92 



Symposium on Microseisms 



less in opposition to the waves gen- 

 erated a few hours previously may be 

 a very effective method of producing 

 the necessary standing wave system. 



One may also refer here to the association 

 of microseisms with cold fronts to support the 

 thought that a relatively sudden reversal of 

 wind over shallow water areas provides a con- 

 dition for microseism generation. Typical 

 weather conditions off the eastern North 

 American coast, prior to the arrival of a cold 

 front, include moderately strong southernly 

 winds. These winds would develop waves 

 travelling in a northerly direction of relatively 

 small amplitude and short period. Following 

 the passage of the cold front the wind direction 

 normally changes abruptly to the northwest. 

 It is reasonable that at some time, shortly after 

 the passage of the front, waves developed by 

 the northwest winds will have periods and 

 wavelengths nearly equal to that of the dying 

 swell from the south. Thus, a standing wave 

 component could exist which would have the 

 potential for excitation of microseisms in ac- 

 cordance with the Longuet-Higgins theory. 



REFERENCES 



Banerji, S. K., Theory of Microseisms. Proc. Indian 

 Acad. Sci., A 1; 727-753, 1935. 



Carder, D. 'C, Earthquake Notes, Vol. 22, Sept. 1951. 



Darbyshire, J., Identification of Microseismic Activity 

 with Sea Waves. Proc. Roy. Soc, 202A; 439-448, 

 Aug. 7, 1950. 



Deacon, G. E. R., Relations between Sea Waves and 

 Microseisms. Nature 160; 419-421, 1947. 



Donn, W. L., Cyclonic Microseisms Generated in the 

 Western North Atlantic Ocean, J. of Meteor. 9; 

 61-71. Feb. 1952. 



Longuet-Higgins, M. S., A Theory of the Origin of 

 Microseisms. Phil. Tran. Roy. Soc. A., 243; 1-35, 

 1950. 



Discussion 



J. G. SCHOLTE 



Royal Netherlands Meteorological Institute 



The existence of an unattenuated pressure 

 variation in the ocean was already suspected 

 by Whipple and Lee (1935) and some years 

 later Bernard (1941) also suggested that a 

 standing wave-system produced in some 

 way microseisms, but the well-known expo- 

 nential decrease of gravity waves precluded 

 any understanding of the process. However, 

 in 1942 Miche proved that in the case of 

 standing gravity waves in an incompressible 



ocean a second order pressure variation exists 

 which is not essentially influenced by the depth. 

 Moreover, as the frequency of this variation 

 is twice that of the ocean waves and as Bernard 

 had observed that the period of microseisms is 

 roughly half that of sea waves, Longuet- 

 Higgins and Ursell (1948) supposed that 

 this second order effect is the primary 

 cause of some microseisms. 



The formula obtained by Miche can be 

 derived by a small extension of the theory of 

 gravity waves. Consider the irrotational mo- 

 tion in an incompressible ocean of infinite 

 depth ; for simplicity's sake we suppose the 

 movement to be two-dimensional. 



The horizontal (u) and vertical (w) com- 

 ponents of the velocity are determined by a 

 velocity-potential : 



u = - d<f>/ dx and w = - di/ 'dz. 

 From the equations of motion 



Du/Dt = 



dP , Dw 



and — - 



Sx Dt 



ep 



dz 



+ gP 



where D/Dt = a differentiation following the 

 motion of the fluid, and p = the pressure, we 

 obtain d< p 1 



St 2 



+ gz 



Po 



the constant 



with q 2 = u 2 + w 2 and p 

 pressure at the free surface. 



Placing the origin in the undisturbed sur- 

 face the equation of this surface is 



= C . eC- 



et / 



L 



The potential <£ has to satisfy the equation 

 of continuity A 4> = and the boundary con- 

 dition 



D/D 



tf^-Iq 2 + gz)=0 for z =C, 

 \dt 2 ) 



or 



dH 

 at 2 = 



d<t> dc > 2 i/ a 2 r y 



g — + + % q A Q Z f or z = C 



dz dt 



(1) 



A wave system consisting of two plane 

 progressive waves travelling in opposite di- 

 rections : 



<p . =— Raisin (kx - ft) - 'a 2 sin ( kx + v t) f e with aj 



