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Diamond potential estimation based on kimberlite
major element chemistry
V.B. Vasilenko
a,
*, N.N. Zinchuk
b
, V.O. Krasavchikov
c
, L.G. Kuznetsova
a
,
V.V. Khlestov
a
, N.I. Volkova
a
a
Institute of Mineralogy and Petrography, SB RAS, Koptuyg Ave. 3, Novosibirsk 630090, Russia
b
Yakutian Joint-Stock Company ‘‘Alrosa’’, Lenin Ave. 6, Mirnyi 678170, Russia
c
Institute of Oil and Gas, SB RAS, Koptyug Ave. 3, Novosibirsk 630090, Russia
Received 16 March 2001; accepted 2 May 2002
Abstract
A strong correlation between the chemical composition of kimberlites and their diamond grade has been established using
statistical methods. The investigation is based upon major element analyses of kimberlite samples, from which xenoliths have
been removed. The samples represent highly diamondiferous, moderately diamondiferous, slightly diamondiferous and
diamond-free rocks from diatremes of the Yakutian Kimberlite Province. In total, the investigation comprises 3792 whole-rock
analyses and 1176 determinations of diamond grade. By means of correlation analysis, the kimberlite chemical analyses were
subdivided into 113 clusters. Regression analysis was carried out between mean major element oxide concentrations of the
clusters and the corresponding average values of diamond contents. The combined use of the regression method with a break-
point and generalized nonlinear discrimination analysis has allowed to correctly estimate the average diamond grade of
kimberlite clusters in more than 85–90% of the cases. The established statistical relations are convincingly justified from a
petrological point of view. The reliable petrochemical description of kimberlite variety, based on averaging 25– 30 whole-rock
analyses or on analyzing of a sample obtained as a result of sequential quartering of a much larger sample, allows to estimate
safely its diamond grade using major oxide contents. The method has worldwide application potential.
D2002 Elsevier Science B.V. All rights reserved.
Keywords: Kimberlite; Diamond grade; Whole-rock composition; Diamond; Exploration; Yakutia
1. Introduction
The relation between diamond grade of kimberlites
and their chemical composition has been widely
discussed. The pessimistic view traditionally consid-
ers kimberlites as hybrid rocks containing variable
amounts of mantle and crust xenoliths of rocks and
minerals. Accordingly, the bulk chemical composition
of kimberlites with enclosed xenoliths does not rep-
resent the composition of the protokimberlitic melts;
neither is there a relation with respect to the degree of
their saturation with xenogenic diamonds (Dawson,
1980; Mitchell, 1986). It is difficult to disagree with
this description of the problem, and most investigators
of kimberlites hold this opinion, thereby ignoring that
0375-6742/02/$ - see front matter D2002 Elsevier Science B.V. All rights reserved.
PII: S 0375-6742(02)00219-4
*
Corresponding author.
E-mail address: titan@uiggm.nsc.ru (V.B. Vasilenko).
www.elsevier.com/locate/jgeoexp
Journal of Geochemical Exploration 76 (2002) 93– 112
petrochemical evolution of kimberlite melts does take
place.
However, if the influence of xenolith material,
represented by sedimentary and igneous rock frag-
ments from crust and metamorphic rocks from crys-
talline basement, on the kimberlite bulk composition
can be eliminated, the petrochemical evolution trends
of these rocks become more clear (Smith et al., 1979;
Vasilenko et al., 1994, 1997). These trends are partly
reflected in regular character of evolution of compo-
sition of some kimberlite indicator minerals, for
example, picroilmenites (Griffin et al., 1997) and in
specific features of some principal kimberlite minerals
including olivine microphenocrysts detected in the
groundmass of freshest kimberlites and lamproites
and containing high-temperature fluid and melt inclu-
sions (Sobolev et al., 1989). Consequently, a relation
between diamond contents in kimberlites and whole-
rock composition may exist.
Earlier, the only successful approach to estimate a
diamond grade of kimberlites was initiated using the
unusual compositional features of some part of prin-
cipal indicator minerals: pyrope and chromespinel.
These features include a low Ca content of some Cr-
rich garnets and Cr enrichment of chromespinels
included in diamonds worldwide (Meyer, 1968;
Meyer and Boyd, 1972; Sobolev et al., 1969a,b,
1975). Unusual low Ca contents along with high Cr
contents of these garnets were explained by para-
genesis lacking clinopyroxene (U.S. Sobolev et al.,
1969a,b). The find of such garnets separately from
diamonds in xenoliths of diamondiferous pyrope
serpentinites (U.S. Sobolev et al., 1969a,b) was a very
important to predict their abundance in concentrates
of diamondiferous kimberlites and to draw the first
Ca–Cr plot for garnets with a specifying a special
lherzolitic trend for the purpose to estimate a diamond
grade using the proportion of subcalcic Cr-rich harz-
burgitic garnets in kimberlites (Sobolev, 1971). This
particular paper was referred to by Lawless (1974) at
his studies of garnet concentrates from South African
kimberlites and number of macrocrysts and even
megacrysts of harzburgitic garnets were subsequently
detected in concentrates of South African and Siberian
kimberlites (Boyd and Dawson, 1972; Gurney and
Switzer, 1973; Sobolev et al., 1973).
Subsequent statistical studies of garnets from kim-
berlites confirmed unusual compositional features of
harzburgitic garnets presenting as group 10 (G 10)
garnets (Dawson and Stephens, 1975). This group,
however, included not only garnets, formed within the
diamond stability field (e.g. Doroshev et al., 1997),
but also garnets from graphite harzburgites. These
mixed, graphite and diamond harzburgite garnets were
used for estimation of diamond grade of South Afri-
can and some other kimberlites (Gurney, 1984; Gur-
ney and Zweistra, 1995). For Siberian kimberlites, the
majority of garnets and chromites typical of diamond-
iferous harzburgites and diamond inclusions were
used for the same purpose (Sobolev, 1984).
It is important to note that isotopic dating of
diamond inclusions, summarized by Pearson and
Shirey (1999), and data on inhomogeneous Sr distri-
bution in garnets included in diamonds (Shimizu and
Sobolev, 1995; Shimizu et al., 1997) show a broad
range of the ages of diamonds including those close to
kimberlite emplacement ages. This means, that at least
a part of diamonds similarly to part of indicator
minerals may be closely related to kimberlite evolu-
tion (Sobolev, 1960).
Attempts to reveal relations between the chemical
composition of kimberlites and their diamond grade
have been undertaken by many researchers. Thus, the
K
2
O/Na
2
O ratio (Krutoyarsky et al., 1959),the
increased contents of Cr and Mg and the decreased
contents of Ti, Fe, Al (Blagulkina, 1969) were
regarded as indicators of the diamond potential of
kimberlites. Milashev (1965, 1972) proposed that the
diamond grade (DG) of kimberlites could be esti-
mated from the rock composition using formula (1):
DG ¼Fe : Ti
logðFe þTiÞþ1=2logðAl þKþNaÞð1Þ
Vasilenko and Kuznetsova (1986) and Vasilenko et
al. (1994, 1997) used nonlinear discriminant analysis
(Vasilenko et al., 1984) of pairs and multiple regres-
sion analysis to show that the relation between rock
chemistry and diamond contents of kimberlites for
different diatremes in the Yakutian Kimberlite Prov-
ince (NE Siberia) could be established with high
accuracy. However, the correlation significance (with
pairs and multiple correlation coefficients < 0.7) was
insufficient for obtaining reliable estimates of the
diamond grade, because this relation differs from
simple functional dependence. This fact explains
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–11294
Fig. 1. Location of diatremes in the Yakutian Kimberlite Province (NE Siberia). (1) Internatsionalnaya, (2) Mir, (3) Aikhal, (4) Yubileinaya, (5)
Sytykanskaya, (6) Molodost, (7) Vostok, (8) Snezhinka, (9) Udachaya (West and East), (10) Leningradskaya, (11) Yakutskaya.
