Synthetic seismograms for P-SV teleseismic waves in a layered anelastic medium are computed by asymptotic ray theory and compared with those computed by a modification of the Thomson-Haskell matrix method for anelastic media, due to Silva (1976). The synthetic seismograms for the two methods agree well with each other, which verifies the validity of the modification of the Thomson-Haskell method. A useful feature of the ray approach is the ability to identify the rays which make up the various events on the seismograms.

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