Algorithm for Spectral Matching of Earthquake Ground Motions using Wavelets and Broyden Updating

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Virginia Tech

This study focuses on creating a spectral matching algorithm that modifies the real strong ground motions in the time domain by adding wavelets adjustment to the acceleration time series. The spectral matching procedure is at its core a nonlinear problem, thus a nonlinear solving method was employed in the proposed algorithm. The Broyden updating method was selected as the nonlinear solving method because it does not require a differentiation analysis. The Broyden updating also makes use the information of spectral misfit and wavelet magnitudes vector to approximate the Jacobian matrix which expected to give an efficient calculation.

A parametric study was numerically conducted to obtain a set of gain factors that reduce the computational time and minimize the spectra misfit. The study was conducted using ten different ground motions, taken from FEMA P-695 (FEMA, 2009), which represent far field, near field-pulse and near field-no pulse earthquake ground motions.

A study of compatible wavelet functions was carried out to determine the appropriate wavelet function for the proposed method. The study include the baseline drift, the frequency and time resolution, and the cross correlation between wavelet adjustments during the spectra matching procedure. Based on this study, the corrected tapered cosine wavelet was selected to be used in the proposed algorithm.

The proposed algorithm has been tested and compared with other methods that are commonly used in spectral matching; the RSPMatch method and the frequency domain method. The comparing parameters were the computational time, the average misfit, the maximum misfit and error, the PGA, PGV, PGD, the Arias Intensity and the frequency content for both acceleration and displacement time histories. The result showed that the proposed method is able to match the target while preserving the energy development and the frequency content of the original time histories.

Spectral Matching, Broyden Updating, Wavelets, Spectrum Compatible Acceleration, Frequency Content