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112 95
Table 1
Average compositions of clusters of Yakutian kimberlites
No SiO
2
TiO
2
Al
2
O
3
Fe
2
O
3
(tot) MgO CaO Na
2
OK
2
OP
2
O
5
LOI A(ct/10 t) V
a
1 25.52 0.52 2.04 5.23 26.20 12.21 0.37 0.61 0.83 23.86 86.0 41.1
2 26.09 0.73 2.78 5.40 22.19 16.01 0.28 1.22 1.03 22.40 56.6 47.5
3 28.67 0.46 8.51 6.91 28.66 2.03 0.40 1.09 0.15 13.72 52.0 57.7
4 25.39 0.56 2.17 5.06 28.06 13.53 0.02 0.71 0.85 23.68 48.7 68.0
5 26.70 0.27 2.04 3.88 28.75 12.06 0.08 0.38 0.34 25.09 42.3 72.7
6 21.52 0.31 2.16 3.32 22.26 20.72 0.03 0.54 0.40 29.09 41.6 44.4
7 26.20 0.38 2.73 3.90 24.63 13.92 0.07 1.16 0.51 25.73 34.4 74.5
8 20.02 0.56 2.27 4.23 23.48 19.59 0.03 0.78 0.90 28.00 30.9 93.3
9 14.23 0.36 2.59 3.16 20.89 21.96 0.14 1.52 0.65 33.93 26.7 59.5
10 24.02 0.36 3.55 3.57 21.64 16.24 0.30 2.72 0.53 24.64 23.7 83.5
11 13.83 0.52 1.91 4.17 11.20 33.05 0.14 0.76 0.99 33.32 23.0 73.5
12 30.96 0.41 2.16 5.22 29.85 8.03 0.56 0.81 0.48 21.79 52.3 82.0
13 29.78 0.39 2.14 7.35 30.02 7.89 0.39 0.40 0.42 21.47 41.9 76.1
14 28.54 0.52 1.70 7.47 25.51 12.33 0.37 0.66 0.75 22.48 41.6 47.2
15 41.70 0.33 4.21 5.63 23.53 8.00 0.32 0.74 0.30 15.49 41.2 78.1
16 38.67 0.82 3.45 5.73 22.91 10.65 0.21 0.79 0.30 16.75 32.9 80.1
17 42.29 0.39 4.67 5.21 19.73 8.40 0.22 1.40 0.32 17.61 21.3 82.7
18 30.40 0.45 3.34 6.01 15.26 19.30 0.16 0.49 0.43 24.32 19.1 63.1
19 39.11 0.96 3.68 7.25 25.37 7.26 0.28 0.87 0.30 14.89 33.8 36.4
20 30.14 1.10 2.63 7.81 20.90 13.18 0.15 0.49 0.25 22.28 28.3 38.3
21 37.67 0.98 2.99 7.86 28.86 6.00 0.14 2.41 0.27 13.16 27.9 61.6
22 31.03 1.30 2.52 5.65 27.62 12.18 0.16 0.96 0.53 17.76 27.3 74.5
23 31.34 1.62 2.11 8.62 28.65 6.63 2.21 1.26 0.37 17.64 27.1 106.5
24 31.79 2.33 2.11 9.59 29.57 6.57 0.20 0.43 0.36 17.34 27.0 85.9
25 35.09 0.88 4.32 6.73 22.18 10.52 0.35 1.34 0.36 17.78 26.7 20.0
26 35.32 1.16 2.77 8.70 26.53 6.76 0.18 0.54 0.22 17.72 26.7 67.5
27 35.54 1.51 2.00 8.75 29.74 5.43 0.24 0.37 0.24 16.47 21.9 33.5
28 30.33 1.60 2.32 8.86 26.66 9.55 0.10 0.33 0.27 19.81 20.7 51.8
29 21.10 1.21 2.77 8.42 14.49 19.80 0.11 0.43 0.27 26.51 20.6 48.4
30 32.82 0.65 2.19 11.66 25.95 7.70 0.09 0.41 0.19 18.05 20.5 39.4
31 37.00 0.17 0.70 8.35 35.58 1.62 0.12 0.14 0.06 16.56 20.3 15.6
32 32.99 1.64 1.80 6.82 31.22 7.53 0.15 0.26 0.31 17.54 18.1 104.6
33 36.22 1.29 2.78 8.71 29.40 6.31 0.27 1.37 0.25 13.79 17.7 68.4
34 27.87 1.65 2.01 8.99 27.58 9.56 0.68 1.08 0.66 20.29 16.9 67.7
35 27.54 1.69 1.89 9.91 29.32 9.55 0.18 0.78 0.55 18.86 15.7 109.8
36 30.75 1.51 1.99 9.25 30.57 7.12 0.25 0.69 0.36 17.77 15.0 62.0
37 32.64 0.84 2.06 7.21 35.00 4.40 0.19 0.46 0.20 17.25 15.7 5.2
38 26.70 0.79 2.15 9.19 27.31 12.70 0.11 0.46 0.34 20.48 14.9 16.7
39 30.73 0.42 2.05 7.58 32.07 7.86 0.19 0.40 0.46 18.46 26.7 144.8
40 26.88 2.39 2.09 10.50 29.97 10.33 0.13 0.67 0.69 18.74 13.0 105.5
41 26.82 1.31 2.24 6.44 24.07 15.03 0.09 0.77 0.70 21.13 12.6 60.9
42 38.23 0.85 3.02 6.96 24.08 7.28 1.96 1.83 0.25 15.96 12.5 9.9
43 34.14 1.02 2.71 6.92 29.56 6.98 0.20 0.52 0.33 17.47 11.9 86.7
44 31.11 1.07 2.74 7.66 27.27 11.32 0.08 1.53 0.49 16.47 6.3 37.8
45 29.77 1.72 2.09 8.64 30.39 8.00 0.20 0.16 0.25 18.30 12.0 159.3
46 30.95 1.39 1.69 8.21 29.85 8.64 0.08 0.12 0.16 17.45 9.8 255.6
47 28.10 1.59 1.29 8.18 25.85 13.75 0.10 0.12 0.15 20.25 8.8 231.1
48 30.04 1.84 2.23 8.12 30.00 8.57 0.09 0.18 0.23 18.32 8.3 338.5
49 24.25 1.61 1.58 8.34 21.42 18.44 0.14 0.14 0.10 23.36 6.2 105.9
50 29.53 2.54 3.07 8.69 28.33 8.87 0.13 0.43 0.61 20.79 5.8 113.9
51 28.00 2.84 2.12 8.18 26.37 12.39 0.10 0.16 0.19 21.41 5.7 141.9
52 27.64 2.78 2.85 7.79 26.63 11.46 0.13 0.33 0.48 22.12 5.6 105.8
53 26.41 1.99 1.87 8.52 28.97 11.40 0.11 0.49 0.47 19.99 12.6 49.6
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–11296
No SiO
2
TiO
2
Al
2
O
3
Fe
2
O
3
(tot) MgO CaO Na
2
OK
2
OP
2
O
5
LOI A(ct/10 t) V
a
54 27.22 1.29 1.86 8.45 30.02 10.75 0.09 0.36 0.34 19.82 10.7 90.0
55 28.86 1.45 1.95 8.86 32.30 8.33 0.13 0.57 0.40 17.17 10.5 58.8
56 24.23 1.30 1.85 6.85 25.20 16.80 0.09 0.34 0.40 23.10 9.2 43.4
57 23.99 0.98 2.30 5.45 25.78 16.14 0.10 0.62 0.30 24.28 8.5 81.9
58 26.05 1.17 1.99 8.50 30.35 11.40 0.10 0.42 0.47 20.19 8.0 53.0
59 27.73 0.98 1.96 5.96 29.19 12.38 0.09 0.35 0.34 21.16 7.1 42.0
