Jökull - 01.12.1989, Qupperneq 69

1. Or
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w
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0. 6
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0.2
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12 3 4
Grain size, <t>
-2 -1
-1
2 3
Grain size, <Þ
12 3 4
Grain size <Þ
Fig- 5. The relationship between form parameters and grain size. The formulas for the parameters and the <J>
scale are given in the text.
Mynd 5. Tengsl milli formþátta og kornastœrðar. Formþœttirnir og kornastœrðarkvarðinn eru skýrðir nánar
i textanum.
population. However, if we redefine the population
to include only tephra grains produced in the H4
eruption, and include only H4 samples in the
analysis of variance, the critical range for elongation
becomes 0.053, for sphericity 0.044, and for the
OP-index 1.985. This indicates a significant
difference between the mean values of the four sam-
ples of H4 in elongation and OP-index, but not in
sphericity. Larsen and Thorarinsson (1978) mapped
the H4 tephra unit and came to the conclusion that
no single section in the vicinity of Hekla contains all
the units of H4 due to changes in wind direction dur-
lng the eruption. As all our H4 samples were taken
at °ne locality, further sampling is clearly necessary
to obtain a full picture of the form characteristics of
this Hekla layer. The same is probably true of H,,
where one of the three samples shows significant
deviation. The diíferences in mean values of the
duplicate analyses on sample 5838 are not
significant for any of the form parameters.
COMPARING SAMPLES AND
VARIABLES WITH CLUSTER ANAIYSIS
The process of selecting the most appropriate
Parameter(s) for characterizing samples and com-
Paring samples may be facilitated considerably by
Performing a cluster analysis. This method involves
a stepwise comparison of samples for which several
parameters have been determined. It can be equally
well used for the comparison of parameters. These
parameters need not be normally distributed, and the
analysis is non-parametric. The method was
described in a geological context by Parks (1966). It
involves the calculation of a similarity coefficient
for all possible sample pairs. The most similar pair
of samples is linked on a tree diagram (dendrogram),
and then the next most similar pair (or linked pairs)
and so on. The tree diagram shows the final step of
the cluster analysis, giving a good visual perception
of the similarities of samples or variables.
The first cluster diagram (Fig. 6) is based on a set
of parameters produced by tallying the number of
plotted points in each cell of the Sneed-Folk
diagram (Fig. 2). Each sample is represented by a
horizontal line, which is joined to its nearest neigh-
bour by a vertical line. This neighbour may be a sin-
gle sample or a cluster of samples, but the scale at
the top of the diagram shows the Pearson correlation
coefficient. To point out an example, the Sneed-Folk
cell parameters cluster the samples from Surtsey
(submarine phreatomagmatic), Katla (subglacial
phreatomagmatic), Heimaey (strombolian-
/hawaiian), and top of the H4 layer (subaerial, last,
non-plinian phase of eruption?). H4 (subaerial, ini-
tial plinian phase) and Hj (subaerial, plinian) are
joined in an equally similar cluster which then joins
JÖKULL, No. 39, 1989 67