Geoscience Reference
In-Depth Information
Figure 5.13.
Free-air
gravity and bathymetry
anomalies along a
north-south line centred
on the Hawaiian island of
Oahu. The volcanic
islands act as a load on
the Pacific plate, bending
it downwards and
resulting in the
symmetrical trough both
in the bathymetry and in
the gravity anomaly.
(After Watts and Daly
(1981). Reproduced with
permission from the
Annual Review and
Planetary Sciences
, vol. 9,
c
1981 by Annual
Reviews Inc.)
Figure 5.14.
A thin plate of thickness
h
is deflected by
w
(
x
)asaresult of an imposed
variable vertical force per unit area
V
(
x
) and a constant horizontal force
H
per unit
length.
the elastic properties of the lithosphere. Thus, given suitable loads, we can make
estimates of mantle viscosity.
The general fourth-order differential equation governing the equilibrium
deflection of an elastic plate as a function of horizontal distance
x
is well known
in engineering:
D
d
4
w
d
x
4
=
V
(
x
)
−
H
d
2
w
d
x
2
(5.56)
where
w
(
x
)isthe deflection of the plate,
V
(
x
)avertical force per unit length
applied to the plate,
H
a constant horizontal force per unit length applied to the
plate and
D
the
flexural rigidity
of the plate (Fig. 5.14). The flexural rigidity is
defined by
Eh
3
12(1
−
σ
D
=
(5.57)
2
)
where
E
is Young's modulus (see Appendix 2),
h
the thickness of the plate and
σ
Poisson's ratio (see Appendix 2).
