Potential Contributors to Common Mode Error in Array GPS Displacement Fields in Taiwan Island

The existence of the common mode error (CME) in the continuous global navigation satellite system (GNSS) coordinate time series affects geophysical studies that use GNSS observations. To understand the potential contributors of CME in GNSS networks in Taiwan and their effect on velocity estimations, we used the principal component analysis (PCA) and independent component analysis (ICA) to filter the vertical coordinate time series from 44 high-quality GNSS stations in Taiwan island in China, with a span of 10 years. The filtering effects have been evaluated and the potential causes of the CME are analyzed. The root-mean-square values decreased by approximately 14% and 17% after spatio-temporal filtering using PCA and ICA, respectively. We then discuss the relationship between the CME sources obtained by ICA and the environmental loads. The results reveal that the independent displacements extracted by ICA correlate with the atmospheric mass loading (ATML) and land water storage mass loading (LWS) of Taiwan in terms of both its amplitude and phase. We then use the white noise plus power law noise model to quantitatively estimate the noise characteristics of the pre- and post-filtered coordinate time series based on the maximum likelihood estimation criterion. The results indicate that spatio-temporal filtering reduces the amplitude of the PL and the periodic terms in the GPS time series.

Discontinuity Detection in GNSS Station Coordinate Time Series Using Machine Learning

Global navigation satellite systems (GNSS) provide globally distributed station coordinate time series that can be used for a variety of applications such as the definition of a terrestrial reference frame. A reliable estimation of the coordinate time series trends gives valuable information about station movements during the measured time period. Detecting discontinuities of various origins in such time series is crucial for accurate and robust velocity estimation. At present, there is no fully automated standard method for detecting discontinuities. Instead, discontinuity-catalogues are frequently used, which provide information about when a device was changed or an earthquake occurred. However, it is known that these catalogues suffer from incompleteness. This study investigates the suitability of machine learning classification algorithms that are fully data-driven to detect discontinuities caused by earthquakes in station coordinate time series without the need for external information. For this study, Japan was selected as a testing area. Ten different machine learning algorithms have been tested. It is found that Random Forest achieves the best performance with an F1 score of 0.77, a recall of 0.78, and a precision of 0.76. Overall, 525 of 565 recorded earthquakes in the test data were correctly classified. It is further highlighted that splitting the time series into chunks of 21 days leads to the best performance. Furthermore, it is beneficial to combine the three (normalized) components of the GNSS solution into one sample, and that adding the value range as an additional feature improves the result. Thus, this work demonstrates how it is possible to use machine learning algorithms to detect discontinuities in GNSS time series.

Comparative Analysis of The Correction Effect of Different Environmental Loading Products On Global GNSS Coordinate Time Series

The global navigation satellite system (GNSS) coordinate time series is affected by the environmental loading (including atmospheric loading (ATML), hydrological loading (HYDL), non-tidal oceanic loading (NTOL), etc.) and many organizations now provide grid products of these loadings. The temporal and spatial resolutions of these products, the loading models and data sources used are not the same, so the effect of correcting the nonlinear deformation of the GNSS coordinate time series is obviously different. This study mainly selects the three agencies, namely, School and Observatory of Earth Sciences (EOST) in France, German Research Center for Geosciences (GFZ) in Germany, and International Mass Loading Service (IMLS) in the United States, including 6 types of ATML models, 7 types of HYDL models and 5 NTOL models. The classification of these 18 environmental loading models was discussed, and the root mean square (RMS) reduction rate of the GNSS coordinate time series after environmental loading corrections (ELCs) was used to evaluate the performance differences of various models. Our results show that both the different models provided by the same organization and the same model provided by different organizations have different correction effects. Regardless of the models, it has a significant impact on the vertical coordinate time series. In order to correct the nonlinear deformation of the GNSS stations to the greatest extent, based on the above analysis, this study selects the optimal model combination of three environmental loadings as ECMWF_IB+MERRA2+ECCO1, and then explores its influence on the periodic signals in the GNSS coordinate time series. Research suggests that environmental loadings have a significant impact on the amplitude and phase of GNSS time series. Especially in the vertical direction, the largest RMS value can reach 8.42 mm. Before and after ELCs, the maximal difference of the annual amplitude and the half-annual amplitude at global 631 stations can reach 8.96 mm and 1.51 mm, respectively. Among them, 84.60% of the stations were corrected by the optimal environmental loading combination model, thus the nonlinear deformation was weakened.

