Detection of geodynamic anomalies in GNSS time series using machine learning methods

Short-term geodynamic displacements of the Earth's surface are studied insufficiently because the unambiguous identification of such geodynamic processes is quite a difficult task. Short-term geodynamic processes can be observed by considering GNSS time series lasting up to 2 months. The coordinate displacements are visually almost unnoticeable comparing annual time series. In this work, an algorithm based on the results of statistical analysis of time series of several GNSS stations on purpose to find simultaneous displacements of the Earth's surface is developed. Authors propose a method for detecting short-term displacements based on sliding correlation and covariance interrelationships between the time series of two GNSS stations for short periods, which are shifted along with the entire time series. The approach allows showing the characteristic of the displacements throughout the study area based on the selection of anomalous displacements of selected GNSS stations. The high correlation coefficient between the periods of stations indicates the presence of simultaneous and identical in absolute value offsets. The high value of covariance indicates the synchronicity and unidirectionality of such displacements. As a result, the time series of 8 GNSS stations of the Geoterrace network for the period from the end of 2017 to the beginning of 2021 are studied according to the presented method. The anomalous altitude displacements in the region for the epoch of 185th day of 2018 and 20 days period is investigated. Based on the processing, maps of the spatial distribution of correlation and covariance coefficients are constructed. The proposed method could be improved and applied to the study of kinematic processes in areas with a dense network of GNSS stations with long time series similarly GNSS networks for monitoring of large electricity produced objects such as HPPs and PSPs.

Understanding the inner structure of the crust and upper mantle is essential to evaluate those mechanisms driving Earth’s dynamics. Usually, surface deformation provides valuable constraints on viscoelastic parameters.  Postseismic deformation following large megathrust earthquakes, offers a unique opportunity to explore the viscoelastic properties of the shallower earth structure since it is strongly influenced by viscoelastic relaxation processes. This postseismic deformation is often recorded by GNSS stations, which offer high temporal resolution and therefore are useful to constrain the relaxation time along convergent margins. However, the spatial coverage of GNSS networks is often sparse,  inhibiting our ability to study the large scale variations in viscoelastic properties of the medium. To solve these issues, we rely on InSAR time series which provide continuous spatial resolution of surface deformation. In this work, we exploit the FLATSIM project (Thollard et al., 2021) initiative considering Sentinel-1 data  over Central Chile that has been processed using the NSBAS processing chain (Doin et al., 2013). Particularly, we focus on Central Chile, with special emphasis on the 2015 8.3 Mw Illapel earthquake. The InSAR data spans 8 years and has been corrected using the global atmospheric models ERA-5. Complementary, we use GNSS time series from 25 stations deployed over the Illapel rupture area, combining stations from Centro Sismologico Nacional and the DeepTrigger project.Since both data sets contain the contribution from multiple tectonic and non-tectonic processes, we employ different techniques to isolate the postseismic deformation of the 2015 Illapel earthquake. Actually,  for GNSS, we apply Independent Component Analysis while for InSAR time series, we perform  a parametric decomposition pixel by pixel. Our findings reveal a very strong postseismic signal with a typical logarithmic decay, lasting at least 8 years.In this work, in order to investigate the underlying rheological properties of the medium, we exploit the PyLith software,  a finite-element model that can take into account the complex rheological structure of the system. To do so, we impose the co-seismic slip model coming from averaged slip solutions, thereby initiating the model to distinguish between viscoelastic and afterslip contributions. By reproducing the surface deformation patterns given jointly by GNSS and InSAR data, we aim to determine the geometrical and rheological variations beneath the Illapel rupture area, particularly those viscoelastic parameters characterizing the crust and upper mantle regions. Our analysis provide insights to better understand how these properties affect both the seismic cycle and long-term deformation patterns at local and regional scales.

