Abstract
In the previous chapters we have discussed various methods to estimate the parameters of the trajectory models for geodetic time series. The observations were written as the sum of a signal plus noise and we emphasized in particular the modelling of the temporal correlated noise in these analyses. In most cases we are interested in the secular motion which is modelled by a linear trend. However, the observations can contain other geophysical signals which need to be included in the trajectory model as well. In this chapter we explain the most common ones such as offsets, seasonal variations and post-seismic relaxation. In addition, in many situations it is beneficial to pre-process the time series before the analysis is performed. We show how the output of various surface loading models can be used to reduce the scattering of the time series. Furthermore, Common Mode and Principal Component Analysis may be applied which again causes a further reduction of the noise and in this way could produce a more accurate estimate of the trajectory model parameters.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Amiri-Simkooei, A. R., Snellen. M., Simons D.G. (2011) Principal component analysis of single-beam echo-sounder signal features for seafloor classification., IEEE Journal of Oceanic Engineering, 36 (2), 259–272, https://doi.org/10.1109/JOE.2011.2122630
Amiri-Simkooei A. R. (2013) On the nature of GPS draconitic year periodic pattern in multivariate position time series, J. Geophys. Res., 118(5), 2500–2511, https://doi.org/10.1002/jgrb.50199
Blewitt G. (1993) Advances in Global Positioning System technology for geodynamics investigations: 1978–1992. Contributions of Space Geodesy to Geodynamics: Technology, 195–213.
Blewitt G., Lavallée D. (2002) Effect of annual signals on geodetic velocity, J. of Geophys. Res., 107, B2145, https://doi.org/10.1029/2001JB000570
Blewitt G., Kreemer C., Hammond W.C., Gazeaux J. (2016) MIDAS Robust Trend Estimator for Accurate GPS Station Velocities Without Step Detection, J. Geophys. Res. Solid Earth, 121, https://doi.org/10.1002/2015JB012552
Blewitt G., Hammond W.C., Kreemer C. (2018) Harnessing the GPS data explosion for interdisciplinary science, Eos, 99, https://doi.org/10.1029/2018EO104623
Bock Y., Wdowinski S., Fang P., Zhang J., Williams S., Johnson H., Agnew D. (1997) Southern California Permanent GPS Geodetic Array: Continuous measurements of regional crustal deformation between the 1992 Landers and 1994 Northridge earthquakes, J. Geophys. Res., 102(B8), 18013–18033
Bogusz J., Klos A. (2015),On the significance of periodic signals in noise analysis of GPSstation coordinates time series, GPS Sol., 20, 655–664, https://doi.org/10.1007/s10291-015-0478-9
Bos M. S., Fernandes R.M.S., Williams S.D.P., and Bastos L. (2008) Fast error analysis of continuous GPS observations, J. Geod., 82 (3), 157–166, https://doi.org/10.1007/s00190-007-0165-x
Bos M. S., Penna N.T., Baker T. F., Clarke P. J. (2015) Ocean tide loading displacements in western Europe: 2.GPS-observed anelastic dispersion in the asthenosphere, J. Geophys. Res., 120(9), 6540–6557
