Some autoregressive models for short-period seismic noise

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Abstract
It is shown that short-period seismic noise at the NORSAR seismic array can be described by a parametric model having the form X(t)−a1(t)X(t−1)−…−ap(t)X(t−p)=Z(t) where X(t) is used to denote the noise process. This is a nonstationary generalization of the standard autoregressive models allowing time-varying autoregressive coefficients and a nonstationary white-noise residual process Z(t). The coefficients a1(t), a2(t), …ap(t) and the residual variance σ2z(t) are estimated using data from the NORSAR seismic array. It is found that the short-period noise at NORSAR is quite satisfactorily described by a third-order (p = 3) model. Also, it is found that the nonstationary character of the noise is due primarily to time variations of the residual variance and the lower order autoregressive coefficients.

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