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Chapter 2 Tsunami Generation

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Chapter 2 Tsunami Generation Chapter 2 Tsunami Generation 2.1 Tsunami-Earthquake Energy Relations, Source Areas I. TSUNAMIMAGNITUDE IN RELATIONTO OTHERPARAMETERS Iida (1970) followed the earlier work by Imamura (1949) to define tsunami magnitude, m, in reference to Japan, as: whereqmaxis the maximum height in meters measured at a coast 10-300 km from the tsunami origin. Iida (1956) gave the tsunami grade scale based on (Table 2.1). Iida (1970) cataloged the earthquakes of magnitude, M, greater than 5.8 accompanied by tsunamis, in and near Japan from 1900 to 1968. The geographic distribution of the epicenters of the tsunamigenic earthquakes (classified according to tsunami magnitude, m) shows that most epicenters lie on the Pacific Ocean side of Japan (not in the Sea of Japan). TABLE2.1. Tsunami grade scale of Iida and Imamura. Depending on the requirement, this scale has been extended occasionally from -3 to 5. (Iida 1956) Grade scale Significance -1 Minor tsunami with max. wave height (h) less than jm 0 h is of the order of 1 m; no damage I h is of the order of 2 m; house damage along coast; ships washed ashore 2 h is of the order of 4-6 m; some destruction of houses; considerable loss of life 3 h is of the order of 10-20 m; damaged area along coast about 400 km 4 h is greater than 50 m; damaged area along coast more than 500 km Iida (1 963b) studied about 100 tsunamigenic earthquakes that occurred from 1700 to 1960 and produced a diagram (not shown here) showing the relation between tsunami magnitude, m,and water depth, D, at the epicenter. From this diagram, the following upperbound on tsunami magnitude can be expressed: m = 1.66 log D - 1.62 where D is expressed in meters. 31 Iida (1963b) also investigated the relation between m and log S where S is the ratio of the water depth at the epicenter to the distance between the epicenter and the point on the coast where m is determined. This is expressed as: log S = 0.12 m + 2.12 (2.3) or inversely m = 8.33 log S - 17.0 (2.4) These relations show that tsunami magnitude is proportional to the slope, S, of the sea bottom at the epicenter and that the water depth, D, at the epicenter has more influence on m than the distance of the epicenter to the coast. The tsunami grade magnitude scale discussed above was originally devised for tsunamis with sources within 600 km of the Sanriku coast. This scale is not linear, even after the logarithmic transformation. Adams ( 1974) devised a new tsunami magnitude scale, based on the logarithm to the base of 2, of the run-up expected at 1000 km from the epicenter. He called this the “logarithmically linear scale” of tsunami magnitude. This scale is better than the tsunami grade magnitude scale, because data are reduced to a fixed epicentral distance, even if not observed there. The linearly logarithmic scale also includes a correction for geometrical spreading. THECONCEPT OF “TSUNAMIINTENSITY” Soloviev (1970, p. 152) pointed out the inappropriateness of the usage “tsunami magnitude.” He stated : “If seismological terminology is applied to description of tsunamis, the grades of the Imamura-Iida scale must be designated as the intensity of the tsunami and not its magnitude. This is because the latter value must characterize dynamically the processes in the source of the phenomenon and the first one must characterize it at some observational point . the nearest point to the source included.” Another important point made by Soloviev was the distinction between the mean height,;, and the maximum height, qmax,of tsunami inundation. This distinc- tion is necessary because, although it is the mean height that is relevant for the estimation of tsunami energy, in older descriptions of tsunamis emphasis was given to the maximum height. The differences between mean height and maximum height could be mostly attributed to topography. Figure 2.1 shows the relation between Si and qmaxfor different tsunamis. Soloviev defined tsunami intensity, i, as : Compared to (2.1), (2.5) differs in three respects. First, instead of magnitude, m, intensity, i, appears. Second, the maximum height, qmax,is replaced by the average height,.Tj. Third, the factor, a,was introduced to account for the average difference in the maximum and mean heights of tsunamis of different intensities. TSUNAMIGENICAND NONTSUNAMIGENICEARTHQUAKES Iida (1970) studied the relation between earthquake magnitude, M, and focal 32 30 20 'I max 10 0 0 5 - 10 7 FIG. 2.1. Correlation between maximum 7) and mean 7 heights of tsunamis (m). 