Relationship between mantle convection
currents and plate motions?
Introduction: Plate tectonics has been regarded as a scientific revolution. If so one might argue that it is incomplete. While we have a detailed understanding of how the plates behave, the relationship between plate motions and convection in the mantle is still vigorously debated. This is evident in the ongoing discussion about mantle plumes and hot spot trails. New information from seismic tomography and compute modeling capacities promise to provide insight in the near future. As we expand our knowledge in science we also expand the boundaries of the unknown. Convection is also a fundamentally important process that controls much of the dynamics of atmospheric, ocean, mantle and outer core systems, and thus well worth understanding better.
Image to right depicting top to bottom mantle convection from http://geomag.usgs.gov/about.php .
Two basic simple end-member models
in the mantle raft the overlying plates around. Traction stresses
at the base of the plates would be critical. This could be akin to sea ice being moved by underlying currents in the sea water.
move due to internal body forces, and influence the shallow convection
current pattern in the mantle.
locally exclusive, but not globally.
Schematic diagram of coupled (left) and decoupled (right) models. In the first case the motion in the asthenosphere rafts the plate above along. The plate would move slower than the underlying asthenosphere, and the relative sense of motion between the two would be as the blue arrows show. In the other case some other force such as trench pull would pull the lithosphere and drag would induce movement in the asthenosphere below, which would diminish downwards, and the relative sense of motion between the two would be the opposite. The second possibility ignores the possibility that some other motion could exist in the asthenosphere due to mantle convection, and treats the asthenosphere as passive. In other words, the arrows in the decoupled case only show the movement component in the asthenosphere that would be created by drag as the over riding plate moves and not movements due to other causes.
Possible driving forces for plate tectonics
Here is a list to start with:
- bottom lithosphere tractions by convection currents.
- trench pull (covered earlier).
- ridge push (sliding off a high, oceanic crust in compression).
- trench suck (rollback, associated with production of rear-arc basins).
- global expanding or contracting forces (controversial).
- membrane forces on a spinning ellipsoid (e.g.
variants of polar fleeing forces).
Lava lake videos that demonstrate possibilities on a small scale:
Conduction vs. convection vs. advection. Advection is often assumed
to be absent in the mantle, but is it (partial melt migration)? We won't have time to really
address that here. Realize that the term advection is used in different ways.
Buoyancy is driven by gravity acting on density
contrasts caused by thermal differences and by phase changes.
Both are important in earth's mantle.
Viscosity of the convecting medium is obviously a crucial parameter. What is the nature of viscosity?
- resistance to flow.
- technically it is ratio of deviatoric stress
(measure of size of shear stress) over shear strain. There are
different types of viscosity defined in slightly different ways
(see Davies for an explanation). There are also different stress-strain
viscosity relationships - linear (Newtonian) vs. power law.
- higher the number the more viscous a material
- typical units are Pascals per second.
- for kinematic viscosity units are meters
squared per second.
Significance of the Rayleigh number in convection
- balance between buoyancy and viscous forces
in a simple layer of thickness D. Dimensionless number.
- input parameters:
- coefficient of thermal expansion.
- temperature gradient in excess of that associated
with increasing pressure (superadiabatic component).
- gravitational acceleration.
- thermal diffusivity (how fast heat moves
- thickness of convecting fluid = d.
- kinematic viscosity
- Ra = gravitational acceleration * density
* volume coefficient of thermal expansion * temperature of interior
fluid * depth of layer cubed all divided by the thermal diffusivity
* viscosity (Davies)
- note that as viscosity increases Ra decreases
and convection less likely. As thermal diffusivity increases
Ra decreases and convection less likely.
- for a given geometry there is a threshold Ra number that
needs to be exceeded for convection to occur. For the spherical
mantle this value is estimated at 2380 (Keary & Vine).
As Ra increases there are also different styles/geometries of convection.
- estimates for even the lower mantle yield
a Ra value of circa 3*E6. In other words buoyancy forces far
overpower viscous retarding forces and convection should be vigorous.
See Turcotte or Davies for a fuller explanation.
Geometries of convection:
- Image to right from http://pubs.usgs.gov/gip/dynamic/unanswered.html, shows a very simple large scale convection cells. How is this simple depiction certainly wrong in detail?? What doesn't it take into account?
- patterns include:
- parallel elongate cylindrical cells (sheet
upwelling and downwelling).
- hexagonal patterns
- spokes, plumes.
- bimodal patter of perpendicular cells.
- stable vs. unstable (turbulent) patterns.
- pattern a function of the Rayleigh number.
- very tall or very wide circulation cells
are not stable (excepting plumes which are only part of the pattern). Often a width to depth ratio
of 2 for cells for earthly conditions.
- below is an experimentally produced convection pattern. How would you describe the pattern? Image is from http://www.etl.noaa.gov/about/eo/science/convection/Table.html .
of mantle convection: flowage in response to buoyancy forces
Importance of Clapeyron slope: For most
mineral transformations the transformation pressure increases
with increasing T (i.e. a positive Clapeyron slope). This means
that in a colder mantle region the transformation can occur at
a shallower level and in a hotter region it occurs at a deeper
level. We already considered this in the context of the olivine
to spinel transition in a subducting slab and the mechanism of trench pull.