60 27.53 1.11 2.26 8.00 30.60 10.97 0.08 0.40 0.02 19.22 6.7 50.5
61 23.51 0.28 3.55 1.23 7.17 32.83 0.42 2.08 0.11 28.92 6.5 54.3
62 26.26 1.09 2.20 7.49 27.82 12.16 0.35 0.91 0.36 19.17 6.3 60.1
63 25.87 1.00 2.37 6.07 24.94 16.03 0.17 1.23 0.38 22.42 13.4 48.8
64 26.63 1.15 2.16 6.71 27.54 13.24 0.13 0.48 0.34 21.83 13.4 70.7
65 27.43 0.67 2.30 6.19 27.35 12.99 0.13 0.44 0.25 22.42 13.2 80.4
66 28.46 0.89 2.20 5.79 28.26 12.63 0.12 0.46 0.32 21.07 12.9 65.0
67 27.04 0.89 2.51 7.10 26.82 13.67 0.11 0.65 0.55 20.81 11.1 44.9
68 28.56 1.38 2.04 8.90 32.62 9.63 0.20 0.83 0.41 15.81 9.7 77.3
69 25.20 0.75 2.28 5.44 23.96 16.45 0.15 0.63 0.27 25.01 8.1 72.6
70 23.73 0.73 2.69 5.85 22.60 16.98 0.42 2.08 0.35 24.93 7.4 48.8
71 21.94 0.73 2.63 5.10 19.55 20.70 0.23 1.20 0.28 27.69 7.1 86.2
72 18.20 0.70 1.69 5.90 12.73 29.88 0.09 0.27 0.39 30.27 9.1 144.8
73 26.03 0.72 3.02 5.25 18.79 20.35 0.12 0.65 0.29 25.18 6.5 217.0
74 33.05 0.67 2.00 6.54 32.53 6.93 0.07 0.28 0.27 17.93 6.1 102.0
75 30.02 0.86 1.25 8.36 32.32 6.97 0.10 0.20 0.22 20.02 5.9 122.8
76 29.58 1.09 1.40 7.53 33.34 6.64 0.06 0.20 0.35 19.97 5.8 120.8
77 30.18 1.02 2.84 6.85 29.86 9.11 0.10 0.30 0.44 19.25 5.7 121.9
78 30.22 1.84 0.97 7.74 29.40 10.19 0.07 0.15 0.24 18.37 4.8 83.7
79 26.17 1.61 1.95 8.21 25.46 14.50 0.11 0.13 0.23 21.60 4.3 101.6
80 28.47 1.89 2.37 7.97 26.03 12.22 0.14 0.37 0.41 21.39 2.9 150.5
81 19.04 0.76 1.17 5.42 16.54 27.76 0.19 0.14 0.15 29.58 2.7 3.0
82 30.35 1.32 2.33 6.52 30.60 9.52 0.42 0.12 0.30 18.05 2.6 150.4
83 31.50 1.91 1.69 9.08 34.55 3.14 0.06 0.21 0.28 14.69 2.6 149.8
84 25.73 2.07 2.42 7.50 18.07 19.82 0.14 0.23 0.23 23.18 2.6 107.0
85 29.42 2.76 2.16 9.48 33.10 3.95 0.09 0.27 0.27 17.15 2.0 153.0
86 19.93 1.49 2.36 6.29 11.94 26.86 0.20 0.35 0.23 30.40 1.7 168.8
87 30.39 2.13 2.09 9.30 34.07 3.13 0.09 0.41 0.34 15.58 1.4 214.8
88 36.79 0.23 1.28 6.47 37.03 1.13 0.07 0.10 0.10 11.60 0.7 98.6
89 25.08 1.15 2.24 6.13 20.54 19.00 0.19 0.58 0.28 25.79 0.5 100.0
90 28.26 2.48 3.92 8.08 26.04 10.43 0.21 0.84 0.84 24.62 0.0 12.3
91 28.06 1.65 2.10 7.51 37.06 12.35 0.07 1.18 0.56 19.73 1.0 96.5
92 24.10 1.18 2.16 6.47 25.58 16.95 0.27 1.19 0.34 22.02 4.0 36.9
93 28.92 1.20 1.56 7.88 31.94 7.57 0.45 0.32 0.49 19.57 4.1 102.8
94 28.59 1.27 1.57 8.57 33.28 6.48 0.09 0.28 0.46 19.55 3.9 63.2
95 26.89 1.36 2.14 6.82 22.54 16.48 0.08 0.32 0.50 22.88 3.4 148.5
96 30.04 1.27 1.68 5.75 30.43 10.22 0.07 0.27 0.44 20.03 3.3 85.4
97 30.32 1.55 1.83 7.95 32.36 6.49 0.12 0.32 0.60 18.81 3.0 97.3
98 26.90 0.97 1.52 6.23 26.75 14.80 0.05 0.22 0.38 22.44 2.9 85.5
99 23.05 1.08 2.62 6.53 17.46 23.68 0.12 0.41 0.78 24.52 2.8 63.9
100 26.38 0.75 1.73 5.79 22.72 18.28 0.11 0.24 0.23 24.04 2.7 82.1
101 24.36 0.92 1.57 8.24 20.33 19.01 0.12 0.27 0.36 25.12 1.8 163.0
102 19.35 0.68 2.76 4.39 16.80 26.36 0.14 0.29 0.24 29.24 1.4 78.0
103 22.49 1.22 2.14 5.17 19.11 23.00 0.12 0.35 0.42 26.28 1.2 134.9
104 15.09 1.14 2.57 4.92 8.25 34.66 0.09 0.42 0.65 32.41 0.0 118.1
105 26.83 2.06 2.79 7.09 27.48 13.41 0.07 0.27 0.55 19.31 0.2 200.0
106 27.37 1.61 2.55 5.00 26.45 14.39 0.00 0.19 0.63 21.43 1.0 213.4
Table 1 (continued)
(continued on next page)
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112 97
why until now, there are no effective and reliable
methods of predicting diamond grade of kimberlites,
based on their chemical composition.
The purpose of the present work is to present a new
method for predicting diamond grade of kimberlites
using their whole-rock compositions, which is based
on the use of more efficient nonlinear statistical
algorithms than used previously. Also, the number
of observations is expanded compared to previous
work (Vasilenko and Kuznetsova, 1986; Vasilenko et
al., 1997, 2000b).
2. Area of investigation
The chemical composition and diamond grade
(parameter A) of commercial kimberlites from the
Yakutian pipes (i.e. Internatsionalnaya, Mir, Uda-
chaya-West, Udachnaya-East, Aikhal, Yubileinaya,
Sytykanskaya) (Fig. 1) and diamondiferous, but non-
economic kimberlites from the diatremes Leningrad-
skaya, Snezhinka, Molodost, Yakutskaya, Vostok,
were investigated in this work.
Detailed descriptions of the geology, petrochemis-
try and mineralogy of kimberlites from these diat-
remes are given by Kharkiv et al. (1991),Zinchuk et
al. (1993),Vasilenko et al. (1994, 1997).
