Geoscience Reference
In-Depth Information
component, normal to the boundary
. Along the coastal line fulfilment is assumed
of the noflow condition through a vertical wall:
u
n
= 0on
G
.
As the initial conditions of the problem, the landslide and the water layer are as-
sumed to be at rest at time moment
t
= 0, i.e. all the velocities and the displacement
of the free water surface are equal to zero.
The set of equations (4.2-4.5) can be resolved by the explicit finite-difference
method. Usually, the staggered leap-frog scheme in space and time is used
[Imamura, Gica (1996)] in calculations.
To suppress the instability of the numerical scheme approximation is used of ad-
vective terms in the equations of motion according to the scheme with upstream dif-
ferences [Roache (1976)]. To avoid generation of small-scale parasitic oscillations
(network noise), it is expedient to set the time step (
Γ
∆
t
) equal to 1.3 of the value
given by the Courant condition.
We shall make use of a hypothetical event in the Malaspina strait (British
Columbia, Canada) [Rabinovich et al. (2003)] as an example in considering the pe-
culiarities of landslide tsunami formation. Numerical simulation of this tsunami is
performed applying the mathematical model, described above. Studies of hypo-
thetical tsunamis are important for estimation of the risk of tsunami hazard. For
the demonstration of research methods of this kind we shall first give a detailed
description of the primary geophysical (geomorphological) information and, then,
present the results of simulation.
The Malaspina strait (Fig. 4.2), located between the continental coast of British
Columbia and Texada island, is about 50 km long and 5 km wide. Its depth along
the axis of the strait varies between 300 and 375 m. In the central part of the strait
there is a thick (
100 m) sedimentary layer, mainly consisting of silt carried out
from the estuary of Fraser River.
In 1946 an earthquake in the central part of Vancouver island, British Columbia,
gave rise to a series of landslides and slumps in the coastal area of Malaspina strait.
∼
(km)
Fig. 4.2 Malaspina strait: map of calculation region. Adapted from [Rabinovich et al. (2003)]
