Abstract
Some computationally efficient procedures that were developed for the precise estimation of the changing point of multivariate locally stationary autoregressive (MLSAR) model are examined for their ability in determining the onset time of S wave in an online system. The details of Householder’s method that is quite efficient in both accuracy and computation are described. The amount of computation is bounded by a multiple of Nm 2 with N being the data length and m the highest model order, and dose not depend on the number of models checked. The univariate locally stationary autoregressive model (LSAR) for one vertical component is sufficient to determine the arrival time of P wave, but not appropriate to determine the arrival time of S wave. The procedure of multivariate AR model (2-V MLSAR) for two horizontal components is most useful for the precise estimation of the arrival time of S wave. Based on the AICs’ of the fitted MLSAR and Akaike’s definition of likelihood of the model, a method of evaluating the posterior distribution of change point of the AR model is also presented.
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© 2003 Springer-Verlag
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Takanami, T., Kitagawa, G. (2003). Multivariate time series model to estimate arrival times of S waves. In: Methods and Applications of Signal Processing in Seismic Network Operations. Lecture Notes in Earth Sciences, vol 98. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0117695
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DOI: https://doi.org/10.1007/BFb0117695
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