Page 91 - Sedimentology and Stratigraphy

78 Field Sedimentology, Facies and Environments

direction. Calculation of the circular mean and circu- the end lies very close to the perimeter of the circle, as
lar variance of sets of palaeocurrent data can be car- happens when all the data are very close together, r
ried out with a calculator or by using a computer will have a value close to 1. If the line r is very short it
program. The mathematical basis for the calculation is because the data have a wide spread: as an extreme
(Swan & Sandilands 1995) is as follows. example, the mean of 0008, 0908, 1808 and 2708
In order to mathematically handle directional data would result in a line of length 0 as the mean values
it is first necessary to translate the bearings into rec- of x and y for this group would lie at the centre of the
tangular co-ordinates and express all the values in circle. The length of the line r is calculated using
terms of x and y axes (Fig. 5.9). Pythagoras’ theorem
1 For each bearing u, determine the x and y values,
2
2
where x ¼ sin u and y ¼ cos u. r ¼ n(x ) þ (y )
2 Add all the x values together and determine the
mean.
3 Add all the y values together and determine the 5.4 COLLECTION OF ROCK SAMPLES
mean.
The result will be a mean value for the average direc- Field studies only provide a portion of the information
tion expressed in rectangular co-ordinates, with the that may be gleaned from sedimentary rocks, so it is
values of x and y each between 1 and þ1. To routine to collect samples for further analysis. Mate-
determine the bearing that this represents use rial may be required for palaeontological studies, to
u ¼ tan 1 (y=x). This value of u will be between determine the biostratigraphic age of the strata
þ90 and 90. To correct this to a true bearing, it is (20.4), or for mineralogical and geochemical anal-
necessary to determine which quadrant the mean will yses. Thin-sections are used to investigate the texture
lie in. and composition of the rock in detail, or the sample
The spread of the data around the calculated mean may be disaggregated to assess the heavy mineral
is proportional to the length of the line r (Fig. 5.9). If content or dissolved to undertake chemical analyses.
A number of these procedures are used in the deter-
mination of provenance.
The size and condition of the sample collected will
depend on the intended use of the material, but for
H most purposes pieces that are about 50 mm across

will be adequate. It is good practice to collect samples
that are ‘fresh’, i.e. with the weathered surface

" removed. The orientation of the sample with respect
to the bedding should usually be recorded by marking

an arrow on the sample that is perpendicular to the
bedding planes and points in the direction of young-
ing (19.3.1). Every sample should be given a unique
, H identification number at the time that it is collected in
the field, and its location recorded in the field note-
book. If collected as part of the process of recording a

sedimentary log, the position of the sample in the
logged succession should be recorded.
Samples should always be placed individually in
appropriate bags – usually strong, sealable plastic
bags. If you want to be really organised, write out

the sample numbers on small pieces of heavy-duty
adhesive tape before setting off for the field and attach
the pieces of tape to a sheet of acetate. Each number is
Fig. 5.9 Directions measured from palaeoflow can be
written on two pieces of tape, one to be attached to
considered in terms of ‘x’ and ‘y’ co-ordinates: see text for
discussion. the sample, the other on to the plastic bag that the