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Fig. 2.8 Geometry of the
Mariana subduction zone.
The brown line represents
the best-fit small circle to
the trench zone, determined
using the algorithm of
Schettino and Tassi ( 2012 ).
The background image
shows the free-air gravity
anomaly field (Sandwell
and Smith 1997 ). The red
line is the active back-arc
spreading center (see text).
The West Mariana Ridge is
an extinct island arc
Schettino and Tassi 2012 ). Figure 2.8 shows the
example of the Mariana subduction zone in the
western Pacific, which forms an almost perfect
small circle arc. We have already mentioned that
the geometry of tectonic plates can be represented
by spherical caps. Therefore, trench zones can be
viewed as the surficial hinge lines of bending of
spherical caps, associated with the subduction of
oceanic lithosphere. Such hinge lines do not have
constant curvature, but their geometry generally
varies to accommodate changes of the relative ve-
locity field of convergence. For example, Fig. 2.8
shows that the present day Mariana Trench is
deforming as a consequence of an extensional
process in the back-arc area, accompanied by the
formation of new oceanic crust along a back-
arc spreading center in the Mariana Trough. This
spreading ridge is placed to the East of an extinct
island arc, the West Mariana Ridge, which is
representative of a previous geometry of sub-
duction. Almost every subduction zone shows
evidence of back-arc activity, either currently or
sometime in the past. Even in the case of Andean-
like trench zones, where the oceanic lithosphere
is subducting beneath a continent, we observe
back-arc deformation of the continental margin
in the geologic past (e.g., Dalziel 1981 ;Ramos
et al. 2002 ), to the point that the present day
western margin of South America has the shape
of a sequence of arcuate hinge lines, which can
be represented anyway by small circle arcs.
An important aspect of the subduction kine-
matics is represented by the velocity relations
between subducting plate, hinge zone, and upper
plate (Fig. 2.9 ). Hamilton ( 2002 ) criticized what
he defined a widespread misconception in the
Earth Sciences community, consisting in the view
that subducting plates roll over stationary hinge
lines and slide down fixed slots. In reality, in
a reference frame fixed to an unsubducted plate
A , the hinge line H always moves toward the
oceanic foreland with some velocity v HA ,justas
the margin of the overriding plate, B , and with
equal velocity (because v BH D 0). If we consider
a reference frame fixed to the top of the transition
zone, O , then the hinge line and the overriding
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