SECT. 5] MICROSEISMS 701 



they were always recorded before the swell arrived at the coast, and he, there- 

 fore, concluded that microseisms were caused by waves at sea and not waves on 

 the coast, the sea-wave energy being transmitted in some way to the sea 

 bottom to cause microseisms. These ideas were a great advance on anything 

 that had been done before, but Banerji was not able to explain satisfactorily 

 how the sea wave energy was transmitted to the sea bottom ; for, as is well 

 known, the effect of ordinary sea waves is negligible at a depth of half a wave- 

 length, and even in shallow depths as the microseism wavelength is much 

 longer than the sea wavelength, the pressure effects of several successive sea 

 waves tend to cancel out. 



Despite the theoretical difficulties, more and more observations confirmed 

 the relationship between the two kinds of waves. P. Bernard (1941) found 

 that the period of the microseisms was always about half that of the sea waves 

 associated with them. This was confirmed by G. E. R. Deacon (1947) who 

 compared sea waves recorded at Perranporth, Cornwall, and microseisms 

 recorded at Kew. Fig. 1 shows the close relation found between the amplitude 

 of waves and that of microseisms, and also between the sea- wave period and 

 twice the microseism period. 



In 1948 (with Ursell) and in 1950, Longuet-Higgins was able to give a con- 

 vincing explanation of this relationship. It had previously been shown by 

 Miche (1944) in another connection that, if there were stationary or standing 

 waves of amplitude a and angular frequency a on the water surface, then the 

 pressure does not disappear at large depths but is given by 



(:P2)oo = Ipa^cr^ cos 2at, 



the pressure variation having half the period (or twice the frequency) of the 

 stationary wave. 



Longuet-Higgins was able to give a physical explanation for this effect. This 

 can be seen by reference to Fig. 2, which shows the various stages in the station- 

 ary wave cycle. The total amount of water is the same in all the stages as there 

 is no net horizontal flow, but in stages (a) and (c) some water has had to be 

 raised up above the mean level, involving an increase in the height of the centre 

 of gravity and hence there must be an extra pressure on the sea bottom to 

 counteract this. This increase in pressure must appear twice per cycle. If one 

 considers a train of such stationary waves, it is clear that, at stage (a) for 

 instance, the centre of gravity of all the waves is lifted up and the waves 

 reinforce each other and the extra pressure can persist over a distance as long 

 as the microseism wavelength. 



Longuet-Higgins extended this argument to the case where two waves of 

 equal wavelength but different amplitude meet head on. A stationary wave is, 

 of course, a particular case of this. The more general case is shown in Fig. 3. 

 The waves have amplitudes ai and az. Suppose the wave of amplitude ai is 

 reduced to rest by superposing on the whole system a velocity —c, then the 

 second w^ave will pass alternately troughs and crests of the first wave, each 

 twice in a complete wave period. One may pass from stage (a) to stage (b) by 



