Effects of time series analysis protocols on transfer functions calculated from earthquake accelerograms

Transfer functions represent the ratio in the frequency domain of one ground motion to another. Transfer functions are a convenient way by which the variation of earthquake ground motions from the free-field to the foundation level of a structure can be quantified for studies of kinematic soil–structure interaction. Aside from ordinary filtering and baseline correction, substantial signal processing occurs in the computation of transfer functions, including windowing (to extract the S-wave portion of the record) and smoothing (to reduce scatter that can obscure physically significant trends). Utilizing several signal processing techniques on a sample data set, we find that detailed features of the transfer function ordinates (i.e., frequency-to-frequency variations) can be affected by the degree of smoothing and by the window length (e.g., whole record versus S-window). However, the overall shape and magnitude of the transfer functions are relatively consistent. More important than signal processing details is the frequency bandwidth over which the results are considered valid, because significant portions of the spectrum can be dominated by stochastic processes with little physical meaning. We argue that transfer functions should be interpreted over those portions of the spectrum having minimal noise impact, as indicated by high coherence.