Geoscience Reference
In-Depth Information
Figure 9.43.
The
geometry of an indented
spherical cap on an
inextensible spherical
shell (e.g., a ping-pong
ball). Radius of shell,
R
;
radius of spherical cap,
r
;
and angle subtended by
spherical cap at centre of
sphere, 2
r
θ
θ
90
−
2
θ
R
θ
.
θ
θ
Oceanic trenches and island arcs are characteristically concave towards the
overriding plate. This shape can be explained by imagining the lithosphere to be
an inextensible spherical shell (like a ping-pong ball). If a portion of the shell is
bent inwards, its edge is circular, and the indented portion has the same curvature
as the original sphere (Fig. 9.43). The radius
r
of the indented circle is therefore
R
is the angle subtended by the circle
at the centre of the sphere. The angle of dip of the indented circle, measured at
the surface, is equal to 2
θ
,where
R
is the radius of the sphere and 2
θ
. This simple model can be applied to the Earth and
tested against observed dip angles of trenches and subduction zones and their
radii of curvature. An arc radius of about 2500 km gives a dip angle of 45
◦
,which
is in reasonable agreement with values for many subduction zones but certainly
not for all (Table 9.6 and Fig. 2.2). Thus, the 'ping-pong-ball' model provides a
partial explanation for the concave shape of many oceanic trenches and island
arcs even though it is an oversimplification of the problem.
θ
9.6.2 Thermal structure
Measurements of heat flow along a cross section perpendicular to a subduction
zone follow a standard pattern. The heat flow is low in the region between the
trench and the volcanic arc. At the volcanic arc, there is a sudden jump in heat
flow from about 40
10
−
3
Wm
−
2
within a very short
horizontal distance. Heat flow then remains high across the volcanic arc and into
the marginal basin. The sudden increase in heat flow at the volcanic arc is due
10
−
3
×
to (75-100)
×
