Symposium on Microseisms Held at Arden House, Harriman, N.Y. 4-6 September 1952, Sponsored by the Office of Naval Research, and the Geophysical Research Directorate of the U.S. Air Force. (1953) / Chapter Skim
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On the Theories of Microseisms
On the Theories of Microseisms
Pages 114-129
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From page 114... ...
Consequently we have to consider waves of compression in a purely elastic system consisting of a fluid layer of finite depth h covering a solid body. Consider a cartesian coordinate system with the x axis in the free surface parallel to the direction of propagation and the z axis vertically downward.
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From page 115... ...
(i v(X Sin Y - ' \ \ c the reflected wave * i = RA exp and two refracted waves: the longitudinal one: u = -- , w = -- -- , with the potential dx dy /x sin a + 2 cos a h cos y h cos a and the transverse wave: u = -- -- , w = -- -- 7 oz ox with the vector-potential ^ in the y-direction: 'x sin p + Z cos p h cos y h cos r /> f = DtAexp / i vl a and b are the velocities of longitudinal and tion (R and D)
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From page 116... ...
i travelling in the Y direction is given by oo « -- r I I Hence n -- o /x sin Y + Z cos exp*
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From page 117... ...
which excites this sure TM of the secondary waves |
From page 118... ...
where J,, is a Bessel function and The motion of the bottom is then given by the same expressions (2) , if we change the factor exp (ivx/c sin y)
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From page 119... ...
= 1 (5) it is obvious that the values YI» corresponding to the roots ^ determine the directions Y for which the reflected elementary wave 4'\ is identical to ^i-2 (the phase shift caused by the two reflections at the boundaries cancels the difference in ohase due to twice transversing the layer)
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From page 120... ...
120 SYMPOSIUM ON MICROSEISMS have used the numerical values a/b b/c = 2 andp/p!
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From page 121... ...
ON THEORIES OF THE ORIGIN OF MICROSEISMS 121 with the root sin (3 = b/S-j, where S-j = the velocity of these waves. Hence the first curve starts at sin jS = b/S, > 1 and tends asymptotically to sin /3 = b/Sj > b/c.
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From page 122... ...
In order to obtain a microseismic amplitude of 5 n the total force Q has to be about 3.10 '"' dynes; assuming the radius of the storm area ss> 18 km it appears that a mean pressure variation of 1/3 mb is necessary to produce the observed microseisms. In this calculation it has been assumed that the pressure variations at widely separated points are correlated; as this will not be the case in actual circumstances, the obtained value of 1/3 mb has to be interpreted as the effective pressure variation.
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From page 123... ...
is the only published treatment which can quantitatively account for energy transfer from the atmosphere to the ocean. Little work has been done on the possibility that pressure fluctuation and gustiness present in turbulent air masses can transfer energy directly to compressional waves in the ocean.
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From page 124... ...
Hydrographic records of pressure and temperature have to be used. There is no microseismic effect observed when cold fronts pass the limit of the continental shelf outside the Norwegian coast, whereas there is generally rapid increase of the microseisms when the cold fronts pass the coast itself.
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From page 125... ...
On the western side of the ocean great emphasis was placed on the possible effect of microbarometric oscillation which looked nothing like the microseism records; if they had any period it was the wrong one, and the theory used to explain the energy transfer required confirmation at many points. The theory used on the eastern side of the ocean was held to be unsatisfactory.
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