Abstract
A new method for investigating the coherence field of the noise component of high-frequency GPS time series is proposed. The method is applied to the main territory of the USA, which is characterized by a dense network of GPS stations. The data are presented in steps of 5 min from February 28, 2013, until June 29, 2019, on the Nevada Geodetic Laboratory Web site. The proposed method estimates the spatial distribution of the mean values of multiple coherence, calculated within nodes of a regular grid, between GPS coordinates of a given number of nearest operable stations and the periods at which the maximum values of coherence are reached. The two-dimensional probability density of the positions of places where the coherence maximum is most often realized is estimated. These estimates can be obtained for the entire history of observations and also in a sliding time window of a given length, which makes it possible to trace the dynamics of changes in time in the coherence field of the earth’s tremor. The entropy of the two-dimensional probability density of places of concentration of maximum values of coherence allows us to distinguish seasonal changes in the structure of the coherence field of GPS noise. To study the temporal dynamics, we use the auxiliary time series of changes in the maximum multiple coherence at 50 reference points located throughout the study area. The study of the coherence properties of this auxiliary 50-dimensional time series (“secondary coherence”) in a 180-day sliding time window highlighted a series of synchronization bursts of earth’s surface tremors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beavan J (2005) Noise properties of continuous GPS data from concrete pillar geodetic monuments in New Zealand and comparison with data from US deep drilled braced monuments. J Geophys Res 110:B08410. https://doi.org/10.1029/2005JB003642
Blewitt G, Lavallee D (2002) Effects of annual signal on geodetic velocity. J Geophys Res 107(B7):2145. https://doi.org/10.1029/2001JB000570
Blewitt G, Hammond WC, Kreemer C (2018) Harnessing the GPS data explosion for interdisciplinary science. Eos 99. https://doi.org/10.1029/2018EO104623
Bock Y, Melgar D, Crowell BW (2011) Real-time strong-motion broadband displacements from collocated gps and accelerometers. Bull Seismol Soc Am 101(6):2904–2925. https://doi.org/10.1785/0120110007
Bos MS, Fernandes RMS, Williams SDP, 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 MS, Bastos L, Fernandes RMS (2010) The influence of seasonal signals on the estimation of the tectonic motion in short continuous GPS time-series. J Geodyn 49(3–4):205–209. https://doi.org/10.1016/j.jog.2009.10.005
Box GEP, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis—forecasting and control, 5th edn. Wiley, Hoboken
Brillinger DR (1975) Time Series. Data analysis and theory, holt, rinehart and winston, Inc, New York, Chicago, San Francisco.
Caporali A (2003) Average strain rate in the Italian crust inferred from a permanent GPS network—I: statistical analysis of the time-series of permanent GPS stations. Geophys J Int 155:241–253. https://doi.org/10.1046/j.1365-246X.2003.02034.x
Chen Q, van Dam T, 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. https://doi.org/10.1016/j.jog.2013.05.005
Duda RO, Hart PE, Stork DG (2000) Pattern classification. Wiley, New York
Filatov DM, Lyubushin AA (2017) Fractal analysis of GPS time series for early detection of disastrous seismic events. Phys A 469(1):718–730. https://doi.org/10.1016/j.physa.2016.11.046
Filatov DM, Lyubushin AA (2019) Precursory analysis of GPS time series for seismic hazard assessment. Pure Appl Geophy First Online: January 7, 2019. https://doi.org/10.1007/s00024-018-2079-3
Goudarzi MA, Cocard M, Santerre R, Woldai T (2013) GPS interactive time series analysis software. GPS Solut 17(4):595–603. https://doi.org/10.1007/s10291-012-0296-2
Gray RM (1990) Entropy and information theory. Springer, New York
Hannan EJ (1970) Multiple time series. Wiley, New York
