During the past decade, there has been renewed interest in seismic wave propagation in anisotropic media. Traveltime analyses of improved shear-wave data gave evidence for shear-wave splitting consistent with azimuthal isotropy (or transverse isotropy with vertical axis of symmetry) in both sedimentary rocks and the earth's deep mantle (Jones and Wang, 1981; Crampin, 1985; Winterstein, 1986). Numerical solutions to line sources in a half-space (Kraut, 1963) and asymptotic plane-wave theory in multilayered media (e.g., Garmany, 1988) were set up; however, a source-amplitude theory is lacking, without which no sound physical understanding of the problem can be achieved. In the present note, I endeavor to demonstrate how simple analytical solutions are able to illuminate the intricate interrelations between inhomogeneity and anisotropy.

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