Geoscience Reference
In-Depth Information
Fig. 2.29 Free-surface perturbations, caused by piston-like and running displacements of the bot-
tom with parameters
a
= 6
,
b
= 2
,
v
= 2(
τ
= 6). Calculations are performed for the time moments
t
indicated in the figure
2
a
/
v
(the reason that such a restriction ex-
ists is expounded in Sect. 2.3.1). The integrals in expressions (2.109)-(2.112) were
calculated numerically.
Figure 2.29 presents the space structure of waves excited by piston-like and run-
ning displacements, which have ultimately resulted in identical residual deforma-
tions (
a
= 6
,
b
= 2). The propagation velocity of a running displacement,
v
= 2, and
the duration of a piston-like displacement,
Formula (2.112) is valid, when
t
v
= 2
a
.
Calculations are performed in accordance with formulae (2.109) and (2.112). From
the figure it is seen that in the case of a piston-like displacement the waves of max-
imum amplitude propagate in the negative and positive directions of axis 0
y
, i.e. in
a direction perpendicular to the direction of maximum extension of the source. In
the case of a running displacement the source emits waves of maximum amplitude
at the Mach angle to the direction of propagation of the displacement (0
x
). More-
over, attention is immediately drawn to the fact that the amplitude of waves caused
by a running displacement is significantly superior to the amplitude of waves in
the case of a piston-like displacement.
For detailed investigation of the orientation of waves emitted from the source
area wave time-bases were calculated at points lying on a circle of a certain radius
(
r
>
max[
a
,
b
]), with its centre coinciding with the origin of the chosen reference
τ
= 6, satisfy the relationship
τ
