Nonlinear Processes in Geophysics
Nonlinear Processes in Geophysics
NPG
Articles | Volume 28, issue 1
Articles | Volume 28, issue 1
https://doi.org/10.5194/npg-28-121-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-28-121-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 28, issue 1
Research article
 | 
15 Feb 2021
Research article |  | 15 Feb 2021

Application of Lévy processes in modelling (geodetic) time series with mixed spectra

Jean-Philippe Montillet, Xiaoxing He, Kegen Yu, and Changliang Xiong

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Cited articles

Anderson, T. W. and Darling, D. A.: Asymptotic theory of certain “goodness-of-fit” criteria based on stochastic processes, Ann. Math. Statist., 23, 193–212, https://doi.org/10.1214/aoms/1177729437, 1952. a
Bevis, M. and Brown, A.: Trajectory models and reference frames for crustal motion geodesy, J. Geod., 88, 283, https://doi.org/10.1007/s00190-013-0685-5, 2014. a
Bock, Y. and Melgar, D.: Physical applications of GPS geodesy: a review, Rep. Prog. Phys., 79, 106801, https://doi.org/10.1088/0034-4885/79/10/106801, 2016. a, b
Bos, M. S., Fernandes, R. M. S., Williams, S. D. P., and Bastos, L.: Fast error analysis of continuous GNSS observations with missing data, J. Geod., 87, 351–360, https://doi.org/10.1007/s00190-012-0605-0, 2013. a
Botai, O. J., Combrinck, L., and Sivakumar, V.: Interferences of α-stable distribution of the underlying noise components in geodetic data, South Afr. J. Geol., 114, 541–548, https://doi.org/10.2113/gssajg.114.3-4.541, 2011. a, b
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Short summary
Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series, together with the estimated geophysical signals. The noise spectrum of these time series is generally modelled as a mixed spectrum, with a sum of white and coloured noise. Here, we are interested in modelling the residual time series after deterministically subtracting geophysical signals from the observations with the Lévy processes.
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