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Fig. 8.6 Preferred attitudes of schistosity planes and B-lineations with extrapolated regional
pattern for crystalline basement of eastern Dolomites near San Stefano (After Agterberg
1961
).
Cells of 100 m on a side, where one or more B-lineations were measured, are shown by
dots
.
Domains for Fig.
8.7
are indicated by
circles
(a and b); outline of boundary of Fig.
8.9
is also
shown (Source: Agterberg
1974
, Fig. 110)
Permian Verrucano conglomerate, at the base of the Permotriassic sedimentary
succession of the Italian Dolomites. During Alpine orogeny, the San Stefano
crystalline formed the core of an anticline in which the Hercynian schistosity planes
were re-activated. The trace of its Alpine NW-SE trending axial plane intersects the
approximately WNW-ESE striking Hercynian schistosity-planes (Fig.
8.6
). Qua-
dratic and cubic unit vector field solutions based on 379 original measurements for
the subarea delineated by heavy line in Fig.
8.6
are shown in Fig.
8.9
.
A difference between the B-axes of Fig.
8.5
and the paleomagnetic measure-
ments analyzed by Fisher (
1953
) is that the latter are directed whereas the B-axes of
Fig.
8.5
are undirected. Unless the scatter of lines representing individual measure-
ments is very large, the vector mean for undirected lines can be estimated in the
same way as that for directed lines. Suppose that
ʸ
i
represents the angle of the
i
-th
measurement and the unit vector mean, then the mean vector method is equivalent
to maximizing
Σ
cos
ʸ
i
representing the sum of cos
ʸ
i
for all measurements. If the
scatter is so large that one or more of values of cos
ʸ
i
for the undirected lines could
cos
2
be negative,
ʸ
i
. The latter method was
first used by Scheidegger (
1965
) for fault-plane solutions of earthquakes and by
Loudon (
1964
) for orientation data in structural geology. The underlying frequency
Σ
ʸ
i
can be maximized instead of
Σ
cos
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