Geoscience Reference
In-Depth Information
PC
2
, this plot shows the variability in the relative contributions from the
two sources to the sedimentary column under investigation. Since we have
worked with a synthetic data set and the actual contribution of the three
source rocks to the sediment is known from
rng(0)
s1 = 10*randn(30,1);
s2 = 7*randn(30,1);
s3 = 12*randn(30,1);
we can estimate the quality of the result by comparing the initial variations
in
s1
,
s2
and
s3
with the (more or less) independent variables PC
1
, PC
2
and
PC
3
stored in the three columns of
newx
.
subplot(3,1,1)
plotyy(1:30,newx(:,1),1:30,s1), title('PC1')
subplot(3,1,2)
plotyy(1:30,-newx(:,2),1:30,s2), title('PC2')
subplot(3,1,3)
plotyy(1:30,newx(:,3),1:30,s3), title('PC3')
h e sign and the amplitude cannot be determined quantitatively and
therefore, in this case, we change the sign of the second PC and use
plotyy
to
display the data on dif erent axes in order to compare the results. As we can
see, we have successfully unmixed the varying contributions of the source
rocks
s1
,
s2
and
s3
to the mineral composition of the sedimentary sequence.
h e approach described above has been used to study the provenance of
the varved lake sediments described in the previous chapter (Section 8.9),
which were deposited around 33 kyrs ago in a landslide-dammed lake in
the Quebrada de Cafayate (Trauth et al. 2003). h e provenance of the
sediments contained in the varved layers can be traced using index minerals
characteristic of the various possible source areas within the catchment.
A comparison of the mineral assemblages in the sediments with those of
potential source rocks within the catchment area indicates that Fe-rich
Tertiary sedimentary rocks exposed in the Santa Maria Basin were the source
of the red-colored basal portion of the varves. In contrast, metamorphic
rocks in the mountainous parts of the catchment area were the most likely
source of the relatively drab-colored upper part of the varves.
9.3 Independent Component Analysis (by N. Marwan)
Principal component analysis (PCA) is the standard method for unmixing
(or separating) mixed variables (Section 9.2). Such analyses produce signals
that are linearly uncorrelated, and this method is also called
whitening
since
