The Haskell–Thomson matrix formulation has been modified to yield synthetic seismograms and theoretical spectral ratios in a system of parallel anisotropic lossy layers. Transfer function matrices are derived for the case of transverse isotropy with a unique vertical axis. Attenuation is included in the analysis through the use of complex elastic coefficients. Short period spectral ratios and time syntheses are found to be significantly affected by the presence of uniaxial anisotropy for a typical continental crustal model while long period spectral ratios are shown to be sensitive to anisotropy in the upper mantle. Normal values of Q for the crust produce almost no change in teleseismic spectral ratios at useful frequencies. Synthetic seismograms for a continental crust indicate that crustal reverberations of teleseismic impulses are attenuated within 5 s of onset

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