We consider transversely isotropic media with vertical axis of symmetry (VTI).? Solutions of P-SV equation of motion in a homogeneous VTI medium contain depth decay factors r 1 and r 2 , which sometimes become complex depending on VTI parameters.? In this case, r 1 and r 2 are complex conjugates.? Using this property, we obtain dispersion equation of Rayleigh waves with real terms for a layered VTI half space through Thomson-Haskell method with reduced delta matrix.? Phase and group velocities as well as surface ellipticity of Rayleigh waves are computed in real domain for a few oceanic and continental VTI structures of the earth.? Present computation in real domain is similar to that in a layered isotropic half space using the same method.? Thus it is presumed that such computation in a layered VTI half space will allow efficient evaluation of a VTI structure of the earth.
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