The results obtained here and in particular (arearranged) and (Pwavep) show in general terms that the P-wave anisotropy parameter is smallest when the variation in the layer Lamé parameter is large, independent of the variation in the shear modulus . This result is therefore important for applications to porous layers containing pore fluids for which Gassmann's (1951) equation shows that the effects of fluids influence only the Lamé constants, not .Thus, the P-wave anisotropy parameter may be a useful hydrocarbon indicator in some situations. This result cannot, however, be considered in isolation, as there may be other effects that produce small P-wave anisotropies, and these should be explored and enumerated before any definitive statement can be made.