and these are not well constrained in the real Earth.

Figure 2: The total force per unit width necessary to break or viscously deform a lithospheric section at a given strain rate. Plots like these are known as the Christmas tree plots, here adopted from Basin Analysis by P.A. Allen and J.R. Allen (without the food).

A geodynamical paradox

It is a paradox that in geodynamical modeling we often use the constraints from flexure studies and at the same time forget about elasticity, without which there would be no such studies at all. Recall that the primary result of shape fitting, for instance of the one depicted in Fig. 1, is that some elastic support is present. As I warned above, one can only hardly distinguish between a purely elastic plate of a given thickness and some other, thicker elasto-brittle or visco-elastic plate when looking at its surface flexure. However, there must be elasticity involved in some form: purely viscous or visco-plastic plates would not form the observed forebulge. Forebulges are related to the way elastic rods and plates transfer bending moment throughout the medium.

The tendency to disregard elasticity may be related to the way we use the word ‘rigid’ in the context of plate tectonics. In physics, rigid means ‘not deforming’. For plate tectonics to work the plates do not have to be rigid. They may not flow apart on geological time scales (they must remain plates), but some relatively small reversible deformation is well compliant with the concept. So the main point is: Be the lithosphere a sandwich or a crème brûlée, it is also flexible, even on geological time scales.

Batman and gummy bears

If you are in numerical modelling then there is good news for you. In the past two decades, several Robins, including myself, have enhanced the Batman codes to account for elasticity. Maybe all you have to do is to switch on the right button. The implementation of visco-elasticity is usually based on a method developed by L. Moresi, who also, according to a previous Geodynamics 101 blog post, coined the hero terminology I just borrowed. Visco-elasticity works in quite a simple way, just like gummy bears. I am currently running an experiment with them. They quickly bend and squeeze when tortured, their resistance governed by their shear modulus, and recover when let go. At the same time they can flow, the resistance being controlled by their viscosity. Let’s put a book on top of one and see if we can find its nose after a week…

The elasticity button

Don’t be afraid to push the elasticity button, if your code has it. Usually it won’t do anything dramatic to your simulations, but exceptions exist [7]. In thermal convection models without plate tectonics there is not much feedback between the lid and the underlying mantle, and so only the build-up of dynamic topography is affected [8]. In subduction modeling your slabs may obtain different dipping angles. In continental extensions the total amount of extension will become more important than the divergence rate [9]. And in the simulation of continental shortening mentioned above [7], the elastic energy accumulated in the entire model gets partially released upon the onset of a shear zone. In such cases, i.e. when large scale elastic strains suddenly influence a much smaller region, one can expect some earthquakes to shake the conventional view of elasticity in geodynamical modeling. And if you still do not care about elasticity but yet you made it all the way here, then you deserve a bonus: the convergence of Stokes solvers is way better for visco-elastic rheologies than for the viscous ones – if you are numerically troubled by large viscosity contrasts of your model, elasticity is the way to go for you.

References
(1) D.L. Turcotte and G. Schubert (2002), Geodynamics
(2) A.B. Watts, S.J. Zhong, and J. Hunter (2013), The Behavior of the Lithosphere on Seismic to Geologic Timescales, doi: 10.1146/annurev-earth-042711-105457
(3) P.A. Allen and J.R. Allen (2005), Basin analysis : principles and applications
(4) E.B. Burov and A.B. Watts (2006), The long-term strength of continental lithosphere: 'jelly sandwich' or 'creme brulée'?, doi: 10.1130/1052-5173(2006)016
(5) E.B. Burov (2009), Time to burn out creme brulee?, doi: 10.1016/j.tecto.2009.06.013
(6) E.H. Hartz, Y.Y. Podladchikov (2008), Toasting the jelly sandwich: The effect of shear heating on lithospheric geotherms and strength, doi: 10.1130/G24424A.1
(7) Y. Jaquet, T. Duretz, and S.M. Schmalholz (2016), Dramatic effect of elasticity on thermal softening and strain localization during lithospheric shortening, doi: 10.1093/gji/ggv464
(8) V. Patocka, O. Cadek, P.J. Tackley, and H. Cizkova (2017), Stress memory effect in viscoelastic stagnant lid convection, doi: 10.1093/gji/ggx102
(9) J.A. Olive, M.D. Behn, E. Mittelstaedt, G. Ito, and B.Z. Klein, The role of elasticity in simulating long-term tectonic extension, doi: 10.1093/gji/ggw044