We can also consider thermal plumes. If there is a density
increase in a colder region of convective downwelling, the phase
transition will occur at a elevated level producing a negative
buoyancy and enhancement of downwelling would be expected. By
the same line of reasoning a hot spot, a positive buoyancy force
would exist. In this case a plume may be self perpetuating once it forms. Which is consistent with the long history of some
mantle plumes (see below). In fact you could ask why would a mantle
plume ever die? What is the slope for the 670 km, spinel to perovskite
Mantle viscosity: a most crucial parameter!!
Shallow mantle viscosity dominated by olivine rheology.
Mantle material is of varying viscosity: lithosphere
vs. asthenosphere, and upper vs. lower mantle. Is there a viscosity
contrast across the 370 km phase change boundary?
Estimations of mantle viscosity from glacio-isostatic
- rebound history takes an exponential form.
- deformation due to ice load will penetrate
to depth comparable to its radius (Davies).
- some larger loadings (bigger ice sheets) reach into lower mantle.
- lower mantle viscosity of 6*E+21Pa-s, upper
mantle viscosity of 3*E+20 Pa-s. This is a large viscosity contrast.
Insight into mantle convection from seismic anisotropy
Basic reasoning: Remember that mantle convection involves the flow of a crystalline solid - i.e. deformation. Such solid-state flow induces a strong preferred direction of crystallographic axes of the deforming minerals. In addition to hardness, seismic velocity varies with crystallographic direction. Seismic velocity anisotropy is observed in the mantle, and can be interpreted to reflect the flow/movement directions.
IRIS and traveling array project.
Map showing azimuthal seismic anisotropy (fast directions) at two different depths in the mantle. Small green circles are hot spot locations. Source of image: Debayle et al. - IRIS website - https://www.iris.edu/gallery3/research/2010proposal/upper_mantle/debayle_fig1 .
Hot spots and mantle plumes
Well known examples: Hawaiian island chain, Iceland, Yellowstone.
- J Tuzo Wilson initial proponent.
- can persist for over 100 Ma.
- oceanic island related hotspots have a different trace element chemistry
than ridge basalts, one less evolved.
- continental hotspot volcanism can be more complex.
- depth of origin?
- birth in an LIP - plume head arrival.
- minority view consider it as a propagating crack, and not driven by a deep plume.
- good place to enter debate: http://www.mantleplumes.org/index.html .
- image to right from http://education.usgs.gov/common/resources/mapcatalog/earthquakes.html, shows the emergent part of the Hawaiian island chain.
Note how the earthquakes are associated preferentially with the southern end, reflecting the younger more active portion.
- Below is an image below the Hawaiian hotspot suggesting the plume extends to substantial depth. Image source: http://www.iris.edu/hq/gallery/photo/9228,
Credit: Cecily Wolfe, University of Hawaii, Sean Solomon, Carnegie Institution of Washington, Gavi Laske, Scripps Institution of Oceanography, Robert S. Detrick, Woods Hole Oceanographic Institution, John A. Orcutt, Scripps Institution of Oceanography, David Berc
- image below from http://pubs.usgs.gov/gip/dynamic/world_map.html . Shows distribution of world's hot spots at present. Are they evenly spread?
Which plates show the largest concentration of hot spots?
- Diagram below from http://oceanexplorer.noaa.gov/explorations/05galapagos/background/mission_intro/media/GSC3D_600.html shows the Galapagos hot spot. Note how the plume is shown to partly feed spreading ridge. As depicted one might be forgiven for wondering why such a broad plume has such a focused volcanic expression.
- Diagram below is 4 frames in the time series result of a numerical model of a Rayleigh-Taylor instability, which might provide insight into the character of mantle plumes.The diagram can be considered upside down to help visualize it as a mantle plume. Specific aspects to note are: the mushroom shaped plume head, the narrower trailing column/tail, the lenticular portion of the column/tail (hinting at the possibility of surface pulses, and the mixing that occurs. Similar behavior is seen in experimental models of plumes. Tomographic images of the mantle at present would not have the resolution to pick up these sorts of details. Image source; https://commons.wikimedia.org/wiki/File:HD-Rayleigh-Taylor.gif , and originally from Shentai Li and Hui Li, Hydrodynamic simulation of the Rayleigh-Taylor instability .
- Image of Mons Olympus, the largest basaltic volcanic construct in the Solar System, found on the Tharsis Bulge of Mars.
- Site describing Tharsis crustal dichotomy, with animation that shows global scale asymmetry convection model.
Stratified vs. whole mantle convection
What is the significance of the upper-lower mantle boundary?
- 670 km phase change: major viscosity barrier,
depth of deepest earthquakes, major velocity changes.
- trace element geochemistry suggest must have
incomplete mixing as can see different reservoirs.
- mantle reservoirs for melts:
- continental lithospheric mantle.
- upper mantle.
- lower mantle via hot spots.
- megaliths (subduction residue), and periodic
penetration of the 670 km boundary.
