Abstract
We present a simple method for identification of seasonal components in GPS displacement time series. The method considers two options for the treatment of long series, considering possible variability in the seasonal phases. The method also proposes a bootstrap scheme to deal approximately with series shorter than one period of the seasonal signal. Tests with synthetic data show that the method gives quite acceptable results, so that results from application to real data, although approximate, should be useful considering the inherent uncertainties in the data.
Similar content being viewed by others
Code availability
The MATLAB programs, diseas.m and syntseas.m, can be downloaded from http://cicese.repositorioinstitucional.mx/jspui/handle/1007/3925. No special hardware or software (besides Matlab) are required. Instructions for the use of these programs are included in the corresponding headers.
References
Bartel BA, Hamburger MW, Meertens CM, Lowry A, Corpuz E (2003) Dynamics of active magmatic and hydrothermal systems at Taal Volcano, Philippines, from continuous GPS measurements. J Geophys Res 108(B10):2475. https://doi.org/10.1029/2002JB002194
Blewitt G, Lavallée D (2002) Effect of annual signals on geodetic velocity. J Geophys ResSolid Earth 107:ETG9
Bogusz J, Figurski M (2014) Annual signals observed in regional GPS networks. Acta Geodyn Geomater 11(2):125–131. https://doi.org/10.13168/AGG.2014.0003
Chanard K, Métois M, Rebischung P, Avouac J (2020) A warning against over-interpretation of seasonal signals measured by the global navigation satellite system. Nat Commun 11(1):1375
Chen Q, Dam TV, Sneeuw N, Collilieux X, Weigelt M, Rebischung P (2013) Singular spectrum analysis for modeling seasonal signals from GPS time series. J Geodyn 72:25–35
Chen B, Bian J, Ding K, Wu H, Li H (2020) Extracting seasonal signals in GNSS coordinate time series via weighted nuclear norm minimization. Remote Sens 2020:12. https://doi.org/10.3390/rs12122027
Davis J, Wernicke B, Bisnath S, Niemi N, Elósegui P (2006) Subcontinental-scale crustal velocity changes along the Pacific-North American plate boundary. Nature 441(7097):1131–1134. https://doi.org/10.1038/nature04781
Davis JL, Wernicke BP, Tamisiea ME (2012) On seasonal signals in geodetic time series. J Geophys ResSolid Earth 117(B1):B01403. https://doi.org/10.1029/2011JB008690
Ding X, Zheng D, Dong D, Ma C, Chen Y, Wang GL (2005) Seasonal and secular positional variations at eight co-located GPS and VLBI stations. J Geodesy 79:71–81. https://doi.org/10.1007/s00190-005-0444-3
Dong D, Fang P, Bock Y, Cheng MK, Miyazaki S (2002) Anatomy of apparent seasonal variations from GPS-derived site position time series. J Geophys Res Earth 107:ETG-9
Freymueller J (2009) Seasonal position variations and regional reference frame realization. In: Drewes H (ed) Geodetic reference frames. Springer Berlin Heidelberg. volume 134 of International Association of Geodesy Symposia, pp 191–196. https://doi.org/10.1007/978-3-642-00860-3 30
Geirsson H, d’Oreye N, Mashagiro N, Syauswa M, Celli G, Kadufu B, Smets B, Kervyn F (2017) Volcano-tectonic deformation in the Kivu Region, Central Africa: results from six years of continuous GNSS observations of the Kivu Geodetic Network (KivuGNet). J Afr Earth Sc 134:809–823
Gonzalez-Ortega A, Sandwell D, Fialko Y, Nava A, Fletcher J, Gonzalez-Garcia J, Lipovsky B, Floyd M, Funning G (2014) El Mayor-Cucapah (Mw 7.2) earthquake: early postseismic deformation from InSAR and GPS observations. J Geophys Res 119(2):1482–1497. https://doi.org/10.1002/2013JB010193
Gruszczynska M, Klos A, Rosat S, Bogusz J (2017) Deriving common seasonal signals in GPS position time series: By using multichannel singular spectrum analysis. Acta Geodyn Geomater 14(3):267–278
Hamming R (1977) Digital filters. Prentice Hall
