地震記象の時系列解析の物理的意味について
1989 年 42 巻 4 号 p. 439-449
詳細
1989 年 42 巻 4 号 p. 439-449
A trial of looking for physical meanings of the statistical time-series model fitted to the seismogram is described. This paper shows that if a particle movement of the elastic displacement field of the Earth due to White-noise body-force equivalent to stochastic displacement discontinuity on the seismic fault plane is observed at the ground surface, the observed wave-form corresponding to the seismogram can be expressed by the innovations representation for time-varying autoregressive moving-average process i. e. the time-varying ARMA model.
As briefly concluding remarks: (1) AR-coefficient matrices of the model can be interpreted as a function of eigen values of vibration of the Crust. (2) MA-coefficient matrices of the model are interpreted as a function not only of the eigen values but also of eigen-functions of vibration of the soil deposits under the observation site and of covariance function of the White-noise body-force. (3) Covariance function of the innovation sequence obtained from fitting the optimal time-varying ARMA or AR model to the digitalized seismogram has mainly relation to the covariance function of the White-noise body-force and also is influenced by both of the covariance functions of filtering and measurement errors.