Bruni S., Zerbini S., Raicich F., Errico M., Santi E. (2014) Detecting discontinuities in GNSS coordinate time series with STARS: case study, the Bologna and Medicina GPS sites, J. Geodesy, 88(12), 1203–1214, https://doi.org/10.1007/s00190-014-0754-4
Chen Q., Van Dam T., Sneeuw N., Collilieux X., Weigelt M., Rebischung P. (2013) Singular Spectrum Analysis for Modelling Seasonal Signals from GPS Time Series, J. of Godyn., 72, 25–35, https://doi.org/10.1016/j.jog.2013.05.005
Davis J.L., Wernicke B.P., Tamisiea M.E. (2012) On seasonal signals in geodetic time series. J. Geophys. Res., 117 (B01403), https://doi.org/10.1029/2011JB008690
Dong D., Fang P., Bock Y., et al. (2002) Anatomy of apparent seasonal variations from GPS-derived site position time series, J. Geophys. Res., 107, 9–16, https://doi.org/10.1029/2001JB000573
Dong D., Fang P., Bock Y., et al. (2006) Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis, J. Geophys. Res., 111, 3405, https://doi.org/10.1029/2005JB003806
Farrell W.E. (1972) Deformation of the Earth by surface loads, Rev. Geophys., 10, 761–797, https://doi.org/10.1029/RG010i003p00761
Freed A.M. (2007) Afterslip (and only afterslip) following the 2004 Parkfield, California, earthquake, Geophys. Res. Lett., 34(6), https://doi.org/10.1029/2006GL029155
Forootan E., Kusche J. (2013) Separation of deterministic signals using independent component analysis (ICA), Stud. Geophys. Geod., 57(1), 17–26, https://doi.org/10.1007/s11200-012-0718-1
Gazeaux J., Williams S.D.P., King M., Bos M., Dach R., Deo M., Moore A. W. et al. (2013) Detecting offsets in GPS time series: First results from the detection of offsets in GPS experiment, J. Geophys. Res., 118 (5), 2397–2407, https://doi.org/10.1002/jgrb.50152
Griffiths J., Ray J.R. (2016) Impacts of GNSS position offsets on global frame stability, Geophys. J. Int., 204(1), 480–487, https://doi.org/10.1093/gji/ggv455
He X., Hua X., Yu K., Xuan W., Lu T., Zhang W., Chen X. (2015) Accuracy enhancement of GPS time series using principal component analysis and block spatial filtering, Advances in Space Research, 55(5), 1316–1327, https://doi.org/10.1016/j.asr.2014.12.016
He X., Montillet J.P., Fernandes R., Bos M., Yu K., Jiang W. (2017) Review of current GPS methodologies for producing accurate time series and their error sources, J. of Geodyn., 106, 12–29, https://doi.org/10.1016/j.jog.2017.01.004
He X., Bos M., Montillet J.P., Fernandes R. (2019) Investigation of the noise properties at low frequencies in long GNSS time series, J. Geod., https://doi.org/10.1007/s00190-019-01244-y
Herring T. A., King R.W., McClusky S. C. (2010) Introduction to GAMIT/GLOBK, report, Mass. Inst. of Technol., Cambridge
Herring T. A., King R. W., McClusky S. C., Floyd M., Wang L., Murray M., Melbourne T., Santillan M., Szeliga W., Phillips D., Puskas C. (2016) Plate Boundary Observatory and Related Networks: GPS Data Analysis Methods and Geodetic Products, Rev. Geophys., 54, 759–808, https://doi.org/10.1002/2016RG000529
Huber P. J. (1964). Robust estimation of a location parameter, Ann. Math. Stat., 35(1), 73–101.
