National Oceanic and
Atmospheric Administration
United States Department of Commerce


FY 1977

Directivity and efficiency of tsunamis

Miyoshi, H.

NOAA-JTRE-190 and HIG-77-4, Hawaii Institute of Geophysics, Honolulu, HI, 32 pp (1977)

After some analyses, the relation between m (the ratio of water depth at the origin to that of the deep sea floor) and r (the ratio of offshore energy of the tsunami to its whole energy) was calculated and is shown in a figure. Most tsunamis radiate offshore from a quarter to a third of its whole energy. Then we calculated the directivity of this offshore energy and found that the biggest energy is radiated at right angles to the bottom contour lines around the origin, and that the shallower is the origin depth, the sharper is this directivity. The calculations were done in accordance with Fermat's principle. Two important conclusions of this theory are as follows: (1) The energy radiated from Chile in 1960 had a remarkable directivity towards Hawaii. Passing through Hawaii, it came to Japan being intensified doubly at most owing to the antipodal effect. (The convex lens effect is rather ambiguous). (2) The angle between the great circle drawn, for example, from Japan (or Hawaii) and the line of circum-Pacific coast can be estimated easily by one globe and a piece of string. The tsunamis generated near the coast where is approximately 90° are dangerous for Japan (or Hawaii). And we need not feel nervous about the tsunamis generated along other coasts. Thus, we can discern handily whether the tsunami is dangerous or not, immediately after a big earthquake occurs across the ocean. It is remarkable that there is a far-reaching area where is approximately 90° for Japan and Hawaii along the coast of South America. When the bottom is uplifted, the efficiency of tsunami generation is some one-thousandth or less, and when the bottom is depressed, the efficiency is the same value but a negative one. The energy exchanged between the earth's crust and the seawater at the time of the generation of tsunami, is tremendous. So when the artificial energy of some 2 × 1023 ergs is given, for example, by nuclear testing, to the sea or the earth's crust, the energy of the tsunami directly caused by the artificial energy must be negligible.

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