Geoscience Reference
In-Depth Information
Table 13.2
(
cont
.)
Ultramafic
Morgan
MORB
Rocks
KIMB
Crust
Picrite
OPX
and Anders (1980)
Ta
0.1
0.03
9
2
0.08
—
0.023
Re
†
1.1
0.23
1
1
0.88
0.08
60
Os
†
0.04
3.1
3.5
5
0.81
3.1
880
Ir
†
0.0011
3.2
7
1
0.80
3.2
840
Au
†
0.34
0.49
4
4
0.38
0.49
257
Tl
†
0.01
0.02
0.22
0.25
0.01
—
0.003 86
Pb
0.08
0.2
10
7
0.11
—
0.068
Bi
0.007
0.005
0.03
0.2
0.01
—
0.002 94
Th
0.035
0.094
16
4.8
0.05
—
0.0541
U
0.014
0.026
3.1
1.25
0.02
—
0.0135
∗
Results in percent.
†
Results in ppb.
Anderson (1983a).
Schematically, primitive mantle can be writ-
opx, cpx, gt and Q, or their low-pressure equiv-
alents) with four composites or averages; peri-
dotite, orthopyroxenite, basalt and Q. In practice,
we can use two different ultramafic rocks (UMR
and OPX) with different ol/opx ratios to decou-
ple the ol
ten
PM
=
MORB
+
UMR
+
CC
+
OPX
+
Q
and
the
proportions
of
each
component
are
opx contributions. The chemistry of
the components (MORB, UMR, OPX and crust) are
given in Table 13.2.
Having measurements of
m
elements in
n
components where
m
far exceeds
n
, we can find
the weight fraction
x
j
of each component, given
the concentration
C
j
of the
j
th element in the
i
th
component, that yields chondritic ratios of the
refractory oxyphile elements. In matrix form,
+
found by the inversion.
The mixing ratios found from Equations 2
and 3 are UMR, 32.6%, OPX, 59.8%, MORB, 6.7%,
crust, 0.555% and Q, 0.11%. This is a model com-
position for primitive mantle (PM) i.e. mantle
plus crust. The Q component is equivalent to
a global layer 3.6 km thick. The MORB compo-
nent represents about 25% of the upper mantle.
This solution is based on 18 refractory elements
and, relative to chondrite (C1) abundances, yields
k
C
ij
x
j
=
kC
j
(1)
46.
The result is given in Table 13.3 under 'mantle
plus crust.' This will be referred to as the bulk
silicate Earth (BSE) composition. Concentrations
normalized to Cl are also given. Note that the
high-charge, small-ionic radius elements (Sc, Ti,
Nb and Hf) have the highest normalized ratios
and may be overestimated. Taking all the refrac-
tory oxyphile elements into account (23 ele-
ments), the normalized enrichment of the refrac-
tory elements in the mantle plus crust is 1.59. If
five elements (Fe, S, Ni, Co and O) are removed
from C1 to a core of appropriate size and density,
the remaining silicate fraction will be enriched
=
1
.
where
C
j
is the chondritic abundance of element
j
and
k
is a dilution or enrichment factor, which
is also to be determined. The least-squares solu-
tion is
(
C
T
C
)
−
1
C
T
C
j
x
j
/
k
=
(2)
where
C
T
is the matrix transpose of
C
,withthe
constraints
x
r
=
1 and
k
=
constant
(3)
Equation 1 then gives the mantle concentrations
of
the
volatile
and
siderophile
elements,
ele-
ments not used in the inversion.