- Cretaceous LIPs, and a model of mantle overturning.
- What happens to a plume head passing through a viscosity barrier?
- core-mantle boundary:
- not sharp and has relief and D'' layer (Peltier 2007).
Viewing present patterns of convection:
- seismic tomography where thermal differences change seismic velocity. Cold
areas are faster than hot. There is a basic assumption that the mantle is compositional homogenous.
- by seismic anisotropy caused by preferred
orientation of mantle crystals due to solid state flowage.
- USArray detection of seismic anisotropy.
- by broader gravity anomalies reflecting deeper
density variation.. New advances with satellite data. GRACE site with maps.
- anomalies in Pacific in Hawaiian area are
parallel to the direction of plate motion relative to the hotspot
reference frame, and about 500 km width. The latter suggest these
are d=w rolls within the upper mantle.
- by hot spot and LIP manifestations.
S- wave velocity anomalies at different levels in the mantle. What patterns do you note. From IRIS site - http://www.iris.edu/hq/gallery/photo/8935. Credit: Sergei Lebedev, Dublin Institute for Advanced Studies, Rob D. van der Hilst, MIT/IRIS Consortium
Shear wave splitting interpreted as due to the direction of mantle flow (and alignment of olivine crystals) beneath western U.S.. Image source: http://www.iris.edu/hq/gallery/photo/8935, Credit: Matthew J. Fouch, Arizona State University, John D. West, Arizona State University/IRIS Consortium
Model simulations of mantle convection
Computer models are only as good as the input and underlying assumptions, but can still inform about possibilities.
Parting thoughts on the mechanisms
- Fact that hot spot is a 'relatively' fixed
reference frame (debated by some) suggests that there is a deep convection pattern
characterized by plumes that are independent of overlying plate motion.
- By necessity there must be shallow plumes
under ridges. Evidence that these are not deeply rooted. This, in connection with hotspots and the scale
of subduction zones, suggests multiple scales and circuits of
- To a first order approximation world stress
maps show a pattern that is consistent with ridge push and trench
- The initiation of continental rifting is
difficult to explain with simple ridge push and trench pull (consider
- Fact that plate changes can occur relatively sudden
(think of kink in Hawaiian hot spot track) needs to be explained.
- May be on the verge of a broad paradigm expansion or shift
explaining interior convection and its surface manifestations.
Through IRIS and other efforts a lot of new data coming in.
- Link to NASA study on core mantle dynamics.
- Anderson, D. & Dziewonski, A.M., 1984, Seismic tomography;
Sci. Am., Oct. issue.
- Bercovici, D. & Mahoney, J., 1994, Double Flood Basalts and Plume Head Separation at the 660-Kilometer Discontinuity; Sciecne, 266, p. 1367-1371, link to pdf can be found here - http://people.earth.yale.edu/publications/david-bercovici .
- Davies, P.A. & Runcorn, S.K., 1980, Mechanisms of Continental
Drift and Plate Tectonics; Academic Press, N.Y., 362p., Collection
of articles - 3 of which have greater pertinence
- Jacoby, Plate sliding and sinking in mantle convection and
the driving mechanism
- Turcotte - Some major questions concerning mantle convection
- Runcorn - Some comments on the mechanism of continental drift
- Davies, G. F., 1999, Dynamic Earth Plates, Plumes and Mantle
Convection; Cambridge University Press, 458 p.
- E. Debayle, B. Kennett and K. Priestley, Global azimuthal seismic anisotropy and the unique plate-motion deformation of Australia, Nature, 433, 509-512, doi:10.1038/nature03247, 2005.
- Holmes, A., 1965, Principles of Physical geology, Nelson-London,
Chapt. XXVIII Heat floor, volcanic activity, and convection.
- Gaherty, J. B., Lizarralde, D., Collins, J. A., Hirth, G., Kim, S., 2004, Mantle deformation during slow seafloor spreading constrained by observations of seismic anisotropy in the western Atlantic; EPSL, 228, 255-265.
- Garfunkel, Z., editor, 1985, Mantle flow and plate theory;
New York: Van Nostrand Reinhold, 304p.
- Long, M. & Becker, T. W., 2010, Mantle dynamics and seismic anistropy; EPSL, 297 341-351.
- McKenzie, D.P. & Richter, 1976, Convection currents in
the earth's mantle, Sci. Am., p. 72-89.
- McKenzie, D.O., Watts, A., Parsons, B., Roufosse, M., 1980,
Platform of mantle convection beneath the Pacific ocean; Nature,
v. 228, p. 442-446.
- McKenzie, D.P., 1983, The Earth's Mantle, Sci. Am., v. 249,
- Peltier, 2007, Mantle Dynamics and the D'' Layer: Impacts of the post Perovskite phase; Geophysical Monograph Series 174, AGU, 217-227.
- Peltier, W.R., eidtor, 1988, Mantle convection; unknown publisher.
- Turcotte, D.L., 1975, The driving mechanisms of plate tectonics;
Reviews of Geophysics and Space Physics, v. 13, #3, p. 333-334.
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