Geoscience Reference
In-Depth Information
Top-down tectonics
thermal, elastic and rheological properties of
solids depend on interatomic distances, or lattice
volumetric strain, and are relatively indifferent
as to what causes the strain (
T
,
P
or crystal struc-
ture). Intrinsic temperature effects are those that
occur at constant volume. The quasiharmonic
approximation is widely used in mineral physics
but not in seismology or geodynamics where less
physically sound relationships are traditionally
used.
A parameter that depends on
P
,
T
, phase (
One can think of mantle convection as having
various origins. The mantle is cooled from above;
instability of the cold upper TBL is a
top-down
mechanism, which is basically plate tectonics.
Heating the mantle from below is a
bottom-up
or
thermal plume mechanism. Lithospheric archi-
tecture provides a
sideways
or EDGE mechanism
that is lacking in Rayleigh--Bénard convection,
or in simple fluids with simple boundary condi-
tions. Internal heating generates time-dependent
upwellings, an
inside-out
mechanism.
Delamination
is a
bottoms-off
thermo-chemical mechanism that
does not involve the whole outer shell. Cooling
of the surface and the motions of plates and
plate boundaries, and their effect on the under-
lying mantle, constitute the main, or large-scale,
mode of planetary convection.
Small-scale
convec-
tion takes the form of gyres and eddies, rolls
and sprouts; these are secondary effects of plate
tectonics.
Edge-driven
convection, and stress vari-
ations and cracks in the plates are all conse-
quences of plate tectonics and offer explanations
of volcanic chains and volcanism that are not at
plate boundaries. Lateral variations in tempera-
ture, melting temperature, density and fertility
of the upper mantle are also consequences of
plate tectonics; recycling, continental insulation
and slab cooling can explain variations in vol-
canic output from place to place. So-called
mid-
plate volcanism, melting anomalies
and
hotspots
can
be consequences of plate tectonics, and do not
require high mantle temperatures or deep fluid
dynamic instabilities.
Early views of plate tectonics treated plates
as responding passively to mantle convection.
Plates and continents drifted about passively
on the surface. Ridges were the upwellings
and slabs were the downwellings. Narrow hot
upwellings were generally held responsible for
'hotspots,' 'hotlines' and 'hotspot tracks'; giant
upwellings or plume heads were held respon-
sible for large igneous provinces and continen-
tal break-up and for influencing plate motions.
These ideas developed from the tacit assumptions
that the lithosphere is rigid and uniform, the
upper mantle is isothermal, generally subsolidus,
and homogenous, and that locations of volcanoes
)
and composition
C
(within limits, e.g. constant
mean atomic weight) can be expanded as
φ
M
(
P
,
T
,φ,
)
=
M
(
V
)
+
ε
C
where
represents higher-order intrinsic effects
at constant molar
V
. Lattice dynamic parameters
and thermodynamic and anharmonic parameters
are interrelated via
V
.
ε
Beyond Boussinesq
The effect of volume changes on thermody-
namic properties are determined by dimension-
less parameters. Scaling parameters for volume-
dependent properties can be written as power
laws or as logarithmic volume derivatives about
the reference state;
Lattice thermal
−
dln
κ
L
/
dln
V
∼
4
conductivity
Bulk modulus
−
dln
K
T
/
dln
V
∼
4
Thermal expansivity
−
dln
α/
dln
V
∼−
3
Volume changes in laboratory convection exper-
iments are small, so the changes of thermal
parameters associated with volume changes are
small, with the possible exception of viscos-
ity. The Boussinesq approximation ignores these
effects. The specific volume at the base of the
mantle is 64% of that at the top. Compression,
composition and phase changes, and to some
extent, temperature, are all involved. When the
above numbers are multiplied by
V
the chan-
ges in physical properties are non-negligible
for the mantle. Although volume scalings such
as the Debye theory and the
quasiharmonic
approximation
are strongly grounded in clas-
sical physics they have not been implemented in
mantle convection codes.
V
/
