source for which QCr) =Q, r^R;Q=0,r>R, the Hankel transform is 

 found to "be 



H(k) = Q R Ji (kR)/k (22) 



wherein J-, (kR) is the first order Bessel function of the variahle (kR). 

 This Bessel function provides the modulation to the wave system expressed 

 "by Equation (2l) and thus effectively defines the beat. Nominally it 

 could "be said that the leading beat length would be defined by the first 

 finite value of kR for which the Bessel function J]_ (kR) is zero, namely 

 kR = 3.832. In the more general case for which Q(r) is some unknown 

 function we should expect kR to have some unknown value 3, that is, 



kR = e (23) 



where R, in this case, would represent some nominal radial limit to the 

 equivalent initial circular disturbance. Thus 2R = S and Equation (23) 

 may be replaced by 



kS = 26 (2i+) 



Because the waves of the Alaskan tsunami have been shown to be effectively 

 nondispersive, we invoke Equations {h) and (5) to express Equation (2^+) in 

 the form 



T /iTd = (^/3) (S/d) (25) 



which immediately shows that T <^ S as predicted by the empirical result. 

 Equation (20). 



If Equations (20) and (25) are combined, the value of g is found to 

 be 



e = 107.6/ /d (26) 



for d in feet. From Equation (25) we should now expect that the wave 

 periods generated would be given by 



T = (tt/107.6 /i") S (27) 



for T in seconds and S in feet. Resorting to the value of S = U25 km 

 (Figure 28), the wave period from Equation (27) is found to be 



T = 1.99 hours (28) 



which is in quite good agreement with the values of 1!-^ given in Table III. 



6. The Transfer of Tsunami Energy to Higher Frequencies 



Aerial photographs of waves reaching a discontinuity, (such as 

 a breakwater end), or passing over a submerged obstruction (such as a 

 rocky outcrop) frequently show odd harmonics of the incident waves in the 



106 



