Geoscience Reference
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Fig. 8.1 Axial symmetric rose diagram of the direction of pebbles in glacial drift in Sweden
according to K¨ster (
1964
). Step from (a) to (b) is accomplished by doubling the angles (After
Koch and Link
1971
, and Batschelet
1965
) (Source: Agterberg
1974
, Fig. 99)
8.1.2 Bjorne Formation Paleodelta Example
The Bjorne Formation is a predominantly sandy unit of Early Triassic age. It was
developed at the margin of the Sverdrup Islands of the Canadian Arctic Archipel-
ago. On northwestern Melville Island, the Bjorne Formation consists of three
separate members which can be distinguished, mainly on the basis of clay content
which is the lowest in the upper member,
C
. The total thickness of the Bjorne
Formation does not exceed 165 m on Melville Island. The formation forms a
prograding fan-shaped delta. The paleocurrent directions are indicated by such
features as the dip azimuths of planar foresets and axes of spoon-shaped troughs
(Agterberg et al.
1967
). The average current direction for 43 localities of Member
C
is shown in Fig.
8.3a
. These localities occur in a narrow belt where the sandstone
member is exposed at the surface. The azimuth of the paleocurrents changes along
the belt (Fig.
8.2
).
The variation pattern shows many local irregularities but is characterized by a
linear trend. In the (
U
,
V
) plane for the coordinates (see Fig.
8.3
), the linear trend
surface is:
x
292.133 + 27.859
u
+ 19.932
v
(degrees). At each point on
the map,
x
represents the tangent of a curve for the paleocurrent trend that passes
through that point, or
¼
F
(
u
,
v
)
¼
dv
dx
du
¼
tan
x
. It readily is shown that:
du
¼
a
1
a
2
tan
x
where
a
1
¼
27.859 and
a
2
¼
19.932. Integration of both sides gives:
1
a
1
þ
u
¼
C
þ
½
a
1
x
a
2
log
e
a
1
cos
x
ð
þ
y
sin
x
Þ
a
2
a
1
a
2
a
1
with
y
¼
a
2
if tan
x
>
and
y
¼
a
2
if tan
x
<
a
2
. The result is applicable when
360
, the quantity 360
may be subtracted from
x
is expressed in degrees. When x
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