Geology Reference
In-Depth Information
Fig. 2.34
Alternate paths of converted boundaries during the splitting of a tectonic plate.
To p
: The new edge links a
free boundary to a conjugate boundary.
Bottom
: Two free boundaries are split
In Sect.
2.7
we have described a method of
construction of flow lines of relative motion,
which can be used only when the two plates
form a conjugate pair. Furthermore, we have
mentioned that it is not generally applicable to
the case of convergent boundaries. Now we want
to describe a technique to produce flow lines in
the general case of two plates separated by a
free boundary for at least some time intervals.
The method is based on the general technique
for determining relative velocity fields discussed
above. Let
r
0
be the present day position vector
of a point belonging to a plate
B
.Wewantto
generate a path on the globe, formed by the
relative positions of this point with respect to
another plate
A
at any time
T
in the geologic
past. The task is easily accomplished calculating
the relative velocity field
v
BA
(
T
) for a sequence
of closed times
T
0
,
T
0
C
•
T
,
T
0
C
2•
T
, ::: in an
interval [
T
0
,
T
00
]. In fact, starting from the position
at the initial time, which is
r
(
T
0
)
D
R
BA
(
T
0
)
r
0
,
we can calculate iteratively the position at any
successive time by the following formula:
The kinematic methods described so far can be
applied equally well to the reconstruction of the
tectonic evolution of oceanic basins and to conti-
nental tectonics. In the former case, the finite re-
construction matrices associated with the rotation
model are determined on the basis of an analysis
of fracture zones and the pattern of marine mag-
In the case of reconstructions that involve defor-
mation of continental crust in the geologic past,
for example during rifting or collisions, or when
the finite rotations must describe relative motions
between continental blocks, these techniques are
inapplicable. In this context, the determination
of the reconstruction parameters (latitude and
longitude of the Euler poles and rotation angles)
mostly relies on geologic data that lack of in-
formation on measurement uncertainty, thereby it
is not generally possible to determine confidence
ellipses for the resulting reconstruction parame-
ters. Nevertheless, it is possible to generate semi-
quantitative reconstructions that correctly predict
the style and timing of tectonic deformation, thus
giving a theoretical framework to the geological
observation at regional or local scale.
r .T
C
•T/
D
r.T/
C
v
BA
.T/•T
(2.56)