3. Analytical methods
The petrochemical database used in the present
work comprises major element analyses of 3792
kimberlite samples, and information on diamond
grade from 1176 samples expressed in carat/10 tons
(ct/10 t). The selected samples are representative of
different types of kimberlites, filling diatremes and
cementing various kimberlite breccia.
The diamond grade of the kimberlites was deter-
mined by processing 10-m core intervals weighing
> 300 kg from prospecting drill holes. Samples for
major element analysis were derived from 2-m inter-
vals of core weighing >60 kg and separate lump
samples. Thus, the diamond grade was determined
in larger samples than analyzed for major element
contents from the same core.
Samples for whole-rock chemistry were crushed
into pieces, 0.5–2 mm in size, and then the amount
was reduced by quartering to 20 g. Prior to grinding,
the rock fragments were examined under binocular
microscope and xenolith fragments of upper mantle
and crustal rocks were removed.
The whole-rock chemistry was determined by X-
ray fluorescence analyses (XRF) at the Institute of
Mineralogy and Petrography, Novosibirsk, Russia,
using a VRA-20R spectrometer (Carl Zeiss, Jena).
The international standard rock samples (gabbro
SGD-1A; Roelandts, 1989) was used as a reference
material. The accuracy of the results was verified by
replicate analyses of standard sample MU-4 (kimber-
lite) for every eight analyzed samples. The analyses
were accepted reliable, if standard major element con-
centrations did not differ from certified values with a
probability of 95% for each oxide. The concentrations
of major oxides were calculated according to Afonin et
al. (1984). The lower detection limits for MgO and
Na
2
O were 0.1–0.2 wt.%. For the other oxides, they
vary from 0.02 to 0.05 wt.%. Each batch of 100
kimberlite samples was accompanied by 5 – 10 dupli-
cate analyses. The analytical results were accepted as
reliable, if the errors of reproducibility did not exceed
those for ordinary silicate analysis (Ostroumov, 1979).
No SiO
2
TiO
2
Al
2
O
3
Fe
2
O
3
(tot) MgO CaO Na
2
OK
2
OP
2
O
5
LOI A(ct/10 t) V
a
107 25.64 1.44 3.68 6.48 23.98 16.59 0.03 0.72 0.67 21.12 0.7 178.5
108 30.35 2.01 2.86 9.36 31.99 5.79 0.09 0.94 0.60 15.66 0.4 221.8
109 28.85 1.75 2.91 8.50 28.87 9.25 0.02 0.50 0.61 18.71 0.3 201.9
110 25.17 1.45 3.80 5.70 20.67 19.50 0.04 1.72 0.70 21.45 0.0 181.3
111 32.78 1.28 3.26 7.22 30.15 7.83 0.01 0.77 0.45 16.20 1.2 235.1
112 28.03 1.13 2.95 6.07 25.44 15.11 0.12 0.42 0.45 19.57 0.1 211.3
113 29.46 1.49 2.68 7.24 28.64 11.03 0.02 0.16 0.34 19.20 0.0 233.3
Average compositions 1– 39 are related to set I, 40 – 77 to subset II
1
and 78 – 113 to subset II
2
.
a
Variation coefficient of diamond grade (V=s/x, where sis standard deviation, xis average value).
Table 1 (continued)
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–11298
All the obtained chemical analyses of kimberlites
for each diatreme were divided by means of statistical
cluster analysis into a few clusters characterizing the
main petrochemical varieties of the studied diatremes.
Clusters lacking information on diamond grade were
discarded. In total, 113 clusters, representing 3792
analyses, were finally accepted. The cluster analysis
was performed using software from the SAS Institute
(USA; i.e. SAS STAT and PROC FASTCLUS).
The mean concentrations of major element oxides
for each cluster together with their average diamond
content are listed in Tab le 1, and the frequency
Fig. 2. Empirical frequency distributions of mean major element contents in 113 clusters. n= frequency; n
X
¯¯
= the number of analyses in clusters.
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112 99
distribution of element concentrations of the cluster
means are shown in Fig. 2.
4. Analysis of correlation between diamond grade
and kimberlite chemistry
Nonlinear pair regressions (Vasilenko et al., 1982)
have shown that significant correlation only exists
between diamond content and some major element
concentrations (Table 2). However, this correlation is
still insufficient to use it as a tool in diamond
exploration.
Linear multivariate regression, using all oxides in
the correlation with the diamond contents of kimber-
lites (Table 3), has considerably reduced the influence
of randomness, whereby the multivariate correlation
coefficient increases to 0.7. Nevertheless, this depend-
ence is still insufficient for prediction purposes.
The results of a previous investigation, using linear
multivariate regression (also considering all the
oxides) of 50 clusters including 839 rock analyses
and diamond contents (Vasilenko et al., 1997), were
very similar to the results presented in Tab le 3.
Therefore, the increase in the number of cases has
not resulted in more reliable estimations of the dia-
mond grade of kimberlites. Apparently, the linear
multivariate regression is insufficiently effective
under the conditions of a polymodal distribution of
parameter A(Fig. 3).
With the aim to reduce random errors, nonlinear
multivariate regression methods were applied. The
highest correlation between the determined and the
Table 2
The parameters of pair regression equations A(ct/10 t) = a+bx +cx
2
+dx
3
Function Argument ni Parameters
ab c d
ATiO
2
113 0.52 + 37.786 29.397 +6.262 –
ANa
2
O 113 0.38 + 4.995 + 62.642 26.189 –
AK
2
O 113 0.40 6.855 + 72.459 56.536 + 12.599
AP
2
O
5
113 0.35 + 6.834 + 64.285 188.704 + 165.600
xis the concentration of a certain oxide, nis the number of clusters and iis the determination coefficient.
Table 3
The parameters of the multiple regression equation
n= 113, r= 0.7 Parameters
of equation
S.E. Criterion
of nonzero
Probability
of nonzero
Absolute term 198.75 92.89 2.14 0.03
SiO
2
1.21 0.98 1.24 0.22
Al
2
O
3
0.80 1.78 0.45 0.65
Fe
2
O
3
(tot) 2.17 1.37 1.58 0.12
TiO
2
10.73 2.20 4.88 < 0.01
MgO 3.18 1.05 3.04 < 0.01
CaO 4.56 1.12 4.07 < 0.01
P
2
O
5
23.98 6.01 3.99 < 0.01
Na
2
O 2.98 4.26 0.70 0.49
K
2
O2.64 2.90 0.91 0.36
LOI 0.57 1.01 0.57 0.57
nis the number of clusters, ris the correlation coefficient.
Fig. 3. Empirical frequency distributions of diamond grade
(parameter A) in 113 distinguished clusters. (1) A< 14.1 ct/10 t
(n= 74), (2) A>14.1 ct/10 t (n= 39).
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112100
calculated values of diamond grade was obtained
using a method of piecewise-linear (break-point)
regression, which was realized by us on the same
pattern as in Statistica for Windows. The mean com-
positions of the clusters were preliminarily standar-
dized by the software package. The break-point was
determined by the program using the Quasi-Newton
method of estimation (Bates and Watts, 1988; Kaha-
ner et al., 1989).
Parameters of the piecewise-linear model for esti-
mating the diamond contents in kimberlites with a
break-point of 14.1 ct/10 t for the 113 cluster means
are given in the Eqs. (2) and (3):
A¼5:473 þ3:824 SiO20:418 TiO2
0:618 Al2O3þ2:501 Fe2O3ðtotÞ
þ6:187 MgO þ6:721 CaO þ1:019 Na2O
þ1:689 K2O0:751 P2O5þ3:064 LOI; for
A>14:1ct=10 t; ð2Þ
A¼23:160 24:893 SiO27:037 TiO2
1:677 Al2O313:309 Fe2O3ðtotÞ
28:039 MgO 44:577 CaO
þ0:361 Na2O7:533 K2O
þ7:578 P2O520:875 LOI; for
A<14:1ct=10 t:ð3Þ
The correspondence between determined and cal-
culated values of diamond grade (parameter A)is
shown in Fig. 4. The correlation coefficient is 0.83
for the case A>14.1 ct/10 t, 0.48 for the case A< 14.1
ct/10 t and 0.93 for the total set of 113 clusters at
significance level >99%.
