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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Can Sea Waves Cause Microseisms
Can Sea Waves Cause Microseisms
Pages 74-93
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From page 74... ...
But until recently there have seemed to be many difficulties, both theoretical and observational, to supposing that sea waves could, by direct action on the sea bed, be the cause of all these microseisms; for the latter have been recorded while the corresponding sea waves were still in deep water, whereas theory seemed to show that the pressure fluctuations associated with water waves were quite insufficient, at such depths, to produce any appreciable movement of the ground. However, recent theoretical work in hydrodynamics has altered this situation: Miche (1944)
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From page 75... ...
In other words, in a progressive wave the contributions to the disturbance from different parts of the sea bed tend to cancel one another out. There is a second reason why progressive water waves may be expected to be relativly ineffective in producing seismic oscillations of the sea bed: not only the mean pressure fluctuation p, but also the pressure fluctuation p at each point decreases very rapidly with, depth and is very small below about one wavelength from the surface.
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From page 76... ...
the external forces acting on the mass are, first, that due to gravity, which is constant, (the total mass being constant) ; secondly the force from the atmosphere, which is also constant, since the pressure p0 at the free surface, if constant, will produce a constant downwards force Xp0 ; thirdly the forces across the vertical planes, which must have zero vertical component, the motion being symmetrical about these planes; and, lastly, the force on the bottom, which equals X p.
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From page 77... ...
a2 a2 cos 2at (11) The mean pressure fluctuation on the bottom is therefore proportional to the product of the two wave amplitudes ai and a2.
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From page 78... ...
This indicates that below a certain depth, in a strictly space-periodic motion, the pressure fluctuations are uniform and equal to the fluctuation p(t) in the mean pressure on the bottom, which has been evaluated.
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From page 79... ...
Indeed this property seems to provide a convenient method of actually measuring the coefficient of reflection from different types of obstacles or from plane beaches. Since standing waves produce only secondorder pressure fluctuations below moderate depths one would expect that, if pressure fluctuations were induced deep in the water, standing waves of half the frequency would be produced at the surface.
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From page 80... ...
. Below this level the displacements are comparatively small, but, instead of the uniform, unattenuated pressure fluctuations in the incompressible fluid, there is now a compression wave, whose planes of equal phase are horizontal: the pressure field in this wave is given by a2 a2 (12)
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From page 81... ...
The expression for the mean pressure variation is therefore the same as if the free surface were the only moving boundary: Similarly in the three-dimensional case P - PD 61 6t2 that is P-P0 (23)
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From page 82... ...
we have oo co (26) a2 A'Al e I0t du dv -co - CO This shows that fluctuations in the mean pressure p arise only from opposite pairs of wave components in the spectrum; that the contribution to p from any opposite pair of wave components is of twice their frequency and proportional to the product of their amplitudes; and that the total pressure fluctuation is the integrated sum of the contributions from all opposite pairs of wave components separately.
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From page 83... ...
11. Practical examples -- We have seen that a necessary condition for the occurrence of the type of pressure fluctuations studied in this paper is that the motion of the sea surface should contain at least some wave groups of the same wavelength traveling in opposite directions.
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From page 84... ...
The effect of an opposing wind on a swell might be investigated on a model scale, by generating progressive 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 fluctuations 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.
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From page 85... ...
nor Rayleigh (1883) evaluated the second-order pressure fluctuations associated with standing waves.
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From page 86... ...
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 movement 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.
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From page 87... ...
DINGEB Naval Research Laboratory As a discussion of the theoretical paper "Can Sea Waves Cause Microseisms," I should like to present some of the data and interpretations obtained by the Naval Research Laboratory on various field trips during the hurricane seasons of the past several years. The data considered here is concerned with hurricanes which have followed paths in the Western Atlantic and Caribbean.
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From page 88... ...
(2) The installation of two wave gages at Cocoa Beach, Florida, through the cooperation of the Beach Erosion Board and the University of California.
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From page 89... ...
This location is approximately 50 miles inland from Cocoa Beach, and therefore can be considered isolated from local surf vibrations, which can cause high seismic noise near the shore. The simultaneous data of microseisms and water waves obtained by these installations during the two hurricanes of the 1951 season is of special interest in that the paths of the storms were radically different.
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From page 90... ...
However, the value of the arbitrary units for A and B is the same. The sharp increase in both wave height and period as shown in curves C and D on the morning of September 8 accompanied the arrival of the swell from "Easy." Data from a Beach Erosion Board gage at Cape Henry and a report from Weather Ship H, several hundred miles east of Charleston, N
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From page 91... ...
We note an abrupt increase in wave amplitude during the early morning of 2 October, reaching a maximum about 1200 and dropping off abruptly about 2000. Referring again to Figure 1 we see that the forward part of the storm entered the Atlantic in the morning of 2 October with strong winds blowing from south-southeast and bringing waves toward Cocoa Beach.
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From page 92... ...
However, in 1942 Miche proved that in the case of standing gravity waves in an incompressible |
From page 93... ...
The only difficulty which it encounters is the fact that microscisms occur very often, while it is a matter of considerable doubt whether standing waves of rather large amplitudes are as common. REFERENCES LoNGUET-HicciNS, M
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