Jiang W., Li Z., Van Dam T. et al. (2013) Comparative analysis of different environmental loading methods and their impacts on the GPS height time series, J. Geod., 87, 687–703, https://doi.org/10.1007/s00190-013-0642-3
Kalnay E., Kanamitsu M., Kistler R., et al. (1996) The NCEP/NCAR 40-year reanalysis project, B. Am. Meteor. Soc., 77(3), 437–471, https://doi.org/10.1175/1520-0477(1996)077
Klos A., Bogusz J., Figurski M., Gruszczynski M. (2015a) Error analysis for European IGS stations, Stud. Geophys. Geod., 60(1) 1–18, https://doi.org/10.1007/s11200-015-0828-7
Klos A., Bogusz J., Figurski M., Kosek W. (2015b) On the handling of outliers in the GNSS time series by means of the noise and probability analysis. In: Rizos, C., Willis, P. (Eds.), IAG 150 Years International Association of Geodesy Symposia, 143. Springer-Verlag, Heidelberg, Germany, https://doi.org/10.1007/1345_2015_78
Klos A., Bos M., Fernandes R., Bogusz J. (2019) Noise-Dependent Adaption of the Wiener Filter for the GPS Position Time Series, Math. Geo., 51 (1), 53–73, https://doi.org/10.1007/s11004-018-9760-z
Langbein J., Borcherdt R., Dreger D. (2005) Preliminary report on the \(28\) September \(2004\), M \(6.0\) Parkfield, California earthquake, Seismol. Res. Lett., 76(1), 10–26, https://doi.org/10.1785/gssrl.76.1.10
Langbein J., Svarc J.L.(2019) Evaluation of Temporally Correlated Noise in GlobalNavigation Satellite System Time Series: Geodetic MonumentPerformance, J. Geophys. Res., 124, 925–942, https://doi.org/10.1029/2018JB016783
Li W., Shen Y., Li B. (2015) Weighted spatiotemporal filtering using principal component analysis for analyzing regional GNSS position time series, Acta Geod. et Geophys., 50(4), 419–436, https://doi.org/10.1007/s40328-015-0100-1
McCarthy D.D., Petit G. (2003) IERS Technical Note 32, Frankfurt am Main: Verlag des Bundesamts fuer Kartographie und Geodaesie
Melbourne T.I., W.M. Szeliga, M. Miller, and V.M. Santillan (2005), Extent and duration of the 2003 Cascadia slow earthquake, Geophys. Res. Lett., 32, L04301, https://doi.org/10.1029/2004GL021790
Ming F., Yang Y., Zeng A., Zhao B. (2016) Spatiotemporal filtering for regional GPS network in China using independent component analysis, J. Geod., 91(4), 419–440, https://doi.org/10.1007/s00190-016-0973-y
Montillet J.P., Williams S.D.P., Koulali A., McClusky S.C. (2015) Estimation of offsets in GPS time-series and application to the detection of earthquake deformation in the far-field, Geophys. J. Int., 200(2), 1205–1219, https://doi.org/10.1093/gji/ggu473
Montillet J.P., Yu K. (2018) Discussion in Geodetic Time Series Analysis of Mixed Spectra and Levy Processes, in Proc. of the Intern. Conf. on Time Series and Forecasting (ITISE), Granada, Spain.
Nikolaidis R. (2002) Observation of geodetic and seismic deformation with the Global Positioning System, Ph.D. thesis, University of California, San Diego, California
Ostini L., Dach R., Meindl M., Schaer S., Hugentobler U. (2009) FODITS: A new tool of the BERNESE GPS software, In EUREF 2008 Symposium, Brussels, Belgium.
Pan Y., Shen W.B., Ding H., Hwang C., Li J., Zhang T. (2015) The Quasi-Biennial Vertical Oscillations at Global GPS Stations: Identification by Ensemble Empirical Mode Decomposition, Sensors, 15(10), 26096–26114, https://doi.org/10.3390/s151026096
Petrov L. (2015) The International Mass Loading Service. arXiv preprint. arXiv:1503.00191.
