Can Sea Waves Cause Microseisms 



85 



13. Historical notes — It was known to FARA- 

 DAY (1831), who refers to earlier work by 

 Oersted, Wheatstone and Weber, that fluid rest- 

 ing on a vibrating elastic plate will form itself 

 into short-crested standing waves. Faraday 

 was the first to show, by an ingenious optical 

 method, that the period of the standing waves 

 is twice that of the vibrations of the plate. The 

 waves that he used were mostly "ripples," con- 

 trolled predominantly by surface tension, since 

 their wavelength lay between 14 and % inch. 

 In the same paper (1831) Faraday describes 

 many other interesting experimental studies 

 of waves in water, mercury and air. 



About fifty years later Rayleigh (1883 

 b) repeated Faraday's experiments and veri- 

 fied, by a slightly different method, the doub- 

 ling of the period. In a theoretical paper 

 (1883 a) Rayleigh gives general consideration 

 to the problem of how a system can be main- 

 tained in vibration with a period which is a 

 multiple of the period of the driving force. He 

 refers in particular to Melde's experiment, in 

 which a stretched string is made to vibrate by 

 the longitudinal oscillation of a tuning fork 

 attached to one end ; such a phenomenon is 

 sometimes called "subharmonic resonance." 



Neither Faraday (1831) nor Ray- 

 leigh (1883) evaluated the second-order 

 pressure fluctuations associated with standing 

 waves. This, however, was done by MICHE 

 (1944) in a different connection, using a La- 

 grangian system of coordinates. Miche noticed 

 the unattenuated terms, and, though he does not 

 mention microseisms, he remarks, "on peut 

 aussi se demander si ces pulsations de pression, 

 malgre leur faible intensity relative, n'exercent 

 pas une action non negligeable sur la tenue des 

 fonds soumis au clapotis." (1944, p. 74.) 



The wave interference theory seems to 

 have arisen as follows. In 1946 Deacon, fol- 

 lowing similar studies by Bernard (1937, 

 1941 a) compared the period and amplitude of 

 swell off the coast of Cornwall, England, with 

 the corresponding microseisms at Kew, and 

 found a two-to-one ratio between the periods 

 (Deacon 1947). F. Biesel, then visiting 

 England, pointed out to Deacon Miche's theo- 

 retical work on standing waves. Miche's re- 

 sults, however, cannot be applied directly to sea 

 waves, since exact standing waves do not oc- 

 cur in the ocean. Moreover, his method is not 

 easily generalized, since it involves a complete 

 evaluation of the second approximation to the 

 wave motion. A very simple proof of Miche's 

 result, however, which depended essentially on 

 the idea of the vertical motion of the center 

 of gravity of the whole wave train, was 

 found by Longuet-Higgins and Ursell (1948) ; 

 the advantage of this method was that 

 the second-order pressure fluctuations on the 

 bottom could then be obtained immediately 

 from the first approximation to the surface ele- 



vation. It then became possible to extend the 

 results to much more general and realistic types 

 of wave motion. A complete theory, giving 

 the necessary conditions for the occurrence of 

 this type of pressure fluctuation, taking into 

 account the compressibility of the ocean, and 

 determining the order of magnitude of the 

 ground movement, was given by Longuet- 

 Higgins (1950). 



It is interesting that Bernard (1941 a, 

 b) had suggested, with intuitive reasoning, that 

 microseisms might be caused by the standing- 

 type waves observed to occur at the center of 

 cyclonic depressions : 



"J'ai cru qu'on pourrait trouver la raison 

 de cette particularity dans le charactere que 

 presentent les mouvements de la mer au centre 

 des depressions cycloniques : la houle s'y dresse 

 aux vagues pyramidales constituant un clapotis 

 gigantesque dont les points de plus ample os- 

 cillation peuvent etre autant des sources de 

 pression periodique sur le fond de la mer, 

 pression qui donnera naissance a un mouve- 

 ment oscillatoire de meme periode du sol . . . " 



"Un clapotis analogue, avec oscillations 

 sur place du niveau de l'eau, se produit lorsque 

 la houle, se reflechissant sur un obstacle, vient 

 interferer avec les ondes incidentes . . . 



"Au contraire, dans le cas d'un train 

 d'ondes de front continu et de deplacement 

 constant, les points ou les mouvements sont de 

 phase opposee donneront sur le fond de la mer 

 des pressions de sens contraire, et la longeur 

 d'onde des oscillations microseismiques etant 

 beaucoup plus grande que celle de la houle, les 

 mouvements transmis par le sol a une certaine 

 distance seront pratiquement simultanes, mais 

 opposes, et ils interfereront, de sorte que 

 l'effet total du train de vagues a l'exterieur sera 

 mil." (BERNARD, 1941 a, p. 7.) 



However, Bernard did not apparently see 

 that the corresponding pressure fluctuations 

 must have a frequency twice that of the waves ; 

 for he suggests other causes for the observed 

 doubling of the frequencies in the case of coast- 

 al waves." (Bernard, 1941a, p. 10.) 



REFERENCES 



Bernard, P., Relations entre la houle sur la cote du 

 Maroc et V agitation microseismique en Europe oc- 

 cidentale, C. R. Acad. ScL, Paris, v. 205, pp. 163- 

 165, 1937. 



Bernard, P., Sur certaines proprietes de la houle etu- 

 diees a I'aide des enregistrements seismograph- 

 iques. Bull. Inst. Oceanogr. Monaco, v. 38, No. 800, 

 pp. 1-19, 1941. 



Bernard, P., Etude sur Vagitation microseismique et 

 ses variations. Ann. Inst. Phys. Globe, v. 19, pp. 

 1-77, 1941. 



