Nonstationary ARMA modeling of seismic motions

Discrete time-varying autoregressive — moving average (ARMA) models are used to describe realistic earthquake ground motion time histories. Both amplitude and frequency nonstationarities are incorporated in the model. An iterative Kalman filtering scheme is introduced to identify the time-varying parameters of an ARMA model from an actual earthquake record. Several model verification tests are performed on the identified model. Applications of these identification and verification procedures are given and show that the proposed models and identification algorithms are able to capture accurately the nonstationary features of real earthquake accelerograms, especially the time-variation of the frequency content. The well-known Kanai-Tajimi earthquake model is covariance equivalent with a subset of the low order ARMA(2,1) model. Using the results and methodology of this study, the parameters of a time-varying Kanai-Tajimi earthquake model can be estimated from a target earthquake record or they can be directly associated with characteristic earthquake features such as predominant frequency and frequency bandwidth.