Perfetti N. (2006) Detection of station coordinate discontinuities within the Italian GPS Fiducial Network, J. Geod., 80(7), 381–396, https://doi.org/10.1007/s00190-006-0080-6
Rodionov S. N. (2004) A sequential algorithm for testing climate regime shifts, Geophys. Res. Lett., 31(9), https://doi.org/10.1029/2004GL019448
Ray J., Altamimi Z., Collilieux X., et al. (2008) Anomalous harmonics in the spectra of GPS position estimates, GPS Solut., 12(1), 55–64, https://doi.org/10.1007/s10291-007-0067-7
Shen Y., Li W., Xu G., Li B.(2013) Spatiotemporal filtering of regional GNSS network position timeseries with missing data using principle component analysis, J. Geod., 88(1), 351–360, https://doi.org/10.1007/s00190-013-0663-y
Stammer D., Wunsch C., Fukumori I. et al. (2002) State estimation improves prospects for ocean research, Eos Trans. AGU, 83(27), 289–295, https://doi.org/10.1029/2002EO000207
Tian Y. (2011) iGPS: IDL tool package for GPS position time series analysis, GPS Solut., 15(3), 299–303, https://doi.org/10.1007/s10291-011-0219-7
Tian Y., Shen Z.K. (2016) Extracting the Regional Common-mode Component of GPS Station Position Time Series from Dense Continuous Network, J. Geophys. Res., 121(2), https://doi.org/10.1002/2015JB012253
Tregoning P., Watson C. (2009) Atmospheric effects and spurious signals in GPS analyses. J. Geophys. Res., 114 (B09403). https://doi.org/10.1029/2009JB006344
Van Camp M., Vauterin P. (2005) Tsoft: graphical and interactive software for the analysis of time series and Earth tides, Comp.. Geosc., 31(5), 631–640, https://doi.org/10.1016/j.cageo.2004.11.015
Van Dam T., Collilieux X., Wuite J., Altamimi Z., Ray J. (2012) Nontidal ocean loading: amplitudes and potential effects in GPS height time series, J. Geod., 86(11), 1043–1057, https://doi.org/10.1007/s00190-012-0564-5
Vitti A. (2012) Sigseg: a tool for the detection of position and velocity discontinuities in geodetic time-series, GPS Solut., 16(3), 405–410, https://doi.org/10.1007/s10291-012-0257-9
Wang W., Zhao B., Wang Q., Yang S. (2012) Noise analysis ofcontinuous GPS coordinate time series for CMONOC, Adv. Space. Res., 49 (5), 943–956, https://doi.org/10.1016/j.asr.2011.11.032
Wang X., Cheng Y., Wu S., Zhang K. (2016) An enhanced singular spectrum analysis method for constructing nonsecular model of GPS site movement, J. Geophys. Res., 121 (10), https://doi.org/10.1002/2015JB012573
Wdowinski, S., Bock Y., Zhang J., Fang P., Genrich J. (1997) Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake, J. Geophys. Res., 102(B8), 18057–18070, https://doi.org/10.1029/97JB01378
Webb F. (2010) A software tool for detecting offsets in geodetic timeseries, Tech. Rep., NTR-47707, NASA New Technology Report.
Williams S.D.P. (2003b) Offsets in Global Positioning System time series, J. Geophys. Res., 108, https://doi.org/10.1029/2002JB002156
Williams, S.D. (2008), CATS: GPS coordinate time series analysis software, GPS Solut., 12(2), 147–153, https://doi.org/10.1007/s10291-007-0086-4
Yuan L.G., Ding X.L., Chen W. et al. (2008) Characteristics of daily position time series from the Hong Kong GPS fiducial network, Chinese J. Geophys., 51, 976–990, https://doi.org/10.1002/cjg2.1292
Acknowledgements
Xiaoxing was sponsored by National key \( R \& D\) Program of China (2018YFC1503600), National Science Innovation Group Foundation of China (41721003), Nation Science Foundation for Distinguished Young Scholars of China (41525014), National Natural Science Foundation of China (41704030, 11662003), Jiangxi Provincial Department of Education Science and Technology Project (GJJ180334). The work carried out by Machiel S. Bos and Rui M. S. Fernandes was sponsored by national Portuguese funds through FCT in the scope of the project IDL-FCT-UID/GEO/50019/2019 and, for Machiel, grant number SFRH/BPD/89923/2012. Computational resources were provided by C4G – Collaboratory for Geosciences (PINFRA/22151/2016).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
He, X., Montillet, JP., Bos, M.S., Fernandes, R.M.S., Jiang, W., Yu, K. (2020). Filtering of GPS Time Series Using Geophysical Models and Common Mode Error Analysis. In: Montillet, JP., Bos, M. (eds) Geodetic Time Series Analysis in Earth Sciences. Springer Geophysics. Springer, Cham. https://doi.org/10.1007/978-3-030-21718-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-21718-1_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21717-4
Online ISBN: 978-3-030-21718-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)