Search

Copyright of Journal of National University of Defense Technology / Guofang Keji Daxue Xuebao is the property of NUDT Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The analysis of the Global NFavigation Satellite System (GNSS) time series provides valuable information for geodesy and geodynamics researcFh. Precise data analysis strategies are crucial for accurately obtaining the linear velocity of GNSS stations, enabling high-precision applications of GNSS time series. This study investigates the impact of different stochastic noise models on velocity estimations derived from GNSS time series, specifically under conditions of environmental loading correction and common mode error (CME) removal. By comparing data from various data centers, we find that post-correction, different analysis strategies exhibit high consistency in their noise characteristics and velocity estimation results. Across various analysis strategies, the optimal noise models were predominantly Power Law with White Noise (PLWN) and Fractional Noise with White Noise (FNWN), with the optimal noise models including COMB/JPL, COMB/SOPAC, and COMB/NGL for approximately 50% of the datasets. Most of the stations (approximately 80%) showed velocity differences below 0.3 mm/year and velocity estimation uncertainties below 0.1 mm/year. Nonetheless, variations in amplitudes and periodic signals persisted due to differences in the processing of raw GNSS observations. For instance, the NGL and JPL datasets, which were processed using GipsyX 2.1 software, showed higher amplitudes of the 5.5-day periodic signal. These findings provide a solid empirical foundation for advancing data analysis methods and enhancing the reliability of GNSS time series results in future research. [ABSTRACT FROM AUTHOR]

While the theory of random isotropic scalar fields on the sphere is well established, it has not been fully extended to the case of vector fields yet. In this contribution, several theoretical results are thus generalized to random isotropic vector fields on the sphere, including an equivalent of the Wiener–Khinchin theorem, which relates the distance-dependent covariance of the field’s components in a particular rotationally invariant basis to the covariance of the vector spherical harmonic coefficients of the field, i.e., its angular power spectrum. A parametric model, based on a stochastic partial differential equation, is proposed to represent the spatial covariance and angular power spectrum of such fields. Such a model is adjusted, with minor modifications, to empirical spatial correlations of the white noise and flicker noise components of 3D displacement time series of ground global navigation satellite system (GNSS) tracking stations. The obtained spatial correlation model may find several applications such as enhanced detection of offsets in GNSS station position time series, enhanced estimation of long-term ground deformation (i.e., station velocities), enhanced isolation of station-specific displacements (i.e., spatial filtering) and more realistic assessment of uncertainties in all GNSS network-based applications (e.g., estimation of crustal strain rates, of glacial isostatic adjustment models or of tectonic plate motion models). [ABSTRACT FROM AUTHOR]

This study addresses the potential of machine learning (ML) algorithms in geophysical and geodetic research, particularly for enhancing GNSS time series analysis. We employed XGBoost and Long Short-Term Memory (LSTM) networks to analyze GNSS time series data from the tectonically active Anatolian region. The primary objective was to detect discontinuities associated with seismic events. Using over 13 years of daily data from 15 GNSS stations, our analysis was conducted in two main steps. First, we characterized the signals by identifying linear trends and seasonal variations, achieving R 2 values of 0.84 for the XGBoost v.2.1.0 model and 0.81 for the LSTM model. Next, we focused on the residual signals, which are primarily related to tectonic movements. We applied various threshold values and tested different hyperparameters to identify the best-fitting models. We designed a confusion matrix to evaluate and classify the performance of our models. Both XGBoost and LSTM demonstrated robust performance, with XGBoost showing higher true positive rates, indicating its superior ability to detect precise discontinuities. Conversely, LSTM exhibited a lower false positive rate, highlighting its precision in minimizing false alarms. Our findings indicate that the best fitting models for both methods are capable of detecting seismic events (Mw ≥ 4.0) with approximately 85% precision. [ABSTRACT FROM AUTHOR]

The time series of GNSS coordinates contain signals caused by the age-related movement of tectonic plates, the deformation of the Earth's surface, as well as errors at different time scales from sub-daily tidal deformation to the long-term deformation of the surface load. Depending on the nature of the signal, specific approaches are used for both the visual interpretation and pre-processing of time series and their statistical analysis. However, none of the present software analyzes the nature of the residual errors but assumes their random nature and obedience to the classical normal distribution. One of the methods for analyzing the time series of coordinates with residual, unaccounted-for systematic errors is the non-classical error theory of measurements. The result of this work is a developed software solution for analyzing the time series of GNSS coordinates to test their normality, or in other words, to test whether a particular GNSS station is subject to the influence of small, unaccounted-for errors. Conclusions: After testing our software on four reference stations in Europe, we concluded that none of the chosen stations followed the normal law of distribution; thus, it is vital to perform such tests before conducting any experiments on the time series from reference stations. [ABSTRACT FROM AUTHOR]

AbstractThe great potential of the Global Navigation Satellite System (GNSS) in monitoring ground deformation is widely recognized. As with other geophysical data, GNSS time series can be significantly noisy, hiding elusive ground deformation signals. Several denoising techniques have been proposed to improve the signal-to-noise ratio over the years. One of the most effective denoising techniques has been proved to be multi-resolution decomposition through the discrete wavelet transform. However, wavelet analysis requires long data sets to be effective, as well as long computation times, that hinder its use as a real or near real-time monitoring tool. We propose training by a Convolutional Neural Network (CNN) to perform the equivalent of wavelet analysis to overcome these limitations. Once trained, the CNN model provides answers within seconds, making it feasible as a real-time data analysis tool. Our Machine Learning algorithm is tested on daily GNSS time series collected in the Campi Flegrei caldera (Southern Italy), which is a highly volcanic risk area. Without significant gaps, the retrieved RMSE and R2 values vary in the ranges 0.65–0.98 and 0.06–0.52 cm, respectively. These results are encouraging, as they hint at the possibility of applying this methodology in more effective real-time monitoring solutions for active volcanoes.