The paper analyzes the vertical displacements of the GNSS sites of civil engineering structures caused by non-tidal atmospheric loading (NTAL). The object of the study is the Dnister Hydroelectric Power Plant №1 (HPP-1) and its GNSS monitoring network. The initial data are the RINEX-files of 14 GNSS stations of the Dnister HPP-1 and 8 permanent GNSS stations within a radius of 100 km, the NTAL model downloaded from the repository of German Research Centre for Geosciences GFZ for 2019-2021, and materials on the geological structure of the object. Methods include comparison and analysis of the altitude component of GNSS time series with model values of NTAL as well as interpretation of the geodynamic vertical displacements, taking into account the analysis of the geological structure. As a result, it was found that the sites of the GNSS network of the Dnister HPP-1 undergo less vertical displacements than the permanent GNSS stations within a radius of 100 km. This corresponds to the difference in thickness and density of the rocks under the GNSS sites and stations, so they undergo different elastic deformations by the same NTAL. In addition, the research detected different dynamics of vertical displacements of GNSS sites on the dam and on the river banks. It leads to cracks and deformations of concrete structures in the dam-bank contact zones. During the anomalous impact of NTAL, the altitude of even nearby sites can change if the geological structure beneath them is different. The work shows that for civil engineering structures it is necessary to apply special models to take into account NTAL deformations for high-precision engineering and geodetic measurements.

The main aim of the article was to analyse the actual accuracy of determining the vertical movements of the Earth’s crust (VMEC) based on time series made of four measurement techniques: satellite altimetry (SA), tide gauges (TG), fixed GNSS stations and radar interferometry. A relatively new issue is the use of the persistent scatterer InSAR (PSInSAR) time series to determine VMEC. To compare the PSInSAR results with GNSS, an innovative procedure was developed: the workflow of determining the value of VMEC velocities in GNSS stations based on InSAR data. In our article, we have compiled 110 interferograms for ascending satellites and 111 interferograms for descending satellites along the European coast for each of the selected 27 GNSS stations, which is over 5000 interferograms. This allowed us to create time series of unprecedented time, very similar to the time resolution of time series from GNSS stations. As a result, we found that the obtained accuracies of the VMEC determined from the PSInSAR are similar to those obtained from the GNSS time series. We have shown that the VMEC around GNSS stations determined by other techniques are not the same.

<p><strong>Abstract: </strong></p> <p><strong> </strong>The increasing development of GNSS techniques enables solving geodetic problems on both local and global scales. Parallelly, complex algorithms have been proposed and can also be solved well by Machine Learning (ML). However, ML techniques are sometimes not sensitive enough to gain results with a high probability for some cases, like sparse data or non-stationary GNSS time series. In this study, we use a combination of Human and Machine learning (H&M) to improve the classification performance of continuous GNSS stations. First, 427 permanent GNSS stations are obtained from the EUREF network to train ML models. The models are then applied to classify the quality of 939 continuous observation stations from two projects, EIFEL and IPOC, carried out by the German Research Centre for Geosciences (GFZ), Potsdam, Germany. Next, we independently validate the ML models' reality through a MATLAB program, GNSS metadata, and seismic data. Finally, all data of these 1366 stations are used to re-train the ML models. The main criteria to classify are the number of outliers, jumps in GNSS time series, root mean square errors, observation time-spans, and stability of the crustal motion velocity fields. Applying the approach of the H&M combination improves the performance of the ML models up to 92% while using only ML methods remains ~68%. These ML-based classification models can be applied to estimate the quality of permanent GNSS stations and to manage big databases. The result is the basis for selecting suitable control and monitoring stations in crustal deformation monitoring as well as in civil and industrial applications.</p> <p><strong>Keywords: </strong></p> <p>GNSS station classification, Machine learning, Human & Machine learning combination.</p>

