Geoscience Reference
In-Depth Information
section). From the figure it is seen that the amplitude of dynamic pressure reaches its
maximum values near the ocean bottom, while the presurface region is characterized
by minimum values of the dynamic pressure. This property is a direct conse-
quence of the boundary condition at the free water surface. When the bottom is
flat, the region of maximum pressures is localized immediately above the source,
and the amplitude of the signal reaches noticeable values near the ocean bottom
(
p
max
∼
200 km, also. In
Fig. 3.12, the amplitude of the dynamic pressure is normalized to the quantity
ρ
0
.
5
ρ
cv
max
) at significant distances from the source,
∼
cv
max
, where
v
max
is the maximum velocity of motion of the ocean bottom. The
appearance of even a very insignificant slope angle in the vicinity of the source leads
to a shift of the region of maximum pressures towards large depths. In this case the
amplitude of the signal in the shallow-water region is noticeably reduced. Further
enhancement of the ocean bottom slope angle results in the maximum pressure
values being achieved already outside the source area (in the deep-water region),
while propagation of the acoustic signal into the shallow-water region is strongly
suppressed. Thus, for example, if
H
1
= 1 km and
H
2
= 8 km in the shallow-water
region, then the dynamic pressure remains at a level
cv
max
, and the main
contribution to this quantity is not due to the acoustic, but to the surface gravitational
wave. At the same time, in the deep-water area the pressure amounts to 3
∼
0
.
02
ρ
ρ
cv
max
and
more.
In the case of short displacements the region of maximum dynamic pressure may
be observed not only near the ocean bottom, but also inside the thick water column,
which is due to the excitation of higher modes of elastic oscillations. In the case
of long-duration displacements the dynamic pressure becomes homogeneous in
the vertical direction, because effects of water compressibility lose their first-priority
significance, and the pressure related to gravitational waves starts to prevail.
In the case of a basin of variable depth, for instance, when the source of waves is
located on the sloping ocean bottom, a most important result consists in the shallow-
water region turning out to be practically closed to the penetration of elastic waves.
The acoustic signal in the shallow-water region being suppressed depends on
two
reasons
:the
first
is trivial. The underwater slope is so oriented that the source emits
elastic waves into the deep-water region. But this reason is not the sole and even
less the principal one. The
second
reason is related to the wave-guide properties of
a column of compressible liquid, limited by a free surface and by an absolutely rigid
bottom. It is known [Brekhovskikh, Goncharov (1982)] or [Tolstoy, Kley (1987)]
that the dispersion relation for normal modes in such a waveguide has the form:
4
T
2
c
2
−
2
1
/
2
H
2
n
1
1
2
k
x
=
π
−
,
(3.35)
where
k
x
is the x-component of the wave vector,
T
is the period of elastic waves
and
n
is the mode number (
n
= 1
,
2
,
3
...
). It is seen that for fixed period
T
and
depth
H
the horizontal wave number will be real only for a finite number of modes.
These modes will be propagating modes. For modes of higher numbers
k
x
becomes
a purely imaginary quantity, consequently, the perturbation in the wave decreases
exponentially in the
x
direction. The situation is possible, when in the deep-water
