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Begin with the exact dispersion relations for P and SV waves.
 

 (2) 
Now convert the cosines under the surd to sines.
Neglecting terms in S^{4}.
Take constant out of bracket.
Expand the surd in powers of S^{2}.
Return factor to original location
Simplify.
Reintroduce cosines.
Next: P plane waves about
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Stanford Exploration Project
12/18/1997