The article proposes to combine a methods based on wavelet denoising (WDN) and Shannon entropy (DSE) for GNSS station position time series denoising and Complementary Ensemble Empirical Mode Decomposition (CEEMD) for the decomposition of the time series into frequency components, namely intrinsic mode functions (IMFs). First, we used WDN as well as DSE to denoise the GNSS time series. They were then decomposed with CEEMD, which is dedicated to analysing non-stationary time series. The proposed WDN + CEEMD and DSE + CEEMD methods were then employed to analyse several GNSS station position time series in Poland. We used daily time series of position residues for 15 GNSS stations of the EUREF Permanent Network (EPN) classified as the Polish national control network. The station time series were decomposed into IMF frequency components, of which IMF5 and IMF6 represented semi-annual and annual signals. We noted an annual oscillation for all the reference stations in the horizontal and vertical components. A semi-annual oscillation was found for all the stations only in the vertical component. The study confirms that the WDN + CEEMD as well as DSE + CEEMD method is capable of limiting the absorption of some noise by seasonal signals. The values of the spectral indices of the station position time series after subtracting the seasonal signals modelled by the WDN + CEEMD or DSE + CEEMD methods assumed values from the range of the power law noise model. GNSS station position time series analysis with WDN + CEEMD and DSE + CEEMD yielded satisfactory results and can be a good alternative for modelling time-dependent seasonal signals in GNSS time series, particularly the annual and semi-annual signals.

Accuracy estimation of site coordinates derived from GNSS-observations by non-classical error theory of measurements

Surface loading effects related to atmospheric, hydrological, non-tidal ocean, are one of the principal sources of the seasonal oscillations in GNSS time series, and it should be taken into account for improving GNSS accuracy. In this study, the daily vertical time series of 9 GNSS stations at Hong Kong was used to investigate the surface loading (sum of atmospheric loading, hydrological loading, non-tidal ocean loading (AHNL)) contributors of seasonal oscillations in GNSS observations. This paper reveals a correlation between the AHNL deformation and the GNSS vertical time series, with an average correlation coefficient of 0.5. The GNSS vertical time series and the corresponding AHNL deformation at all stations exhibit identical amplitudes and phases. The average root mean square (RMS) reduction is 15% at all stations after removing the AHNL deformation from the GNSS vertical time series, implying that AHNL may contribute to non-linear fluctuations in GNSS observations at Hong Kong. Furthermore, the independent component analysis (ICA) method was performed to extract periodic signals from the GNSS time series. ICA method can effectively separate the seasonal signals related to AHNL, the seasonal signals show a strong correlation with AHNL deformations, with Lin correlation coefficients above 0.6. Finally, we carried out cross wavelet transform (XWT) method to quantitatively express the annual phase relationship between GNSS vertical time series and AHNL deformation. The XWT result shows AHNL mainly contribute to the annual oscillation in GNSS observations.

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.

This study investigates the effects of non-tidal atmospheric loading on GNSS time series for a network covering the Nordic countries, with a specific focus on Finland. We processed a 5-month dataset from the year 2015 using GAMIT/GLOBK software, implementing two distinct non-tidal atmospheric loading grid models, namely ‘atmfilt’ and ‘atmdisp’. Our results reveal that both grid models yield similar improvements in the variability of GNSS coordinate time series, albeit with a slightly better performance for ‘atmdisp’ grid. Our results show that implementing these built-in models in the time series analysis yields up to a 14% improvement (reduction in scatter) in the vertical component for 75% of the selected stations. However, the enhancement diminishes for the horizontal components (increase in scatter), exacerbating the eastern component of time series. The corrections lead to a 10% improvement of the North component. We also examined the effectiveness of the loading corrections by comparing our processing-level corrected time series to the daily averaged time series improved by the loading model provided by EOST loading service as a post-processing approach. Given the relatively short 5-month duration of the time series, drawing definitive conclusions when comparing models is challenging. However, it is evident that the GNSS time series exhibits distinct variations related to atmospheric loading in their vertical positions across the various models that were examined.

