Table III shows five waves in the leading envelope for North American 

 stations south to San Diego. Variations from this number are explained as 

 interference effects of merging wave trains . 



The number of waves in the leading envelope increases to 8 and 9 

 along the South American coast, but again this development is found to 

 be incipient in the two leading envelopes for San Francisco and Rincon 

 Island, California (Figures 50 and 51), and again the explanation is an 

 interference effect of competing wave trains of the basic type (5 waves 

 per beat). The 5-waves-per-beat character of the tsunami is still re- 

 tained in the waves reaching the Hawaiian Islands (Figures 57 to 59), 

 but is then lost to much longer envelopes in the records for the more 

 distant stations in the West Pacific. Tsunami signatures shown in 

 Figures 6l to GG have about 8 waves in the leading envelopes, but since 

 these tsunamis originated from a restricted part of the source region at 

 the southwest end, they may have been of fundamentally different shape 

 at the outset. 



The periods T]_ of Table III range from 1.5T to 2.33 hours and average 

 1.79 hours (l08 minutes). When this information is plotted in Figure 71, 

 which is adapted from original data of Takahasi (1961) supplemented by 

 other data (Wilson et al, 1962; Wilson, 196i+), a best fit curve to the 

 total data yields the relationship 



log^Q T = (5/8) M - 3.31 (19) 



where T is the tsunami period in minutes and M the earthquake magnitude. 



Equations (3) and (19), empirically derived from statistical data, 

 suggest a relationship between the tsunami period and the effective source 

 diameter S. Elimination of M between these equations, gives 



T = 0.3l6S^^/^^ (20) 



for T in minutes and S in kilometers. 



This result clearly implies that the tsunami period is directly 

 proportional to the source diameter, a relationship which can be shown 

 to have some theoretical support. It was shown, for instance, by Wilson, 

 et al (1962), Wilson (196U) that Kranzer and Keller's (1959) result for 

 the surface disturbance n at a great distance r from an arbitrary radially 

 symmetric initial surface elevation Q(r) of the water surface, centered at 

 a source (r = 0), could be expressed (in the case of shallow water) as 



n = [H(k)/rd]cos (kr-at) (2l) 



in which H(k) is the Hankel transform in the variable k of the function 

 Q(r). 



For the case of a supposed cylindrical rise of water level at the 



104 



