Geoscience Reference
In-Depth Information
Fig. 2.15 Maximum amplitude of wave caused by piston-like displacement,
τ
= 1, versus distance
from the boundary of the source for different source sizes
therefore, as the wave propagates, the front 'overtakes' it, thus causing enhance-
ment of the amplitude. Variation of the wave amplitude, as it travels away from
the source, is shown in Fig. 2.15. Dispersive amplification can be seen to be capable
of enhancing the wave amplitude by 25%, but it is not always present and exists only
in such cases, when the size of the source is noticeably greater than the basin depth.
The effect of dispersive tsunami amplification was first dealt with in [Mirchina,
Pelinovsky (1987)] for volcanogenic tsunamis.
Figures 2.12 and 2.13 show the dependences of wave amplitudes upon the dis-
placement duration (curves 1-3), calculated within the framework of potential
theory. In the case of a piston-like displacement the behaviour of these dependencies
does not differ very strongly from the broken line, corresponding to the long-wave
theory. Significant differences are observed only in the case of small-size sources
and at large distances from it. In the case of waves due to a membrane-like displace-
ment, also, no noticeable difference exists at the boundary of the generation area be-
tween calculations performed by the long-wave and potential theories. But, already
at a small distance from the source the dependence of the amplitude essentially
changes in character and becomes monotonous. Such a character of the dependence
is conserved for any horizontal dimensions of the source. It is important to note
that rapid membrane-like displacements do not cause tsunami waves of significant
amplitudes.
We shall now turn to the relationship between the wave energy and the source pa-
rameters, presented in Fig. 2.14. It can be seen that in the case of a large-size source
or of significant displacement durations, the energy values calculated by potential
and long-wave theories comply quite well with each other. The most essential dif-
ference is again observed in the case of short membrane-like displacements. Taking
into account that in the case of real tsunami sources
τ
∗
<
1 clarifies the leading role
of seabed motions with residual displacements in the excitation of strong tsunamis.
A similar conclusion is made, for example, in [Dotsenko, Soloviev (1990)] from
analysis of a source with axial symmetry.
