Geoscience Reference
In-Depth Information
the parameter
ε
Nd
(epsilon Nd) is the deviation in parts per ten thousand:
1
[
143
Nd
/
144
Nd]
0
10
4
ε
Nd
=
−
×
(6.52)
144
Nd]
CHUR
0
[
143
Nd
/
[
143
Nd
144
Nd]
0
where
/
is
the
initial
ratio
of
a
whole-rock
sample
and
[
143
Nd
144
Nd]
CHU
0
is the initial neodymium ratio of the CHUR model (calcu-
lated from Eq. (6.51)) at the same time
t
ago. Indeed,
/
ε
Nd
values can be calculated
at any time from the formation of a system to the present day: they should always
be accompanied by the time at which they were calculated.
As shown in Fig. 6.7,arock that was derived directly from the CHUR would
have an initial ratio equal to the CHUR ratio for that age and hence a zero epsilon
value (
0). However, partial melts of the CHUR develop negative epsilon
values as time passes, so a rock derived from the melting of older crustal rocks
will have a negative epsilon value (
ε
Nd
=
0). Likewise, rocks derived from the
residue left after the CHUR had been partially molten and the melt withdrawn
will have positive epsilon values (
ε
Nd
<
0). Such a source is generally referred to
as
depleted mantle
because it is depleted in the highly incompatible elements such
as rubidium and the light rare-earth elements. Equations (6.50) and (6.51) can be
used together to calculate a model age
T
,which represents the time that has elapsed
since the neodymium in the rock sample had the same isotopic ratio as that of the
CHUR model (i.e., since the rock separated from a chondritic reservoir such as
primordial mantle). Such an age has a meaning only provided that the samarium-
neodymium ratio of the rock has not been altered since the rock separated from
the CHUR mantle. However, the Sm
ε
Nd
>
Nd ratio is relatively insensitive to crustal
processes such as metamorphism, weathering and diagenesis, so the model age
T
can be used, with caution, as a time estimate. Equation (6.50)gives the initial
neodymium ratio for a rock as
143
Nd
144
Nd
/
0
=
143
Nd
144
Nd
147
Sm
144
Nd
(e
λ
T
now
−
−
1)
(6.53)
now
From Eq. (6.51), the neodymium ratio in the CHUR at a time
T
ago was
143
Nd
144
Nd
CHUR
1967(e
λ
T
=
0
.
512 638
−
0
.
−
1)
(6.54)
0
Equating these two expressions and rearranging terms to obtain a value for
T
gives
log
e
[
143
Nd
/
+
1
144
Nd]
now
−
0
.
512 638
[
147
Sm
/
1
λ
T
=
(6.55)
144
Nd]
now
−
0
.
1967
If the rock came from a depleted mantle source instead of the CHUR, such an age
estimate would be too low. Since there is little evidence for the existence of any
primordial mantle since
4 Ga, it is generally conventional to calculate model
ages with respect to depleted mantle rather than to the CHUR. Age estimates
∼
