RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 8, ES6003, doi:10.2205/2006ES000212, 2006

Results of Numerical Modeling

Calculation of Historical Tsunami

[17]  Solovieva and Kuzin, [2005] considered the main earthquakes and tsunamis at the Russian coast of the Black Sea. Events were selected from these data, for which the dates of earthquakes, coordinates of the earthquake epicenters, and run-up data were known. This makes possible adequate modeling of the past events for analyzing possible dynamic displacements within the seismic source. The results of the calculations were checked with the data of observations on run-up at the coast for each event and with the results of calculations performed by other authors [Solovieva and Kuzin, 2005; Zaitsev et al., 2002]. Thus, we selected three seismic events on 26 June 1927; 12 September 1927; and 12 July 1966 with coordinates of the sources 34.4oE, 44.4oN; 34.5oE, 44.5oN; and 37.3oE, 44.7oN, respectively (see Table 1).

[18]  We obtained approximate sizes of tsunami source and altitude, at which water could be displaced in the source using Iida relation (see, for example [Pelinovsky, 1982]) for estimating the parameters of tsunami source at given magnitude of the earthquake M.

eq004.gif(4)

where R is radius of the source, and h is displacement of water over the seismic source. It is noteworthy that owing to incompressibility of the fluid, the displacement at the surface would repeat exactly the bottom displacement in the seismic source. Thus, formation of the tsunami source would occur during the time of dynamic displacements in the seismic source, in our case, during t seconds of the rising of the block. The size of the tsunami source R allows us to specify the approximate size of the block (or blocks) comprising the seismic source, while the displacement of the wave surface over the seismic source would allow us to calculate the altitude of the elevation of the block (or blocks) in the seismic source.

Calculation 1.
[19]  Let us consider earthquake on 26 June 1927 (M = 5.8) with coordinates of the epicenter: 34.4oE, 44.4oN. Using relations (4) we get that the radius of the source is R = 6.3 km, and the altitude of the displacement of water surface is h = 0.12 m.

[20]  Thus, we assume that approximate parameters of the seismic source are: D = 12.6 km is the size of the key-block; B = 0.2 m is the altitude of the key-block.

2006ES000212-fig03
Figure 3
[21]  The location of the earthquake source on 26 June 1927 is schematically shown in Figure 3.

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Figure 4
[22]  Patterns of the locations of wave fronts for four time moments are shown in Figures 4a, 4b, 4c, and 4d: in 200 s after the beginning of tsunami wave generation by the seismic source, after 1200 s, after 2200 s, and after 8800 s. It is clearly seen that after 20 min (1200 s) the wave front reached Yalta and Feodosiya, and approximately after 40 min, the wave front reached the Turkish coast of the Black Sea. Almost in two and a half hours, the wave reached all points at the Black Sea coast.

2006ES000212-fig05
Figure 5
[23]  The distribution of maximal wave heights at 10-meter isobath is shown in Figure 5. It is seen well that the maximal wave heights at this isobath do not exceed 20 cm, which agrees well with the results of calculation of other authors [Solovieva and Kuzin, 2005; Zaitsev et al., 2002].

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Figure 6
[24]  Pressure gauge series calculated at three points of the Black Sea coast for the first 500 s of the tsunami wave generation and propagation are shown in Figure 6.

[25]  It is clearly seen from the pressure gauge series that at each of the three points, tsunami started with sea level rise. For example, in Eupatoria, the first sea level rise was 2 cm, and only the fifth wave caused a rise of 9 cm. Fluctuations of the sea level continued for a long time and ranged from - 8 to 9 cm. In Yalta, the height of the first wave was 8 cm, while the second was already equal to 15 cm. After this, the fluctuations of the sea level decreased and continued for a long time ranging from - 7 to 8 cm. In Feodosiya, the height of the first wave was 4 cm, and for a long time the fluctuations of the level ranged from - 10 to 8 cm. It is clearly seen that the distribution of maximal wave heights along the Russian coast of the Black Sea has a small scatter (Figures 5 and 6).

