84 



Symposium on Microseisms 



parallel to the crests of some wave components 

 of the incoming waves, but refraction of the 

 waves by the shoaling water will tend to bring 

 the crests parallel to the shore. 



If the incoming waves are represented by 

 a region Q i in the spectrum, then we may as- 

 sume that the reflected waves are represented 

 by a region Q 2 which is the reflection of Qi in 

 the line through parallel to the shoreline (see 

 figure 10, in which the x-axis is taken parallel 

 to the shoreline). Q2- is then the reflection 

 of Q 1 in the line through perpendicular to 

 the shoreline (the y-axis) . 



Suppose that the period of the incoming 

 swell lies between 12 and 16 seconds, that its 

 direction is spread over an angle of 30°, and 

 that its mean direction makes an angle of 10° 

 with the perpendicular to the shoreline. Then 

 we find Qj = Q 2 = 1.4 x 10" 8 cm/ 2 , Q 12 

 = 1/3 0, = 0.47 x 10" 8 cm." 2 . If the ef- 

 fective shoreline is 600 km. in length and the 

 region of interference extends, on the average, 

 10 km. from the shore, then A = 6,000 km 2 . 

 If also a 1 =2m, a 2 = 0. lm(a reflection coeffi- 

 cient of 5%) and if r = 2,000 km., then we find 

 from (26) (assuming h = 0) that 2|5|= 0.3(x. 

 Since this amplitude is somewhat smaller than 

 in case (a), we may conclude that coastal re- 

 flection does not give rise to the largest disturb- 

 ances at inland stations, though it may be a 

 more common cause of microseisms near to the 

 coast. 



Besides the examples given above there is 

 another possible class of cases, namely when a 

 swell meets an opposing wind. For example, 

 coastal swell may be subject to an offshore 

 wind, or there may be a sudden reversal of the 

 direction of the wind at the passage of a cold 

 front.* The wind will doubtless tend to dim- 

 inish the amplitude of the original swell, but 

 it may also tend to generate waves travelling 

 in the opposite direction, the amplitude of 

 which may increase rapidly on account of the 

 roughness of the sea surface. However, in 

 none of the first three cases discussed above is 

 it necessary to assume that such action takes 

 place. 



12. Observational tests — The present theory 

 suggests several possible kinds of experimental 

 investigation. The first is a comparison of the 

 periods of microseisms and of the sea waves 

 possibly associated with them, (which should 

 be about twice the microseism periods). There 

 is a general agreement between the periods, in 

 that the range of microseism periods is from 

 about 3 to 10 seconds while the periods of high 

 sea waves vary from about 6 to 20 seconds. 

 Further, the periods of both microseisms and 

 sea waves both increase, in general, during a 

 time of increased disturbance. The close two- 

 to-one ratio between the periods of sea waves 

 and of the corresponding microseisms which 

 was found by Bernard (1937 and 1941) and re- 



* See also the author's comment on the paper by 

 Frank Press. 



lated by Deacon (1947) and Darbyshire 

 (1948) is highly suggestive, though not conclu- 

 sive. A similar, though less detailed study by 

 Kishinouye (1951) during the passage of a 

 tropical cyclone, has not confirmed the relation- 

 ship. Comparisons of this kind are, however, 

 inconclusive, unless it can be shown that the 

 microseisms can be associated uniquely with 

 the recorded sea waves. The meteorological 

 conditions are rarely so simple, and the record- 

 ing stations so well placed, that it is possible 

 to be certain of the connection ; the examples se- 

 lected by Darbyshire (1950) were, how- 

 ever, chosen with this requirement in mind. 



Figure 7 shows that the displacement of 

 the "sea bed" may vary by a factor of the order 

 of 5, depending on the depth of the "ocean." 

 Although the model chosen is extremely simpli-. 

 fied, we can nevertheless infer that the ampli- 

 tude of microseisms should, on the present the- 

 ory, depend considerably on the depth of water 

 in the path of the microseisms ; the depth in the 

 generating area itself, where the energy-den- 

 sity is greatest, should be of the most critical 

 importance. Comparisons between the micro- 

 seisms due to storms in different localities 

 would therefore be of considerable interest. It 

 should be noticed that the unequal response of 

 the ocean to different frequencies may result 

 in a displacement of the spectrum towards 

 those frequencies for which the response is a 

 maximum. 



The nature of the frequency spectrum of 

 sea waves under various conditions is of fun- 

 damental importance, and further studies 

 should be undertaken. The wavelengths and 

 directions of the components of the spectrum, 

 both for swell and for waves in the generating 

 area, could be studied by means of aerial photo- 

 graphs or altimeter records taken from an air- 

 plane. An estimate of the amount of wave re- 

 flection from a coast might be obtained by tech- 

 niques similar to those which were used in the 

 model experiments described in Section 7, that 

 is, by comparing the frequency spectra of pres- 

 sure records taken at different depths in the 

 water, or off different parts of the same coast 

 where the bottom gradient varied. The effect 

 of an opposing wind on a swell might be in- 

 vestigated on a model scale, by generating pro- 

 gressive waves in the usual manner and then 

 exposing them to an artificial wind ; the growth 

 of the opposing waves would be measured by 

 means of the second-order pressure fluctua- 

 tions deep in the water. 



It would be of great interest to record 

 the pressure fluctuations on the ocean floor 

 directly, if the practical difficulties of making 

 measurements at such depths can be overcome. 

 A pressure recorder has been designed for this 

 purpose by F. E. Pierce, of the National Insti- 

 tute of Oceanography. 



