tsunami on a distant shoreline. Waves which diverge near their source 

 will converge again at a point on the opposite side of the ocean. An 

 example of this was the 1960 tsunami whose source was on the Chilean 

 coastline, 39.5° S., 74.5° W. (Pararas-Carayannis, 1969). The coast of 

 Japan lies between 30° and 45° N. and about 135° to 140° E., a difference 

 of 145° to 150° longitude from the source area. As a result of the con- 

 vergence of unrefraoted wave rays, the coast of Japan suffered substantial 

 damage and many deaths occurred (U.S. Army Engineer District, Honolulu, 

 1960; Hirono, 1961). Figure 8 illustrates the convergence of the wave 

 rays due to the Earth's sphericity. 



120° 135° 150° 165° 180° 165° 150° 135° 120° 105° 90° 75° 60° 45 c 



Figure 8. Convergence of wave rays. 



Chao (1970) gives the equation for wave refraction in spherical 

 coordinates as 



dx 

 ds 



C \dw/ 



cos a tan \j> 

 R 



where ray separation is defined by the equation 



d 2 3 d3 D n 



ds z ds 



(70) 



(71) 



and the coefficients p and q are defined as 

 P = 



— ( — I - — sin a tan w 

 C Vds/ R 



(72) 



48 



