Geoscience Reference
In-Depth Information
Fig. 8.5 Two examples of minor folds in the Pustertal quartzphyllite belt.
Left side
: East-dipping
minor folds near Welsberg (Monguelfo; location near midpoint of western boundary of subarea
delineated in Fig.
8.16
);
Right side
: ditto along TRANSALP profile near subvertical contact with
Permotriassic (grid coordinates 206-767; part of MS112, see Fig.
8.16
) (Source: Agterberg
2012
,
Fig. 1)
8.1.3 Directed and Undirected Unit Vectors
Directional features play an important role in structural geology. Basic principles
were originally reviewed and developed by Sander (
1948
) who associated a
3-dimensional (A, B, C) Cartesian coordinate system with folds and other struc-
tures. A-axis and C-axis were defined to be parallel to the directions of compression
and expansion, respectively, with the B-axis perpendicular to the AC-plane
representing the main plane of motion of the rock particles. Two examples of
Hercynian minor folds with clearly developed B-axes are shown in Fig.
8.5
(from
Agterberg
1961
) for quartzphyllites belonging to the crystalline basement of the
Dolomites in northern Italy. Measurements on B-axes from these quartzphyllites
were analyzed previously (Agterberg
1959
,
1961
,
1974
,
1985
,
2004
,
2012
) and will
again be used here with re-interpretations as needed.
Stereographic projection using either the Wulff net or the equal-area Schmidt net
continue to be useful tools for representing sets of directional features from
different outcrops within the same neighbourhood or for directions derived from
crystals in thin sections of rocks. Contouring on the net is often applied to find
maxima representing preferred orientations, which also can be estimated using
methods developed by mathematical statisticians, especially for relatively small
sample sizes (see, e.g., Fisher et al.
1987
).
Reiche (
1938
) used the vector mean to find the preferred orientation of direc-
tional features. Using a paleomagnetic data set, Fisher (
1953
) further developed this
method for estimating the mean orientation from a sample of directed unit vectors.
The frequency distribution of unit vectors may satisfy a Fisher distribution, which is
the spherical equivalent of a normal distribution. The mean unit vector is estimated
as follows. For a sample of measurements, the average direction cosine is deter-
mined along each of the three axes of a Cartesian coordinate system. The strength
|
R
| of the vector
R
described by the three average direction cosines is less than one
Search WWH ::
Custom Search