3. Numerical Simulation of Tsunami Generation, Propagation and Run-up:
Keyboard Model of Source (Direct Subduction Zone)
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Figure 5
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Figure 6
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[9] There was considered a dynamical source consisting of 5 rectangular
keyboard blocks. In first set of computations keyboard blocks with the same size
100 km
50 km (Figure 5) were taken. In a second set of computations,
lengths of corresponding five blocks were taken to be equal to 50, 100, 150,
50, and 150 km, respectively, and the width of all blocks was the same and equal
to 50 km (Figure 6). Thus, source length for both sets of computations was equal
to 500 km. The value of vertical displacement (upwards or downwards) of keyboard
blocks from initial position, at water depth equal to 1000 m, was taken to be equal
to 3 m for each keyboard block in both sets.
[10] The following scenarios were considered:
- uplift of first to fifth blocks, successively, one after another with the same velocities (0.05 m s-1 or 0.075 m s-1 or 0.15 m s-1 );
- uplift of first to fifth blocks in various sequence but with the same velocities (0.05 m s-1 or 0.075 m s-1 and 0.15 m s-1 );
- uplift of first to fifth blocks in various sequence but with different velocities;
- vertical displacement of blocks upward or downward in various sequence but with the same velocities (0.05 m s-1 or 0.075 m s-1 or 0.15 m s-1 );
- uplift of first to fifth blocks but the motion of each next block begins before stopping of preceding one.
[11] Variations of these five scenarios are presented in Table 1.
[12] From Table 1 it is seen that value of run-up on a beach depends on the
distance between the source and the coast (lines 2.2; 2.4; 2.5 in Table 1),
on the velocity of block vertical motion in the source: slower motion, smaller
run-up (lines 1.1; 1.2 in Table 1), and on the block size: at the same source
(500 km long), its cutting to 5 blocks with lengths of 50, 100, 150, 50, and 150 km
(with maximum size 150 km
100 km) leads to run-up increase from 3 m to 4 m
(lines 1.2; 2.1 in Table 1), as compared with cutting of the same source to
5 equal blocks with size of each block 100 km
50 km (Figure 6).
It is also seen that if the motion of the next block begins before stopping
of preceding one then run-up value
R max increases to 20 percents,
and run-down value
R min increases into 1.5 times (lines 1.1; 1.3 in
Table 1).
3.1. Vertical Displacements of Keyboard Blocks in the Source Only Upwards
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Figure 7
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[13] The analysis of the results obtained permits to separate them on two
characteristic features. To the first group there are related events in which keyboard
blocks in the earthquake source move only upwards (see, Table 1). As an example,
let us consider events for lines 1.1 and 2.6. Figure 7 presents a space-time
picture of behaviour of moving shoreline for 600 km part of the coast for these
cases. There are well seen two wave fronts coming to a beach. The first front
reaches the beach nearly after 25 min from the onset time of wave propagation
from the source. And, at the same value of keyboard blocks (see Figure 5), first wave comes as
continuous front and it reaches the beach near simultaneously almost in all points
of the coast (Figure 7a). In the second case, the bend of the wave front is connected
with different keyboard block size in the source and with sequence taken for the
motion of blocks (Figure 7b). The second run-up wave front (Figure 7) is of more complex shape
with alternation of crests and troughs along all the 500 km wave front. Such shape
of front is formed depending on sequence of keyboard block motion in the source
and on different velocity of their vertical motion.
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Figure 8
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[14] Figure 8 presents a distribution of maximum and minimum
run-ups
Rmax at the coast for cases considered. It is well seen that
for both cases maximum run-up
Rmax
is about 4 m and maximum run-down
from a beach
Rmin is near 2.8 meters. However, distribution of maximum
run-up values along the coast is essentially different for each case considered.
So, in the case of motion of the same keyboard blocks the maximum run-up is
practically uniformly distributed along the coast with divergence of 10-17
percents (Figure 8a). Quite different situation arises for
distribution of maximum run-ups in the case of upward motion
of keyboard blocks with different sizes. The maximum run-up value distribution
along the coast is between 0.5 m and 4 m (Figure 8b). The maximum
values of water run-down from a beach
Rmin along the coast differ in 3.5 times.
3.2. Vertical Displacements of Keyboard Blocks in the Source
Upwards and Downwards
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Figure 9
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[15] Quite another picture appears when there is presented the motion of keyboard
blocks upward as well as downward. In Figure 9 it is presented an example of
space-time picture for the case of vertical motion in the source of equal blocks,
when 1, 3, 5 blocks are removed upward to 3 meters, and 2 and 4 blocks are
displaced downward also to 3 meters (line 1.4 in Table 1). In this case, there
appears a quite another picture of distribution of crests and troughs at the wave
run-up on a beach. There are well seen three wave fronts. First of them is an
insignificant run-down in ones points and a small run-up in another ones.
The next wave front is alternation of maximum run-down
Rmin (vertical component) and
run-ups
Rmax
between
- 4 m and 4 m height. And third front with scattering
of these values between
- 3 m and 3 m also is an alternation of crests and troughs.
At analogous sequence of displacements but for keyboard blocks of different lengths
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Figure 10
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it appears a very similar picture (Figure 10). Here, most values of run-up on the coast
are for waves of the second front while most run-down is for waves of the first
front. In the first place, it can be related to the waves generated by keyboard block
downward motion since at various combinations of blocks in the source the
depression wave can be followed by the elevation wave with larger height than that
generated by motions of blocks only upwards
[Mazova and Ramirez, 1999].
It is necessary to note that at rupture process in the source of tsunamigenic earthquake,
surface water wave comes towards rupture spreading with velocity determined by
that of vertical motion of keyboard blocks along the subduction zone. The wave
generated by such source simultaneously comes along the subduction zone and
propagates from source with different velocities.
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Figure 11
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[16] In Figure 11 it is presented the propagation of surface water wave along the source
at rupturing in the source during the earthquake.
[17] The analysis performed demonstrates that at motion of keyboard blocks in the
earthquake source the sequence of their displacements, the change of the keyboard
block size in 1.5-2 times, and the change of rise velocity in two times provides
only insignificant change of the run-up value. However, the distribution of
maximum run-ups and maximum run-downs along the coast is essentially different,
this difference can be of up to 8-10 times.
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