Abstract
The accuracy by which velocities can be estimated from GNSS time series is mainly determined by the low-frequency noise, below 0.2–0.1 cpy, which are normally described by a power-law model. As GNSS observations have now been recorded for over two decades, new information about the noise at these low frequencies has become available and we investigate whether alternative noise models should be considered using the log-likelihood, Akaike and Bayesian information criteria. Using 110 globally distributed IGS stations with at least 12 years of observations, we find that for 80–90% of them the preferred noise models are still the power law or flicker noise with white noise. For around 6% of the stations, we found the presence of random-walk noise, which increases the linear trend uncertainty when taken into account in the stochastic noise model of the time series by about a factor of 1.5 to 8.4, in agreement with previous studies. Next, the Generalised Gauss–Markov with white noise model describes the stochastic properties better for 4% and 5% of the stations for the East and North component, respectively, and 13% for the vertical component. For these stations, the uncertainty associated with the tectonic rate is about 2 times smaller compared to the case when the standard power-law plus white noise model is used.
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References
Akaike H (1974) A new look at the statistical model identification. IEEE T Automat Contr 19:716–723
Amiri-Simkooei AR (2016) Non-negative least-squares variance component estimation with application to GPS time series. J Geodesy 90:451–466. https://doi.org/10.1007/s00190-016-0886-9
Amiri-Simkooei A, Tiberius C, Teunissen P (2007) Assessment of noise in GPS coordinate time series: methodology and results. J Geophys Res-Solid. https://doi.org/10.1029/2006JB004913
Bertiger W, Desai SD, Haines B, Harvey H, Moore AW, Owen S (2010) Weiss JP 84:327–337. https://doi.org/10.1007/s00190-010-0371-9
Bevis M, Brown A (2014) Trajectory models and reference frames for crustal motion geodesy. J Geodesy 88:283–311. https://doi.org/10.1007/s00190-013-0685-5
Blewitt G (1993) Advances in global positioning system technology for geodynamics investigations: 1978–1992. Contributions of Space Geodesy to Geodynamics: Technology 25:195–213
Bos MS, Fernandes RMS, Williams SDP, Bastos L (2013a) Fast error analysis of continuous GNSS observations with missing data. J Geodesy 87:351–360. https://doi.org/10.1007/s00190-012-0605-0
Bos MS, Williams SDP, Araújo IB, Bastos L (2013b) The effect of temporal correlated noise on the sea level rate and acceleration uncertainty. Geophys J Int 196(3):1423–1430. https://doi.org/10.1093/gji/ggt481
Burnham KP, Anderson DR (2002) Model selection and multimodel inference. Springer, New York. https://doi.org/10.1007/b97636
Dmitrieva K, Segall P, DeMets C (2015) Network-based estimation of time-dependent noise in GPS position time series. J Geodesy 89:591–606. https://doi.org/10.1007/s00190-015-0801-9
Dmitrieva K, Segall P, Bradley A (2017) Effects of linear trends on estimation of noise in GNSS position time-series. Geophys J Int 208:281–288. https://doi.org/10.1093/gji/ggw391
Fernandes RMS, Bos MS (2016) Applied automatic offset detection using HECTOR within EPOS-IP Time- series, AGU Fall Meeting, G51A-1084, San Francisco, USA
Fernandes RMS, Ambrosius BAC, Noomen R, Bastos L, Wortel MJR, Spakman W, Govers R (2003) The relative motion between Africa and Eurasia as derived from ITRF2000 and GPS data. Geophys Res Lett. https://doi.org/10.1029/2003GL017089
Finnegan NJ, Pritchard ME, Lowman RB, Lundgren PR (2008) Constraints on surface deformation in the Seattle, WA, urban corridor from satellite radar interferometry time-series analysis. Geophys J Int 174:29–41. https://doi.org/10.1111/j.1365-246X.2008.03822.x
Gordon RG, Stein S (1992) Global tectonics and space geodesy. Science 256:333
Hacker RS, Hatemi JA (2018) Model Selection in Time Series Analysis: Using Information Criteria as an Alternative to Hypothesis Testing. arXiv preprint arXiv:1805.08991
He X, Montillet JP, Fernandes R, Bos M, Yu K, Hua X, Jiang W (2017) Review of current GPS methodologies for producing accurate time series and their error sources. J Geodyn 106:12–29
Hill EM, Davis JL, Wernicke BP, Malikowski E (2009) Niemi NA (2009) Characterization of site-specific GPS errors using a short-baseline network of braced monuments at Yucca Mountain, southern Nevada. Journal of Geophysical Research: Solid Earth. https://doi.org/10.1029/2008JB006027
Johnson HO, Agnew DC (1995) Monument motion and measurements of crustal velocities. Geophys Res Lett 22:2905–2908. https://doi.org/10.1029/95GL02661
King MA, Williams SD (2009) Apparent stability of GPS monumentation from short-baseline time series. Journal of Geophysical Research: Solid Earth. https://doi.org/10.1029/2009JB006319
Langbein J (2004) Noise in two-color electronic distance meter measurements revisited. J Geophys Res 109:B04406. https://doi.org/10.1029/2003JB002819