Calculation 2.
[26]  The earthquake on 12 September 1927 (M = 6) corresponds to the following coordinates of the epicenter: 34.5oE, 44.4oN. The coordinates of the source are close to the case considered above, however, the recorded magnitude of the earthquake was higher (M = 6). The parameters of the tsunami source calculated from relations (4) are the following: radius of the tsunami source is R = 7.9 km, while the elevation of water at the source is h = 0.18 m.

[27]  Thus, we assume approximate parameters of the seismic source: D = 15.8 km is the size of the key-block; B = 0.3 m is the altitude of the key-block.

2006ES000212-fig07
Figure 7
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Figure 8
[28]  Localization of the source for this earthquake is shown in Figure 7.

[29]  Locations of tsunami wave fronts at four time moments: after 220 s, after 2200 s, after 3550 s, and after 7100 s are shown in Figure 8.

2006ES000212-fig09
Figure 9
2006ES000212-fig10
Figure 10
[30]  It is clearly seen that less than in one hour the wave reaches Anapa, Novorossiysk, and Gelendzhik. Although the arrival time of waves from this source to specific points at the coast is practically the same as in the previous case (localization of the sources is close) but the distribution of wave heights in the second case is different (see Figure 9, Figure 10). The greatest wave heights are observed in Yalta, Feodosiya, and Eupatoria, which agrees well with the available data.

[31]  Pressure gauge series calculated at three points of the Black Sea coast: Yalta, Novorossiysk, and Tuapse are shown in Figure 10. The choice of the towns is related to the possibility of testing the results of the calculations on the basis of the available data of measurements and calculations.

Calculation 3.
[32]  The earthquake on 12 July 1966 (M = 5.8) corresponds to the following coordinates of the epicenter: 37.3oE, 44.7oN. The parameters of the tsunami source calculated from relations (4) are the following: radius of the tsunami source is R = 6.3 km, while the elevation of water at the source is h = 0.12 m.

[33]  Thus, we assume approximate parameters of the seismic source: D = 12.6 km is the size of the key-block; B = 0.22 m is the altitude of the key-block.

2006ES000212-fig11
Figure 11
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Figure 12
[34]  The location of the source of this earthquake is shown in Figure 11.

[35]  Locations of tsunami wave fronts and spatial distribution of sea level at four time moments after wave propagation from this source are shown in Figure 12: after 310 s, after 1200 s, after 3500 s, and after 9100 s. It is clearly seen that already in 20 min after the earthquake, the waves would reach Anapa, Novorossiysk, and Gelendzhik. In half an hour, the waves would reach Tuapse, and in 40 min they would reach Sochi. Less than one hour would be necessary for the waves to reach the Turkish coast of the Black Sea (see Figures 12 a-d).

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Figure 13
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Figure 14
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Figure 15
[36]  The distribution of maximal wave heights at 10-meter isobath over the entire perimeter of the Black Sea for this earthquake is shown in Figure 13. It is clearly seen that unlike the previous cases, when the distribution of maximal heights was localized in the region of Yalta, in the third case, the distribution is localized in the region of Anapa-Gelendzhik (see Figures 13 and 14).

[37]  One can see that localization of the earthquake source near Anapa yields in a peak of maximal wave heights at the coast in the region of Anapa, Novorossiysk, and Gelendzhik. The greatest heights reach 42 cm in Gelendzhik (see Figure 15a, and Table 1).

[38]  It is clearly seen that the results obtained by numerical modeling using the dynamic keyboard model of subduction [Zaitsev et al., 2002] agree well with the data of field observations and calculations of other authors almost at all points. However, to our opinion, a certain difference from the calculations made by other authors for the earthquakes on 26 June 1927 in Eupatoria and on 12 September 1927 in Yalta is related to a better physical basis of the earthquake source model.

Calculation of Possible Catastrophic Tsunami at the Black Sea Coast Generated at Hypothetical Seismic Sources

[39]  Let us consider generation and propagation of a tsunami wave over the basin of the Black Sea for six sources with equal size, the same localization, and assume that in all six cases (scenarios) the magnitude of the possible catastrophic earthquake is M = 8.5. The motion of blocks in the source is considered with the same velocity 0.54 km h -1. The displacement is the same: up or down. The location of the source corresponds to the coordinates of the earthquake on 26 June 1927: 34.4oE-33.6oE; 44.3oN-43.5oN. From relations (4) we get the size of the tsunami source R = 141.2 km and height of water displacement at the tsunami source h = 2.5 m. Rising of block (blocks) in the seismic source occurs during 30 s, then the recalculated elevation of the block at the bottom would be equal to 4.5 m. We assume that the size of the seismic source is approximately D = 282 km.

