Reading: Chapt. 11 of text. A nice overview.

Two basic models:

• coupled: currents in the mantle raft the overlying plates around. Traction stresses at the base of the plates would be critical.
• decoupled: plates move due to internal body forces, and influence the shallow convection current pattern in the mantle.
• locally exclusive, but not globally.

Possible driving forces for plate tectonics:

• bottom tractions by convection currents.
• trench pull.
• ridge push (sliding off a high).
• trench suck (rollback).
• see Fig. 11.10 of text for various forces involved.
• global expanding or contracting forces.
• membrane forces on spinning ellipsoid (e.g. variants of polar fleeing forces).

Conduction vs. convection vs. advection. Advection is often assumed to be absent in the mantle, but is it? We won't have time to really address that here.

Buoyancy is driven by gravity acting on density contrasts caused by thermal differences and by phase changes. Both are important.

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 the 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 bouynacy force would exit. 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 boundary?

Mantle viscosity:

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 is.
• units are Pascals per second.
• for kinematic viscosity units are meters squared per second.

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:

• rebound history takes an exponential form.
• deformation due to ice load will penetrate to depth comparable to its radius (Davies).
• some larger loadings 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.

Significance of the Rayleigh number in convection behavior:

• 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 by conduction)
  • 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 number that needs to be exceeded for convection to occur. For the spherical mantle your text indicates this value is 2380 (Keary & Vine). As R increases there are 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:

• parallel elongate cylindrical cells (sheet upwell 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). Often a width to depth ratio of 2 for cells for earthly conditions.

Hot spots:

• can persist for over 100 Ma.
• have a different trace element chemistry than ridge basalts, one less evolved.
• depth of origin?
• birth in an LIP - plume head arrival.
• minority view as a propagating crack.

Stratified vs. whole mantle convection:

• 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:
  • 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.

Model simulations of mantle convection:

• physical models vs. computer models.
• dragging mylar over the system.
• internal heat production vs. heat from below.
• convection movies from Caltech.
• Los Alamos convection movies.

Viewing present patterns of convection:

• seismic tomography where thermal differences change seismic velocity. Cold areas are faster than hot.
• by seismic anisotropy caused by preferred orientation of mantle crystals due to solid state flowage.
• by broader gravity anomalies reflecting deeper density variation.. New advances with satellite data.
• anomalies in Pacific in Hawiaan 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.

Parting thoughts on the mechanisms:

• Fact that hot spot is a relatively fixed reference frame suggests that there is a deep convection pattern characterized by plumes that is independent of plate motion.
• By necessity there must be shallow plumes under ridges. This in connection with hotspots and the scale of subduction zones suggests multiple scales and circuits of convection.
• To a first order approximation world stress maps show a pattern that is consistent with ridge push and trench pull.
• The initiation of continental rifting is difficult to explain with simple ridge push and trench pull (consider EAR).
• Fact that 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 shift explaining interior convection and its surface manifestations.

Some References:

• Anderson, D. & Dziewonski, A.M., 1984, Seismic tomography; Sci. Am., Oct. issue.
• 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.
• Holmes, A., 1965, Principles of Physical geology, Nelson-London, Chapt. XXVIII Heat floor, volcanic activity, and convection.
• Garfunkel, Z., editor, 1985, Mantle flow and plate theory; New York: Van Nostrand Reinhold, 304p.
• 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, #3, 14p.
• Turcotte, D.L., 1975, The driving mechanisms of plate tectonics; Reviews of Geophysics and Space Physics, v. 13, #3, p. 333-334.
• Peltier, W.R., eidtor, 1988, Mantle convection; unknown publisher.

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