Effects on Chilean Vertical Reference Frame due to the Maule Earthquake co-seismic and post-seismic effects

Accurate 3D surface deformation analysis is essential for understanding geodynamic processes and mitigating related hazards. We present a methodology that fuses GNSS and InSAR time series to achieve robust deformation estimates. Our case study focuses on the Groningen region in the Netherlands, an area undergoing significant subsidence and seismicity due to decades of gas extraction. In addition, Groningen benefits from a dense GNSS network spanning approximately 50 × 50 km, offering an ideal testbed for integrated deformation analyses.The proposed workflow involves preparing GNSS time series from Nevada Geodetic Laboratory by removing common-mode errors and detrending for plate motion, then referencing all stations to a central GNSS antenna. A moving average filter further refines the GNSS time-series. In parallel, we refine the “Basic” EGMS InSAR products by applying smoothed calibration trends derived from the “Calibrated” products. Subsequently, the daily average deformation of InSAR Line-of-Sight (LOS) points near the reference GNSS station is subtracted from all persistent scatterers, ensuring consistent reference frames across both datasets.To combine InSAR LOS deformation with GNSS 3D data, we identify persistent scatterers within a 100-meter radius of each GNSS antenna and synchronize the reference epochs between both datasets. We then rotate the GNSS East-North-Up coordinates so that one axis aligns with the InSAR LOS, apply an error-weighted least-squares solution to fuse the measurements, and finally reintroduce the out-of-LOS components derived from the pre-processed GNSS data. The resulting full 3D deformation field is then converted back to the ENU coordinate system.Preliminary analyses suggest that integrating GNSS and InSAR improves reliability in all three components, with particularly notable benefits in the north component. Moving forward, this fusion strategy can be extended to smaller-scale monitoring projects (e.g., dams or bridges), offering a versatile approach to detecting and characterizing localized deformation anomalies.

<p><span>Detecting small Slow Slip Events (SSEs) is still an open challenge. The difficulty in revealing low magnitude events is related to their detection in the geodetic data, which must be improved either by employing more powerful equipment or by developing novel methods for the systematic discovery of small events, which can be crucial for the precise characterization of the slip spectrum</span><span>. The improvement of the ability to detect small SSEs and the associated seismic response can play a decisive role in the understanding of the mechanics of active faults, remarkably subduction in which tremors cannot serve as a proxy for the slow slip or Episodic Tremor and Slip (ETS) is not regularly observed, making it necessary to provide new observations and methods to perceive potential bursts of slow slip.</span></p><p><span>Here we explore three Deep Learning–based strategies applied to GNSS data to characterize earthquakes and SSEs. Unlike seismic data, geodetic observations are crucial for dealing with SSEs, since they contain the required spatiotemporal information. Yet, since the low number of available labelled events (earthquakes or SSEs) producing significant displacement at GNSS station does not allow to adequately train Deep Learning models, we adopt synthetic geodetic data (Okada, 1985), obtained by generating events with uniformly distributed parameters. Thus, the model will not be biased towards the most numerous parameters, with a possibly stronger predictive power. The approach inspired by (van den Ende, Ampuero, 2020) was used for the characterization (i.e., estimation of epicentral location and magnitude), which associates geodetic time series with the location information of the GNSS stations. Yet, rearranging the geodetic displacement from GNSS time series into images can let Convolutional Neural Networks (CNN) to better account for the data spatial consistency, leading to more precise results. Furthermore, Transformers have also been tested with image time series of ground deformation. To assess the reliability of the tested methods, a magnitude threshold on the synthetic test set has been estimated, which depends on the depth and the hypocenter location of the event, showing a trade-off between the Signal-to-Noise (SNR) ratio and the relative position of the test events with respect to the GNSS network, revealing physical consistence. The results are also spatially consistent, as the location and magnitude errors tend to increase as the actual epicenters move offshore, with the location error showing a strong inverse proportionality on the magnitude. The employment of time series of deformation with Transformer networks lead to the best results and may allow us to better handle the noise complexity and to account for a spatio–temporal analysis of the ground deformation linked to SSE triggering. Nevertheless, the image–based model outperforms the other two on real data, showing evidence that the synthetic data does still not overlap with the real one, opening towards several perspectives. A more complex synthetic noise can be produced by allowing for synthetic data gaps and outliers (e.g., common modes), or machine learning–based denoising strategies can be envisioned to pre–process the data to improve the SNR ratio.</span></p>