When using the piecewise-linear model, the main
difficulty is a choice between the two linear functions,
e.g. between the Eqs. (2) and (3). For this purpose, we
have applied the universal nonlinear discriminator
(Vasilenko et al., 1984), which is a special nonlinear
procedure realized in the author’s software program
package Visual Analysis of Data and Initial Classifi-
Fig. 4. Correlation between determined and calculated values of parameter Ausing piecewise-linear regression with break-point 14.1 ct/10 t for
the Yakutian kimberlites.
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112 101
cation (VADIC). The used algorithm represents our
adaptation of the known Rosenblatt – Parzen’ method
(Rosenblatt, 1956; Parzen, 1962; Devroye and Gyorfi,
1985) of nonparametric estimation of a probability
density function, which was developed by us for multi-
variate distributions. It should be noted that the choice
of a metrical tensor for the corresponding multivariate
space and of radius of averaging kernel is carried out
using a special minimax estimation of likelihood
function, providing the greatest stability of results.
The mean whole-rock compositions of the 113
clusters were divided into two sets: I containing
clusters with A>14.1 ct/10 t, and II with A< 14.1 ct/
10 t. Then, using Vasilenko’s universal nonlinear
discriminator, the control partition of the sampling
into the same two sets was carried out, which showed
that 97.5% of the highly diamondiferous kimberlites
were identified correctly (Fig. 5).
One can see that the linear discriminator (the
distribution of figured points along y-axis) gives
considerable overlap of the compared subsets with a
rather high rate of ambiguous solutions as a result,
whereas the nonlinear discriminator (the distribution
of figured points along x-axis) provides an almost
error-free result. The zero points at the axes in Fig. 5
correspond to dividing borders.
As shown in Fig. 4, the relative prediction error is
much higher when predicting low diamond values,
than for the high values.
The distribution of diamond contents with A< 14.1
ct/10 t is a clearly polymodal distribution. Therefore,
the question arose whether the estimates of low
diamond contents also can be improved by the method
of piecewise-linear regression. In Fig. 6, the corre-
spondence between the determined and the predicted
values calculated by means of piecewise-linear regres-
Fig. 5. Average composition of clusters for sets I and II in the diagram of values of linear (D
I/II
) and nonlinear [log( f
I
/f
II
)] discriminators.
f
I
= probability density in set I; f
II
= probability density in set II. D
I/II
=5.523 + 0.004 SiO
2
+0.369 TiO
2
+0.108 Al
2
O
3
0.013
Fe
2
O
3
(tot) + 0.152 MgO + 0.178 CaO + 0.544 Na
2
O0.142 K
2
O0.692 P
2
O
5
0.047 LOI.
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112102
sion for clusters with diamond contents less than 14.1
ct/10 t is shown. As can be seen, the correlation is
considerably improved.
The parameters of piecewise-linear regression for
the data set with diamond contents A< 14.1 ct/10 t are
given in the Eqs. (4) and (5):
A¼1:682 þ2:160 SiO2þ0:474 TiO2
1:118 Al2O3þ0:977 Fe2O3ðtotÞ
þ2:849 MgO þ4:153 CaO
þ1:001 Na2Oþ0:135 K2O
þ0:047 P2O5þ0:708 LOI;
for 5:5<A<14:1ct=10 t; ð4Þ
A¼9:208 2:728 SiO20:401 TiO2
0:972 Al2O31:170 Fe2O3ðtotÞ
1:652 MgO 1:388 CaO
þ1:016 Na2O0:801 K2O
þ1:349 P2O53:281 LOI;
for A<5:5ct=10 t:ð5Þ
When using Eq. (4), the correlation coefficient
between determined and calculated values of param-
eter Ais 0.80 (n= 38). The correlation coefficient for
set II as a whole (A< 14.1 ct/10 t) is already equal to
0.90, and the reduced index of correlation by quad-
ratic regression is equal to 0.95. The value of break-
point 5.5 ct/10 t, as would be expected, corresponds to
a gap between the dense clusters of points in the
regression curve (see Fig. 6) and to a minimum in the
frequency curve of parameter A(see Fig. 3).
In this case, the choice of the linear function in the
model of piecewise-linear regression for the prognosis
of diamond content can be made with using the
universal nonlinear discriminator. The control parti-
tioning of set II with diamond contents A< 14.1 ct/10 t
into subsets: II
1
(5.5 ct/10 t < A< 14.1 ct/10 t) and II
2
(A< 5.5 ct/10 t) is shown in Fig. 7. Here the universal
nonlinear discriminator allowed to distinguish 100%
of the values of both subsets. It is noteworthy that the
use of the universal nonlinear discriminator for iden-
tification reduces the probability of the decision er-
ror by 10–20% in comparison with algorithms of
linear discrimination.
When calculating estimates of diamond abundance
for kimberlites belonging to set II, it is sufficient to
determine whether the mean composition belongs to
Fig. 6. Correlation between determined and calculated values of parameter Ausing piecewise-linear regression with break-point 5.5 ct/10 t for
the Yakutian kimberlites with A< 14.1 ct/10 t.
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112 103
subsets II
1
or II
2
. This can be obtained using the
universal nonlinear discriminator with a probability
>95%.
5. Practical recommendations
Necessary conditions for the successful application
of the proposed method are the correct selection and
the correct petrochemical description of an object
under examination. Such object can be a block of
rather uniform kimberlite weighing c1 t from which
the 25–30 samples for XRF analysis are collected in a
random way. The obtained major element analyses are
examined for homogeneity. The mean whole-rock
composition of the object under study should be
related to kimberlite type and should fall into the rock
composition field, used in the present work. Whether
the object under examination belongs to the kimberlite
rock type can be tested using the criterion proposed by
Vasilenko et al. (2000c). Comparison of chemical rock
composition under examination with the average
compositions of the clusters in Table 1 can be made
by plotting of determined mean contents of major
oxides in polygons in Fig. 2. If the plotted points of
major element contents of a studied kimberlite fall
within the polygons, this rock is related to one of the
predefined clusters.
The main stage of diamond potential estimation is
the attribution of the chemical composition under
examination to one of subsets I, II
1
or II
2
. For any
average chemical composition to be assigned to one
of sets I or II, the probability densities f
I
and f
II
are
calculated for it (a description of an algorithm is given
in Appendix A). If f
I
>f
II
, the composition under
examination is assigned to set I; otherwise, it falls
into set II. In the latter case, f
II1
and f
II2
values are
calculated, and depending on their ratio, a conclusion
can be drawn regarding to which subset II
1
or II
2
this
kimberlite belongs.
ThedecisiontowhichsubsetI,II
1
or II
2
the
examined composition belongs is an important dia-
mond grade estimate, which can be refined for subset
I using Eq. (2), for subset II
1
using Eq. (4), and for
subset II
2
using Eq. (5). The proposed method can be
improved by increasing the number of chemical
Fig. 7. Average compositions of clusters for subsets II
1
and II
2
in the diagram of values of linear (D
II1/II2
) and nonlinear [log( f
II1
/f
II2
)]
discriminators. f
II1
= probability density in subset II
1
;f
II2
= probability density in subset II
2
.D
II1/II2
= 11.04 0.084 SiO
2
+ 0.103 TiO
2
0.061
Al
2
O
3
0.203 Fe
2
O
3
(tot) 0.129 MgO 0.097 CaO + 0.223 Na
2
O0.436 K
2
O + 0.809 P
2
O
5
0.132 LOI.
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112104
analyses of kimberlites and their diamond grade in
Table 1 and by improving the computing algorithms.
