| Abstract
| - Abstract. If knowledge of our theories on the directivity of tsunamis had received worldwide attention, the following operations could have been carried out internationally just after the large earthquake of 19 September 1985 which occurred near Acapulco, Mexico. Having found the great circle, “line S” which is perpendicular to the coast around Acapulco, we could have calculated the angles between line S and line A and between line S and line D, where line A and line D are the great circle connecting Acapulco and Auckland, New Zealand and that connecting Acapulco and Duke of York Island (Chile), respectively. The resultant angles are 30‡43′ and 41‡49′(>68‡48′/2), we could thereafter neglect the eastern half of the offshore energy flux. When we assume that the speed of trans-Pacific tsunami is 400 knots, the probability that the actual tsunami will come earlier than the calculated arrival time proves to be$$\frac{1}{{\sqrt {2\pi } }}\int_{ - {\text{ }}\infty }^{ - {\text{ }}0.689} {e^{ - t^{{2 \mathord{\left/ {\vphantom {2 2}} \right. \kern-ulldelimiterspace} 2}} } dt = 0.2454} $$ Contact with New Zealand prior to the forecasted arrival time was essential, but the tsunami attention for the Japanese coast was unnecessary. Without such application of our directivity theories, frequent fruitless warnings will be issued for future trans-Pacific tsunamis. Quick improvements in warning procedures are required.
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