Geology Reference
In-Depth Information
10.3.3.1 The model
In Sec. 5.5, the reader saw that the crust's composition in terms of elements is
reasonably known, with the data of Rudnick and Gao (2004) one of the most ac-
cepted ones. Unfortunately, for the Model of Crepuscular Crust, the composition in
terms of minerals, not of chemical elements is required. To the authors' knowledge,
only one single author (Grigor'ev, 2007) has provided a preliminary estimation of
it. After the authors' extensive review of Grigor'ev's mineralogical composition, an
update was carried out in Valero D. et al. (2010a) ensuring that all species com-
prising the analysis were mathematically, chemically and geologically consistent. A
mass balance of the species was undertaken, ensuring that the total sum of the
mineral mass (vector i ) was equal to that of the total chemical elements mass as
given by Rudnick and Gao (2004) (vector j ). A matrix with the elements as rows
and minerals as columns was obtained:
i!
1
2
3
4
5
j
SiO 2 CaCO 3 NaAlSi 3 O 8 Al 2 SiO 5
#
1
0
3
1
Si
1
2
3
8
5
O
2
R[j i] =
0 1 0 0 Ca 3
0 1 0 0 C 4
0 0 1 0 Na 5
0 0 1 2 Al 6
7
If R is the coe cient r j;i matrix , then Eq. (10.1) must be satisfied:
r j;i i = j
(10.1)
Vector i is the unknown.
If the continental crust is assumed to be a closed system, the elements contained
in the minerals must be equal to the chemical composition of the crust. And, if
the chemical composition defined by Rudnick and Gao (2004) given in Table 5.13 is
assumed to be correct, the application of Eq. (10.1) in Grigor'ev's analysis, should
give the same values as Rudnick and Gao (2004).
Yet, the output of the mass balance between compounds and elements for
Grigor'ev (2007) analysis does not correspond to the chemical composition of the
upper Earth's crust determined by Rudnick and Gao (2004), i.e. ^ j 6= j (see
Table D.8 in the Appendix) 9 . Additionally, not all the elements compiled in the
chemical composition were taken into account (Grigor'ev considers 56 elements, as
opposed to the 78 included in Rudnick and Gao (2004)). This is because many
elements that are missing in Gri gor'ev's analysis, are minor elements that do not
9 In table D.8, the values are expressed in g of substance per g of crust, since this is the usual
way of expressing the chemical composition of the crust. This means that j is multiplied by the
molecular weight of the substance MW j .
 
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