GNSS systems allow precise resolution of the geodetic positioning problem through advanced techniques of GNSS observation processing (PPP or relative positioning). Current instrumentation and communications capabilities allow obtaining geocentric and topocentric geodetic high frequency time series, whose analysis provides knowledge of the tectonic or volcanic geodynamic activity of a region. In this work, a GNSS time series study is carried out through the use and adaptation of R packets to determine their behavior, obtaining displacement velocities, noise levels, precursors in the time series, anomalous episodes and their temporal forecast. Statistical and analytical methods are studied; for example, ARMA, ARIMA models, least-squares methods, wavelet functions, Kalman techniques and CATS analysis. To obtain a geodynamic model of the Central American region, the horizontal and vertical velocities obtained by applying the above methods are taken, choosing the velocity with the least margin of error. Significant GNSS time series are obtained in geodynamically active regions (tectonic and/or volcanic). [ABSTRACT FROM AUTHOR]

Accurate noise model identification for GNSS time series is crucial for obtaining a reliable GNSS velocity field and its uncertainty for various studies in geodynamics and geodesy. Here, by comprehensively considering time span and missing data effect on the noise model of GNSS time series, we used four combined noise models to analyze the duration of the time series (ranging from 2 to 24 years) and the data gap (between 2% and 30%) effects on noise model selection and velocity estimation at 72 GNSS stations spanning from 1992 to 2022 in global region together with simulated data. Our results show that the selected noise model have better convergence when GNSS time series is getting longer. With longer time series, the GNSS velocity uncertainty estimation with different data gaps is more homogenous to a certain order of magnitude. When the GNSS time series length is less than 8 years, it shows that the flicker noise and random walk noise and white noise (FNRWWN), flicker noise and white noise (FNWN), and power law noise and white noise (PLWN) models are wrongly estimated as a Gauss–Markov and white noise (GGMWN) model, which can affect the accuracy of GNSS velocity estimated from GNSS time series. When the GNSS time series length is more than 12 years, the RW noise components are most likely to be detected. As the duration increases, the impact of RW on velocity uncertainty decreases. Finally, we show that the selection of the stochastic noise model and velocity estimation are reliable for a time series with a minimum duration of 12 years. [ABSTRACT FROM AUTHOR]

Estimating the height component of Global Navigation Satellite System (GNSS) stations is widely known to be more challenging than estimating the horizontal position. In this study, we utilized height time series data from 37 continuous GNSS stations that were part of the Turkish RTK CORS Network called TUSAGA-Active (Turkish National Permanent GNSS Network Active). The data covered the period from 2014 to 2019, and the selection of stations focused on the Eastern Anatolia region of Turkey due to its topographic characteristics and the pronounced influence of seasonal changes, which facilitated the interpretation of the effects on the height component. The daily coordinates of the GNSS stations were derived using the GAMIT/GLOBK software solution. We identified statistically significant trends, periodic variations, and stochastic components associated with the stations by applying time series analysis to these daily coordinate values. As a result, the vertical velocities of the GNSS stations were determined, along with their corresponding standard deviations. Furthermore, examining the height components of the continuous GNSS stations revealed seasonal effects. We aimed to investigate the potential relationship between these height components and meteorological parameters. The study provides evidence of the interconnectedness between the height components of continuous GNSS stations and various meteorological parameters. Simple linear regression analysis and ARMA time series modeling were utilized to establish this relationship. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

David Glacier and Drygalski Ice Tongue are massive glaciers in Victoria Land, Antarctica. The ice from the East Antarctic Ice Sheet is drained through the former, and then discharged into the western Ross Sea through the latter. David Drygalski is the largest outlet glacier in Northern Victoria Land, floating kilometers out to sea. The floating and grounded part of the David Glacier are the main focus of this article. During the XXI Italian Antarctic Expedition (2005–2006), within the framework of the National Antarctic Research Programme (PNRA), two GNSS stations were installed at different points: the first close to the grounding line of David Glacier, and the second approximately 40 km downstream of the first one. Simultaneous data logging was performed by both GNSS stations for 24 days. In the latest data processing, the kinematic PPP technique was adopted to evaluate the dominant diurnal components and the very small semi-diurnal variations in ice motion induced by the ocean tide and the mean ice flow rates of both GNSS stations. Comparison of the GNSS time series with predicted ocean tide calculated from harmonic coefficients of the nearest tide gauge stations, installed at Cape Roberts and Mario Zucchelli Station, highlight different local response of the glacier to ocean tide, with a minor amplitude of vertical motion at a point partially anchored at the bedrock close to the grounding line. During low tide, the velocity of the ice flow reaches its daily maximum, in accordance with the direction of seawater outflow from the fjord into the ocean, while the greatest daily tidal excursion generates an increase in the horizontal ice flow velocity. With the aim to extend the analysis in spatial terms, five COSMO-SkyMED Stripmap scenes were processed. The comparison of the co-registered offset tracking rates, obtained from SAR images, with the GNSS estimation shows good agreement. [ABSTRACT FROM AUTHOR]

