In the Pacific-Antarctic area near longitude 130° W, Figure 27 

 suggests a strong focusing of vave rays, and pronounced tsunami effects 

 probably resulted if the tsunami remained relatively unaffected by the 

 screen of islands in the Tuamotu Archipelago and nearby island clusters. 

 That the tsunami did breach the island barriers without sensible loss 

 of its identity is shown by the sequence of analyses in Figures 5T 

 through 60. 



For Midway Island; Mokuoloe Island, Oahu, and Hilo, Hawaii; repre- 

 sented by Figoores 57 through 59, the primary signatures are similar and 

 comprise a leading beat of about five waves of 1.8 hours period with a 

 maximum beat-height at Hilo of 1.8 feet. 



Lyttelton, New Zealand, has an elongated rocket-shaped beat of 10 

 waves with periods of 1.8 to 1.5 hours and a maximum height of 3.8 feet 

 (Figure 60). The waves reaching Lyttelton had to penetrate the Hawaiian 

 Islands, cross the Christmas Island Ridge, and then follow a ray parallel 

 to the Tonga Trench (Figure 27). Their emergence in such pure form and 

 high amplitude (Figure 60c), even after radial spreading caused by the 

 Tonga Trench bathymetry, indicates not only that the island barriers were 

 ineffective scatterers of the large waves, but that the signal strength 

 was significant to excite so large a response. 



This raises the interesting question whether Lyttelton provided 

 appropriate conditions for pseudoresonance of the tsunami. Lyttelton 

 lies about half-way up a l6-mile long inlet (Port Lyttelton) on the east 

 coast of South Island, New Zealand. This inlet (Figure 69) is about 1 

 mile wide along most of its length and shelves almost uniformly from a 

 depth of about 7 fathoms at the mouth. We use the eigenperiod formulas 

 for a uniformly sloping rectangular open-mouthed basin (cf. Wilson, I966). 



(i) T^ = 5.236 L/v^i 



(10) 

 (ii) T2 = O.I135 Tj^ 



where T-|_ and T2 are the first and second mode periods of free oscillation 

 of the inlet, L is its length and d-|_ its depth at the mouth. For L = I6 

 miles, d-]_ = k2 feet; T-^ is 3.35 and T2 is l.UG hours. It is thus inferred 

 that the tsunami would have excited a near-resonant response from the 

 second mode of the free oscillation. 



We now enquire into the amplification that could be expected of waves 

 entering the inlet with periods of 1.8 and 1.6 hours. We require the 

 generalized formula for wave height amplification a at a specified distance 

 x from the head of the inlet. This formula developed from Lamb (1932) and 

 akin to Equation (8) is: 



2 



in which K, a wave number, has the same definition as given in Equation (9) 



a Ml - ^) (1+1^) (11) 



95 



