86 



Symposium on Microseisms 



COOPER, R. I. B., and LONGUET-HlGGINS, M. S., An ex- 

 perimental study of the pressure variations in 

 standing water waves. Proc. Roy. Soc. A, v. 206, 

 pp. 424-435, 1951. 



Darbyshire, J., Identification of microseismic activity 

 with sea waves. Proc. Roy. Soc. A., v. 160, pp. 439- 

 448, 1950. 



Deacon, G. E. R., Relations between sea waves and 

 microseisms. Nature, v. 160, pp. 419-421, 1947. 



Faraday, M., On a periodic class of acoustical figures, 

 and on certain forms assumed by groups of parti- 

 cles upon vibrating elastic surfaces. Appendix: 

 On the forms and states assumed by fluids in con- 

 tact with vibrating elastic surfaces. Phil. Trans. 

 Roy. Soc, pp. 319-340,, 1831. 



Kishinouye, P., Microseisms and sea waves. Bull. 

 Earthqu. Res. Inst., v. 29, pp. 577-582, 1951. 



Longuet-Higgins, M. S., and Ursell, F., Sea waves 

 and microseisms. Nature, v. 162, p. 700, 1948. 



Longuet-Higgins, M. S., A theory of the origin of mic- 

 roseisms. Phil. Trans. Roy. Soc. A., v. 243, pp. 1- 

 35, 1950. v 



Longuet-Higgins, M. S., On the decrease of velocity 

 with depth in an irrotational surface wave. (In 

 press) 1953. 



Martin, J. C, Moyce, W. J., Penney, W. G., Price, 

 A. T., and Thornhill, C. K., Some gravity-wave 

 problems in the motion of perfect liquids. Phil. 

 Trans. Roy. Soc. A., v. 244, pp. 231-281, 1952. 



MlCHE, M., Mouvements ondulatories de la mer en pro- 

 fondeur constante ou decroissante. Ann. Ponts 

 et Chaussees, v. 114, pp. 25-87, 131-164, 270-292, 

 396-406, 1944. 



Rayleigh, Lord, On maintained vibrations. Phil. Mag. 

 vol. 15, pp. 229-235, 1883. 



Rayleigh, Lord, On the crispations of fluid resting upon 

 a vibrating support. Phil. Mag., v. 16, pp. 50-58, 

 1883. 



Whipple, F. J. W., and Lee, A. W., Notes on the theory 

 of microseisms. Man. Not. Roy. Astr Soc 

 Geophys. Suppl., v. 3, pp. 287-297, 1935. 



Discussion 



G. E. R. Deacon (National Institute of Ocean- 

 ography at Teddington) 



The wave-interference theory explains, 

 for the first time, how energy sufficient to gen- 

 erate long, regular, microseisms is communi- 

 cated to the ground. It has been clear for a 

 long time that the occurrence of microseisms is 

 associated with the presence of sea waves, but 

 it could not be proved that the waves played an 

 essential part in the energy transfer. 



Although each breaker, as it crashes on 

 the coast, must cause a local disturbance, and 

 has been shown to do so, the variations in the 

 moment of impact along a stretch of coast, and 



the shortness of the wavelength compared with 

 that of 3 to 10 second microseisms, make it 

 most unlikely that the actual beating of surf on 

 a coast could produce the long microseismic 

 waves that can be detected far from the coast. 



The exponential decrease in wave move- 

 ment with depth was sufficient reason why a 

 train of progressive waves should not disturb 

 the sea bottom at great depths, and at lesser 

 depths the contributions from different parts 

 of the sea bed would tend to cancel each other 

 out. Taking account of the compressibility of 

 the water made no significant difference to this 

 conclusion. 



If the conviction held by many who had 

 studied microseisms, that sea waves are di- 

 rectly concerned in the generation of micro- 

 seisms were to be confirmed, we had to find a 

 theory which showed that sea waves were modi- 

 fied in such a way that they were able to cause 

 regular changes in pressure, acting simultane- 

 ously over large areas of the sea bed. During 

 the past few years it has, in addition," become 

 necessary to explain why the periods of the 

 microseismic waves are half those of the sea 

 waves, and how the effect of wind and wave- 

 height could vary with the depth of water, 

 being sometimes greater in deep water than in 

 shallow. 



The new wave-interference theory seems 

 to fill these requirements, and to be capable of 

 withstanding the test of more precise and well- 

 directed observations. 



It is not easy for the non-mathematician to 

 understand the precise demonstration that two 

 trains of waves of the same wavelengths, meet- 

 ing each other in opposite directions, will cause 

 variations in pressure on the sea bed with twice 

 the frequency of the surface waves, but Dr. 

 Longuet-Higgins has done his best to explain 

 it in non-technical terms. The deduction is 

 simplified by considering the vertical move- 

 ments of the centre of gravity of a water mass 

 bounded by two vertical nodal planes, and by a 

 comparison with the changing tension in the 

 string of a pendulum. It is perhaps not very 

 difficult to accept the result intuitively, as 

 Bernard (1941) did, particularly if we re- 

 member the convincing agreement between 

 theory and observation obtained by measure- 

 ments in a tank. 



There is also confirmation of the mean 

 pressure changes and their ability to produce 

 microseisms that can be detected far from the 

 coast, in the work of Darbyshire (1950). 

 As Dr. Longuet-Higgins says in his paper, 

 confirmation of the two to one relationship 

 between wave and microseism periods does not 

 completely verify the theory, but when, as 

 Darbyshire showed, the trend of a band of swell 

 from long to short periods was exactly par- 

 alleled by proportionate changes in the micro- 

 seism periods there is little room to doubt that 

 the waves caused the microseisms. 