Continuously Operation Reference Stations (CORS) networks provide surveying, mapping, and positioning services and play a crucial role in determining crustal displacement. This study processed the continuous Global Navigation Satellite System (GNSS) data collected from 55 CORS stations in the TAST's CORS in Vietnam to determine the crustal displacement in Vietnam from 2018 to 2021. The processing was performed using online Precise Point Positioning (PPP) services and the displacement model to estimate the velocity of the position time series. The result showed that the horizontal velocity field of all CORS stations is uniform in magnitude and direction, ranging from 25.3 to 42.6 mm/year with accuracy from ±0.1 to ±1.0 mm/year in the south-east direction in the International Terrestrial Reference Frame 2014 (ITRF2014). This study confirms the stability and accuracy of GNSS data from the TAST's CORS network for crustal displacement analysis. [ABSTRACT FROM AUTHOR]

The vertical movements of the Earth’s surface affected by non-tidal atmospheric loading (NTAL) are analyzed using satellite radar interferometry data. A clear relationship between deformation maps data derived from radar interferometry data and the GNSS time series of permanent stations has been established. The object of the study was the areas around the GNSS stations BYCH (Buchach), GORD (Horodok), CRNT (Chernivtsi). The input data were four pairs of radar interferometric images for the specified areas.Radar satellite images were obtained from the Sentinel-1A spacecraft. Data type — SLC (Single Look Complex) with vertical polarization. Acquisition mode — wideband interferometric IW (Interferometric Wide Swath). Data were processed using SNAP (Sentinel Application Platform) software. The processing yileded maps of vertical displacement of the specified territories where the earth’s surface displacement caused by influence of non-tidal atmospheric loading had taken place. The values obtained on the basis of vertical displacement maps have a high agreement with the results of time series of changes in the altitude position of permanent GNSS stations. The results obtained in the article are of both scientific and practical importance for studying the impact of non-tidal atmospheric loading in large areas. The practical significance is in improving the accuracy of terrestrial geodetic measurements’ processing, in particular high-precision levelling. The research data allow to make corrections of the results of levelling for short-period displacements affected by the influence of non-tidal atmospheric loading (NTAL).

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

It is an indisputable fact that the GNSS time series contain colored noise. However, we find that colored noise greatly affects parameter estimation of general linear trajectory models. For the post-seismic timescale parameters, ignoring the colored noise will increase the iteration times of the calculation parameters by 10–11 times. For parameters of coefficients, ignoring colored noise will obviously increase the deviation of parameter estimates. To overcome the above problems, we first estimate colored noise by maximum likelihood estimation. Then, the nonlinear least square algorithm with colored noise as the stochastic model is used to calculate timescale parameters. Finally, general linear trajectory models are constructed by using the calculated timescale parameters, and their optimal parameters are estimated by maximum likelihood estimation. The method is validated by lots of simulation experiments. The results show that the number of iterations is reduced by 90% compared with the traditional method; the deviation for parameters of coefficients decreased significantly. These methods are applied to the 2011 Tohoku-Oki earthquake. The results show that a nonlinear least square algorithm based on an appropriate stochastic model can provide strong constraints for timescale parameters. Among them, the timescale parameters of logarithmic terms decay exponentially with the increase in the distance from the epicenter; timescale parameters of exponential terms increase linearly northward. On the other hand, colored noise is an important factor affecting the extraction of seismic signals. For co-seismic displacement, ignoring colored noise will seriously underestimate small amplitude co-seismic signals. In the northern of Tohoku with the smallest co-seismic displacement, ignoring the colored noise will underestimate the co-seismic displacement by 20 mm. For post-seismic displacement, the float caused by ignoring colored noise is up to 500 mm, and the larger float (> 200 mm) is randomly distributed in the spatial domain. Therefore, it is necessary to consider the influence of colored noise on post-seismic deformation. [ABSTRACT FROM AUTHOR]

Global navigation satellite system (GNSS) site coordinate time series provides essential data for geodynamic and geophysical studies, realisation of a regional or global geodetic reference frames, and crustal deformation research. The coordinate time series has been conventionally modelled by least squares (LS) fitting with harmonic functions, alongside many other analysis methods. As a key limitation, the traditional modelling approaches simply use the functions of time variable, despite good knowledge of various underlying physical mechanisms responsible for the site displacements. This paper examines the use of machine learning (ML) models to reflect the effects or residential effects of physical variables related to Sun and the Moon ephemerides, polar motion, temperature, atmospheric pressure, and hydrology on the site displacements. To form the ML problem, these variables are constructed as the input vector of each ML training sample, while the vertical displacement of a GNSS site is regarded as the output value. In the evaluation experiments, three ML approaches, namely the gradient boosting decision tree (GBDT) approach, long short-term memory (LSTM) approach, and support vector machine (SVM) approach, are introduced and evaluated with the time series datasets collected from 9 GNSS sites over the period of 13 years. The results indicate that all three approaches achieve similar fitting precision in the range of 3–5 mm in the vertical displacement component, which is an improvement in over 30% with respect to the traditional LS fitting precision in the range of 4–7 mm. The prediction of the vertical time series with the three ML approaches shows the precision in the range of 4–7 mm over the future 24- month period. The results also indicate the relative importance of different physical features causing the displacements of each site. Overall, ML approaches demonstrate better performance and effectiveness in modelling and prediction of GNSS time series, thus impacting maintenance of geodetic reference frames, geodynamics, geophysics, and crustal deformation analysis. [ABSTRACT FROM AUTHOR]

