Seismic waves and correlation autoregressive processes

Stochastic models appropriate for seismic records of earthquakes and underground nuclear explosions are considered and a selective review of the existing models is presented. Special models of stationary processes, periodically correlated processes, and uniformly modulated stationary processes as well as a new class called correlation autoregressive processes are studied. Relevant properties of correlation autoregressive processes are presented. It is shown that the successful models presently used are all subclasses of the correlation autoregressive processes. Shortcomings of the existing nonstationary models and merits of the new class for seismic wave modeling are discussed and directions for the further research and development are suggested. It is hoped that the model and the ideas introduced in this article will provide a stimulation for further examination of correlation autoregressive processes and will promote statistical modeling of seismic records.