and recorded at 
, the data trace (Figure 3.3(a)) reaches steady state after 8 secs, assuming 8 secs is long enough to include all the arrivals.
According to equation 3.6, the latter half of the trace (8-16 secs) is used to extract the frequency response. The red line in Figure 3.3(b) shows the frequency spectrum of the latter 8 secs in panel (a), which clearly only contains a 25-Hz frequency component. In contrast, the frequency spectrum of the former 8 secs is far from a spike, and the peak frequency amplitude is weaker compared to the red line. Therefore, it is of significant importance to run a time-domain finite-difference simulation long enough to reach steady state before extracting frequency responses. Figure 3.3(c) shows the zoom view of the spectrums between 20-30 Hz.
When the single frequency modeling is repeated 400 times over all the frequencies spanned by the Ricker wavelet, the resulting reconstruction (black line in Figure 3.4(a)) is almost identical to the red line, which is the recorded trace with a 20-Hz Ricker wavelet as source for time-domain simulation. Also, their spectrums are very similar. Figure 3.4 verifies that the single frequency simulation based on individual frequencies yields the same results as a broadband simulation.