660 MUNK [chap. 18 



If the oceans were of constant depth and of infinite extent, the disturbance 

 following the initial arrival would be of very short duration. This is because the 

 waves are almost non-dispersive. For any (angular) frequency to the group 

 velocity is given by 



V = {gh)y^[l-h{co%^l9)+...] 



and for waves of 5-min period at a depth of 4 km this equals roughly V — 

 0.9\/{gh). Thus the group velocity is diminished by 10% relative to waves of 

 infinite length, and the travel time is increased accordingly. If the initial arrival 

 took 10 h, waves of 5-min period should arrive 1 h later. Relatively little energy 

 goes into waves of periods shorter than 5 min, and the entire disturbances 

 should be a matter of hours. The foregoing estimates are confirmed by a more 

 rigorous examination of the appropriate initial value problem (Prins, 1956). 



In fact, the disturbances following a major tsunami are noticeable for a 

 week. The amplitude decays to 1/e of its value once every twelve hours (Munk, 

 1961). What is the cause of the prolonged oscillation? Trapping of tsunami 

 energy into slow-edge waves along the continental shelves is a possibility. The 

 scatter of tsunamis by sea mounts and other bottom irregularities would lead 

 to reverberations. Probably a more important factor is multiple reflections at 

 the continental boundaries, and in some instances it has been possible to 

 identify second arrivals with definite refiected paths (Cochrane and Arthur, 

 1948; Shimozuru and Akima, 1952). 



In all events the subsequent stages of tsunamis resemble in their complexity 

 the day-to-day background oscillation (except for being higher), and the 

 power-spectral analysis is enlightening even though we are not dealing with 

 stationary time series. Fig. 9 shows comparative spectra of a tsunami and of 

 background activity at Acapulco. The tsunami spectrum is two to three orders 

 of magnitude above background. The outstanding feature is the principal peak 

 at 0.57 c/ks in both spectra. A smaller peak at 1.5 c/ks is also reproduced 

 whereas a third peak at 1.15 c/ks is found only in the tsunami spectrum. 



In general it is found that the spectra of different tsunamis at any one 

 station look alike, whereas one tsunami at different stations has no reproducible 

 spectral features. The inevitable conclusion is that tsunami records are governed 

 principally by the bottom topography near the recording station, and not by 

 the character of the source. In the case of stations in harbours, the deep-sea 

 spectrum is viewed through the additional "harbour filter", and the distortion 

 is even more extreme. 



Some efforts to remove the effect of harbour resonances have been made by 

 Rikitake (1949). Perhaps the use of analogue models (Ishiguro, 1959) can lead 

 to realistic appraisals of the response function of harbours and bays. An alter- 

 native (and perhaps preferable) scheme is to install stations on small steep 

 islands with resonances (if any) well above the frequencies characteristic of the 

 tsunamis. The latter point of view has been pioneered by Van Dorn (Van Dorn 

 and Donn, 1960). He has demonstrated that, for waves the length of which 

 equals the circumference of a circular island, the wave height will be 50% higher 



