Geology Reference
In-Depth Information
polygon is moved back to the original reference
frame before applying the rigid transformation
listed in the rotation model.
Another problem that often must be solved, in
the context of continental tectonics, is associated
with the impossibility to determine a priori, inde-
pendently from the specific kinematic history, a
list of finite reconstruction poles to be included
in a rotation model. The reason is that the typical
geological data are generally represented by par-
tially incoherent geologic structures (faults, fold
axes, etc.), which result from the superposition of
two or more phases of deformation, as illustrated
in Fig.
2.37
. Even assuming that it is possible
to separate the original data in coherent subsets,
and to identify the timing of the deformation
phases through a precise dating of the geologic
structures, the oldest tectonic structures cannot
be used to determine finite reconstruction pa-
rameters, because it is likely that their strike
has been affected by the more recent phases
of deformation. In these conditions, the typical
approach is to reconstruct the tectonic history
of a region starting from the most recent phase
of deformation and going back through time. If
we can identify the most recent set of geologic
structures, for example between some time
T
k
and
the present (Fig.
2.37
), then it is possible to de-
termine the parameters of a stage transformation
S
(0,
T
k
), which clearly coincides with the finite
reconstruction matrix at time
T
k
:
S
(0,
T
k
)
D
R
(
T
k
).
At this point, all the structures that are older than
T
k
, and that have been affected by the most recent
phase of deformation, are rotated using the matrix
R
(
T
k
), in order to remove the “overprint” of this
phase. After this operation, these structures be-
come coherent with other data that had not been
affected by the recent deformation. The resulting
data set can be used, at the next step, to determine
a second stage pole,
S
(
T
k
,
T
k
1
),whichinturnal-
lows to calculate the finite reconstruction matrix
at time
T
k
1
:
R
(
T
k
1
)
D
S
(
T
k
,
T
k
1
)
R
(
T
k
), and
Fig. 2.36
Stretching and shortening continental blocks
by a factor “. In a reference frame (
x
0
,
y
0
,
z
0
)wherethe
stage pole,
S
, has been moved to the North Pole, the
northernmost and southernmost vertices,
q
n
and
q
s
,ofa
plate polygon are used to divide the block perimeter in two
halves. Then, each point along the eastern half is moved
along its parallel of latitude to stretch or shorten by factor
“ the corresponding
small circle
arc •
¥
that separates it
from the western boundary
Fig. 2.37
Superposition of two phases of deformation
of a tectonic element. During phase 1, between
T
1
and
T
2
, a rift forms with extension axes having direction
WNW
E
SE. Note that the resulting offset
L
between
the two separating blocks is always less than the width
W
of the stretched zone. This phase is followed by a
second episode of extension between
T
3
and
T
4
,having
NW
the original transfer zones and rift axes. At the end of this
phase the original block has been divided in four distinct
tectonic elements (
A
,
B
,
C
,and
D
). To determine a finite
reconstruction pole and angle of rotation for phase 1, it
is necessary to remove the effects of the second phase of
deformation, by reconstructing the shape of the tectonic
element at time
T
3
S
E
direction, which modifies the strike of some of
