The top figure is the time history from the El Centro earthquake, North-South horizontal component. The second is the corresponding Waterfall FFT with 4 second segments and with 50% overlap.
The Waterfall FFT is calculated by first taking the complete response time history for each natural frequency of interest. Then the time history for each is divided into segments. Finally, the shock response spectrum (SRS) is taken for each natural frequency and for each segment, by taking the peak positive and peak negative responses.
The Waterfall SRS function is given in:
Matlab script: Vibrationdata Signal Analysis Package
>> vibrationdata > Time History > Shock Response Spectrum, Various > Waterfall FFT
See also: El Centro Earthquake
– Tom Irvine