The velocities of tectonic plates derived from GNSS time series are regularly used as input data for geophysical models. However, as shown by numerous researches, the coordinates time series contain residual errors of a systematic nature, which can significantly affect the reliability of the obtained velocity estimates. This research shows that using non-classical error theory of measurement (NETM) for processing GNSS time series allows detecting the presence of weak, not removed from GNSS processing, sources of systematic errors. Based on the coordinate time series of selected permanent GNSS stations in Europe, we checked the empirical distributions of errors by the NETM on G. Jeffries' recommendations and on the principles of the theory of hypothesis tests according to Pearson's criterion. It is established that the obtained coordinates time series of GNSS-stations only partially confirm the hypothesis of their conformity to the normal Gaussian distribution law, and this may be the main reason for their unrepresentative classification. In the future, it is necessary to identify and take into account the causes of residual errors that distort the real distribution of the results of the GNSS time series.

Estimating the height component of Global Navigation Satellite System (GNSS) stations is widely known to be more challenging than estimating the horizontal position. In this study, we utilized height time series data from 37 continuous GNSS stations that were part of the Turkish RTK CORS Network called TUSAGA-Active (Turkish National Permanent GNSS Network Active). The data covered the period from 2014 to 2019, and the selection of stations focused on the Eastern Anatolia region of Turkey due to its topographic characteristics and the pronounced influence of seasonal changes, which facilitated the interpretation of the effects on the height component. The daily coordinates of the GNSS stations were derived using the GAMIT/GLOBK software solution. We identified statistically significant trends, periodic variations, and stochastic components associated with the stations by applying time series analysis to these daily coordinate values. As a result, the vertical velocities of the GNSS stations were determined, along with their corresponding standard deviations. Furthermore, examining the height components of the continuous GNSS stations revealed seasonal effects. We aimed to investigate the potential relationship between these height components and meteorological parameters. The study provides evidence of the interconnectedness between the height components of continuous GNSS stations and various meteorological parameters. Simple linear regression analysis and ARMA time series modeling were utilized to establish this relationship.

GNSS systems allow precise resolution of the geodetic positioning problem through advanced techniques of GNSS observation processing (PPP or relative positioning). Current instrumentation and communications capabilities allow obtaining geocentric and topocentric geodetic high frequency time series, whose analysis provides knowledge of the tectonic or volcanic geodynamic activity of a region. In this work, a GNSS time series study is carried out through the use and adaptation of R packets to determine their behavior, obtaining displacement velocities, noise levels, precursors in the time series, anomalous episodes and their temporal forecast. Statistical and analytical methods are studied; for example, ARMA, ARIMA models, least-squares methods, wavelet functions, Kalman techniques and CATS analysis. To obtain a geodynamic model of the Central American region, the horizontal and vertical velocities obtained by applying the above methods are taken, choosing the velocity with the least margin of error. Significant GNSS time series are obtained in geodynamically active regions (tectonic and/or volcanic).

In this paper, the mathematical derivation of the underlying probability distribution function for the normalized least-squares wavelet spectrogram is presented. The impact of empirical and statistical weights on the estimation of the spectral peaks and their significance are demonstrated from the statistical point of view both theoretically and practically. The simulation results show an improvement of approximately 0. 02 mm (RMSE) for annual signal estimation when statistical weights are considered in the least-squares wavelet analysis (LSWA). The weighted LSWA estimates the signals more accurately than the ordinary LSWA for different percentage amount of missing data. As a real-world application, Global Navigation Satellite Systems (GNSS) time series for a station in Rome, Italy are analyzed. The analyses of the GNSS time series provided by different agencies for the same station reveal statistically significant annual peaks, more significant in 2010 but less significant between 2018 and 2020, while the higher frequency components show different spectral patterns over time. A declining trend of approximately − 0. 42 mm/year since 2004 is estimated for the GNSS height time series, likely due to gradual land subsidence. The results not only highlight the advantages of LSWA but can also help to better understand the uncertainties involved in signal estimation. • The Least-Squares Wavelet Analysis (LSWA) of GNSS time series in Rome is presented. • The mathematical derivation of stochastic surfaces for spectrograms in LSWA is shown. • Considering statistical weights improved the accuracy of signal estimation. • Jumps and missing data affect signal estimation but can be greatly treated by LSWA. • Annual signals were more significant in 2010 but less between 2018 and 2020. [ABSTRACT FROM AUTHOR]

