

or, alternatively, 



cos 



E. = E. + E (167) 



i t cos 6j J 1 



where b^ is the distance between adjacent wave rays for the transmitted 

 wave, and b{, the distance between adjacent wave rays for the incident 

 wave. Rewriting equation (167), 



E^ cos 0„ E 



t 2 r 



which gives 





E. 



cos 



e l 





E. 

 ^ 





H l 



\ 



COS 



e 2 



+ 



H 2 

 r 



H? 



L 



H? 



1 



L. 



COS 



e l 



L. 



(168) 



= 1 (169) 



Noting that L^/L^ = C^/C^ = /d 2 /d 1 and that Ly/Lj; = C^/Ci = /d 1 /d 1 = 1, 

 and substituting equations (163) and (165) into equation (169) , 



2/d^ cos X \ 2 / d 2\ 1/2 COS 6 2 



/dT cos 1 + Sd7 cos 2 / \d n / cos 0, 



yiT cos 0, + /d^ cos 2> 



which reduces to 



VdT" cos 0, + /d^ cos Y 

 vuT cos + v^a~" cos 0„ / 



(170) 



= 1 (171) 



proving that the equations of Cochrane and Arthur conserve the energy of 

 the incident wave. 



Cochrane and Arthur (1948) compared a calculated value for a wave 

 from the 1946 tsunami, which reflected from the continental slope off 

 southern Oregon, with an actual recorded wave height at Hanasaki, Japan. 

 Using a rough approximation for the wave height at the top of the conti- 

 nental slope, it was determined that the reflected wave arriving at 

 Hanasaki would have a height of 17 centimeters (0.56 foot). The observed 



72 



