Skip to main content
Earth, Planets and Space
Download PDF
  • Article
  • Published:

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

Earth, Planets and Space volume 52, pages 155–162 (2000)Cite this article

Abstract

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.

References

  • Akaike, H., Information theory and an extension of the maximum likelihood principle, in 2nd International Symposium on Information Theory, edited by B. N. Petrov and F. Csaki, pp. 267–281, Akademiai Kiado, Budapest, 1973.

    Google Scholar 

  • Bock, Y., S. Wdowinski, P. Fang, J. Zhang, S. Williams, H. Johnson, J. Behr, J. Genrich, J. Dean, M. van Domselaar, D. Agnew, F. Wyatt, K. Stark, B. Oral, K. Hudnut, R. King, T. Herring, S. Dinardo, W. Young, D. Jackson, and W. Gurtner, Southern California Permanent GPS Geodetic Array: Continuous measurements of regional crustal deformation between the 1992 Landers and 1994 Northridge earthquakes, J. Geophys. Res., 102, 18013–18033, 1997.

    Article  Google Scholar 

  • Brockwell, P. J. and R. A. Davis, Time Series: Theory and Methods, 577 pp., Springer-Verlag New York, Inc., 1991.

  • El-Fiky, G. S., T. Kato, and Y. Fujii, Distribution of vertical crustal movement rates in the Tohoku district, Japan, predicted by least-squares collocation, J. Geod., 71, 432–442, 1997.

    Article  Google Scholar 

  • Fujii, Y. and N. Nakane, Horizontal Crustal Movements in the Kanto-Tokai District, Japan, as Deduced from Geodetic Data, Tectonophys., 97, 115–140, 1983.

    Article  Google Scholar 

  • Fujii, Y., K. Miyashita, and Y. Kitazawa, Crustal deformation and seismicity in and around the Ibaraki prefecture, Earth Mon., 7, 2, 79–84, 1985 (in Japanese).

    Google Scholar 

  • Hashimoto, M., Horizontal strain rates in the Japanese islands during inter-seismic period deduced from geodetic surveys (Part I): Honshu, Shikoku and Kyushu, Zisin, 43, 13–26, 1990 (in Japanese with English abstract).

    Google Scholar 

  • Hashimoto, M. and D. Jackson, Plate Tectonics and Crustal Deformation Around the Japanese Islands, J. Geophys. Res., 98, 16149–16166, 1993.

    Article  Google Scholar 

  • Hashimoto, M., T. Sagiya, H. Tsuji, Y. Hatanaka, and T. Tada, Co-seismic displacements of the 1995 Hyogo-ken Nanbu Earthquake, J. Phys. Earth, 44, 255–279, 1996.

    Article  Google Scholar 

  • Hein, G. A. and R. Kistermann, Mathematical foundation of nontectonic effects in geodetic recent crustal movement models, Tectonophys., 71, 315–334, 1981.

    Article  Google Scholar 

  • Ishibashi, K., On the mechanism of the Tokai earthquake, Earth Mon., 7, 128–131, 1985 (in Japanese).

    Google Scholar 

  • Ishibashi, K., A possible large earthquake near Odawara city in near future, Earth Mon., 7, 420–426, 1985 (in Japanese).

    Google Scholar 

  • Japanese University Consortium for GPS Research, Crustal Deformation Observed at the Sagami Bay Area, Japan, by Means of GPS Interferometry, J. Geod. Soc. Japan, 39, 107–119, 1993.

    Google Scholar 

  • Kato, T., G. S. El-Fiky, E. N. Oware, and S. Miyazaki, Crustal strains in the Japanese islands as deduced from dense GPS array, Geophys. Res. Lett., 25, 3445–3448, 1998.

    Article  Google Scholar 

  • Kuwayama, T. and Y. Fujii, Change of mode of crustal deformation in the Izu peninsula, Honshu, Japan and bending of the Northernmost part of the Philippine Sea plate, Zisin, 43, 101–110, 1990 (in Japanese with English abstract).

    Google Scholar 

  • Li, Q. and B. Tao, Theory of Probability and Statistics, and Its Applications to Geodesy, 321pp., Survey and Mapping, China, 1982 (in Chinese).

    Google Scholar 

  • Ljung, L., System identification, theory for the user, 519 pp., Prentice-Hall, New York, 1987.

    Google Scholar 

  • Ljung, L., System identification toolbox for use with Matlab-user’s guide, Natick, Mass., 266 pp., The MathWorks, Inc., 1995.

  • Minster, J. B. and Y. H. Jordan, Rotation vectors for the Philippine Sea and Vivera Plates, Eos Trans. AGU, 60, 958, 1979.

    Google Scholar 

  • Miyazaki, S. and Y. Hatanaka, Crustal deformation observed by GSI’s new GPS array, Eos Trans. AGU, 78, S104, 1997.

    Google Scholar 

  • Miyazaki, S. and Y. Hatanaka, About Continuous GPS monitoring system of GSI, in Kishyo Kenkyu Note, edited by H. Nakamura, 192, 105–131, Meteorological Society of Japan, 1998 (in Japanese).

  • Oware, E. N., A New Tectonic View of the Japanese Islands Based on GPS Dense Array Data, Ph.D. thesis, 214 pp., University of Tokyo, 1998.

  • Sagiya, T., A. Yoshimura, E. Iwata, K. Abe, I. Kimura, K. Uemura, and T. Tada, EstablishmentofPermanent GPS Observation Network and Crustal Deformation Monitoring in the Southern Kanto and Tokai Areas, Bull. Geogr. Surv. Inst., 41, 105–118, 1995.

    Google Scholar 

  • Seno, T., The Instantaneous Rotation Vector of the Philippine Sea Plate Relative to the Eurasian Plate, Tectonophys., 42, 209–226, 1977.

    Article  Google Scholar 

  • Shimada, S. and Y. Bock, Crustal Deformation Measurements in Central Japan Determined by a Global Positioning System Fixed-Point Network, J. Geophys. Res., 97, 12437–12455, 1992.

    Article  Google Scholar 

  • Tada, T., T. Sagiya, and S. Miyazaki, Deforming Japanese islands as seen from GPS observations, Kagaku, 67, 917–927, 1997 (in Japanese).

    Google Scholar 

  • Tsuji, H., Y. Hatanaka, T. Sagiya, and M. Hashimoto, Coseismic crustal deformation from the 1994 Hokkaido-Toho-Oki Earthquake Monitored by a nationwide continuous GPS array in Japan, Geophys. Res. Lett., 22, 1669–1672, 1995.

    Article  Google Scholar 

  • Zhang, J., Y. Bock, H. Johnson, P. Fang, S. Williams, J. Genrich, S. Wdowinski, and J. Behr, Southern California Permanent GPS Geodetic Array: Error analysis of daily position estimates and site velocities, J. Geophys. Res., 102, 18035–18055, 1997.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Environmental Sciences, Ibaraki University, Mito, 310-8512, Japan

    Jianxin Li & Kaoru Miyashita

  2. Earthquake Research Institute, University of Tokyo, Tokyo, 113-0032, Japan

    Teruyuki Kato

  3. Geographical Survey Institute, Tsukuba, 305-0811, Japan

    Shinichi Miyazaki

Authors
  1. Jianxin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kaoru Miyashita
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Teruyuki Kato
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shinichi Miyazaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianxin Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Miyashita, K., Kato, T. et al. GPS time series modeling by autoregressive moving average method: Application to the crustal deformation in central Japan. Earth Planet Sp 52, 155–162 (2000). https://doi.org/10.1186/BF03351624

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03351624

Keywords