With reference to the influence of local geology on earthquake ground motions, a more complete analytical formulation is made of the well-known problem of a horizontally stratified, linearly-elastic half-space subjected to vertically traveling, sinusoidal, plane waves. A more general interpretation of a result of Kanai is given, and a recursion formula is derived for computing amplification spectra. Some special properties of the system are pointed out and numerical examples are given.

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