Geoscience Reference
In-Depth Information
[Shoemaker et al. (1990); Toon et al. (1994)]. Large objects collide with our planet
approximately once every 100,000 years. The authors of [Ward, Asphaug (2000)]
point out that the dependence presented in Fig. 4.13 is not quite accurate, but that it
is the best estimate of all that could be made for objects with radiuses of 1-1,000 m,
using presently available information. The actual collision frequency of the Earth
with celestial bodies within the range of dimensions indicated may differ by a factor
of 3 as compared to the dependence proposed.
The dotted line in Fig. 4.13 shows the number of objects that are not destroyed in
the atmosphere and that are capable of reaching the Earth's surface. From the point
of view of tsunami generation we will be interested precisely in these objects, since
they are capable of effectively influencing the water column. Of course, large me-
teor bodies, exploding in the atmosphere at small heights (such as the Tungus me-
teorite, 1908) over the surface of the ocean are probably also capable of causing
gravitational waves, but, most likely, their energy will be insufficient for exciting
dangerous tsunami waves.
The typical density of stony asteroids amounts to about 3,000 kg/m
3
, their veloc-
ity to 20 km/s. Assuming the object to have a spherical shape, it is easy to estimate
its kinetic energy. Thus, for example, a meteor body of diameter 100 m will have
a kinetic energy
10
17
J. This value corresponds to the energy of a very strong
seismotectonic tsunami (see Fig. 3.1). Now, if the diameter of the object amounts to
1 km, then its energy will be colossal,
≈
·
3
10
20
J. This value is already many times
greater than the energy of the source of the strongest earthquake of the twentieth
century that occurred in Chile in 1960. It is not difficult to estimate that such an en-
ergy is sufficient to evaporate 10
11
m
3
of water (the heat required to evaporate water
is 2
.
3
≈
3
·
10
6
J/kg). It is interesting to note that precisely such a volume of water is
ousted by ocean bottom deformations in the case of very strong earthquakes (source
area of 1,000
·
100 km, average vertical deformation of bottom of 1 m). At any rate,
a relatively small part of the energy is, most likely, spent on the evaporation of water.
Following [Ward, Asphaug (2002)], we shall assume a meteorite falling into
the ocean to create, at the initial stage, a radially symmetric cavity, described by
the following function:
×
0
(
r
)=
D
C
r
2
1
1
R
D
)
,
ξ
R
C
−
−
θ
(
r
−
(4.36)
where
D
C
is the depth of the cavity,
R
C
and
R
D
are its internal and external radii,
respectively and
is the Heaviside step function. The case, when
R
D
=
R
C
cor-
responds to water being released into the atmosphere (or to its evaporation). T
h
e
θ
initial perturbation, here, represents a depression (Fig. 4.14a). When
R
D
=
R
C
√
2,
the water ejected from the cavity, forms an external circular structure (a splash or
circular swell), the volume of which is exactly equal to the volume of the water,
ejected from the cavity (Fig. 4.14b).
From the shape of the cavity it is possible to estimate the tsunami energy as
the potential energy of the initial elevation,