Langbein J (2008) Noise in GPS displacement measurements from Southern California and Southern Nevada. J Geophys Res 113:5405. https://doi.org/10.1029/2007JB005247
Langbein J (2012) Estimating rate uncertainty with maximum likelihood: differences between power-law and flicker–random-walk models. J Geodesy 86:775–783. https://doi.org/10.1007/s00190-012-0556-5
Langbein J, Bock Y (2004) High-rate real-time GPS network at Parkfield: utility for detecting fault slip and seismic displacements. Geophys Res Lett 31:L15S20. https://doi.org/10.1029/2003GL019408
Langbein J, Svarc J (2019) Evaluation of temporally correlated noise in GNSS time series: geodetic monument performance. J Geodesy. https://doi.org/10.1029/2018JB016783
Lidberg M, Johansson JM, Scherneck H-G, Davis JL (2007) An improved and extended GPS-derived 3D velocity field of the glacial isostatic adjustment (GIA) in Fennoscandia. J Geodesy 81:213–230. https://doi.org/10.1007/s00190-006-0102-4
Mao A, Harrison CGA, Dixon TH (1999) Noise in GPS coordinate time series. J Geophys Res 104:2797–2816. https://doi.org/10.1029/1998JB900033
Melbourne TI, Webb FH (2003) Slow But Not Quite Silent. Science 300(5627):1886–1887. https://doi.org/10.1126/science.1086163
Montillet JP, McClusky S, Yu K (2013) Extracting colored noise statistics in time series via Negentropy. IEEE Signal Proc Lett 20(9):857–860. https://doi.org/10.1109/LSP.2013.2271241
Montillet JP, Williams SDP, Koulali A, McClusky SC (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):1207–1221. https://doi.org/10.1093/gji/ggu473
Montillet JP, Melbourne TI, Szeliga WM (2018) GPS vertical land motion corrections to sea-level rise estimates in the Pacific Northwest. J Geophys Res 123(2):1196–1212. https://doi.org/10.1002/2017JC013257
Neres M, Carafa MMC, Fernandes RMS, Matias L, Duarte JC, Barba S, Terrinha P (2016) Lithospheric deformation in the Africa-Iberia plate boundary: improved neotectonic modeling testing a basal-driven Alboran plate. J Geophys Res 121(9):6566–6596. https://doi.org/10.1029/2003GL017089
Proakis JG (2001) Digital communications, 4th edn. McGraw-Hill Higher Education. ISBN: 0072321113
Santamaría-Gómez A, Bouin M-N, Collilieux X, Wöppelmann G (2011) Correlated errors in GPS position time series: implications for velocity estimates. J Geophys Res 11:1405. https://doi.org/10.1029/2010JB007701
Santamaría-Gómez A, Gravelle M, Dangendorf S, Marcos M, Spada G, Wöppelmann G (2017) Uncertainty of the 20th century sea-level rise due to vertical land motion errors. Earth Planet Sci Lett 473:24–32
Schwarz G (1978) Estimating the dimension of a model. Ann Statist 6:461–464. https://doi.org/10.1214/aos/1176344136
Steffen H, Wu P (2011) Glacial isostatic adjustment in Fennoscandia—a review of data and modeling. J Geodyn 52:169–204. https://doi.org/10.1016/j.jog.2011.03.002
Tregoning P, Watson C (2009) Atmospheric effects and spurious signals in GPS analyses. J Geophys Res. https://doi.org/10.1029/2009JB006344
Williams SDP (2003) The effect of coloured noise on the uncertainties of rates from geodetic time series. J Geodesy 76:483–494. https://doi.org/10.1007/s00190-002-0283-4
Williams SDP, Bock Y, Fang P, Jamason P, Nikolaidis RM, Prawirodirdjo L, Miller M, Johnson DJ (2004) Error analysis of continuous GPS position time series. J Geophys Res 109:B03412. https://doi.org/10.1029/2003JB002741
Zhang J, Bock Y, Johnson H, Fang P, Williams S, Genrich J, Behr J (1997) Southern California permanent GPS geodetic array: error analysis of daily position estimates and site velocities. J Geophys Res 102(B8):18035–18055. https://doi.org/10.1029/97JB01380
Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102(B3):5005–5017
Acknowledgements
We would like to acknowledge Dr. Jürgen Kusche (Editor-in-Chief) and the anonymous reviewers for their valuable comments and suggestions. Machiel Bos was sponsored by national Portuguese funds through FCT in the scope of the Project IDL-FCT-UID/GEO/50019/2019 and Grant Number SFRH/BPD/89923/2012. The Portuguese team used computational resources provided by C4G—Collaboratory for Geosciences (PINFRA/22151/2016), supported by FCT (Portugal). Note that the latest version of the software Hector used to produce the results in this work is available at (http://segal.ubi.pt/hector/). Xiaoxing was sponsored by National key R&D Program of China (2018YFC1503600), Nation science foundation for distinguished young scholars of China (41525014), National Natural Science Foundation of China (41704030, 41804007, 41604013, 41674005, 41501502, 41761089), Jiangxi Province Key Lab for Digital Land (DLLJ201801 & 03), Natural Science Foundation of Jiangxi Province (20181BAB203027) and Chongqing Bureau of Quality and technology Supervision (CQZJKY2018004).
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He, X., Bos, M.S., Montillet, J.P. et al. Investigation of the noise properties at low frequencies in long GNSS time series. J Geod 93, 1271–1282 (2019). https://doi.org/10.1007/s00190-019-01244-y
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DOI: https://doi.org/10.1007/s00190-019-01244-y