Model identification and validation of nonstationary seismic signals

The modeling of transient geophysical signals is addressed. The generating mechanisms of seismic signals are time-varying. Therefore, modeling tools associated with the property of nonstationarity have to be employed. The authors use time-dependent ARMA and AR models in order to describe the signals in the time domain. The models are validated by various time-varying second-order spectral measures. They use the second-order cumulant spectrum and the spectogram to initially qualify and identify the nonstationary structure of the seismic signals. Then after the modeling they use the second cumulant spectrum and the rational time-varying spectrum as measures of the statistical validity and/or significance of the model fits. Finally, the application of the proposed algorithms to real seismic data is studied.