f Orthorhombic media: Elastic waves in a vertically fractured earth

Anisotropy in the Earth's crust seems to be well modeled by orthorhombic symmetry (three mutually orthogonal planes of symmetry. In many places rocks can be regarded as a transversely isotropie (t.i.) background with a vertical symmetry axis (due mainly to fine horizontal layering ) in which is embedded a system of vertical parallel fractures (equivalent to aligned microcracks ), which themselves are assumed to be orthorhombic with respect to the natural coordinate system, with x3 positive downward and x1 perpendicular to the fractures (Schoenberg and Douma, Geophysical Prospecting 36, 571-.590, 1988).