The linear theory of viscoelasticity is used to study the effects of anelasticity on SH body waves propagating through a layered medium. The mathematical properties of SH waves in a viscoelastic medium are outlined. Reflection and transmission coefficients for SH plane waves impinging upon a plane boundary separating two anelastic media are calculated and compared with the coefficients for the perfectly elastic case. Synthetic seismograms for teleseismic SH body waves are computed for a plane-layered crustal model in both the elastic and anelastic cases, using a ray theory approach.

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