Aligned vertical fractures provide one commonly recognized source of azimuthal (surface angle dependent) seismic anisotropy in oil and gas reservoirs (Lynn et al., 1995). While layering in the earth also results in seismic anisotropy (Backus, 1962), horizontal layering of isotropic rock produces vertical transversely isotropic (VTI) media, and could not produce horizontal transversely isotropic (HTI) symmetry without some very significant uplift phenomena being present simultaneously. Of course, anisotropic layers such as shale beds bring seismic anisotropy with them, but again this anisotropy will more typically be VTI, rather than HTI.
On the other hand, VTI earth media seem much easier to understand and analyze than HTI media. Nevertheless, when the source of the anisotropy is aligned vertical fractures, we can make very good use of the simpler case of horizontal fracture analysis by making a rather minor change of our point of view that easily gives all the needed results.
Together with the simplifications already noted, we can also understand very directly the sources of the anisotropy due to fractures by considering a method introduced by Sayers and Kachanov (1991). We find that elastic constants, and therefore the Thomsen (1986) parameters, can be very conveniently expressed in terms of the Sayers and Kachanov (1991) formalism. Furthermore, in the low crack density limit [which is also consistent with the weak anisotropy approach of Thomsen (1986)], we obtain direct links between the Thomsen parameters and the fracture properties. These links suggest a method of inverting for fracture density from wave speed data.