Geoscience Reference
In-Depth Information
Fig. 2.34 Directional co-
efficient versus duration of
bottom displacement. Curves
1, 2 correspond to piston-
like displacement, 3, 4 to
membrane-like displacement.
Curves 1, 3 are obtained for
a
= 1
,
b
= 5
,
r
= 10, curves 2,
4for
a
= 3
,
b
= 15
,
r
= 30
of the model source. Calculations have been performed for various deformation
durations of the bottom. The main part of energy is seen to be emitted in a direction,
perpendicular to the direction of maximum extension of the source, independently
of the time law satisfied by motion of the bottom. But as the displacement duration
increases, the diagram undergoes significant changes, the character of which does
depend on the type of time law of motion of the bottom.
We shall now introduce the directional coefficient of emission as the ratio of
energy fractions emitted in directions
= 0
◦
and 90
◦
. Figure 2.34 shows the depen-
dence of the directional coefficient upon the displacement duration. For a piston-
like displacement the quantity
W
0
◦
/
W
90
◦
decreases monotonously as the duration
increases. But the corresponding dependence for a membrane-like displacement
exhibits a non-monotonous character. It is interesting to note that in the case of
a membrane-like displacement the directional coefficient may assume larger values
than for a piston-like displacement. From the figure it can also be concluded that
a decrease in the size of a source, if its shape (the ratio
a
/
b
) is conserved, results in
a weakening of the directionality, especially when its size becomes comparable to
the depth.
Why does the duration of the bottom deformation (or type of time law) influence
the orientation of wave emission? The point is that an asymmetric source forms
waves of differing wavelengths in different directions. In other words, there exists
an effective horizontal size of a source, depending on the direction. Above, it was
shown (Fig. 2.12) that, when the displacement duration increases, the wave ampli-
tude falls more rapidly in the case of a source of smaller horizontal extension. There-
fore, if the source is elongated, then the degree of emission orientation inevitably
decreases, as the displacement duration rises. The behaviour of the directional coef-
ficient in the case of a membrane-like displacement is explained in a similar manner.
Figure 2.35 presents the total wave energy (integrated over all directions) ver-
sus the duration of the bottom displacement. In the case of a piston-like displace-
ment the energy monotonously decreases as the duration increases, while in the case
of the membrane-like displacement there exists a certain 'optimal' duration, for
which the energy is maximal. For this 'optimal' duration the membrane-like dis-
placement turns out to be more effective, than even a piston-like displacement of
small duration. Similar dependences were obtained in [Dotsenko, Soloviev (1990);
Dotsenko (1996)] within the framework of linear theory of long waves.
α