Hackl M, Malservisi R, Hugentobler U, Jiang Y (2013) Velocity covariance in the presence of anisotropic time correlated noise and transient events in GPS time series. J Geodyn 72:36–45. https://doi.org/10.1016/j.jog.2013.08.007
Hamilton JD (1994) Time series analysis. Princeton University Press, Princeton
Hsien PA, Bredehoft JD (1981) A reservoir analysis of the denver earthquakes: a case of induced seismicity. J Geophys Res 86(B2):903–920. https://doi.org/10.1029/JB086iB02p00903
Jolliffe IT (1986) Principal component analysis. Springer, Berlin
Khelif S, Kahlouche S, Belbachir MF (2013) Analysis of position time series of GPS-DORIS co-located stations. Int J Appl Earth Observ Geoinf 20:67–76. https://doi.org/10.1016/j.jag.2011.12.011
Langbein J (2008) Noise in GPS displacement measurements from Southern California and Southern Nevada. J Geophys Res 113:B05405. https://doi.org/10.1029/2007JB005247
Langbein J, Johnson H (1997) Correlated errors in geodetic time series, implications for time-dependent deformation. J Geophys Res 102(B1):591–603. https://doi.org/10.1029/96JB02945
Li J, Miyashita K, Kato T, Miyazaki S (2000) GPS time series modeling by autoregressive moving average method, application to the crustal deformation in central Japan. Earth Planets Space 52:155–162. https://doi.org/10.1186/BF03351624
Lyubushin AA (1998) Analysis of canonical coherences in the problems of geophysical monitoring. Izv Phys Solid Earth 34(1):52–58
Lyubushin AA (1999) Analysis of multidimensional geophysical monitoring time series for earthquake prediction. Ann Geofis 42(5):927–937. https://doi.org/10.4401/ag-3757
Lyubushin AA (2014) Analysis of coherence in global seismic noise for 1997–2012. Izv Phys Solid Earth 50(3):325–333. https://doi.org/10.1134/S1069351314030069
Lyubushin A (2018a) Synchronization of geophysical fields fluctuations. In: Chelidze T, Telesca L, Vallianatos F (eds) Complexity of seismic time series: measurement and applications. Elsevier, Amsterdam, pp 161–197
Lyubushin A (2018b) Global coherence of GPS-measured high-frequency surface tremor motions. GPS Solutions 22:116. https://doi.org/10.1007/s10291-018-0781-3
Mao A, Harrison CGA, Dixon TH (1999) Noise in GPS coordinate time series. J Geophys Res 104(B2):2797–2816. https://doi.org/10.1029/1998JB900033
Marple SL Jr (1987) Digital spectral analysis with applications. Prentice-Hall Inc, Englewood Cliffs
Teferle FN, Williams SDP, Kierulf HP, Bingley RM, Plag HP (2008) A continuous GPS coordinate time series analysis strategy for high-accuracy vertical land movements. Phys Chem Earth, Parts A/B/C 33(3–4):205–216. https://doi.org/10.1016/j.pce.2006.11.002
Wang W, Zhao B, Wang Q, Yang S (2012) Noise analysis of continuous GPS coordinate time series for CMONOC. Adv Space Res 49(5):943–956. https://doi.org/10.1016/j.asr.2011.11.032
Williams SDP, Bock Y, Fang P, Jamason P, Nikolaidis RM, Prawirodirdjo L, Miller M, Johnson DJ (2004) Error analysis of continuous GPS time series. J Geophys Res 109(B3):B03412. https://doi.org/10.1029/2003jb002741
Zhang J, Bock Y, Johnson H, Fang P, Williams S, Genrich J, Wdowinski S, Behr J (1997) Southern California permanent GPS geodetic array: Error analysis of daily position estimates and site velocities. J Geophys Res 102(B8):18,035–18,055. https://doi.org/10.1029/97JB01380
Acknowledgements
The author is grateful to the Nevada Geodetic Laboratory, University of Nevada, Reno, for providing free access to three-component GPS time series with sampling time step 5 min from the global network all over the world. This work was supported by the Russian Foundation for Basic Research, Project No. 18-05-00133 “Estimation of fluctuations of seismic hazard on the basis of complex analysis of the Earth’s ambient noise.”
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Lyubushin, A. Field of coherence of GPS-measured earth tremors. GPS Solut 23, 120 (2019). https://doi.org/10.1007/s10291-019-0909-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-019-0909-0