Skip to content


  • Article
  • Open Access

GPS time series modeling by autoregressive moving average method: Application to the crustal deformation in central Japan

  • Jianxin Li1Email author,
  • Kaoru Miyashita1,
  • Teruyuki Kato2 and
  • Shinichi Miyazaki3
Earth, Planets and Space201452:BF03351624

Received: 29 July 1999

Accepted: 24 December 1999

Published: 20 June 2014


Autoregressive moving average (ARMA) method is applied to modeling the time series of position changes of GPS sites, obtained by the Geographical Survey Institute (GSI) of Japan during the period from April 1996 to March 1998. The present application is focused on denoising of the GPS time series data where only white noise is considered, and detection of data discontinuities and outliers in order to obtain time-averaged velocity and strain fields in central Japan. The data discontinuities are detected by a typical Kalman filter algorithm. The outliers are eliminated by using robust estimation techniques during the ARMA process. The averaged strain field, calculated by the least-squares collocation method from the improved two-year time series data, distinguishes clearly between the tectonically active and inactive regions. Higher maximum shear strain rates were detected in the southern area of the Kanto district. In the areas with very high seismicities, however, the difference between the maximum shear strain rates, that were estimated from the raw time series data and the ARMA-analyzed data, amounted to about 0.2 microstrain/yr. This indicates that the existence of noise and discontinuities can lead to an over-prediction of the strain field.


Time Series DataCrustal DeformationJapanese IslandData DiscontinuityBoso Peninsula