Geology Reference
In-Depth Information
Fig. 2.32
Nucleation of a new plate by splitting of an
existing
n
-th order plate. Free plate boundaries are shown
as
dashed lines. Left
: The new plate boundary splits two
conjugate boundaries through the insertion of two new
triple junctions,
J
0
and
J
00
. In this case, the new boundary
is a free boundary and there is no need for a global
reorganization.
Right
: If one of the two boundaries that are
cut is a free boundary, then a large scale reorganization,
involving several conversions between free and conjugate
boundaries, is necessary. In this instance, a new conju-
gate boundary separates the parent plate from the newly
formed tectonic element
a small circle arc about a stage pole. When
a boundary separates two plates whose relative
motion occurs about a continuously changing
Euler pole, we say that this is a
free boundary
.In
this case, strike-slip faults, in particular transform
faults, and fracture zones have a quite complicate
pattern, as illustrated in Fig.
2.26
.If
C
is a plate
circuit containing
p
nodes, then its size (i.e.,
the number of edges) is given by
e
D
p
1. The
following theorem proves that this number does
not
coincide with the total number of conjugate
pairs in a plate tectonic configuration, that is, with
the total number of conjugate boundaries, but is
always lower.
that in this configuration only two of the three
boundaries can be conjugate boundaries, thereby
we would have
f
D
1and
c
D
2, in agreement
with Eqs. (
2.54
)and (
2.55
). Now let us assume
that the theorem holds for a system with
p
plates.
We want to prove that in this case it also holds
if one of these plates splits, thus adding a new
tectonic element to the system.
Figure
2.32
shows two possible mechanisms
for generating a new additional tectonic plate
from an existing one. Clearly, in order to create
a new boundary that splits an existing plate, two
of its boundaries must be broken by insertion
of triple junctions. If the edges that are split
are conjugate boundaries, two extra conjugate
boundaries and one additional free boundary are
created and there is no need to change the tectonic
style of the remaining plate boundaries. In this
instance,
f
increases by one, while
c
increases
by two, thereby Eqs. (
2.54
)and(
2.55
) remain
valid and the theorem is proved. The new plate
boundary separating the two parts of the original
plate is always a free boundary when this kind
of plate nucleation occurs. A much more com-
plicated situation follows if at least one of the
two boundaries that are split is a free boundary.
In this instance, the proof relies on the fact that
for any pair of triple junctions in
G
,thereexistat
least three
alternate paths
that link the two nodes.
An alternate path is a path formed by an alternate
sequence of conjugate and free edges.
The example of Fig.
2.33
shows the tree struc-
ture that can be formed with the set of all alternate
Topological Theorem (for Plate Tectonic Con-
figurations)
If G
(
j
,
b
)
is a global plate configuration, then
the number of free and conjugate boundaries are
given, respectively, by:
1
3
b
D
e
1
D
p
2
f
D
(2.54)
2
3
b
D
j
D
2f
c
D
(2.55)
Proof
In this proof, we always assume that in
normal conditions
a system of tectonic plates
tries to maximize the number of conjugate bound-
aries during any episode of reorganization, be-
cause this is clearly a minimum energy configura-
tion. In a three-plates system, it results by (
2.34
)
that
b
D
3and
j
D
2. We have already proved
