Geoscience Reference
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of waves. Owing to tsunami waves being subject to dispersion, it is expedient to
resolve the problem within the framework of potential theory.
In conclusion, we shall briefly dwell upon one more possible mechanism of
tsunami formation in the case of underwater earthquakes. Experience of the in-
vestigation of catastrophic and strong seismic events shows that numerous seismic
cracks of lengths exceeding tens of kilometers and widths amounting to 5-15 m
arise at the epicentral zone. Dilatant changes of the state of rock in the same area
develop, enhancement of the specific volume of the medium takes place, as well as
revelation of microcracks and growth of its permeability. In the case of underwater
earthquakes such processes should clearly take place in the rock of the ocean bot-
tom. Rapid opening of the cracks at the ocean bottom should lead to an impetuous
drainage of water.
Evidence provided by witnesses of the 1999 Izmit earthquake revealed that
one of the shallow regions of the Sea of Marmara was dried up by the exclusive
drainage of water through cracks in the sea-floor; large areas of the sea-floor were
completely uncovered. In scientific literature, such phenomena are conventionally
termed the Moses effect, in memory of the biblical Exodus through the Red Sea.
Naturally, the dried areas of the sea-floor remain for a short time, until the water
fills up the entire volume formed by the created set of cracks.
The impetuous drainage of water into cracks results in a local lowering of
the ocean level. Such an initial perturbation is also capable of generating tsunami
waves. The first results of mathematical simulation of the formation mechanism of
a tsunami, caused by a fault opening up in the bottom, are presented in [Levin,
Nosov (2008)].
2.1.3 Calculation of Deformations of the Ocean Bottom
For simulating tsunami waves of seismotectonic origin it is necessary to have real-
istic data concerning the residual deformations of the ocean bottom, resulting from
an underwater earthquake. Residual deformations can be calculated on the basis of
seismic data, making use of the analytical solution for the stationary problem of
elasticity theory, presented in [Okada (1985)].
In this chapter, formulae are presented for surface displacements due to inclined
shear and tensile faults in an isotropic homogeneous elastic half-space. The expres-
sions have been carefully checked to be free from any singularities and misprints.
The Yoshimitsu Okada formulae are quite cumbersome and contain numerous
variables. Therefore, in this section, in order to avoid errors, instead of our tradi-
tional notation, we shall accurately follow [Okada (1985)] and apply the original
notation adopted therein.
We take the Cartesian reference system as it is shown in Fig. 2.5. The elastic
medium occupies the region of
z
0. The 0
x
axis is taken to be parallel to the strike
direction of a finite rectangular fault of length
L
and width
W
. Burger's vector
D =(
U
1
,
U
2
,
U
3
) shows the movement of the hanging-wall side block relative to