2006ES000212-fig16
Figure 16
[40]  Let us consider possible scenarios of the block motion in the seismic source (Figure 16):

[41]  1. The source consists of one block moving upwards (Figure 16a);

[42]  2. The source consists of one block moving downwards (Figure 16b);

[43]  3. The source consists of two blocks simultaneously moving upwards and downwards and the negative motion in the source is oriented to the sea side (Figures 16c, 16d);

[44]  4. The source consists of two blocks simultaneously moving upwards and downwards and the negative motion in the source is oriented to the coast side (Figures 16e, 16f).

Calculation 1.
[45]  Let us, first, consider the motion of the block as a whole (Figure 16a). We shall consider propagation of waves in the basin of the Black Sea. Distribution of maximal wave heights at 10-meter isobath for the entire Black Sea coast of Russia for this calculation is shown in Figure 15a.

2006ES000212-fig17
Figure 17
[46]  Since we consider local tsunamis, the maximal wave heights are found at small distances from the sources, i.e. in Yalta, Feodosiya, and Eupatoria, which is clearly seen in Figure 17, where pressure gauge series are shown at eight points of the Russian Black Sea coast

[47]  Analysis of pressure gauge series indicates that at all points the wave would reach the coast in 15-50 minutes, and only in Yalta, the first front would be observed almost instantaneously, in 3-5 m. after the beginning of the seismic process. The greatest values of run-up and run-down in Yalta would be equal almost to three meters, after this the amplitudes would decrease but however, for a long time the maxima of the approaching wave trains would remain within 1.7-1.2 m. In Feodosiya and Eupatoria, the wave heights would reach 1.5-1.8 m, while the maximal run-down values would reach 1.5 m. In Gelendzhik, Novorossiysk, Tuapse, and Sochi, the first maximal waves of run-up and run-down would be in the interval 0.5-1 m. It is worth noting that since we consider only local tsunamis and the source is located close to the coast, the first wave that reaches the coast (10-meter isobath), would be a run-up wave at all points of the coast.

Calculation 2.
[48]  Let us consider the same formulation of the problem, but the block as a whole moves downwards (Figure 16b). Distribution of maximal wave heights at 10-meter isobath for the entire Black Sea coast of Russia for this calculation is shown in Figure 15b.

2006ES000212-fig18
Figure 18
2006ES000212-fig19
Figure 19
[49]  It is clearly seen in Figure 18 that at all points, tsunami starts with a run-down motion, i.e. water flows off the coast. The distributions of maximal and minimal run-up values along the Russian coast of the Black Sea for the first and second calculations are shown in Figure 19.

[50]  It is interesting to note that it follows from the comparison of Figures 19a and 19b that the patterns of the distribution of wave heights for the maximal and minimal values calculated along the coast are overturned. It is seen well that maximal values of run-up and run-down are observed in the region left of Yalta.

Calculation 3.
[51]  Let us consider a seismic source (Figure 16c) consisting of two blocks of equal size. The blocks move simultaneously upwards and downwards with equal speed of 0.54 km h -1. The calculated values of vertical displacement of blocks are equal to 4.5 m and - 4.5 m, respectively.

[52]  The distributions of maximal wave heights at 10-meter isobath along the entire Russian coast of the Black Sea for this calculation are shown in Figure 15c.

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Figure 20
[53]  A comparison of Figure 15b and Figure 15c clearly demonstrates a significant difference in the distribution of wave heights along the coast. In Anapa and Gelendzhik, the run-up and run-down values are significantly smaller, in Yalta, the run-up is approximately the same, but the run-down is significantly greater, while in Novorossiysk, in the third scenario the run-up and run-down values are much greater (Figure 20).

[54]  It is clearly seen that the wave arrived to Eupatoria with a negative height, i.e. the water, first, flowed off the coast (60 cm in the vertical direction), and then returned with a height of 1.3 m. At all other points, tsunami started with run-up. The maximal run-up reaching 3.5 m is possible in Yalta.

