Why are subduction zones curved?

The Pacific Ring of Fire, North America to the left, the Aleutian arc in the center, the Kurile arc, Northeast Japan arc to the right. Image from google.

One of the most prominent features when looking on the large-scale topography of Earth are subduction zones. Since I have often wondered why they usually are arc-shaped I decided to delve a bit into the topic and share my findings in this post. It is mainly from a perspective of a geometrical model proposed in  “Why subduction zones are curved” from Mahadevan, Bendick, and Haiyi Liang, Tectonics (2010). The post is not meant to be a full synopsis of driving mechanisms for plate tectonics in general, or subduction in specific. For general information I for example recommend to listen to this talk on plate tectonics and subduction by Geoscience professor Robert Stern from the University of Texas at Dallas. As always, excuse this interested laywoman for leaving out important aspects which you are invited to point out below.

Introduction

Prinsesstårta, a traditional Swedish cake filled with a.o. whipped cream, custard and jam, and covered with green marzipan (Wikimedia Commons).

Subduction zones are convergent margins that can be classified as Andean-type arcs and intra-oceanic arcs. They are either arcs – concave in respect to the oceanic plate – or straight. Along the Pacific Ring of Fire the subducting slabs of adjacent arcs are usually fold over like a Prinsesstårta rather than being loose flaps.

Seismicity at the Andean-type Southern Chile trench. The relatively young and thin subducting slab is melted in the upper 300 km below which no more earthquakes occurr.  http://www.iris.edu/ieb

Andean-type arcs are characterized by forced subduction of relatively buoyant, young, still viscous lithosphere beneath an overriding plate. They often have straight sections and relatively shallow dip of the subducting slab (37°± 16°). Examples are the Chile trench or the Cascadia subduction zone.

Seismicity below 33 km at the intra-oceanic Mariana trench. Earthquakes occurr deeper than 500 km and the slab has a very steep dip.  Made with the 3D viewer at http://www.iris.edu/ieb

Intra-oceanic arcs develope by free subduction because of the gravitational pull (slab pull) of relatively dense, elastic lithosphere. They have a characteristic length (500 to 5000 km) and are usually arc-shaped. The subducting slab usually has a steep dip (49° ± 18°). Examples are the Mariana trench and the Aleutian arc.

Arc-trench systems (“island arcs”) of new or magmatically transformed lithosphere may arise on top of the hanging wall of the subduction zone which may emerge as islands or grow into mountain ranges. They are superficial phenomena, but visible and directly measurable and therefore much better studied than the subducting slab itself.

 

Ocean basin recycling

http://www.ngdc.noaa.gov/mgg/ocean_age/data/2008/ngdc-generated_images/whole_world/2008_age_of_oceans_plates.jpg

Subduction is an inevitable consequence of oceanic plate growth because the Earth´s total surface remains constant. Relatively thin, elastic to viscous oceanic lithospheric plates grow out of the spreading ridges and slowly move as if on a conveyer belt of thick, dense, incompressible, viscous mantle for thousands of kilometers. When they reach their final grave, the subduction zones, they bend into the upper mantle within a couple of hundred kilometers. Along their journey they become stiffer as they cool down to 500°C or less. They grow in thickness and become heavier, due to sedimentation, intraplate volcanism and mainly underplating by serpentinization, the hydration and metamorphic transformation of ultramafic rock from the Earth’s upper mantle. The solid, but elastic mechanical lithosphere starts at 6 km thickness and ends at up to 42 km (Kurile trench) to 55 km (Mariana trench) thickness. Remember that, unlike ice, solid rock is more dense than liquid rock.

Global growth and destruction of oceanic lithosphere takes place at a rate of about 3 km² per year over the extend of 55000 kilometers of spreading ridges and 55000 kilometers of convergent zone margins. That equals 18 km³ of emerging hot lithosphere, equivalent to more than four 1991 Pinatubo eruptions. A multiple thereof disappears from the surface of Earth every year, equivalent to the volume of several 1815 Tambora eruptions. Over 30000 kilometers of ridge-ridge transform faults accommodate tensions.

Why arcs?

Illustration of the spherical Earth in a medieval manuscript. 14th century copy of a 12th century original by Gossuin de Metz – L’image du monde (Wikimedia Commons).

Because the surface of the Earth is not flat but curved equal to the inverse of Earth´s radius, the subducting lithosphere is not a flat plate like visualized in many illustrations. It is also not a complete spherical shell, but rather a thin, ragged spherical cap, as animated youtube video. The thick underlying mantle is supporting the seafloor until it becomes too heavy and plunges or is pushed down by an overriding plate. The convex curvature of the oceanic slab then somehow becomes inverted to a concave shape like a dent in a table tennis ball – a table tennis ball with hot interior which melts everything that enters.

Striking similarity of subduction arc morphology with this simualation of a growing spherical shell that buckles inside an (invisible) hollow sphere. Image by Norbert Stoop, Dr. Falk K. Wittel, ETH Zürich http://www.ifb.ethz.ch/comphys/research

Whereas spreading ridges are linear, subduction zones are in most cases curved. While the Prinsesstårta comparison gives us some intuitive understanding to the phenomenon complex simulations are neccessary to understand the theoretical background of how thin spherical shells fold when they grow, like shown in the left image.

Keep in mind that an egg shell is able to sustain a lot more pressure than if the same material was flat. Similarly, to break the symmetry of the spherical lithosphere into a buckled shape (obviously, because of gravity, down and not up) a relatively high “activation” barrier has to be overcome, because first the lithosphere has to be stretched and bend. High stiffness and low viscosity of old plates higher the stakes. This resistance has to be overcome by high enough applied load or negative bouyancy. The resulting shape of the margin will be that which consumed the least energy. Apparently, the most favourable solution is a slim ring (forebulge) of switching curvature, minimizing the zone of energetically costly bending and stretching.

