A discrete-time analysis of seismic site amplification in layered medi
a for vertically propagating shear waves is presented. The discrete-ti
me approach not only is simpler and more accurate than the previously
suggested frequency-domain techniques but also provides better physica
l insight into the problem. The discrete-time domain equations of wave
propagation can be derived by using the upgoing and downgoing waves a
s auxiliary variables, and require only three parameters for each laye
r: the reflection coefficient at the bottom of the layer, the travel t
ime of waves in the layer, and the damping. The discrete-time formulat
ion results in simple analytical models for site amplification. When c
ompared with the previous ones, these new models have important advant
ages: (1) They use the physical parameters of the site; (2) for a sing
le soil layer over bedrock subjected to vertically propagating waves,
the model is exact; (3) amplitudes and phase characteristics of the si
te are accounted for in the models; (4) the models can incorporate mul
tiple reflections in the layer; and (5) the models result in simple ti
me-domain filters for simulating ground motions. They also provide con
venient tools to develop random vibration models, generate site-specif
ic response spectra, and identify site characteristics from recorded m
otions.