Geology Reference
In-Depth Information
files, used by dedicated algorithms during the
process of construction of some hierarchical data
structures (or
trees
in the sense of Computer Sci-
positions of a set of tectonic plates at any given
time. A
rotation tree
can be considered as a data
structure that specifies the multilevel tectonic
hierarchy of a plate system at an assigned time
T
(Ross and Scotese
1988
). It is often referred to
as a
plate circuit
, although this term is also used
when relative velocities are specified rather than
relative positions, usually in studies on current
plate motions. The nodes of these data structures
are tectonic elements, while an edge between any
pair of nodes indicates that their relative motion
can be described by a sequence of stage rotations.
Therefore, given a stage
S
, the edges of a plate
circuit
C
for time
T
2
S
define a set of
conjugate
plate boundaries
in a system of interacting tec-
tonic elements during the stage
S
, not the whole
set of active plate boundaries, although all the
existing plates at time
T
are represented in
C
.
Thus, if
e
and
p
are respectively the size (that
is, the number of edges) and the order (number
of plates) of
C
,thenby(
2.34
) it always results:
e
<3(
p
2). It is also important to note that the
topology of plate circuits is not constant through
time, but changes as a consequence of major
plate boundary reorganizations. In general, the
definition of a plate circuit topology for each
tectonic stage is based on the geological or geo-
physical evidence and the identification of a set
of conjugate boundaries, such that the resulting
graph is a connected tree (that is, for any two
nodes
u
and
v
there exists a unique path from
u
to
v
). The topology is specified implicitly during the
compilation of a rotation model, while the duty of
the reconstruction algorithms is to build a rotation
tree for any assigned reconstruction time
T
.
In the example of Fig.
2.28
, we assume
that the relative motion between the plate pairs
(
A
,
C
), (
B
,
C
), (
C
,
D
), and (
D
,
E
) is represented
by rotations at constant angular velocity during a
time interval
S
[
T
0
,
T
00
]. Therefore,
S
is assumed
to be a tectonic stage. This assumption most
likely relies on the geometry of fracture zones
in
Fig. 2.28
Sketch map illustrating the construction of
plate circuits.
Left
: A system of five plates. Finite rotations
of
A
with respect to
C
,
B
to
C
,
D
to
C
,and
E
to
D
are
known.
Right
: The corresponding plate circuit
evidence regarding the tectonic activity along
the transcurrent faults that separate
D
from
C
and
E
. In this instance, four finite reconstruction
matrices must be defined for the conjugate
boundaries, which allow to determine four inde-
pendent stage rotations,
S
AC
(
T
0
,
T
00
),
S
BC
(
T
0
,
T
00
),
S
DC
(
T
0
,
T
00
), and
S
ED
(
T
0
,
T
00
) through Eq. (
2.44
).
If
R
AC
(
T
),
R
BC
(
T
),
R
DC
(
T
), and
R
ED
(
T
)arethe
finite reconstruction matrices at any time
T
2
[
T
0
,
T
00
], then any other relative position at time
T
can be calculated by combining these basic
rotations.
For example, it is possible to determine the
relative position of
A
with respect to
B
and that
of
E
with respect to
C
at time
T
:
R
AB
.T/
D
R
CB
.T/R
AC
.T/
I
R
EC
.T/
D
R
DC
.T/R
ED
.T/
In general, the tree structures associated with
plate circuits are arranged so that the greater is
the degree of a node in a plate circuit
C
,that
is, the number of edges incident with the node,
the higher will be its level in the hierarchical
structure. Therefore, the neighborhoods of nodes
in
C
will increase in size when we move toward
higher levels in the data structure.
Plate circuits are built by reconstruction al-
gorithms starting from a rotation model. This
table specifies, for any stage boundary, the fi-
nite reconstruction pole and rotation angle of
each identified pair of conjugate plates. A sample
fragment of these data structures is shown in
Fig.
2.29
. In these tables, the tectonic elements
the
oceanic
area
and
on
geological
field
