Geology Reference
In-Depth Information
10.8.4 Modelling evolution in the MORB and OIB sources
A key test of the proposed residence of mantle noble gases in hybrid pyroxenites
is whether the difference in residence times between the MORB source and the
D
region can explain the differences between the noble gas signatures of MORBs
and OIBs. This requires a way to calculate the evolution of the noble gases in the
mantle. Such a calculation can also test the overall plausibility of the proposal in
the light of results from numerical models of mantle evolution [156]. Here a simple
method is presented for calculating the evolution of noble gas concentrations in
the mantle, taking account of degassing and radioactive generation. This method
is then applied in the next section, using the estimated ranges just discussed as
boundary conditions.
We used the 'model time' of Section 10.4.3 to calculate the remaining primitive
fraction of the mantle and the rate of accumulation of subducted crust in the mantle
as a function of time, and later to calculate tracer residence times (Section 10.7.3).
The same approach can be used to estimate rates of degassing of the mantle. By
the same logic as the survival of primitive mantle, the mantle's complement of
primordial volatiles will also decline exponentially with model time if the rate of
degassing is constant with respect to
t
m
:
exp
,
t
m
τ
g
c
i
=
−
c
i
(10.9)
where
c
i
is the concentration of species
i
,
c
i
is its initial concentration, and
τ
g
=
m
i
/r
i
is the
degassing timescale
,where
m
i
is the mass of species
i
in the mantle
and
r
i
is the rate at which it is being removed from the mantle.
More generally, the concentration of a radiogenic species will change according
to
c
i
t
m
=−
c
i
τ
g
+
g
i
,
(10.10)
where
g
i
is the rate of radioactive generation of the species and
τ
g
need not be
constant.
From the previous section, the observed degassing rate of
3
He is
r
3
=
1060 mol/yr, and the conventionally inferred concentration in the mantle source
is about
c
3
=
10
9
atoms
3
He/g (Table 10.5(a)). The mass of
3
He in the mantle is
10
27
g. The degassing timescale
m
3
=
Mc
3
, using the mass of the mantle
M
=
4
×
for
3
He is then
τ
g
=
6.7 Gyr. If the concentration of
3
He is two or three
times higher, then
m
3
is larger and the degassing timescale is correspondingly
longer. Thus the degassing of the MORB source may be relatively slow.
m
3
/r
3
=