Задача обнаружения аномалий – является одной из ключевых при создании киберфизических систем, так как позволяет в режиме реального времени анализировать данные, поступающие с различных устройств, и оценивать состояние среды. В данной статье сравниваются 14 одномерных методов обнаружения аномалий во временных рядах, использующих статистический подход и методы машинного обучения. Эта работа позволит оценить различные подходы к задаче обнаружения аномалий. Сравнение данных методов проводится на тестовых наборах данных из открытых источников. Результатом работы является анализ точности и производительности методов обнаружения аномалий в одномерных числовых рядах. Как итог, статистические методы являются более точными, обнаруживая точечные и коллективные аномалии, при этом требуя меньше времени на вычисления. Измерения, приведенные в данной статье, проводились на одномерных рядах, обнаружение аномалий в многомерных временных рядах будет предметом дальнейшего изучения. The task of detecting anomalies is one of the key tasks in creating cyber-physical systems, as it allows you to analyze data coming from various devices in real time and assess the state of the environment. This article compares 14 one-dimensional methods for detecting anomalies in time series using a statistical approach and machine learning methods. This work will allow us to evaluate different approaches to the problem of detecting anomalies. The comparison of these methods is carried out on test data sets from open sources. The result of the work is an analysis of the accuracy and performance of methods for detecting anomalies in one-dimensional numerical series. As a result, statistical methods are more accurate, detecting point and collective anomalies, while requiring less time for calculations. The measurements given in this paper were performed on one-dimensional time series, and the detection of anomalies in multidimensional time series will be the subject of further study.

<p>Permanent GNSS stations have become fundamental for geodynamic studies thanks to their capability of providing consistent coordinate time series. The time series analysis is becoming more and more sophisticated and there are several approaches, fully automated or not, helping the users to derive the main parameters of interest such as: trends, periodical signals, discontinuities, types of noises, blunders. Typically, however, the analysis of the time series is still performed considering separately each of the three coordinate components. Actually, this neglects the three-dimensional nature of the GNSS position solutions, which are computed simultaneously, and may have some impact on the analysis. We should also bear in mind that the values of the coordinates time series depend on the reference system orientation. For instance, the time series values expressed in geocentric coordinates (X, Y, Z) are usually different from the same ones represented in a topocentric (E, N, V) reference. Therefore, if the analysis is performed separately on the three coordinate components, results will be different depending on the adopted reference system.<br>The aim of this work is to address the issue concerning the automated rejection of outliers potentially present in the GNSS time series. This is a fundamental aspect considering the large amount of data that nowadays shall be continuously processed and analyzed, thus requiring procedures as automated as possible. A viable approach is to search for outliers by analyzing the error distribution of the coordinates after having removed trends and signals, assuming that these behave like casual errors and follow a normal density distribution. It is then possible to set a statistical threshold in order to reject iteratively all the solutions with higher residual values. This approach is usually implemented by considering mono-dimensional time series in which the three coordinate components are processed separately. Nevertheless, from a statistical point of view, each GNSS position solution should be considered to be a 3D variable, thus characterized by a probability density function defined in a 3D space. In particular, by considering a chi-square distribution with three degrees of freedom it is possible to consider an ellipsoidal density function that well fit the error distribution of a 3D casual variable such as the GNSS coordinates.<br>In this work, numerical results obtained from the analysis of real dataset will be presented. In particular, six years of daily position solutions obtained from 12 GNSS permanent stations have been considered. The time series have been analyzed starting from both geocentric and topocentric coordinates using alternatively two different approaches: a classical one, in which the three coordinate components have been processed separately, and the 3D approach that allowed to consider the three coordinates at once. Results show that the second approach is mostly independent from the starting reference system, whereas the classical approach is affected by the orientation of the Cartesian axes used to project the same positions.</p>