Range of the P - wave anisotropy parameter for nely layered VTI

Since the work of Postma (1955) and Backus (1962), much is known about elastic constants in vertical transversely isotropic (VTI) media when the anisotropy is due to ne layering of isotropic elastic materials. I review earlier work and then show that the P-wave anisotropy parameter c 11 =c 33 lies in the range 1 4 c 11 =c 33 h + 2i h1=(+ 2)i, when the layers are themselves composed of isotropic elastic materials with Lam e constants and and the vertical average of the layers is symbolized by hi. The upper bound is true for all nely layered media of this type, while the lower bound is the best possible for ne layering with two constituents. This lower bound corrects an error in Postma's (1955) paper on two-component VTI media. The method used here shows in general terms that the P-wave anisotropy parameter is smallest when the variation in the layer Lam e parameter is large, independent of the variation in the shear modulus. This result is therefore important for applications to porous layers where the eeects of uids innuence only the Lam e constants, not. Thus, the P-wave anisotropy parameter may be a useful hydrocarbon indicator in some situations.