Negative bouyancy is sufficient to cause free subduction in a certain range between minimum (L_min, requiring some 10 to 50 million years of growth, e.g. South Sandwich trench) and maximum cap length (L_max, up to 180 million years, e.g. Mariana trench) from the spreading ridge, depending on the extrusion velocity. Within this range the lithosphere is subcritically stable, so it may bend upon small changes in applied forces, but need not. If the cap length is over L_max it must subduct. Bending preferably, but not exclusively, starts at the plate edges.

Louisville Seamount range aligned with the syntaxis between the Tonga and the Kermadec trench. Image by google.

Local variations in density and rigidity may influence the exact location of the arcs and the links between them, the syntaxes. Seamount chains may increase stiffness and therefore are sometimes aligned with syntaxes, like the Emperor Seamount chain ending between the Kuril-Kamchatka trench and the Aleutian trench and the Louisville Seamount chain in the image on the right.

One obstacle for understanding is that we are used to two-dimensional illustrations of subduction zones, idealized cross-sections with exaggerated vertical dimension. For me they create the association of a sheet of paper which gently bends when pushed over the edge of a table. To perform a more realistic simple 3D experiment, try to hold the paper like a tunnel and apply gentle pressure onto the curved edge. You will see the developement of an indentation with a narrow bending curve. Alas, it requires special technical and programming skills for more sophisticated three-dimensional simulations. In this simulation the authors show the time developement of buckling of an incomplete sphere.

 

What determines the arc radius?

Wikimedia Commons

Looking at the Ring of Fire above and in the first image, the width of the subduction arcs is peculiarly uniform, varying by less than one order of magnitude. So what determines the radius of the trenches? First of all, there is no correlation between the radius of the arc and the dip of the downgoing slab. The dip angle mainly is a consequence of negative bouyancy, the more dense the slab, the steeper the plunge. The older the slab and the faster the convergence rate, the deeper is the observed seismic zone of the still rigid and fragile slab. So if bouyancy and speed do not influence the radius of the arc, what else is the reason?

There actually is an energy trade-off between the deformation of the curved lithosphere, which favors broad and wide arcs and the deformation of the upper mantle to acommodate for the subducting slab and the vacancy under the forebulge, which favors slim and small arcs. The observed arc widths are thus the energetically optimal balance. The most profound parameters that influence this balance are the curvature of the lithosphere due to the curvature of Earth, viscosity and elasticity of lithosphere and mantle, and lithosphere thickness. Especially the curvature of Earth sets a limit on the width of arcs and leads to the segmentation seen along long oceanic plate edges like the Pacific.

Why not arcs?

The Juan Fernandez ridge in the center intersecting the Chile trench. Image by google.

In the case of forced subduction young, positively bouyant plates are forced under a continental shelf. In this case the mechanical model predicts a straight subduction zone, because the load comes from the opposite plate as a horizontal force and the lithosphere still has relatively low stiffness. The forebulges are also segmented into trenches of characteristic length according to the balance between bending energy of the curved lithosphere and mantle deformation energy.

 

Conclusions

The presented mechanical model of subduction is sufficient to explain the large-scale structure and location of subduction arcs. If this model is correct and if the Atlantic oceanic basin continues to grow, sometimes in the future subduction will set in. It has already started at two locations, namely at the South-Sandwich trench and the Lesser Antilles subduction zone. It´s worth noting that both subduction zones are located between two continental plates, North and South America, and South America and Antarctica, respectively. Subduction most likely was initiated at the free oceanic plate edges assumed to have been present between the continental plates. Some big questions remain, for example when did subduction in general start and when will it end? Did the recycling rate of oceanic plates change over time? And is subduction unique in the solar system and why?

chryphia

 

And, thanks to Matt, here are the Friday riddles, this time with a zoologic theme! The answers may be volcanoes, volcanic features, geology terms or lavas.  2 points will be awarded for each correct answer and 1 point after a clue is given. These is the last riddle session for this quarter and Sissel is firmly holding the top position, but as always, everyone´s a winner! 

 

 

 

 

 

 

1) The two images. Clue: The worms are headed towards Mexico. Basin and Range. 19th century geologist Clarence Dutton described the basin and range province as an “army of caterpillars headed towards Mexico”. The second image is a wash basin and a gas range in one! Inanamoon667, 1 point.

 

2) Duran Duran and the Palace of the Lion. Answer: Sigiriya, Duran Duran recorded a video here, and an ancient kingdom built a palace
here with a great lion as the gate. dinojura44, 2 points. 

3) This island of small frogs is always getting into everyone’s business. Answer: Nosy Be, an island off the northwest coast of Madagascar. A play on nosy, it is home to one of the world’s smallest frogs. Evan Chugg, 2 points. 

4) The sheep are the color of lava, and a dragon is chained within me. Answer: Mount Damāvand. Iranian red sheep live there, and Zoroastrian legend says a three-headed dragon is chained within this mountain. Shérine France, 2 points. 

5) I ran like water, but now I have become a butterfly. Answer: Komatiite. This ancient lava was so hot, 1600+ degrees, that it had a viscosity similar to water. All known examples have been metamorphosed, so becoming a butterfly is a reference to metamorphosis. Inannamoon667, 2 points. 

Final score board of season 2: 

25 Sissel
17 Inannamoon667
13 KarenZ
8 Kelda
8 Shérine France
8 Evan Chugg
7 Dinojura44
4 Bobbi
2 Alison
2 Stephanie Alice Halford
2 Agimarc
1 Diana Barnes
1 Edward
1 mikegrimsvotn

MATT

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