Seismic Deformation of the Lithosphere - Quantitative Plate Tectonics - page 300

Fig. 11.4 Vertical cross-section across the Nazca slab,
which is subducting beneath the Chile Trench. Black
dots represent foci of intra-plate earthquakes, while un-
derthrusting events are shown as green circles . All the
earthquake foci in a vertical stripe 200 km wide have been
projected onto this vertical cross-section. The Wadati-

Benioff zone is modelled by a 30 km thick seismogenic
slab, built around a cubic spline regression curve of the
events locations ( red line ). Most world's slabs bend down-
wards (increasing dip) in the asthenosphere and upwards
in the transition zone (decreasing subduction angles)

Fig. 11.5 Vertical cross-section illustrating the main geometric features of accretionary prisms and the typical focal
mechanisms associated with slab underthrusting

The second source of intra-plate seismicity
requires a more complex explanation. In Chap. 2 ,
we have seen that the Earth's subduction zones, in
particular the island arcs, are represented geomet-
rically by small circle arcs. Frank ( 1968 )wasthe
first to prove that the curvature of the subduction
zones is a function of the slab dip '. He proposed
a suggestive explanation that is known as the
“ping-pong ball” model. In this model, the litho-
sphere is considered as a flexible-inextensible

spherical shell that bends downwards, determin-
ing a deformation pattern that can be assimilated
to the dent of a ruptured ping-pong ball. In this
process, there is a quantity that is conserved:
the Gaussian curvature of the Earth's surface. To
understand the concept of Gaussian curvature, let
us consider a surface S having arbitrary shape.
The curvature of S at a point P clearly varies if
we consider different directions along the tan-
gent plane at P . Euler in 1760 showed that the