Geoscience Reference
In-Depth Information
g
k
sinh(
kz
)
sinh(
kH
)+
p
2
p
cosh(
kz
)
p
2
−
∞
s
+
i
∞
F
(
r
,
ϕ
,
z
,
t
)=
−
d
k
dp
exp
{
pt
}
g
k
cosh(
kH
)
0
s
−
i
∞
J
0
(
kr
)
A
0
2
n
=1
J
n
(
kr
)
A
n
cos(
n
ϕ
)
H
0
(
p
,
k
)+
∞
×
)
H
n
(
p
,
k
)
.
+
B
n
sin(
n
ϕ
(2.51)
Making use of expression (2.51), it is not difficult to obtain formulae for calcu-
lation of the displacement of the surface and of the velocity components
v
r
=
∂
F
r
,
∂
v
ϕ
=
1
r
∂
F
∂ϕ
,
v
z
=
∂
F
z
, the explicit expressions for which will not be written out
here, because they are too cumbersome.
Below we shall turn to the case, when the source of waves exhibits axial symme-
try. The solution of the problem, here, will be of the following form:
∂
F
(
r
,
z
,
t
)
p
cosh(
kz
)
g
k
sinh(
kz
)
sinh(
kH
)+
p
2
p
2
−
∞
s
+
i
∞
−
X
(
p
,
k
)
,
=
d
k
d
p
exp
{
pt
}
J
0
(
kr
)
g
k
cosh(
kH
)
(2.52)
0
s
−
i
∞
where
∞
∞
1
2
X
(
p
,
k
)=
{−
}
η
(
r
,
t
)
.
d
t
d
r
exp
pt
J
0
(
kr
)
r
π
i
0
0
2.3 Plane Problems of Tsunami Excitation by Deformations
of the Basin Bottom
In this section two-dimensional models (in the vertical plane) are dealt with.
Solution of the plane problem permits to demonstrate clearly many important
peculiarities of the physical processes taking place during tsunami generation. A
significant part of the results, obtained within the framework of the two-dimensional
model, remains valid in the three-dimensional case also. The 2D
⇒
3D transition for
problems of the type considered actually permits to investigate only two new points:
the direction of wave irradiation and changes in their characteristics, as the distance
from the source increases.
