Abstract
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.
Highlights
Group velocities; surface ellipticity of Rayleigh waves is obtained using equation (48)
8.2 Continental structure As a continental structure, let us consider the VTI model obtained by Huang et al [2010] for SW China using Love and Rayleigh waves up to the period 40 s
R1 and r2 are complex conjugates; using this property, we get these matrices with real elements. (d) Using T-H method with reduced delta matrix, we obtain Rayleigh dispersion equation (47) with real terms in a layered VTI half space. (e) We evaluate Rayleigh wave phase and group velocities for oceanic and continental VTI models through dispersion equation (47) (Figures 2, 3 and 5)
Summary
Group velocities; surface ellipticity of Rayleigh waves is obtained using equation (48). 8.2 Continental structure As a continental structure, let us consider the VTI model obtained by Huang et al [2010] for SW China using Love and Rayleigh waves up to the period 40 s.
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