Geoscience Reference
In-Depth Information
Fig. 5.12
Ni-Fe-SiO
2
and Ni-MgO-Co ternary diagrams
Fig. 5.13
Centered Ni-Fe-SiO
2
and Ni-MgO-Co simplexes
�
1
1
“
(
)
(
)
−
−
5.5.3.4 Operations
Two common operations for manipulating data and for dis-
playing various geometric images within the ternary diagram
are powering and perturbation (Aitchison
1986
; Pawlowsky-
Glahn and Olea
2004
; Pawlowsky-Glahn and Egozcue
2006
). Pertinent geometric images may be zones discrimi-
nating compositional observations into classes and ellipses
denoting confidence intervals of distributions.
A particular form of perturbation called data centering is
used when data are compressed to a small region of the ter-
nary diagram (simplex) offering poor visual analysis of the
data. The perturbing vector is set as the inverse geometric
mean of the compositional data and such that it obeys the
unit sum property.
∏∏
u
=
�
ζ
x
,...,
x
N
N
”
1
D
�
•
Centered data for subcompositions Ni-Fe-SiO
2
and Ni-MgO-
Co (Fig.
5.13
) give a much better picture of the data distribu-
tion. The segregation of ore type classes (color coded points)
is more visible in both plots. An important problem to note
here is the occurrence of zeros and missing values in the sam-
ple data. Because the geometric mean is used, these values
must be handled with care. For the purposes of centering in the
nickel laterite example, missing values were ignored and zeros
were set to 1 such that the products did not resolve to zero.
