Rayleigh Waves: An Overview for Beginners

[Awsom Guy]

Hi,
I need some really really basic information on Rayleigh waves as the only website I could ind was Wikipedia. This page is too in depth or either not enough information on the basics. So I need much information as possible on how Rayleigh waves work.
Thanks.

 

[billiards]

Hi Awsom Guy,

In wikipedia it says:

Rayleigh waves are generated by the interaction of P- and S- waves at the surface of the earth, and travel with a velocity that is lower than the P-, S-

So the truth is that Rayleigh waves are just a mix of P and S waves. If you don't know what P and S waves are then I strongly recommend finding out about those before you try to understand Rayleigh waves. Rayleigh waves are formed under the conditions where multiple reflections of P and S waves sum up to make a bigger, slower (group velocity) wave which expands cylindrically.

Also, Rayleigh waves are "surface waves", which means that they only propagate at and a few hundred km below the surface (they get weaker with depth).

 

[Awsom Guy]

Yes I know what P and s waves are and I know what surface waves are.
Thankyou

 

[adrianpoll]

Longitudinal and shear waves are subject to the continuity conditions of infinite media. However, a surface imposes a different elastic condition. The key condition on a surface is that the stress component perpendicular to the surface must tend to zero as one approaches the surface (otherwise on would have infinite acceleration, bad news!).

The elastic wave types in terms of which we think, are our "solutions to the wave equation" (BTW the solid doesn't have to think about the "wave equation", it just obeys it!). The Rayleigh wave is the "solution to the wave equation" that comes up when you do the math for a wave traveling on a surface. Specifically, traveling on the surface of a semi-infinite body with motion in the plane perpendicular to the surface and parallel to the direction of propagation (i.e. no transverse motion). Unlike the longitudinal and shear waves, the particles move in ellipses. The motion is greatest on the surface and by the time you are a few wavelengths below the surface there is very little motion. Like the longitudinal and shear waves, the Rayleigh wave has a well defined velocity (it depends on Poisson's ratio) that is the same at all frequencies. Thus it is "non-dispersive" and the waveform propagates without changing shape. At least, that's for a straight wave front. If it's spreading from a point source it's a little different.

So as you can see, the Rayleigh wave is not limited to earthquakes, although it is especially important in earthquakes (and applies to the extent that the crust of the Earth can be approximated as a semi-infinite solid). It is not correct to say that the Rayleigh wave is a mixture of longitudinal and shear waves. If it is earthquakes that you are interested in, I recommend you also take a close look at Love waves. These also propagate on surfaces but the direction of particle motion is parallel to the surface plane and TRANSVERSE to the direction of propagation. Rayleigh waves are much discussed in seismology but also, I have read on the Internet that it is mainly Love waves that one feels during an earthquake.