Convection and complexity - New Theory of the Earth - page 76

sinkers may equilibrate at upper mantle or tran-
sition zone depths; they then warm up and rise.
The basic law governing ascent and settling,
Stokes' Law , expresses a balance between grav-
itational and viscous forces,

magma temperatures and large degrees of partial
melting, allowing for specific and latent heats,
melting probably initiates at depths of order
200 km under oceanic ridges and large volcanic
provinces, assuming that the mantle is mainly
peridotite. The solidus temperature of dry peri-
dotite at this depth is at least 2100 ◦ C. One ques-
tion is, how fast can material rise between about
200 and 90 km, and is the material at 90 km rep-
resentative of the deeper mantle source region or
has it been fractionated upon ascent? Viscosities
in silicates are very stress- and temperature-
dependent, and diapirs occur in regions of the
mantle that have higher than normal stresses
and temperatures. Diapiric emplacement itself
is a high-stress process and occurs in regions
where mantle convection may have oriented crys-
tals along flow lines. Diapirs may rise rapidly
through such low-viscosity material. A 50 km par-
tially molten diapir at a depth of 200 km can
rise at a rate of about 40 cm/s. Kimberlites travel
an order of magnitude faster still. Crystal set-
tling velocities in magmas are of the order of
cm/s. It appears therefore that deep diapirs can
rise rapidly enough to entrain both melt and
crystals. At depth the melt content and the per-
meability are low, and melt segregation may be
very slow. The fertile low-melting point blobs may
be encased in relatively impermeable subsolidus
peridotite and can therefore melt extensively as
they rise.
In a chemically stratified mantle, for example
residual peridotite over eclogite or fertile peri-
dotite, there is a conductive thermal boundary
between the convecting layers. In such a region
the thermal gradient is in excess of the melting
gradient, and melting is likely to initiate at this
depth. Eclogite has a melting temperature about
200 ◦ C below that of dry peridotite and melting
of fertile blobs is also likely between TBLs. Partial
melting causes a reduction in density, and a
Rayleigh--Taylor instability can develop. Material
can be lifted out of the eclogite or piclogite --
eclogite plus peridotite -- layer by such a mecha-
nism and extensive melting occurs during ascent
to the shallower mantle. At shallow depths peri-
dotite elevated adiabatically from greater depths
can also melt and magma mixing is likely, par-
ticularly if the diapir is trapped beneath thick

gR 2 V = 2 ρ / 9 η

where R is the radius of a spherical particle
or diapir, is the

dynamic viscosity and V is the terminal veloc-
ity. This equation can be applied to the rising or
sinking of blobs through a mantle or a magma
chamber, with modifications to take into account
non-spherical objects and non-Newtonian viscos-
ity. Additional complications are introduced by
turbulence in the magma chamber and finite
yield strengths.
Diapirs are usually treated as isolated spheres
or cylinders rising adiabatically through a static
mantle. Because of the relative slopes of the
geotherm, and the melting curve, diapirs become
more molten as they rise. At some point, because
of the increased viscosity or decreased density
contrast, ascent is slowed and cooling, crystal-
lization and crystal settling can occur. The litho-
sphere serves as a viscosity or strength barrier,
and the crust serves as a density barrier. Melt
separation can therefore be expected to occur
in magma chambers at shallow depths. In a
convecting mantle the actual temperatures (adi-
abatic or subadiabatic) diverge from the melt-
ing point as depth increases. In a homogenous
mantle, melting can therefore only occur in the
upper parts of the rising limbs of convection
cells or in thermal boundary layers. The addi-
tional buoyancy provided by melting contributes
to the buoyancy of the ascending limbs. Although
the melts will attempt to rise relative to the
adjacent solid matrix, they are embedded in a
system that is itself rising and melting further.
If broad-scale vertical convection is fast enough,
diapirs can melt extensively without fractionat-
ing. Fertile, low-melting-point patches, such as
eclogite, can melt extensively if surrounded by
subsolidus peridotite.
The stresses and temperatures in the vicinity
of rising plumes or diapirs are high, and these
serve to decrease the mantle viscosity; thus rapid
ascent is possible. In order to achieve observed

ρ is the density contrast, η