PSN-L Email List Message

Subject: Re: Rayleigh Waves
From: Bob Hancock icarus@.........
Date: Tue, 22 Dec 2009 08:12:10 -0700

```Bob McClure is absolutely correct about visualization of the Rayleigh =
wave.  The particle motion for the Rayleigh wave was difficult for me to =
grasp until I hand plotted the data through several phase differences.  =
After making the plots I was able to visualize the particle motion of =
the Rayleigh wave.  I used the following instructions found in the SAC =
manual for particle motion plots:

"...In a particle-motion plot one evenly spaced file is plotted =
against
another.  For each value of the independent variable, normally time, the =
value
of the dependent variable of the first file is plotted along the y axis =
and
the value of the dependent variable of the second file is plotted along =
the x
axis.  For a pair of seismograms this type of plot shows the motion of a
"particle" in the plane of the two seismograms as a function of time.
A square plot is generated, with the limits along each axis being =
the
minimum and maximum values of the dependent variable...."

As previously pointed out the Rayleigh wave is made up of two separate =
motions.  There is a radial wave and a vertical wave.  To achieve the =
optimum retrograde circular motion, the radial wave (similar to a P =
wave) precedes the vertical wave motion by 1/4 of the wavelength.  It =
was particularly interesting to vary the phase difference and amplitude =
of each wave component, and note the changes in the shape of the =
Rayleigh wave particle motion.  I did this at 1/8 wave length intervals =
from a -1 to a + 1 phase differential to better understand this motion.

Particle motion can be viewed either by hand plotting or by rotating the =
data in the two horizontal channels.  When rotated two additional files =
are generated which are called the Radial and Transverse channels.  =
Following is a simple explanation of the process of rotation from Prof. =
George Zandt, University of Arizona:

"...Rotation, or more precisely, rotation of seismograms from the ZNE =
coordinates to ZRT coordinates is relatively straightforward. The choice =
of recording the NS and EW components of ground motion is rather =
arbitrary, right? You just need to record two orthogonal (at rt angles) =
directions, could be NE and SE, but by convention sesimologists always =
use N and E. If your events are coming from N or S or E or W, then the =
data is called "naturally rotated" and you can clearly see the =
separation of Love and Rayleigh, for example. But for any other =
direction, its not naturally rotated. So, you can rotate the data =
yourself to the radial and transverse directions. Mathematically, this =
is quite simple and involves multiplying the data by cosine of the =
difference in angles...."

I am unaware of any programs that run on Windows that will perform the =
functions of rotation and particle motion as applied to seismograms, in =
particular PSN4 format data.

Bob Hancock
Three Points, AZ

On Dec 21, 2009, at 9:37 PM, Robert McClure wrote:

>  It helps to visualize the various seismic waves that propagate in
> the body and on the surface of the earth. To this end, I refer you to
> web site
>=20
> http://www.daleh.id.au/seismic_theory.html.
>=20
> There,  you will find instructive animations of P, S, Love, and
> Rayleigh waves. These animations are borrowed from Lawrence W. Braile,
> Professor, Department of Earth and AtmosphericSciences, Purdue
> University, West Lafayette, Indiana. No doubt they appear on his
> website as well.
>=20
> http://web.ics.purdue.edu/~braile/
>=20
>  You will see that the particle motions of the surface waves (Love
> and Rayleigh, do indeed decrease with depth. The shorter the period
> the greater the rate of attenuation. Borehole seismometers take
> advantage of this decrease with depth to reduce the sensed amplitude
> of microseisms and cultural noise.
>=20
> Bob
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>=20
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