The analysis of long time series of Global Navigation Satellite System (GNSS) observations has recently evidenced that the slow tectonic processes are not the only ones producing the observed slow deformations, but the Earth's crust reacts also to stresses induced by pressure variations and water circulation. The basic mechanisms are substantially of two kinds: deformations induced by the elastic response of the loaded surface and deformations due to the poroelastic properties of the ground. These mechanisms are quite different, in the first case the water load causes subsidence, in the second uplift; both create horizontal deformations moving away from the centre of deformation. Under anisotropic conditions, water pressure changes in poroelastic soils can induce large horizontal deformations especially where highly fractured rocks may provide permeability for fluid flow. Both elastic and poroelastic phenomena are observable and measurable by continuous GNSS monitoring of ground deformations. Both can be triggered by periodical atmospheric processes but also by extreme events, like heavy rainfalls. We will show a few case studies, observed in the Italian area, that demonstrate how the deformation patterns, at different repeating periods, clearly correlate with groundwater circulation in different environmental condition. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate the effect of the Baltic Sea non-tidal loading in the territory of Latvia using observations of the GNSS continuously operating reference stations (CORS) of LatPos, EUPOS®-Riga, EPN and EstPos networks. The GNSS station daily coordinate time series obtained in a double-difference (DD) mode were used. For representation of the sea level dynamics, the Latvian tide gauge records were used. Performed correlation analysis is based on yearly data sets of these observations for the period from 2012 up to 2020. The approach discloses how the non-tidal loading can induce variations in the time series of the regional GNSS station network. This paper increases understanding of the Earth's surface displacements occurring due to the non-tidal loading effect in Latvia, and is intended to raise the importance and necessity of improved Latvian GNSS time series by removing loading effects. [ABSTRACT FROM AUTHOR]

Abstract Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model.

Abstract The goal of any nonlinear dynamical analysis of a data series is to extract features of the dynamics of the underlying physical and chemical processes that produce that spatial pattern or time series; a by-product is to characterise the signal in terms of quantitative measures. In this paper, we briefly review the methodology involved in nonlinear analysis and explore time series for GNSS crustal displacements with a view to constraining the dynamics of the underlying tectonic processes responsible for the kinematics. We use recurrence plots and their quantification to extract the invariant measures of the tectonic system including the embedding dimension, the maximum Lyapunov exponent and the entropy and characterise the system using recurrence quantification analysis (RQA). These measures are used to develop a data model for some GNSS data sets in New Zealand. The resulting dynamical model is tested using nonlinear prediction algorithms. The behaviours of some RQA measures are shown to act as precursors to major jumps in crustal displacement rate. We explore synchronisation using cross- and joint-recurrence analyses between stations and show that generalised synchronisation occurs between GNSS time series separated by up to 600 km. Synchronisation between stations begins up to 250 to 400 days before a large displacement event and decreases immediately before the event. The results are used to speculate on the coupled processes that may be responsible for the tectonics of the observed crustal deformations and that are compatible with the results of nonlinear analysis. The overall aim is to place constraints on the nature of the global attractor that describes plate motions on the Earth.

In this study we compared weekly GNSS position time series with modelled values of crustal deformations on the basis of Gravity Recovery and Climate Experiment (GRACE) data. The Global Navigation Satellite Systems (GNSS) time series were taken from homogeneously reprocessed global network solutions within the International GNSS Service (IGS) Reprocessing 1 project and from regional solutions performed by Warsaw University of Technology (WUT) European Permanent Network (EPN) Local Analysis Center (LAC) within the EPN reprocessing project. Eight GNSS sites from the territory of Poland with observation timespans between 2.5 and 13 years were selected for this study. The Total Water Equivalent (TWE) estimation from GRACE data was used to compute deformations using the Green's function formalism. High frequency components were removed from GRACE data to avoid aliasing problems. Since GRACE observes mainly the mass transport in continental storage of water, we also compared GRACE deformations and the GNSS position time series, with the deformations computed on the basis of a hydrosphere model. We used the output of Water GAP Hydrology Model (WGHM) to compute deformations in the same manner as for the GRACE data. The WGHM gave slightly larger amplitudes than GNSS and GRACE. The atmospheric non-tidal loading effect was removed from GNSS position time series before comparing them with modelled deformations. The results confirmed that the major part of observed seasonal variations for GNSS vertical components can be attributed to the hydrosphere loading. The results for these components agree very well both in the amplitude and phase. The decrease in standard deviation of the residual GNSS position time series for vertical components corrected for the hydrosphere loading reached maximally 36% and occurred for all but one stations for both global and regional solutions. For horizontal components the amplitudes are about three times smaller than for vertical components therefore the comparison is much more complicated and the conclusions are ambiguous.

This study evaluates the EUREF Permanent Network (EPN) station position time series of approximately 200 GNSS stations subject to the Repro 2 reprocessing campaign in order to characterize the dominant types of noise and amplitude and their impact on estimated velocity values and associated uncertainties. The visual inspection on how different noise model represents the analysed data was done using the power spectral density of the residuals and the estimated noise model and it is coherent with the calculated Allan deviation (ADEV)-white and flicker noise. The velocities resulted from the dominant noise model are compared to the velocity obtained by using the Median Interannual Difference Adjusted for Skewness (MIDAS). The results show that only 3 stations present a dominant random walk noise model compared to flicker and powerlaw noise model for the horizontal and vertical components. We concluded that the velocities for the horizontal and vertical component show similar values in the case of MIDAS and maximum likelihood estimation (MLE), but we also found that the associated uncertainties from MIDAS are higher compared to the uncertainties from MLE. Additionally, we concluded that there is a spatial correlation in noise amplitude, and also regarding the differences in velocity uncertainties for the Up component.

