Bob,

I quite agree with your analysis.  Some transverse motion would 
happen with an acoustic wave travelling down a steel rod, for 
example, but that assumes a free surface, which isn't the case inside 
the earth.  The fact that the formula for the P-wave velocity uses 
the bulk modulus of the earth's material rather than its elastic 
modulus pretty well proves your case.

However it is still true that P-waves will have a substantial 
vertical component, arising from the fact that the wave front will 
always to some degree be coming up from under the station.

Thanks,

Brett

At 11:42 AM 3/25/2011, you wrote:
>I disagree with your hypothesis. Transverse motion is only possible 
>with a wave of finite cross-section. A P wave has a 
>more-or-spherical wavefront and is not a beam of sound. Even a 
>beamed wave would have no transverse motion at its center axis.
>
>Bob
>
>On Thu, Mar 24, 2011 at 5:17 PM, Brett Nordgren 
><brett3nt@.............> wrote:
>Dave,
>
>I think in real world seismology, not everything always exactly 
>follows the simple theory.  We see P waves quite well on our 
>verticals.  For one thing they are body waves and commonly approach 
>the station from an angle below the horizontal.  Also I think there 
>is always a transverse motion associated with compression waves like 
>P waves--look up Poisson's Ratio.  I would normally expect them to 
>have a transverse motion of very roughly 1/3 the amplitude of their 
>longitudinal motion.
>
>Regards,
>Brett


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