Geoscience Reference
In-Depth Information
s3
) could, for example, rel ect climatic variability within the catchment area
of the sedimentary basin. It may therefore be possible to use the sediment
compositions in the array
x
(from which we calculate
s1
,
s2
and
s3
using a
PCA) to derive information on past variations in climate
We need to create a synthetic data set consisting of three measurements
representing the proportions of each of the three minerals in the each of
the thirty sediment samples. We i rst clear the workspace, reset the random
number generator with
rng(0)
and create thirty values
s1
,
s2
and
s3
. We use
random numbers with a Gaussian distribution generated using
randn
, with
means of zero and standard deviations of 10, 7 and 12.
clear
rng(0)
s1 = 10*randn(30,1);
s2 = 7*randn(30,1);
s3 = 12*randn(30,1);
We then calculate the varying proportions of each of the three minerals in
the thirty sediment samples by summing up the values in
s1
,
s2
and
s3
, at er
i rst multiplying them by a weighting factor.
x(:,1) = 15.4+ 7.2*s1+10.5*s2+2.5*s3;
x(:,2) = 124.0-8.73*s1+ 0.1*s2+2.6*s3;
x(:,3) = 100.0+5.25*s1- 6.5*s2+3.5*s3;
h e weighting factors, which together represent the mixing matrix in our
exercise, rel ect not only dif erences in the mineral compositions of the source
rocks, but also dif erences in the weathering, mobilization, and deposition of
minerals within sedimentary basins. Hence if two minerals have weighting
factors with dif erent signs, one could be (for example) the weathering
product of the other mineral, which would explain why their proportions in
the thirty sediment samples were anti-correlated. Alternatively, the dif erent
signs could indicate a dilution ef ect, i.e., if the proportions of one of the
minerals in the sediment samples remain constant but the proportions of
all other minerals vary in a similar way, they will be anti-correlated with
the proportions of the i rst mineral. To complete the generation of the data
set, we add some Gaussian noise with a standard deviation of 3.8 to the
proportions of the minerals and save the result as
sediment_1.txt
.
x = x + 3.8*randn(size(x));
save sediments_1.txt x -ascii
Having seen how the sedimentary record was created and the dependencies