This work is motivated by an application for the homogenization of global navigation satellite system (GNSS)-derived integrated water vapour series. Indeed, these series are affected by abrupt changes due to equipment changes or environmental effects. The detection and correction of the series from these changes are a crucial step before any use for climate studies. In addition to these abrupt changes, it has been observed in the series a non-stationary of the variability. We propose in this paper a new segmentation model that is a breakpoint detection in the mean model of a Gaussian process with heterogeneous variance on known time intervals. In this segmentation case, the dynamic programming algorithm used classically to infer the breakpoints cannot be applied anymore. We propose a procedure in two steps: we first estimate robustly the variances and then apply the classical inference by plugging these estimators. The performance of our proposed procedure is assessed through simulation experiments. An application to real GNSS data is presented. [ABSTRACT FROM AUTHOR]

The objective of this study is to discover the geodynamic processes of the Earth's crust in the territory of Latvia occurred due to the effect of the Baltic Sea non-tidal loading, by way of using GNSS permanent station daily coordinate time series and tide gauge data to find correlations between two data sets for the period from 2012 up to 2018. For this study observations of 31 Latvian and 2 Estonian GNSS stations were used. Stations belong to the LatPos, EUPOS®-Riga, EPN and EstPos networks. Station daily coordinate time series were computed using Bernese GNSS software v5.2 in a double-difference mode with 9 fiducial stations from International GNSS Service and EUREF Permanent GNSS Network. The analysis of obtained data significantly increases understanding of the Earth's surface displacements occurring due to the loading effect in Latvia. [ABSTRACT FROM AUTHOR]

With the improvement of Global Navigation Satellite System (GNSS) observation accuracy and the establishment of large continuously operating networks, long GNSS time series are now widely used to understand a range of Earth deformation processes. The continuously operating stations of the Crustal Movement Observation Network of China capture deformation signals due to time‐dependent tectonic, nontectonic mass loading, and potentially unknown geophysical processes. In order to separate and recover these underlying sources accurately and effectively, we apply the independent component analysis (ICA) to decompose the observed time series of vertical displacements. Then, we compare these signals with those predicted from independently developed geophysical process models of atmospheric, nontidal ocean, snow, soil moisture mass loading, and the Land Surface Discharge Model, as well as with Gravity Recovery and Climate Experiment observations. For comparison, we also perform the principal component analysis decomposition of time series and find that the ICA achieves a more consistent representation of multiple geophysical contributors to annual vertical GNSS displacements. ICA can decompose the long‐term trend and different seasonal and multiannual signals that closely correspond to the independently derived mass loading models. We find that independent contributions from atmospheric, soil moisture, and snow mass loading can be resolved from the GNSS data. Discrepancies are likely due to the correlated nature of some of the loading processes and unmodeled contributions from groundwater and surface water changes in South Central China and the Ganges Basin. Key Points: We extract the seasonal sources of vertical GNSS displacements in China using independent component analysisComparison of the independent components with mass loadings and GRACE shows that atmospheric and soil moisture seasonal loads are dominantWe estimate of mass loading cycles due to unmodeled surface and groundwater changes [ABSTRACT FROM AUTHOR]

Unmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model. Key Points: We modify Least Square Harmonics Estimation(LSHE) through design matrix supervision and introduction of a priori alternative frequenciesFull periodicity models of 25 CMONOC GNSS time series in Yunnan Province, China are established with the proposed MLSHESpectral indices, ACF and RMS of residuals analysis indicates that MLSHE reduces colored noise through full periodicity model estimations [ABSTRACT FROM AUTHOR]

In this paper we propose a network-based Kalman filter combined generalized simulated annealing algorithm approach to decompose a group of GPS position time series into secular trend, annual and semi-annual signals as well as noise components. This approach treats east, north and vertical components of the whole network separately and estimates network-average process-noise parameters to constrain the time variability of the seasonal signals and noise components. Each coordinate component for each station is modeled in state-space model (SSM) individually. The noise components are described as the combination of flicker noise (FN), random walk noise (RWN) and observation white noise (WN). Each component, except for the trend, is allowed to variate over the time, and their amplitudes are estimated by maximization of likelihood function using a generalized simulated annealing (GSA) algorithm. The proposed approach is applied to 10 reprocessed GPS position time series from the Tectonic and Environmental Observation Network of Mainland China (CMONOC II), and its output is compared with that of ordinary maximum likelihood estimation (MLE). The results show that the proposed approach is an effective tool for the decomposition of GPS position time series. Finally, the advantages and limitations of the proposed approach are also discussed. [ABSTRACT FROM AUTHOR]

