P-wave velocity increases with depth. This causes the wave paths to not 
be linear (and the wavefront is not spherical). The paths can be 
visualized as upward curving concave arcs. P-wave motion is therefore 
predominantly vertical when it reaches the surface at all distances from 
the epicenter.

Mike

On 3/25/2011 9:30 AM, Brett Nordgren wrote:
> 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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