With the increase of incidence angle, a portion of a P-wave converts into a S-wave, how does this behaviour occur?

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    Do you have a reference that states this? (I am intrigued!) – user889 Mar 23 '15 at 9:35
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    @SabreTooth This phenomenon, known as mode conversion, is described by the Zoeppritz equations, which are solutions to the wave equation. Here's a nice demo video. How this happens is, I think, rather a tricky question to answer without a lot of arm-waving. – kwinkunks Mar 23 '15 at 17:22

The way I imagine this phenomenon is illustrated in the picture below. I have to warn you that it lacks scientific accuracy and is just a simple way to imagine the effects we observe on a reflective boundary. However, it can be useful as a simple model you can easily imagine.
In the upper picture you can see an illustration of a reflection event at a horizontal boundary.
The lower picture illustrates how the vector of particle motion in a down-going P-wave is 'decomposed' into two vectors. First component is a vector of particle motion in an up-going S-wave, the second corresponds to particle motion in an up-going P-wave.

Once again, this is not how the rays exactly behave in a reflection event. Here we do not take into account transmitted waves and lots of other factors. Nevertheless, sometimes you can use this 'approximation' because it satisfies two conditions:

  • At normal incidence, there is no mode conversion (shear wave does not appear)
  • As the incident angle increases, the amount of shear-wave energy increases too.

These effects are also observed in real life.
Exact description of a reflection event on a plane boundary, as kwinkunks has mentioned above, is given by Zoeppritz equations. They take into account all details and are widely-used. No doubt, they are much more difficult (but physically correct!) than a simple sketch I suggest.

a very simple illustration of mode conversion.

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    Modelling shear-wave conversion does not show a monotonous increase of conversion energy as you can see here which is taken from Crewes. – Way of the Geophysicist Apr 3 '15 at 18:08
  • Yes, thank you @WayoftheGeophysicist for your comment. As I have mentioned, Zoeppritz equations should be used for precise calculations. A useful and intuitive tool can be found here: CREWES Zoeppritz Explorer. However, as you probably may have noticed, conversion energy always increases (by its absolute value) at small incidence angles and is equal to zero at normal incidence. And just to clarify: I do not propose an accurate model of reflection event, but rather a way to imagine this phenomenon. – antongrin Apr 23 '15 at 14:03

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