Page 146 - Statistics and Data Analysis in Geology

S patia I Analysis

Figure 5-16. Effect of choice of segment size and origin on appearance of rose diagrams.
Data are directions of glacial striations from file FINLAND.TXT: (a) 5" segments, 0"
origin, outer ring 20%; (b) 15" segments, 0" origin, outer ring 30%; (c) 30" segments,
0" origin, outer ring 40%; (d) 15" segments, 10" origin-compare to (b). Alternative
graphical forms include (e) kite diagram, 15" segments, 0" origin-sometimes used
in statistical presentations; (f) circular histogram, 15" segments, 0" origin-widely
used to plot wind directions.
The dominant direction in a set of vectors can be found by computing the
vector resultant. The X- and Y-coordinates of the end point of a unit vector whose
direction is given by the angle 8 are
xi = cos ei
=sin& (5.39)
Three such vectors are shown plotted in Figure 5-17. Also shown is the vector
resultant, R, obtained by summing the sines and cosines of the individual vectors:

(5.40)

From the resultant, we can obtain the mean direction, 3, which is the angular av-
erage of all of the vectors in a sample. It is directly analogous to the mean value of
a set of scalar measurements
(5.41)
Obviously, the magnitude or length of the resultant depends in part on the amount
of dispersion in the sample of vectors, but it also depends upon the number of

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