Stochastic Time-Series Prediction Equation Using Wavelet Packets for Iran

In this study, a stochastic simulation model proposed by Yamamoto and Baker (Bulletin of the Seismological Society of America 103:3044–3056, 2013) is applied to the Iranian strong motion database, which comprises more than 3828 recordings for the period between 1975 and 2018. Each ground motion is decomposed into wavelet packets. Amplitudes of wavelet packets are divided into two groups, and for each group, model parameters are estimated using the maximum likelihood method. Regression coefficients are then obtained relating model parameters to seismic characteristics such as earthquake magnitude, distance, and site condition. Inter-event residuals of coefficients and correlation of total residuals of those parameters are also calculated. An inverse wavelet packet transform is used to reconstruct the amplitudes in the time domain and perform the simulation. Finally, a validation test is performed. The comparison of ground motion intensity measures for recorded and simulated time series shows acceptable conformity in the application. The estimated parameters using the simulated data agree with the real data, indicating the acceptable validity of the estimated stochastic simulation model. The obtained regression equations can generate ground motions for future earthquake scenarios in Iran.