In the matter of tvo-dimens.ional (jr, radial) propagation of disper- 

 sive waves, Wilson, et al C1962I, Wilson ( I96U ) , had concluded that height 

 decays as r-1 in the body of the waves and as r'-5/6 near the wave front. 

 Some experimental evidence seemed to support those conclusions at that 

 time, particularly the experiments of Takahasi C1961) and the field re- 

 sults reported by Van Dorn (1961). However, Kajuira C1963), using more 

 rigorous theory, has shown the amplitude decay of the leading wave of a 

 tsunami will conform to the law H « r-2/3 in two-dimensional propagation 

 from a rectangular source, provided 



(a/d) (6 v/dTi /t)^/2 > 3 (16) 



where a is the half-length of the major axis and propagation is in the 

 direction of that axis (see also Van Dorn, I965). 



Data represented by the third group of points in Figure TO, which 

 apply to stations west and southwest of the tsunami source region, are 

 clearly representative of two-dimensional (radial) wave propagation. 

 Their scatter appears to be centered around the line H « ]--2/3 near a 

 value of r/d - 1,000. Kajiura's condition would then require 



a/d > 3 (r/6d)l/3 (IT) 



For a depth d - 15,000 feet. Equation (iT) stipulates that 



a > 75 km (18) 



In this condition Equation (18) is well satisfied by the inferred dimen- 

 sions of the tsunami source region. 



5. Period Characteristics of the Main Tsunami 



Table III shows that the periods Ti, the average of the first 

 three waves in the beat of the primary wave system, are remarkably uniform. 

 This suggests that these large waves were, in effect, nondispersive. 



Because of the smallness of the relative depth kd, where k(= 2it/X) 

 is the wave number, and X the wave length, the group velocity of the wave 

 envelopes would not be sensibly different from the phase velocity of the 

 individual waves in the bpats. Thus kd is normally less than I/60 for 

 waves of 2 hours approximate period in an ocean 12,000 feet deep. Over 

 a travel distance as long as 10,000 nautical miles the waves would out- 

 pace the envelope by only about 10 seconds. This implies that the beat 

 structure of the main tsunami should remain largely unchanged. The 

 stations from Yakutat to San Diego, Figures k3 to 52, suggest that this 

 was generally true, and the earth movement along the fault length must 

 have been of a rather uniform character, probably well symbolized by 

 Figures 3^, 36 and 37. 



103 



