Examples of nonstationarity

A typical seismic trace, as shown in Figure 1, is nonstationary since it includes parts of low and high variance, albeit its mean is approximately zero. A shot gather, as shown in Figure 2, is nonstationary since each individual trace is usually nonstationary. Furthermore, the hyperbolic shape of the reflection events causes spatial spectral variations.

 

nStatVar
Figure 1 Nonstationary seismogram. The seismogram in the top panel has three distinct regions: The relatively quiet period before the event, the event, and the ringing of the coda. The bottom panel displays an estimate of the signal's local variance.

 

gather Figure 2 Shot gather. Shot gathers are nonstationary, because they show regions of distinct variance: The early quite zone, the hyperbolic reflections and the noisy coda at the bottom.

Many synthetic data sets are stationary since they are generated by simple statistical models. In practice, data sets are often nonstationary. However, the decision if a data set is assumed stationary or nonstationary depends on an application's tolerance for deviations from strict stationarity.