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
Heflin M, Donnellan A, Parker J, Lyzenga G, Moore A, Ludwig L, Rundle J, Wang J, Pierce M (2020) Automated estimation and tools to extract positions, velocities, breaks, and seasonal terms from daily GNSS measurements: illuminating nonlinear Salton Trough deformation. Earth Space Sci 7:e2019EA000644. https://doi.org/10.1029/2019EA000644
Janssen V (2007) Volcano deformation monitoring using GPS. J Spat Sci 52(1):41–54. https://doi.org/10.1080/14498596.2007.9635099
Ji K, Shen Y, Wang F (2020) Signal extraction from GNSS position time series using weighted wavelet analysis. Remote Sens 12:992. https://doi.org/10.3390/rs12060992
Klos A, Bos M, Fernandes R, Bogusz J (2019) Noise-dependent adaption of the Wiener filter for the GPS position time series. Math Geosci 51:53–73
Larson KM, Poland M, Miklius A (2010) Volcano monitoring using GPS: developing data analysis strategies based on the June 2007 Kilauea Volcano intrusion and eruption. J Geophys Res. https://doi.org/10.1029/2009JB007022
Lee S-W, Yun S-H, Kim DH, Lee D, Lee YJ, Schutz BE (2015) Real-time volcano monitoring using GNSS single-frequency receivers. J Geophys Res Solid Earth 120:8551–8569. https://doi.org/10.1002/2014JB011648
Mann D, Freymueller J, Lu Z (2002) Deformation associated with the 1997 eruption of Okmok volcano. Alsk J Geophys Res 107(B4):2072
Miyagi Y, Freymueller JT, Kimata F, Sato T, Mann D (2004) Surface deformation caused by shallow magmatic activity at Okmok volcano, Alaska, detected by GPS campaigns 2000–2002. Earth Planets Space 56:e29–e32
Puglisi G, Bonforte A (2004) Dynamics of Mount Etna Volcano inferred from static and kinematic GPS measurements. J Geophys Res 109:B11404. https://doi.org/10.1029/2003JB002878
Ray J, Altamimi Z, Collilieux X, Van Dam T (2008) Anomalous harmonics in the spectra of GPS position estimates. GPS Solut 12:55–64
Ruttner P (2021) Analysis and prediction of long term GNSS height time series and environmental loading effects. Master's thesis, ETH Zurich
Tregoning P, Watson C (2009) Atmospheric effects and spurious signals in GPS analyses. J Geophys Res 114:B09403. https://doi.org/10.1029/2009JB006344
Tucikešić S, Božić B, Mulić M (2020) Absolute time series GNSS point positioning-data cleaning and noise characterization. Tehnički Vjesnik 27(4):1229–1236
Wang K, Jiang W, Chen H, An X, Zhou X, Yuan P, Chen Q (2018) Analysis of seasonal signal in GPS short-baseline time series. Pure Appl Geophys 175:3485–3509
Wernicke B, Davis J (2010) Detecting large scale intracontinental slow-slip events (SSEs) using geodograms. Seismol Res Lett 81:694–698. https://doi.org/10.1785/gssrl.81.5.694
Acknowledgements
L. A-B. was supported by CONAHCYT Investigadoras e Investigadores por México Program, project 2602. We are deeply grateful to the Servicio de Geodesia Satelital, from Instituto de Geofísica, Universidad Nacional Autónoma de México (UNAM), especially to Enrique Cabral-Cano and Luis Salazar-Tlaczani. We are grateful to two anonymous reviewers and to the editor Ramón Zúñiga.
Funding
This study had no external funding.
Author information
Authors and Affiliations
Contributions
FAN contributed to conceptualization, program code, writing—first draft, and review of subsequent drafts. LÁ-B performed data curation and analysis, writing—contributions to and review of all drafts, and editing. Both authors approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there are no conflicts of interest or competing interests.
Additional information
Edited by Prof. Ramón Zúñiga (CO-EDITOR-IN-CHIEF).
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Nava, F.A., Ávila-Barrientos, L. Seasonal components in GPS displacement time series. Acta Geophys. (2023). https://doi.org/10.1007/s11600-023-01245-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11600-023-01245-8