Two reasons which intensified the Chilean tsunami of 1960 along the Japanese coast, have been supposed as follows;
(1) The distance between the Chilean coast and the Japanese coast is 17, 100km. (which is roughly 20, 000km) —Antipode Effect—
(2) The Hawaiian Islands and the shallows around them have the convex-lens effect on the orthogonals of the tsunami wave. And the energy converges into Japan.
The present author, in this paper, pursues the primary reason, regarding the abovementioned two reasons as the secondary ones. The thought that the bottom topography causes refraction of the tsunami wave and much energy is radiated at right angles to the bottom contour lines around the origin, was picked up. Many past examples, such as the tsunami caused by the Lisbon earthquake of 1755 and that was generated at the Aleutian Trough on April 1, 1946, support this thought impressively.
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 off-shore energy of the tsunami to the whole) was calculated and shown in a table and a figure. Most tsunamis radiate off-shore a quarter of the whole energy or so. And it is natural that the deeper is the origin depth, the bigger is the ratio of off-shore energy.
Then we calculated the directivity of this off-shore energy, and found that the shallower is the origin depth, the sharper is the directivity. Directivities of many tsunamis, the origin depths of which are various, are shown in a table and a figure.
These two facts of rather opposite meanings shown in two tables, are combined into new theorem that “the deeper is the origin depth, the larger are the energy radiated in any direction”. This theorem suggests the possibility of the larger (along the Japanese coast) Chilean tsunami than that of 1960, in future.
Two important conclusions of this paper are as follows;
(1) The energy radiated from Chile in 1960, had a remarkable directivity towards Hawaii. Passing through Hawaii, it was intensified doubly at most—more accurately, maintaining its energy owing to the antipode effect, it came to Japan.
(2) The angle Θ between the great circle drawn from Japan and the line of circum Pacific coast, can be observed or calculated. The tsunami generated near the coast whereΘis approximately 90°, is dangerous for Japan. And we need not feel nervous about other coasts. Along the coast of South America, there is a far-stretching area whereΘis approximately 90°. And there are dangerous coasts fragmentarily, in other areas. The warnings against the tsunamis from these fragmentary areas are haunted with some probabilities
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