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410-km discontinuity and
60 km downward
depression of the 670-km discontinuity. The
diverse amounts of displacement are clearly
a consequence of the different magnitudes
of the Clapeyron slopes associated with the
transformations of '-olivine and ”-spinel.
These quantities were calculated assuming pure
isochemical phase transitions at the transition
zone boundaries, in agreement with the pyrolite
model. Although some seismic studies have
confirmed the existence of these deflections
(e.g., Shearer and Masters
1992
), their negative
correlation and the predicted relative magnitude
are not always observed experimentally (Bina
and Helffrich
1994
). However, there is a
general consensus about the validity of a
model based on phase transitions rather than
chemical boundaries. Part of the discrepancies
can be explained by taking into account that the
transformations of majorite garnet and pyroxene
to perovskite at the base of the transition zone
and in the uppermost lower mantle have
positive
Clapeyron slopes (Weidner and Wang
1998
),
thereby their effect is opposite to that of spinel.
Another important consequence of the pyrolite
model is represented by the effect of phase tran-
sitions on buoyancy and mantle convection, in so
far as they determine variations of density and
heat transfer (e.g., Christensen
1995
). According
to the Clausius-Clapeyron relation, the Clapeyron
slope of a single-component system is given by:
Fig. 1.13
Phase diagram of pyrolite in
P
-
T
space,
showing phase transitions at the 410-, 520-, and 670 km
discontinuities (Modified from Christensen
1995
)
670 km depth. The magnitude of
dp
/
dT
for the
transition of olivine to wadsleyite is
positive
,
and a recent estimate gives
C
3.1 MPa K
1
at
13.4 GPa and 1,400 K (Akaogi et al.
2007
).
Conversely, the breakdown of the ringwoodite
to perovskite and magnesiowüstite has a
negative
Clapeyron slope of
2.6
˙
0.2 MPa
K
1
at 670 km depth (Akaogi et al.
2007
).
Therefore, a negative thermal anomaly across the
transition zone, for example associated with the
presence of subducted material, will determine
simultaneously a downward deflection of the
670-km discontinuity and an upward deflection
of the 410-km discontinuity, as illustrated in
Fig.
1.13
. Consequently, we expect that in general
the topography of these primary surfaces of
discontinuity be negatively correlated.
For example, the thermal anomaly associated
with a stagnant slab in the transition zone could
be as high as 700 K. Helffrich and Wood (
2001
)
estimated that such a difference of temperature
would determine
30 km upward offset of the
¡
2
S
¡
D
¡
2
Q
L
T¡
dp
dT
D
S
V
D
”
D
(1.13)
where
S
and
V
are respectively the variations
of entropy and specific volume, ¡ is the mean
density of the two phases,
¡
is the density con-
trast between the phases, and
Q
L
is the latent heat.
Therefore, the phase transition is exothermic if
”>0, otherwise it will be endothermic.
ThesketchinFig.
1.14
illustrates the predicted
behaviour of negative thermal anomalies placed
in the vicinity of the 410- and 670-km disconti-
nuities. At 410 km depth, the transition of olivine
to wadsleyite has positive ”, so that it is exother-
mic. Therefore, a small downgoing body with
negative thermal anomaly (•
T
< 0) just above the