For the practical realization, we have created a special
software package.
6. Discussion
Statistical solutions of the problem of diamond
potential estimation based on kimberlite chemical
compositions have two major restrictions: (1) a prob-
ability of obtaining of an erroneous result, and (2) a
prohibition of extrapolation of the obtained results to
objects, not involved into the statistical set.
In the discussed case, the first restriction can be
eliminated, if the calculated correlations between oxide
contents of the analyzed rocks and diamond grade
correspond to variation in formation conditions of these
rocks and can be verified by independent methods.
Oxides of K, Na, Ti, Ca and Mg are of major impor-
tance for the estimation of diamond potential. In the
calculation results of pair nonlinear regressions, such
significant correlations were established for oxides of
K, Na, Ti, and Ca. Additionally, factors of these oxides
in the calculations of linear multivariate functions are
the most reliable. Comparison of the average compo-
sitions of sets I, II
1
and II
2
suggests that the contents of
K
2
O, Na
2
O and MgO increase and the contents of TiO
2
and CaO decrease with increasing diamond grade
(Table 4).
Consequently, the behavior of K
2
O, Na
2
O, MgO,
TiO
2
and CaO and distribution of diamond grade in
the studied sets (Fig. 3), should be evaluated against
kimberlite petrology. Justification is conveniently
performed by using the generalized petrochemical
model of genetic kimberlite types (Vasilenko et al.,
1997), developed for the Yakutian Kimberlite Prov-
ince. Here verification of the model is done by data
derived from thermodynamic experiments. Accord-
ing to this model, the petrochemical diversity of
kimberlites is determined by the depth of kimberlite
melt generation, the temperature of magmatic
source, the composition of magma-generating rocks
and the differentiation of kimberlite melts within
diatremes. These factors will be briefly discussed
below.
6.1. Depth
In the depth range where pyrope-diamond subfacies
associations are stable (Sobolev, 1974),thereare
approximately seven discrete levels of generation of
kimberlite melts. Melts generated at each of these depth
levels are characterized by discrete compositions,
termed petrochemical populations in the petrochemical
model. Kimberlites of the deepest population are char-
acterized by minimal average contents of TiO
2
(0.33
wt.%) and MgO (24.20 wt.%) and maximal average
contents of K
2
O (0.85 wt.%) and Na
2
O (0.46 wt.%). As
the melt generation depth increases, the content of TiO
2
and MgO in the petrochemical kimberlite populations
increases and the content of K
2
O and Na
2
O decreases.
As a result, the least deep-seated population 7 displays
highest TiO
2
(2.60 wt.%) and MgO (28.33 wt.%)
contents and is characterized by low K
2
O (0.44
wt.%) and Na
2
O (0.15 wt.%) contents.
The above-mentioned peculiarities in major oxide
distribution may relate to compositional changes of
clinopyroxene of the magma-generating substrate (i.e.
clinopyroxene–olivine cotectics). Experimental inves-
tigations (Herzberg, 1983; Gasparik, 1989, 1990, 1994;
Ringwood et al., 1992) show that Ti leaves the clino-
pyroxene to the garnet structure with increased pres-
sure. This generates clinopyroxene–olivine cotectic
melt with depletion in Ti. The potassium behavior is
also function of the compositional variation of clino-
pyroxene. Indeed, with increasing pressure, Kis accu-
mulated in clinopyroxene, entering into its structure
(Sobolev, 1974; Edgar and Vukadinovic, 1993;
Schmidt, 1996; Harlow, 1997; Andre et al., 1998;
Table 4
Average concentrations of major element oxides and diamond grade in the distinguished sets of kimberlites
Set nSiO
2
TiO
2
Al
2
O
3
Fe
2
O
3
(tot) MgO CaO Na
2
OK
2
OP
2
O
5
LOI A(ct/10 t)
I 39 30.25 0.88 2.66 6.91 25.94 11.07 0.27 0.82 0.43 20.54 29.9
II
1
38 27.62 1.28 2.23 7.13 26.70 13.02 0.19 0.61 0.34 21.03 8.89
II
2
36 26.96 1.45 2.31 7.03 25.61 14.18 0.12 0.44 0.43 21.39 1.86
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112 105
Sobolev and Shatsky, 1990). Thus, there exists a
vertical zoning of the lithosphere with respect to
clinopyroxene compositions, which is characterized
by decreasing Ti and increasing Kcontents with depth.
There are also some evidences of a pressure-depend-
ent chemical differentiation in kimberlite types. Based
on seismic data, Vasilenko et al. (2000b) showed that
the lithosphere thickness under diamondiferous kim-
berlite fields (populations 1 – 4) is estimated to be 220
km. This is confirmed by the data on xenoliths and REE
spectra in garnets of Yakutian kimberlites (Griffin et al.,
1996), showing that the lithosphere thickness under the
Daldyn kimberlite field in the Palaeozoic can be
estimated at 220–230 km. This depth corresponds
approximately to the Lehman Discontinuity at the top
of a pronounced low-velocity zone, observed in deep
seismic sounding experiments across this part of the
Siberian Platform (Griffin et al., 1996).
On the contrary, kimberlites of population 7 and
other types of alkaline picrites, which are less deep-
seated than kimberlites, are widely distributed and
occur in areas where the lithosphere thickness
decreases down to 150 km.
6.2. Temperature
Within the kimberlite populations a pronounced
negative correlation between CaO and MgO contents
exists. The individual CaO and MgO values form dis-
crete clusters, named by us as varieties. The average
values of CaO/MgO ratio of these varieties exhibit a
regular trend from 8.20 to 0.18. This trend reflects in-
creasing temperature, as evidenced from experimental
data (Dalton and Presnall, 1998; Wyllie and Lee, 1998).
It seems likely that the population formation began
with the carbonate varieties and ended with the most
magnesianvarieties.Basedonexperimentsonthe
CaO–(Na
2
O+K
2
O) –(MgO + FeO) –(SiO
2
+Al
2
O
3
)–
CO
2
system, Wyllie and Lee (1998) showed that car-
bonatite magmas correspond to the low-temperature
part of a continuous set of low-capacity partial melts,
including kimberlites. At 70 kbar, even a slight temper-
ature rise usually results in a change of partial melt
compositions from carbonatite to kimberlite (Dalton
and Presnall, 1998).
The study of the diamond potential of Yakutian kim-
berlites in the petrochemical model (Vasilenko et al.,
1997) showed that kimberlite varieties with CaO/MgO
ratio >6.0 contain small amounts or lack diamonds. As
the CaO/MgO ratio decreases, diamond grade in-
creases, reaching maximal values in kimberlite vari-
eties with CaO/MgO ratios between 0.5 and 0.35. The
kimberlite varieties with CaO/MgO ratios of < 0.35 are
characterized again by decreasing diamond grade.
Experiments on diamond crystallization in alkaline
silicate, carbonate, and carbonate – silicate melts, with-
out and with the participation of H–C–O fluid (Borz-
dov et al., 1999) suggest that diamond nucleation is
determined mainly by reaction kinetics. Based on
experiments of the CaCO
3
–C, MgCO
3
–C,
CaMg(CO
3
)
2
–C systems, Pal’yanov et al. (1998,
1999a) and Sokol et al. (1999) showed that the catalytic
activity of alkaline-earth carbonates during diamond
crystallization at P= 7 GPa and T= 1700 –1750 jC
varied in the successive order: CaMg(CO
3
)
2
>Ca-
CO
3
>MgCO
3
. These results can be used to account
for the lower diamond grade of essentially calcic and
essentially magnesian varieties in comparison with
intermediate (Mg –Ca) varieties.