This article presents an analysis of the extent of the impact of deformations of the earth's crust resulting from geophysical models on changes in the coordinates of Global Navigation Satellite System (GNSS) stations. The author presents the results of analyses of the spatial correlation coefficient of deformation components for the non-tidal atmospheric loading (NTAL), non-tidal ocean loading (NTOL) and hydrological loading (HYDRO) models of geophysical deformation. In addition, the author calculated the correlation coefficients between station's coordinate series to determine whether the deformations of the earth's crust have a more global, large-area (regional scale) or local-range (local scale) impact, limited to the nearest of stations. In addition to correlation coefficients, the author analysed the similarity in periodic components between station coordinates by calculating the coherence between them. The results of the analysis showed that for the height components (Up), we observe the global range of deformation models, and the NTAL deformation has the greatest influence on the change in them. The lack of correlation between coordinate signals for horizontal components may result from specific local conditions in the place of the station, low-resolution of geophysical models and small amplitudes of these signals in relation to noise. An analysis of the coherence coefficients showed that each station coordinates shows completely different periodic components in the North, East and Up directions. [ABSTRACT FROM AUTHOR]

In Antarctica, the severe climatic conditions and the thick ice sheet that covers the largest and most internal part of the continent make it particularly difficult to systematically carry out geophysical and geodetic observations on a continental scale. It prevents the comprehensive understanding of both the onshore and offshore geology as well as the relationship between the inner part of East Antarctica (EA) and the coastal sector of Victoria Land (VL). With the aim to reduce this gap, in this paper multiple geophysical dataset collected since the 1980s in Antarctica by Programma Nazionale di Ricerche in Antartide (PNRA) were integrated with geodetic observations. In particular, the analyzed data includes: (i) Geodetic time series from Trans Antarctic Mountains DEFormation (TAMDEF), and Victoria Land Network for DEFormation control (VLNDEF) GNSS stations installed in Victoria Land; (ii) the integration of on-shore (ground points data and airborne) gravity measurements in Victoria Land and marine gravity surveys performed in the Ross Sea and the narrow strip of Southern Ocean facing the coasts of northern Victoria Land. Gravity data modelling has improved the knowledge of the Moho depth of VL and surrounding the offshore areas. By the integration of geodetic and gravitational (or gravity) potential results it was possible to better constrain/identify four geodynamic blocks characterized by homogeneous geophysical signature: the Southern Ocean to the N, the Ross Sea to the E, the Wilkes Basin to the W, and VL in between. The last block is characterized by a small but significant clockwise rotation relative to East Antarctica. The presence of a N-S to NNW-SSE 1-km step in the Moho in correspondence of the Rennick Geodynamic Belt confirms the existence of this crustal scale discontinuity, possibly representing the tectonic boundary between East Antarctica and the northern part of VL block, as previously proposed by some geological studies.

Following the 2004 seismic unrest at Tenerife and the 2011–2012 submarine eruption at El Hierro, the number of Global Navigation Satellite System (GNSS) observation sites in the Canary Islands (Spain) has increased, offering scientists a useful tool with which to infer the kinematics and present-day surface deformation of the Canary sector of the Atlantic Ocean. We take advantage of the common-mode component filtering technique to improve the signal-to-noise ratio of the velocities retrieved from the daily solutions of 18 permanent GNSS stations distributed in the Canaries. The analysis of GNSS time series spanning the period 2011–2017 enabled us to characterize major regions of deformation along the archipelago through the mapping of the 2D infinitesimal strain field. By applying the triangular segmentation approach to GNSS velocities, we unveil a variable kinematic behaviour within the islands. The retrieved extension pattern shows areas of maximum deformation west of Tenerife, Gran Canaria and Fuerteventura. For the submarine main seismogenic fault between Tenerife and Gran Canaria, we simulated the horizontal deformation and strain due to one of the strongest (mbLg 5.2) earthquakes of the region. The seismic areas between islands, mainly offshore Tenerife and Gran Canaria, seem mainly influenced by the regional tectonic stress, not the local volcanic activity. In addition, the analysis of the maximum shear strain confirms that the regional stress field influences the E–W and NE–SW tectonic lineaments, which, in accordance with the extensional and compressional tectonic regimes identified, might favour episodes of volcanism in the Canary Islands.

Abstract After the 2004 unrest on Tenerife (Canary Islands), the Global Navigation Satellite System (GNSS) network called TEGETEIDE was designed and deployed with seven survey mode stations to contribute to a volcanic alert system. Starting in 2008, public access data from continuous GNSS stations, managed by public institutions, were included in this network allowing measurement of ground displacement at 14 locations in Tenerife. Data acquired from 2005 to 2015 was analysed to assess ground deformation in Tenerife following the 2004 volcanic unrest. The overall ground deformation depicted compression in the central Las Cañadas Caldera possibly caused by gravitational subsidence of the high central volcanic cone. This sinking is generalised around the whole island but is less in the northeast (Anaga Massif) where we found an extension rate close to 200 strain/y that could be related to a secondary submarine fault accommodating rifting to the northeast and isolating the behaviour of this massif. At the south volcanic field (south rift), another localized area with an extensional deformation was detected, possibly resulting from the subsurface fluid migration or mass addition that caused the 2004 volcanic unrest because is located following the seismic swarm alignment along Icod Valley towards Roque del Conde massif that persists since that event. We also detected residual plate velocity indicating movement of Tenerife towards Gran Canaria that should be studied in the context of the entire Canary Islands archipelago. [ABSTRACT FROM AUTHOR]

