112 



Symposium on Microseisms 



surface, the pressure amplitude at the bottom 

 is greater than P in the ratio P b c b / w c w 



where Q b and o w are the densities and Cb and 

 Cw are the compressional wave velocities in the 

 bottom and water respectively. If we take o w 

 = 1, q = 3, c w = 5000 ft/sec, c b = 22,000 ft/ 

 sec, this ratio is 13.2, giving about 80 dynes/ 

 cm" at the bottom for a 6 dyne/cm" amplitude at 

 the surface. The displacement amplitude at 

 the bottom for an oscillation of period T will 

 be of the order of TP b /2rcP b c b = TP /2rr p„c w 

 which is about 0.3 micron for T = 5 sec and 

 the other quantities having the values assumed. 

 This should be a value characteristic of the 

 immediate area of generation and the ampli- 

 tude at a seismic station at some distance 

 should be considerably less, yet the amplitudes 

 of microseisms attributed to the passage of 

 cold fronts over deep water may run to more 

 than 2 microns. There seems to be a discrep- 

 ancy by a factor of 10 or more. 



I rather doubt that the idea of resonant 

 coupling between elastic waves in- two different 

 media due to coincidence between the phase ve- 

 locities of different wave types will turn out 

 to have a great deal to do with the coupling 

 of atmospheric pressure oscillations to the 

 ocean bed. Where it has been possible to cor- 

 relate wave forms of microbarometric waves 

 across a tripartite array, the apparent phase 

 velocity has usually come out to be very much 

 less than sound velocity and comparable with 

 the wind velocity at some moderate altitude. 

 Gravity surface waves on the ocean also have 

 phase velocities of the same order as wind ve- 

 locities, so that if microbarometric oscillations 

 are coupled with anything in the ocean it is 

 presumably with gravity rather than compres- 

 sional waves. 



Gravity waves only 1 meter high would 

 give pressure oscillations of the order of 10 6 

 dynes/cm" near the surface and bottom pres- 

 sures exceeding the 80 dynes/cnf estimated for 

 the direct excitation of the "organ pipe" modes 

 for all water depths less than 1.25 wave lengths, 

 or about 160 feet for waves of 5 sec. period. 

 So far as pressures go, surface waves in shal- 

 low water seem to be adequate to generate 

 observable microseisms. 



However, there seems to be a good deal of 

 statistical evidence that at least some micro- 

 seismic activity, and perhaps most of it in some 

 areas, has a deep water origin. Whipple 

 and Lee (1935), investigating Banerji's 

 (1930) suggestion that gravity waves should 

 generate compressional waves that were not 

 attenuated exponentially with depth, showed 

 that the compressional wave travelling with the 

 velocity of gravity surface waves would neces- 

 sarily have an exponential attenuation rather 

 than a sinusoidal variation with depth. 



If therefore appears to me that neither the 

 direct action of atmospheric pressure oscilla- 



tions nor indirect coupling via gravity waves 

 in the first order linear approximation are ade- 

 quate to explain the generation of microseisms 

 in deep water, and the second order term in the 

 expression for the bottom pressure as discussed 

 by Longuet-Higgins (1950) is the only mecha- 

 nism that has been proposed so far that 

 looks quantitatively adequate. The failure of 

 some observers to verify the two-to-one ratio 

 between the periods of ocean waves and of mi- 

 croseisms as deduced from this theory may in- 

 dicate nothing more than that the wave peri- 

 ods observed on a swell recorder in shallow wa- 

 ter near the coast are not necessarily the same 

 as the periods of the interfering wave systems 

 that produce microseisms in the storm area. A 

 deep-water bottom pressure recorder should 

 throw a great deal of light on this question. 



REFERENCES 



Banerji, S. K., Microseisms Associated with Disturbed 

 Weather in the Indian Seas. Phil. Trans. Royal 

 Soc. A., 229, 287 (1930). 



Daniels, F. B., Acoustical Energy Generated by the 

 Ocean Waves. Journ. Acoust. Soc. Amer., 24, 83 

 (1952). 



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

 Microseisms. Phil. Trans. Royal Soc, A., 242 

 (1950). 



Roschke, W. H., Jr., The Relationship Between Air 

 Pressure Micro-Oscillations and Concurrent Synop- 

 tic Patterns. Journ. Met., 9, 213 (1952). 



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

 of Microseisms. Mthly. Notes Royal Astrom. Soc, 

 Geo., Suppl., 3, 287 (1935). 



Discussion from the Floor 



Lynch. Since the purpose of this conference 

 is to reconcile contradictory views on micro- 

 seisms as far as possible, I should like to call 

 attention to a contradiction or at least an ap- 

 parent contradiction presented by the opening 

 part of Dr. Press' paper. He states, on the 

 basis of Dr. Wm. Donn's work that micro- 

 seismic activity on the East Coast begins only 

 when the cold front enters the Atlantic. The 

 speaker in a paper yesterday states that he 

 and his colleagues feel positive that microseis- 

 mic activity on the East Coast from cold fronts 

 originates in the Great Lakes. Here then we 

 have an apparent contradiction — one author 

 claims the activity originates in the Great 

 Lakes, another author claims the activity origi- 

 nates in the Atlantic — to the casual listener 

 surely a contradiction! 



This, however, is one contradiction that 

 we can easily reconcile. I should like to point 

 out that the time taken for a microseismic wave 

 to reach New York from the Great Lakes is a 

 matter of minutes. I should like to point out 