An alternative mechanism to explain the diamond
abundances in the kimberlite varieties assumes a xeno-
genic nature; whereby an increase in the extent of par-
tial melting is responsible for the correlation between
diamond grade and CaO/MgO ratio of kimberlites.
Diamond grade decreases commonly from the deepest
kimberlite population 1 to the least deep-seated pop-
ulation 7, but is also variably dependent on the variety
composition. For example, Vasilenko et al. (1997)
showed that diamond grade of the variety with CaO/
MgO ratio of 0.45 gradually decreases from 14.4 ct/10 t
in population 1 up to 0.01 ct/10 t in population 7.
Thus, one can assume that the increase of diamond
grade of deep-seated populations is due to the rise of
catalytic activity of system with increasing pressure.
6.3. Composition of the substrate
The rock compositions of magma-generating sub-
strates for kimberlite melts, can be constrained from the
compositions of mantle xenoliths. Comparison of xen-
olith compositions and kimberlite host rocks (Vasi-
lenko et al., 2001) suggests that the xenoliths of
peridotite–dunite compositions with low values of
CaO/MgO ratio originated from an evolution of P–T
conditions of pyrolith melting. They can be considered
as restites with respect to the kimberlite melts with high
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112106
values of CaO/MgO ratio. The presence of eclogite and
pyroxenite xenoliths in kimberlites leads to increased
contents of sodium and potassium, respectively. This
increase of the melt alkalinity is usually accompanied
by increasing diamond grade of kimberlites relating to
the populations 1–3. There is some experimental
evidence in support of this phenomenon (Pal’yanov
et al., 1999b): i.e. the introduction of alkaline carbo-
nates into the system promotes the increase of catalytic
activity of diamond formation, with Na
2
CO
3
having a
greater effect than K
2
CO
3
.
6.4. Differentiation
Viscous differentiation of kimberlite melts within
diatremes (Vasilenko et al., 2000a) originates when
kimberlite magma entraps wall-rock xenoliths as well
as formerly crystallized kimberlites (autolith kimberlite
breccia). As a result, the melt in the system melt – xen-
olith is characterized by increasing viscosity, energy
loss, lowering of basicity, and decreasing solidus tem-
perature. This leads to earlier crystallization of a more
magnesian melt as compared to the same melt lacking
xenoliths. This observation suggests that kimberlite
breccia are commonly more diamondiferous than mas-
sive kimberlites. It is assumed that the lowering in
crystallization temperature of magma in the system
melt–xenolith reduces the quantity of graphitized
diamond crystals.
The higher diamond grade in more magnesian parts
of the melt is consistent with the general correlation
between diamond grade and kimberlite chemical
composition. The data suggest that the proposed
method of diamond potential estimation of kimberlites
is not accidental, but reflects the main factors of
kimberlite petrology.
The second restriction, i.e. a prohibition of extrap-
olation of the obtained results, can be lifted, if kimber-
lites from other regions display comparable behavior in
chemical composition with Yakutian kimberlites.
For this purpose, chemical compositions of Yaku-
tian diamoniferous kimberlites were compared with
kimberlites from South and West Africa and Lesotho
(Table 5). The results showed that the Yakutian
Kimberlite compositions vary over a broader range.
Among the South and West African kimberlites,
kimberlites of population 1 do not found. Populations
1–3 are absent in kimberlites from Lesotho. More-
Table 5
Average composition of kimberlite populations in Yakutia and
Africa
a
Population 1 2 3 4 5 6 7
Yakutia
n326 230 1358 1343 394 295 103
SiO
2
27.00 24.11 27.43 28.67 28.88 29.39 29.29
TiO
2
0.33 0.52 0.81 1.23 1.62 1.93 2.60
Al
2
O
3
2.58 2.58 2.25 2.08 1.86 1.85 2.28
Fe
2
O
3
(tot) 4.22 5.81 5.53 7.57 8.37 8.33 9.27
MgO 24.20 24.29 25.90 28.50 27.91 29.71 28.93
CaO 14.57 16.38 14.12 11.06 10.65 8.93 8.57
Na
2
O 0.46 0.16 0.16 0.16 0.21 0.09 0.15
K
2
O 0.85 0.69 0.56 0.52 0.40 0.27 0.44
P
2
O
5
0.43 0.62 0.30 0.36 0.36 0.31 0.46
South Africa
n0 64 42 8 18 21 34
SiO
2
– 33.91 37.93 33.20 35.49 29.23 33.63
TiO
2
– 0.68 0.96 1.41 1.76 2.09 2.43
Al
2
O
3
– 4.32 5.05 3.88 3.49 2.30 3.68
Fe
2
O
3
(tot) – 6.29 6.02 5.64 6.21 5.42 7.71
MgO – 18.63 23.51 25.70 23.64 28.61 24.21
CaO – 12.85 6.56 8.47 9.96 11.66 9.34
Na
2
O – 0.28 0.99 0.52 0.43 0.25 0.43
K
2
O – 0.95 1.07 2.44 1.63 0.89 1.81
P
2
O
5
– 0.59 0.56 1.58 1.14 1.07 1.51
West Africa
n033 13 13372112
SiO
2
– 37.09 36.92 35.20 33.22 32.37 31.99
TiO
2
– 0.78 1.07 1.34 1.68 2.17 2.63
Al
2
O
3
– 4.01 5.18 4.81 4.84 3.15 2.85
Fe
2
O
3
(tot) – 5.57 7.64 6.91 7.25 8.49 6.63
MgO – 28.55 24.19 21.51 24.92 28.31 27.00
CaO – 5.21 6.89 10.43 8.24 6.37 7.42
Na
2
O – 0.54 0.95 0.82 0.27 0.32 0.31
K
2
O – 1.03 1.46 1.81 1.52 1.13 0.74
P
2
O
5
– 0.35 0.59 0.61 0.57 0.87 0.57
Lesotho
n00 0 4349
SiO
2
– – – 32.14 31.55 29.68 31.85
TiO
2
– – – 1.42 1.79 2.08 2.67
Al
2
O
3
– – – 2.38 3.44 3.74 4.22
Fe
2
O
3
(tot) – – – 5.48 4.26 6.50 7.59
MgO – – – 29.29 31.09 23.56 23.52
CaO – – – 8.05 7.13 10.09 8.77
Na
2
O – – – 0.11 0.19 0.15 0.17
K
2
O – – – 2.04 1.34 0.39 1.15
P
2
O
5
– – – 0.81 0.74 0.84 0.24
nis the number of analyses.
a
Chemical analyses of African kimberlites are taken from
Fairbairn and Robertson (1966),Dawson and Hawthorne (1973),
Nixon (1973a,b),Fesq et al. (1975),Robinson (1975) and Paul and
Potts (1976).
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112 107
over, the African kimberlites contain larger propor-
tions of magnesian varieties. However, these differ-
ences don’t hamper the use of the proposed method of
diamond potential estimation.
In recent years, much of the current interest in the
kimberlite investigation is centered on the mineralog-
ical and geochemical characteristics of these rocks,
while their petrochemical characteristics are usually
neglected. The latter statement can be illustrated by
the number of abstracts, published in abstract volumes
of the Sixth and Seventh International Kimberlite
Conferences (1995, 1998), where among the 615
abstracts, only 12 abstracts focus on the petrochemical
properties of kimberlites. Despite this lack of interest,
we hope that the present results show the relevance of
whole-rock compositions of kimberlites and the reli-
ability of the obtained conclusions in diamond explo-
ration.