Calculation 4.
[55]  In this calculation we consider an "overturned" seismic source (relative to Calculation 3) oriented as shown in Figure 16d. Negative displacement is oriented in the region of Gelendzhik, Tuapse, and Sochi. The blocks move simultaneously upwards and downwards with equal speed of 0.54 km h -1. The calculated values of vertical displacement of blocks are equal to 4.5 m and - 4.5 m, respectively.

2006ES000212-fig21
Figure 21
2006ES000212-fig22
Figure 22
[56]  It is clearly seen in Figures 15d, 21, and 22 that unlike Calculation 1 (simple elevation of the block over the bottom) at all points except for Eupatoria, tsunami starts with run-down while the maximal values of run-up are significantly greater than in the first scenario of calculations. A consideration of more complex seismic source, in which displacements are oriented not only upwards but also downwards, yield in another pattern of the arrival of the first wave as well as in the other pattern of the distribution of maximal and minimal heights along the coast.

Calculation 5.
[57]  In this calculation, in the source of the earthquake of the same size as in the previous calculations the negative displacement is oriented into the open sea (Figure 16e). The blocks move simultaneously upwards and downwards with equal velocity of 0.54 km h -1. The displacement of the blocks is the same with the same velocity.

[58]  Distribution of maximal wave heights at 10-meter isobath is shown in Figure 15e.

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Figure 23
[59]  The analysis of the distribution shown here demonstrates that in this version of calculation the values of run-up at the Russian coast of the Black Sea are relatively small. In Gelendzhik, Tuapse, and Sochi (Figure 23) tsunami starts with a run-down flow, but the run-up waves, which arrive later, are not high. They would not exceed a few tens of centimeters. However, in Yalta, the height of the first wave would reach 2.6 m; it will be followed by a strong run-down, whose value along the vertical would reach 5.5 m. The second run-up as expected would be significantly greater and reach 4 m.

Calculation 6.
[60]  In this calculation, the source is similar to the previous one; however, the negative displacement is oriented to the coast (Figure 16f). The blocks move simultaneously upwards and downwards with equal velocity of 0.54 km h -1. The displacement of the blocks is the same with the same velocity as in the previous calculation. Localization of the source and magnitude of the earthquake M = 8.5 is the same as in the previous calculations (see Figure 15f).

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Figure 24
[61]  Pressure gauge series in eight towns of the coast are shown in Figure 24. It is seen well that in Yalta and Feodosiya, tsunami starts with run-down. In Yalta, the first wave is maximal (of the order of 4 m). The waves arrive at the Russian coast with a positive phase of run-up, and the maximal values of the run-up are of the order of 1 m.

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Figure 25
[62]  Distributions of maximal and minimal wave heights along the Russian coast of the Black Sea are shown in Figure 25. It is seen well that distributions (a) and (b) differ significantly from each other. In scenario (b) the values of maximal run-up heights reach 10 meters, and minimal run-down values reach 7 m, while in case (a) the values of maximal run-up heights reach 5 meters, and minimal run-down values reach 9.5 m.

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Figure 26
[63]  A histogram of the distribution of maximal wave heights for all six calculations of tsunamis from a hypothetical source is shown in Figure 26. It is clearly seen that the maximal values of wave heights up to 10 m are observed in the region left of Yalta. The greatest waves are generated in the realization of the sixth scenario, when the negative displacement in the seismic source is oriented to the coast. This agrees well with the results of paper [Pelinovsky and Mazova, 1992], in which the authors speak about possible increase in tsunami wave height at the coast in the case of a local source with negative displacement in the source oriented to the coast. The next peak of maximal values is located in the region of Novorossiysk for scenarios 3 and 4. The Gelendzhik and Sochi regions appeared the safest. The maximal wave heights are of the order of 40 cm and 70 cm, respectively.


RJES

Citation: Mazova, R. Kh., and E. A. Tresvyatskaya (2006), Numerical modeling of the generation of long waves by a dynamic seismic source and their propagation in the Black Sea, Russ. J. Earth Sci., 8, ES6003, doi:10.2205/2006ES000212.

Copyright 2006 by the Russian Journal of Earth Sciences

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