A new approach on numerical modeling of wave propagation is introduced and is used to analyze the effect of earthquake magnitudes (ground motion amplitudes) on wave propagation. In this method, the sum of the maximum amplitudes of the first output model at time 0 s and rest of the output models at different times are normalized to unity. Considering this as a constraint, the sum of the weighted-squared Fourier amplitudes is minimized by using the Lagrange multiplier method. The proposed method can reveal the relationship of actual time histories by showing simple clear peaks. This method is used to analyze the time histories of various earthquake events at different vertical array sites of the Kashiwazaki–Kariwa nuclear power plant of Tokyo electric power company (TEPCO). The wave arrival times obtained from this method and down-hole measurements are compared. The results show increase in the arrival times at surface layer when the magnitude of earthquake is large. The results reveal that the amplitudes of small magnitude earthquakes at depths are small and are largely amplified at surface, whereas in case of large magnitude earthquakes, the amplitudes are large at depths and are deamplified at surface reflecting the effects of the strain-dependent soil properties that result in non-linear site response to strong shaking. The results also show that the reflected peak amplitudes are higher for small magnitude earthquakes than for large magnitude earthquakes. Copyright © 2010 John Wiley & Sons, Ltd.