Geoscience Reference
In-Depth Information
Fig. 2.6 Cross section of slip distribution. A big black arrow indicates the strike of the fault
plane. The gray level shows the amplitude of dislocations and white arrows represent the
motion of the hanging wall relative to the footwall. Contours show the rupture initiation time
in seconds and the black star indicates the hypocentre location. The figure is adapted from
http://earthquake.usgs.gov/eqcenter/eqinthenews/2006/usvcam/finite fault.php (see also Plate 3 in
the Colour Plate Section on page 311)
2.2 General Solution of the Problem of Excitation
of Gravitational Waves in a Layer of Incompressible Liquid
by Deformations of the Basin Bottom
2.2.1 Cartesian Coordinates
The goal of this section is the construction of a mathematical model describ-
ing the motion of a layer of homogeneous incompressible liquid in the case of
deformation of the basin bottom, proceeding in accordance with a certain given
space-time law. The liquid is limited from above by its free surface and is in a gravi-
tational field, characterized by the acceleration of gravity, g. We shall only deal with
the case of a basin of constant depth
H
—such an approach will permit to obtain
an analytical solution of the problem. We shall consider the amplitude of motions
of the basin bottom,
H
.In
practice, this condition is actually always satisfied (the average depth of the ocean
is
H
η
0
, a small quantity as compared to the depth,
η
0
η
0
<
10 m even in the case of catastrophic earthquakes).
The amplitude of gravitational surface waves,
A
, excited by one or another mo-
tion of the basin bottom with the amplitude
∼
4
,
000 m, while
η
0
, will clearly be of the same order
