A probabilistic approach for the construction of regional earthquake response spectra

Five scenario earthquakes plausible for the Los Angeles metropolitan region, and one numerical approximation of the 1994 Northridge Mw 6.7 event, provide the database of the proposed methodology that is applied for the construction of regional earthquake response spectra. The methodology involves two main stages of data compaction. In the first stage, the Karhunen–Loève (K–L) decomposition of the excitation temporal covariance matrix is performed. In the second stage, the dominant eigenvectors are analytically approximated with Chebyshev polynomials, thus being converted from eigenvectors to eigenfunctions. This compact analytical representation of the nonstationary excitation data provides an exact closed-form solution for the nonstationary response of linear multi-degree-of-freedom systems. Furthermore, statistical inference analysis for the response variables is conducted, which leads to the construction of regional probabilistic response spectra based on the Log-Normal probability model for the response variables.