The book 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. 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 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.