7. Conclusions
Kimberlite rocks comprise a number of discrete
petrochemical clusters. Whole-rock composition and
diamond grade of kimberlite clusters vary depending
on P–Tparameters of protokimberlitic melts and
magma-generating substrate composition.
That is the reason that the linear multivariate regres-
sions turned out to be insufficiently effective for
prediction purposes, and the method of piecewise-
linear regression (with a break-point) was chosen for
estimation of diamond potential of kimberlites, based
on their major element chemistry.
The use of piecewise-linear regression combined
with a universal nonlinear discriminator allows to
place, with a certainty of >90%, a group of kimberlite
samples within one of three sets of kimberlites with the
diamond contents: A< 5.5 ct/10 t; 5.5 < A>14.1 ct/10 t;
A>14.1 ct/10 t. For each of the sets, the diamond grade
canbecorrectlyestimatedinmore than 85 – 90% of cases.
The reliable description of whole-rock composition
of a certain kimberlite variety (based on the average
composition of 25 –30 chemical analyses or on the
analysis of a sample obtained by step-by-step reduction
in volume of a large sample) allows to estimate dia-
mond grade of this rock, based on major element
chemistry, with a reliability which is clearly higher
than deduced by other methods.
Acknowledgements
We thank N.V. Sobolev, S.M. Bezborodov and
S.D. Chernyi for constructive discussions of the
proposed method. The authors have benefited greatly
from the comments of R.A.J. Swennen, A. Steenfelt
and F.V. Kaminsky, who helped to improve the
original manuscript.
Appendix A. Calculation of empiric probability
densities for sets I and II and subsets II
1
and II
2
For calculating probability density f
X
(X= I, II, II
1
,
II
2
), the corresponding table of metric tensor coeffi-
cients (Tables A1– 4), as well as the corresponding
Table A1
Metric tensor coefficients for set I
SiO
2
TiO
2
Al
2
O
3
Fe
2
O
3
(tot) MgO CaO Na
2
OK
2
OP
2
O
5
LOI
SiO
2
0.0324 0.0811 0 0.0466 0.0129 0 0.0129 0.0700 0 0
TiO
2
0.0811 6.5098 0 1.1473 0.0138 0 1.1977 0.5271 0 0
Al
2
O
3
0000 000000
Fe
2
O
3
(tot) 0.0466 1.1473 0 0.5408 0.0255 0 0.1227 0.4991 0 0
MgO 0.0129 0.0138 0 0.0255 0.0517 0 0.0681 0.0772 0 0
CaO 0 0 0 0 0 0 0 0 0 0
Na
2
O0.0129 1.1977 0 0.1227 0.0681 0 9.7155 1.7004 0 0
K
2
O0.0700 0.5271 0 0.4991 0.0772 0 1.7004 4.4009 0 0
P
2
O
5
0000 000000
LOI 0 0 0 0 0 0 0 0 0 0
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112108
lines from Tab le 1 (the numbers from a
X
to x
X
inclusive: a
I
=1, x
I
= 39; a
II
= 40, x
II
= 113; a
II1
= 40,
x
II1
=77;a
II2
= 78, x
II2
= 113), are used.
Let gis a metric tensor for set X,Ris a 10-variate
vector, describing a composition of kimberlite sample
under study (R
1
is the SiO
2
content, ...,R
10
is the LOI
Table A2
Metric tensor coefficients for set II
SiO
2
TiO
2
Al
2
O
3
Fe
2
O
3
(tot) MgO CaO Na
2
OK
2
OP
2
O
5
LOI
SiO
2
0.1344 0.0042 0 0.0461 0.0734 0 0.9053 0.2057 0 0
TiO
2
0.0042 4.4606 0 1.4264 0.0819 0 2.8682 0.3323 0 0
Al
2
O
3
0000 000 000
Fe
2
O
3
(tot) 0.0461 1.4264 0 0.9300 0.1351 0 2.4625 0.4168 0 0
MgO 0.0734 0.0819 0 0.1310 0.0776 0 0.4780 0.1005 0 0
CaO 0 0 0 0 0 0 0 0 0 0
Na
2
O0.9053 2.8682 0 2.4625 0.4780 0 136.4692 27.5336 0 0
K
2
O 0.2057 0.3323 0 0.4168 0.1005 0 27.5336 13.1840 0 0
P
2
O
5
0000 000 000
LOI 0 0 0 0 0 0 0 0 0 0
Table A4
Metric tensor coefficients for subset II
2
SiO
2
TiO
2
Al
2
O
3
Fe
2
O
3
(tot) MgO CaO Na
2
OK
2
OP
2
O
5
LOI
SiO
2
0.7060 1.4573 0.7506 0 0 0.4042 1.0455 0.7345 0 0
TiO
2
1.4573 7.4348 3.5847 0 0 0.9928 2.1841 3.6302 0 0
Al
2
O
3
0.7506 3.5847 4.6824 0 0 0.5571 6.5936 6.3640 0 0
Fe
2
O
3
(tot) 0 0 0 0 0 0 0 0 0 0
MgO 0 0 0 0 0 0 0 0 0 0
CaO 0.4042 0.9928 0.5571 0 0 0.2522 0.1088 0.5942 0 0
Na
2
O 1.0455 2.1841 6.5936 0 0 0.1088 158.5699 23.7786 0 0
K
2
O 0.7345 3.6302 6.3640 0 0 0.5942 23.7786 22.4888 0 0
P
2
O
5
0000 00 0 000
LOI 0 0 0 0 0 0 0 0 0 0
Table A3
Metric tensor coefficients for subset II
1
SiO
2
TiO
2
Al
2
O
3
Fe
2
O
3
(tot) MgO CaO Na
2
OK
2
OP
2
O
5
LOI
SiO
2
0.4763 0.3680 0.9422 0 0 0.2354 0.4233 0.3356 0 0
TiO
2
0.3680 3.0680 1.9527 0 0 0.2616 2.2261 2.3737 0 0
Al
2
O
3
0.9422 1.9527 8.7919 0 0 0.5031 1.7523 5.3945 0 0
Fe
2
O
3
(tot) 0 0 0 0 0 0 0 0 0 0
MgO 0 0 0 0 0 0 0 0 0 0
CaO 0.2354 0.2616 0.5031 0 0 0.1595 0.2369 0.0377 0 0
Na
2
O 0.4233 2.2261 1.7523 0 0 0.2369 313.5831 39.6839 0 0
K
2
O 0.3356 2.3737 5.3945 0 0 0.0377 39.6839 14.7356 0 0
P
2
O
5
0000 00 0 000
LOI 0 0 0 0 0 0 0 0 0 0
V.B. Vasilenko et al. / Journal of Geochemical Exploration 76 (2002) 93–112 109
content) and r
k
is the same vector, corresponding to
line kin Table 1.
The distance S
k
between points r
k
and Rin metrics
of set Xis determined by the matrix equation:
S2
k¼ðRrkÞgðRrkÞ
¼X
10
i¼1
X
10
j¼1
gijðRrkÞiðRrkÞj:
Taking this into account and using the Rosenblatt–
Parzen method (Rosenblatt, 1956; Parzen, 1962; Dev-
roye and Gyorfi, 1985), we derive:
fXðRÞ¼ 1
NX
x
k¼a
UðSkÞ;
where N=x
X
a
X
+1 and U(S
k
) is a function of
standardized normal distribution (i.e. Gaussian distri-
bution with mean equal to 0 and standard deviation
equal to 1).
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