Discrete-Time Analysis of Seismic Site Amplification

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Abstract
A discrete-time analysis of seismic site amplification in layered media for vertically propagating shear waves is presented. The discrete-time approach not only is simpler and more accurate than the previously suggested frequency-domain techniques but also provides better physical insight into the problem. The discrete-time domain equations of wave propagation can be derived by using the upgoing and downgoing waves as auxiliary variables, and require only three parameters for each layer: the reflection coefficient at the bottom of the layer, the travel time of waves in the layer, and the damping. The discrete-time formulation results in simple analytical models for site amplification. When compared with the previous ones, these new models have important advantages: (1) They use the physical parameters of the site; (2) for a single soil layer over bedrock subjected to vertically propagating waves, the model is exact; (3) amplitudes and phase characteristics of the site are accounted for in the models; (4) the models can incorporate multiple reflections in the layer; and (5) the models result in simple time-domain filters for simulating ground motions. They also provide convenient tools to develop random vibration models, generate site-specific response spectra, and identify site characteristics from recorded motions.