Jökull - 01.12.1989, Page 67

new, deep caldera lake within the Askja caldera
(Sigurdsson and Sparks, 1978; Sæmundsson, 1982).
An early phase of the eruption was classified as
phreatoplinian by Self and Sparks (1978). The sam-
ple (1004) was taken at Sviðanes, and was supplied
by Gudrún Larsen.
The Skógar tephra sample was collected by the
authors at the locality Skógar in Fnjóskadalur. The
Skógar tephra has been described by Norðdahl
(1983). Only light coloured white-gray particles
were measured in the present study, but it is not cer-
tain that all the grains are derived from the same
eruption as the tephra is clearly reworked. The
unpublished Si02 value was kindly supplied by
Hreggviður Norðdahl.
The Kúðafljót sample was collected from a soil
section at the river Kúðafljót. The sample is from a
tephra layer which is widespread in Southeast Ice-
land and is known as "the needle layer". The data on
the chemistry of this layer was obtained from Ólafs-
son and others (1984).
RESULTS
general form of
SAND SIZED ASH PARTICLES
To get an overall picture of the form of the
analyzed samples, the mean values were plotted on a
Sneed-Folk diagram (Fig. 2). Most of the samples
form a fairly dense cluster in the centre of the
diagram although some trend from the compact
bladed form towards the elongate form is observed.
A similar pattern is produced by plotting the mean
values on the Zingg diagram (Fig. 1).
STATISTICAL DISTRIBUTION
OF FORM PARAMETERS
Many 0f the parametric statistical tests commonly
applied to samples assume that the samples are
derived from populations which can be modelled by
ihe normal distribution. Clarke and Cooke (1983)
list the following conditions, that point to the con-
sideration of the normal random variable as a model
for a variate: (1) strong central tendency, (2) equally
likely positive and negative deviations from the cen-
tral value, and (3) rapid falloff of deviation
frequency as the deviations become larger. Blatt
and others (1972) have summarized geological
parameters that tend to be normally distributed.
These include grain size (measured on the <I> scale),
grain roundness, and grain sphericity. To investigate
the normality of the form parameters used in the
present study, histograms were plotted for each one
using the combined data for sample 5838 (two ran-
dom samples for all grain sizes, giving a total of 160
data points). Fig. 4 shows the plots for elongation,
sphericity, and OP index. The probability plots
(marked A on the diagram) offer a better comparison
with the normal distribution, which would plot as a
perfectly straight line. All the parameter plots
resemble a straight line, and the histograms form
unimodal, bell shaped pattems. We therefore con-
clude that the normal distribution is a reasonable
model for the form parameters elongation, spheri-
city, and OP-index.
GRAIN SIZE AND FORM PARAMETERS
The statistical results in the present study are
based on tephra grains within the size range
0.125 mm to 2.0 mm. To answer the question
whether the form parameters are related to grain
size, elongation, sphericity, and OP index for all
measured grains are plotted against size in Fig. 5.
There is obviously no systematic change in these
parameters within the size range. The question may
also be answered by using the sample correlation
coefficient (r) to evaluate the linear relationship
between two measured (or calculated) parameters.
The results are shown in Table III. Obviously, the
correlation is very poor in all cases. We therefore
conclude that the size grades' may be combined and
regarded as one sample. All subsequent plots for the
data involve sample means without respect to grain
size. The values t and P in Table III show the results
of t-tests for the statistical signilicance of the corre-
lation coefficient, r, for each pair of variables. The P
value gives the probability of obtaining a calculated
sample value of the correlation coefficient greater
than r from a population with a correlation
coefficient of zero. For elongation, the chances of
obtaining the sample value r = 0.059 from a
JÖKULL, No. 39, 1989 65