Due to the scarcity of near-fault records with forward-directivity effects, synthetic near-fault pulse-like ground motions through superimposing pulse models and high-frequency components are commonly used in the earthquake engineering. However, in existing studies, the cross-over frequency in generating high-frequency components is usually empirical and unclear. In this article, a hybrid decomposition and resynthesis method is developed to quantify the cross-over frequency, in which the wavelet decomposition and high-pass filter are, respectively, used to get the pulse and high-frequency components for near-fault records. Using the 30 near-fault pulse-like records, the distribution of cross-over frequencies is obtained. It is interestingly found that the cross-over frequency is inversely proportional to the pulse period.
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