In this paper, we present the first velocity field from cGNSS (continuous GNSS) stations in the Continuous Monitoring GNSS Network (REGME) in Ecuador. We have analyzed data from 33 cGNSS REGME stations for the 2008–2014 period in order to characterize horizontal crustal motion and deformation in Ecuador. Prior to this, we analyzed the time series for the 33 REGME stations in order to determine their seasonality and the type of spectral noise. For most stations, we found a predominance of uncorrelated white noise with annual and semi-annual variations as the predominant first and second periods. Velocity was estimated by introducing the trend, seasonality and noise in each series in the general model, thus allowing us to improve accuracy as well as magnitude. The velocity and strain distribution correspond to the transpressive right-lateral slip of the westward-dipping faults of the Major Dextral System and the NNE movement of the North Andean Block (NAB) relative to the South American plate. The distributions of our deformation rate and velocity field indicate a differentiated tectonic behavior between northern, central and southern Ecuador. In northern Ecuador, there is an estimated right-lateral motion of 7.6 ± 0.5 mm/yr, consistent with the NNE movement of the NAB relative to the South American plate. In central Ecuador, the right-lateral motion decreases to 5.3 ± 0.4 mm/yr. In the southern region of Ecuador (from the Guayaquil Gulf to Peru) there is no strain accumulation, GNSS velocities decrease and turn to south. This zone belongs to the so-called Inca or Peru sliver. These results are consistent with the distinct behavior of subduction in Ecuador, with no coupling in southern Ecuador, and increased coupling towards the north, in the zone where megathrust earthquakes have occurred over the last century. The southern part of the Carnegie Ridge marks the limit between the two zones. We suggest that the main driving force responsible for the ongoing crustal deformation in Ecuador is the convergence between the Nazca and South American plates with the variable coupling pattern and the collision of the Carnegie Ridge. This results in different velocity patterns for the northern and the southern parts of Ecuador. [ABSTRACT FROM AUTHOR]

Global navigation satellite system (GNSS) datasets suffer from common mode error (CME) and other unmodeled errors. To decrease the noise level in GNSS positioning, we propose a new data-driven adaptive multiscale denoising method in this paper. Both synthetic and real-world long-term GNSS datasets were employed to assess the performance of the proposed method, and its results were compared with those of stacking filtering, principal component analysis (PCA) and the recently developed multiscale multiway PCA. It is found that the proposed method can significantly eliminate the high-frequency white noise and remove the low-frequency CME. Furthermore, the proposed method is more precise for denoising GNSS signals than the other denoising methods. For example, in the real-world example, our method reduces the mean standard deviation of the north, east and vertical components from 1.54 to 0.26, 1.64 to 0.21 and 4.80 to 0.72 mm, respectively. Noise analysis indicates that for the original signals, a combination of power-law plus white noise model can be identified as the best noise model. For the filtered time series using our method, the generalized Gauss-Markov model is the best noise model with the spectral indices close to − 3, indicating that flicker walk noise can be identified. Moreover, the common mode error in the unfiltered time series is significantly reduced by the proposed method. After filtering with our method, a combination of power-law plus white noise model is the best noise model for the CMEs in the study region. [ABSTRACT FROM AUTHOR]

Mass redistribution within the Earth system deforms the surface elastically. Loading theory allows us to predict loading induced displacement anywhere on the Earth’s surface using environmental loading models, e.g., Global Land Data Assimilation System. In addition, different publicly available loading products are available. However, there are differences among those products and the differences among the combinations of loading models cannot be ignored when precisions of better than 1 cm are required. Many scholars have applied these loading corrections to Global Navigation Satellite System (GNSS) time series from mainland China without considering or discussing the differences between the available models. Evaluating the effects of different loading products over this region is of paramount importance for accurately removing the loading signal. In this study, we investigate the performance of these different publicly available loading products on the scatter of GNSS time series from the Crustal Movement Observation Network of China. We concentrate on five different continental water storage loading models, six different non-tidal atmospheric loading models, and five different non-tidal oceanic loading models. We also investigate all the different combinations of loading products. The results show that the difference in RMS reduction can reach 20% in the vertical component depending on the loading correction applied. We then discuss the performance of different loading combinations and their effects on the noise characteristics of GNSS height time series and horizontal velocities. The results show that the loading products from NASA may be the best choice for corrections in mainland China. This conclusion could serve as an important reference for loading products users in this region.

Common mode error (CME) in Chuandian region of China is derived from 6-year continuous GPS time series and is identified by principal component analysis (PCA) method. It is revealed that the temporal behavior of the CME is not purely random, and contains unmodeled signals such as nonseasonal mass loadings. Its spatial distribution is quite uniform for all GPS sites in the region, and the first principal component, uniformly distributed in the region, has a spatial response of more than 70%. To further explore the potential contributors of CME, daily atmospheric mass loading and soil moisture mass loading effects are evaluated. Our results show that ~15% of CME can be explained by these daily surface mass loadings. The power spectral analysis is used to assess the CME. After removing atmospheric and soil moisture loadings from the CME, the power of the CME reduces in a wide range of frequencies. We also investigate the contribution of CME in GPS filtered residuals time series and it shows the Root Mean Squares (RMSs) of GPS time series are reduced by applying of the mass loading corrections in CME. These comparison results demonstrate that daily atmosphere pressure and the soil moisture mass loadings are a part of contributors to the CME in Chuandian region of China.