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Subject: Rayleigh waves
From: Randall Peters PETERS_RD@..........
Date: Mon, 21 Dec 2009 08:52:51 -0500

     I agree with you that the vertical strain will give rise to a transver=
se strain also, because of the Poisson ratio.  However, I don't see in this=
 a mechanism for the required phase difference between the two components. =
 In a Rayleigh wave the vertical and horizontal motions are out of phase wi=
th each other by 90 degrees--what is called phase quadrature.  If what you =
say is true, then why are there no significant Rayleigh components associat=
ed directly with the vertical component of an earthquake rupture?  In other=
 words I would expect two surface waves following arrivals of P and S--one =
from the rupture itself and the other from the superposition of P and S, as=
 described in all seismology textooks. (The textbook argument for their gen=
eration is one of P and S waves combining at the surface after they have tr=
aveled a distance that is a significant fraction of the radius of the Earth=
).  This description involving superposition is one that I fully appreciate=
 from a conceptual point of view.   The physics ought to be the same whethe=
r for teleseismic surface waves of Rayleigh type and for solid state filter=
s called surface acoustic wave (SAW) devices.  The saw devices use interlea=
ved electrodes that operate on the basis of the force that exists between a=
djacent strips because of their capacitance.  Moreover, they are a coherent=
 array, meaning enough strips to provide several wavelengths.  I believe th=
e force between strips must involve both vertical and horizontal components=
; i.e., a source of shear.  I must admit that my description is one based o=
n intuition that could be erroneous.  The full description of math-type wou=
ld be complicated and one with which the venerable A.E. H. Love would be pl=
eased  There is still another feature of fundamental physics that I believe=
 should be considered in relation to the microseisms, no matter whether my =
hypothesis is true.  The crust of the Earth has some very special propertie=
s when it comes to geoscience.  The Moho (crustal thickness) was discovered=
 as the result of the discontinuity in phase velocity of P-waves as they cr=
oss the interface between crust and mantle.  Thus I expect that microseisms=
 should be confined to the crust, behaving in a manner similar to electroma=
gnetic guided waves.  Since the crust as a waveguide cannot support waves w=
hose wavelength is greater than the crustal thickness, this results in a lo=
w frequency cutoff.  In other words, the longest period limit should be est=
ablished (assuming crust average thickness of 15 km) at about 6 s, assuming=
 P-wave velocity of 3 km/s.  Is it just a coincidence that micro's with a p=
eriod longer than 15 s are not (to my knowledge) observed? =20

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