Geoscience Reference
In-Depth Information
Fig. 3.6 Time evolvents of surface displacements of liquids at the centre of the active zone for dif-
ferent displacement propagation velocities
v
. The thick and thin lines correspond to incompressible
and compressible liquids, respectively
to the excitation of standing acoustic waves in the natural resonator of a 'column
of compressible liquid with a free surface on the rigid bottom'. Similar oscilla-
tions arise in the case of piston-like and membrane-like displacements of the ocean
bottom (Fig. 3.2).
Within the framework of the model applied, the damping of oscillations is due to
the outflow of elastic wave energy from the generation area. The oscillation damp-
ing process proceeds, in this case, faster, than in the case of vertical displacements of
the ocean bottom, which is related to the existence of a large number of elastic wave
rays, deviated from the vertical direction. In real natural conditions the damping will
proceed even more rapidly owing to losses occurring, when the elastic waves are re-
flected and scattered from the boundaries 'water-bottom' and 'water-atmosphere'.
In Fig. 3.7, the dependence of the maximum amplitude of surface displacement
at the centre of the active zone (
x
= 5) is presented in a semilogarithmic scale as
a function of the velocity
v
. From the figure it is seen that for propagation velocities
of the displacement inferior to
v
= 4(
v
=
c
/
2
750 m/s) practically no difference
exists between the models for compressible and incompressible liquids. Both theo-
ries reveal the presence of a local maximum at
v
= 1, corresponding to resonance
excitation of gravitational waves. At high velocities the model for incompressible
liquids more than twice underestimates the free-surface displacement.
∼