1. Sanriku, 1933; 2. Tonankaido, 1944; 3. Nankaido, 1946; 4. Tokachi-Oki, 1952; 5. Kam- chatka, 1952; 6. Boso, 1953; 7. Iturup, 1958; 8. Chile, 1960; 9. Urup, 1963; 10. Alaska, 1964; 11. Niigata, 1964. (Soloviev 1970) depth, H, of submarine earthquakes that occurred from 1926 to 1968 in and near Japan (Fig. 2.2). The solid line represents the boundary between tsunamigenic and nontsunamigenic earthquakes, i.e. tsunamigenic earthquakes occur to the right side of this line. This (lower) limiting magnitude for tsunamigenic earthquakes is ex- pressed as : M = 6.3 + 0.005 H (2.6) where the focal depth, H, is expressed in km. However, there are three tsunamigenic earthquakes to the left of the solid line (not shown here). If these are included then the smallest magnitude of a tsunamigenic earthquake is given by: M = 5.6 + 0.01 H (2.7) Iida (1970) also gave the following relation for the lower limit for the magnitude of earthquakes which have generated disastrous tsunamis (i.e. tsunamis of magni- tude > 2): M = 7.7 + 0.05 H (2.8) 33 80 -- I I I I 60 -- I I I I I I H(krn) 40 -- I I I I I I 20 -- I I I I I I I I, 0 I FIG. 2.2. Relation between earthquake magnitude and focal depth of submarine earthquakes, 1926-68. (Iida 1970) This limit is shown by the dashed line in Fig. 2.2. In the data represented in Fig. 2.2, there were 79 earthquakes with magnitudes greater than given by (2.6) and yet they were not followed by tsunamis. Of these, 32 were aftershocks and 15 were relatively deep-focus shocks. Both types are unlikely to produce tsunamis. Iida used the concept of faulting to explain the fact that the remaining 32 earthquakes were nontsunamigenic. For these 32 earthquakes, Iida considered focal-plane solutions. Radiation patterns from both P and S waves were used, and faulting along the nodal plane was assumed, to calculate the dip and strike components of the unit vector of motion because of faulting. The faulting is classified as dip-slip type if the dip component exceeds the strike component. The reverse situation is called strike-slip. Iida found that for more than 60% of the tsunamigenic earthquakes studied, faulting was the dip-slip type. Iida ( 1970) investigated the relation between earthquake magnitude and tsun- ami magnitude classified according to the type of faulting. He concluded that tsunami magnitude is proportional to earthquake magnitude and that most large tsunamis result from earthquakes associated with dip-slip faulting. For other detailed studies on Japanese tsunamis see Hatori (1970) and Watanabe (1970). For the source mechanism of tsunamigenic and nontsunamigenic earthquakes in the north- west part of the Pacific Ocean see Balakina (1970). SEISMICENERGY VERSUS TSUNAMI ENERGY Iida ( 1963b) gave the following relation between earthquake magnitude, M, and tsunami magnitude, m: m = (2.61 f 0.22) M - (18.44 f 0.52) (2.9) Gutenberg and Richter (1956) gave the following relation between M and seismic energy, Es (expressed in ergs): logEs = 11.8 + 1.5 M (2.10) 34 From these two equations, one can write: log E, = 22.4 + 0.6 m or (2.1 1) E, = E, X with E, = 2.5 X IOzz ergs (2.12) Takahasi ( 195 1) gave the following relation between tsunami magnitude, m, and tsunami energy, E, : E, = E: X (2.13) with E, = 2.5 X loz1ergs In Takahasi’s method, the tsunami energy is estimated from the following relation (based on symmetry, for example Equation (1.143)): (2.14) where g is gravity, p is water density, r is the distance between the observation location and tsunami source, D is the water depth at the observation point, 5 is the average observed height of tsunami, and T is the duration of tsunami. From (2.9) and (2.13) log E, = 21.4 + 0.6 m = 10.3 + 1.5 M (2.15) Hence, comparing (2.1 1) with (2.15) (2.16) Thus, about a tenth of the seismic wave energy appears as tsunami energy. Table 2.2 supports this statement quite well (actually E, /El has been observed to vary over a substantial range with an average value of about 10). TABLE2.2. Tsunami energy, E,, versus seismic wave energy, E,. (lida 1963a) Seismic wave Tsunami energy Earthquake Magnitude energy (E,) (E,) (MI ioz3 ergs ergs Chile, May 22, 1960 8.5 35.5 3.0 Sanriku, Mar. 2, 1933 8.3 17.8 1.7 Nankaido, Dec. 20, 1946 8. I 8.9 0.8 Tokachi, Mar. 4, 1952 8. I 8.9 0.8 Tonankai, Dec. 7, 1944 8.0 6.3 0.79 Aomori, Feb. IO, 1945 7.3 0.56 0.004 35 Iida ( 1963a) gave the following empirical relation between earthquake magni- tude, M, and the area, A, of aftershock activity (expressed in km2). log A = 0.9 M - 3.0 (2.17) He also deduced that the area over which crustal deformation occurs (which might lead to tsunami generation) is equal to the area of aftershock activity.
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