Geoscience Reference
In-Depth Information
temperature gradient exceeds the adiabatic gra-
dient by a given amount. The adiabat does
not define a unique temperature; it defines a
gradient. The average temperature variation with
depth is called the geotherm. Its basic form is
almost always assumed to consist of adiabatic
regions where temperatures rises slightly with
depth (approximately 0.3 to 0.5
◦
C/km), and of
narrow thermal boundary layers (TBL) where tem-
peratures increase rapidly (approximately 5 to
10
◦
C/km) over a depth of a few hundred kilo-
meters. If the mantle were entirely heated from
below, was not experiencing secular cooling and
if the mantle were a fluid with constant proper-
ties, the horizontally averaged temperature gra-
dient would be adiabatic. Material brought up
rapidly from depth without cooling by conduc-
tion or heating by radioactivity will follow an
adiabatic path. The mantle geotherm is not,
in general, along the adiabat; departures from
an adiabat are due to secular cooling, internal
radioactive heat production and the cooling from
below by material that sank from the upper cold
TBL. As a volume element rises through the man-
tle its temperature decreases in response to adia-
batic decompression but at the same time its tem-
perature increases due to internal heat released
from radioactive decay. The actual temperature
gradient in the mantle can be slightly subadia-
batic. The mantle geotherm away from thermal
boundary layers may depart by as much as 500 K
from the adiabat.
or impossible, even under the best of conditions,
to generalize from a small number of simulations
or experiments.
Volume
Equations of state can be cast into forms that
involve
P
and
T
,or
V
and
T
. Many physical prop-
erties depend on
P
and
T
only in-so-far as the spe-
cific volume is changed. The intrinsic effect of
T
is often a small perturbation. This is not true
for radiative conductivity, rigidity and viscosity.
Various laws of corresponding states, Debye the-
ory, and the quasi-harmonic approximation are
cast in terms of inter-atomic distances or volume.
Usually, volume refers to specific volume. In dis-
cussions of sampling theory, volume will refer to
the size of the sampled domain.
Composition
Density, seismic velocity, melting temperature,
fertility and so on are affected by changes in
composition or lithology. The mantle is a multi-
component system. Yet it is often assumed that
the mantle is homogenous and that variations in
seismic velocity and magmatism are controlled
only by variations in temperature.
Phase changes
Phase changes are responsible for most of the
seismic velocity and density increases at 410- and
650-km depth. There are other seismic reflectors
and scatterers in the mantle and some of these
may be due to chemical or lithologic changes.
Chemical boundaries are generally harder to
detect than phase boundaries because they
are more variable in depth and reflectivity or
impedance, and their existence is not controlled
by
P
and
T
. The absence of features similar to 410-
and 650-km discontinuities does not imply that
there are no chemical variations in the mantle
or that the mantle is not chemically stratified.
Pressure
Pressure is not an intuitive parameter, at least
in the pressure range of the deep mantle. For
geophysical purposes it is the compression, or
the volume, that controls physical properties.
The
specific volume
,or
inverse density
, of the man-
tle decreases by about 30% from the top to the
bottom and most physical properties are strong
non-linear functions of volume. This is ignored
in most simulations of mantle convection and
the insight gained from these simulations is
therefore restricted. Laboratory simulations of
mantle convection cannot model this pressure
effect. Since mantle dynamics is an example of
a
far-from-equilibrium system
that is sensitive to
small perturbations in initial or boundary con-
ditions, or changes in parameters, it is difficult,
Ratios
Geophysics, fluid dynamics and geochemistry
abound in dimensionless ratios such as the
V
p
/
V
s
ratio, Poisson's ratio, Rayleigh number and iso-
topic ratios such as
3
He/
4
He. Ratios are handy
but they do not constrain absolute values of the
numerator and denominator. For example, high
3
He/
4
He ratios do not imply high
3
He-contents,