Determination of the correlation degree between GNSS stations of Ukraine based on time series

Using GNSS for many years is the most common technology for the collection, processing, and interpretation of Earth observation data, in particular for the high-precision study of plate tectonics. The results of GNSS observations, such as coordinate time series, allow us to do continuous monitoring of stations, and modern methods of satellite observation processing provide high-precision results for geodynamic interpretation. The aim of our study is to process the results of observations by DD and PPP methods and determine the degree of correlation between GNSS stations based on coordinate time series. For our study, we selected 10 GNSS stations, which merged into two networks - Lviv (SAMB, STOY, STRY, SULP та ZLRS) and Ukrainian (BCRV, CHTK, CNIV, CRNI, GLSV та SULP). The duration of observations on each of them is about 1.5 years (2019-2020). The downloaded observation files were processed in two software packages: Gamit and GipsyX. After applying the «cleaned» procedures based on the iGPS software package, the residual time series were obtained and the coefficients of the interstation correlation matrices were calculated. After the procedure of "cleaning" the time series, we obtained the RMS value decrease for all components of the coordinates by an average of 7-30%, and some stations by 55%. Based on the obtained RMS values, we can conclude that the influence of unextracted or incorrectly modeled errors can significantly affect the results of satellite observations. The obtained interstation correlation coefficients for both networks show different results depending on the used method for processing satellite observations. The larger correlation values of the DD method can be explained by the fact that the effect of errors is distributed evenly to all network stations, whereas in the PPP method errors for each station are individual. The obtained graphs of the common-mode errors values, after their removal from the residual time series, confirm the more uniform nature of the DD method. The results of our study indicate the feasibility of using the PPP method, as the autonomous processing of stations allows you to see the real geodynamic picture of the studied region.

Imputation of GPS Coordinate Time Series Using MissForest

The global positioning system (GPS) can provide the daily coordinate time series to help geodesy and geophysical studies. However, due to logistics and malfunctioning, missing values are often “seen” in GPS time series, especially in polar regions. Acquiring a consistent and complete time series is the prerequisite for accurate and reliable statical analysis. Previous imputation studies focused on the temporal relationship of time series, and only a few studies used spatial relationships and/or were based on machine learning methods. In this study, we impute 20 Greenland GPS time series using missForest, which is a new machine learning method for data imputation. The imputation performance of missForest and that of four traditional methods are assessed, and the methods’ impacts on principal component analysis (PCA) are investigated. Results show that missForest can impute more than a 30-day gap, and its imputed time series has the least influence on PCA. When the gap size is 30 days, the mean absolute value of the imputed and true values for missForest is 2.71 mm. The normalized root mean squared error is 0.065, and the distance of the first principal component is 0.013. MissForest outperforms the other compared methods. MissForest can effectively restore the information of GPS time series and improve the results of related statistical processes, such as PCA analysis.

Characterizing the astrometric instability of extragalactic radio source positions measured with geodetic VLBI

Context. Geodetic very long baseline interferometry (VLBI) has been used to observe extragalactic radio sources for more than 40 yr. The absolute source positions derived from the VLBI measurements serve as a basis to define the International Celestial Reference Frame (ICRF). Despite being located at cosmological distances, an increasing number of these sources are found to show position instabilities, as revealed by the accumulation of VLBI data over the years. Aims. We investigate how to characterize the astrometric source position variations, as measured with geodetic VLBI data, in order to determine whether these variations occur along random or preferential directions. The sample of sources used for this purpose is made up of the 215 most observed ICRF sources. Methods. Based on the geodetic VLBI data set, we derived source coordinate time series to map the apparent trajectory drawn by the successively measured positions of each source in the plane of the sky. We then converted the coordinate time series into a set of vectors and used the direction of these vectors to calculate a probability density function (PDF) for the direction of variation of the source position. For each source, a model that matches the PDF and that comprises the smallest number of Gaussian components possible was further adjusted. The resulting components then identify the preferred directions of variation for the source position. Results. We found that more than one-half of the sources (56%) in our sample may be characterized by at least one preferred direction. Among these, about three-quarters are characterized by a unique direction, while the remaining sources show multiple preferred directions. The analysis of the distribution of these directions reveals an excess along the declination axis that is attributed to a VLBI network effect. Whether single or multiple, the identified preferred directions are likely due to source-intrinsic physical phenomena.

Improving the products of global GNSS data analysis by correcting for loading displacements at the observation level

<p>In recent years, the sensitivity of the GNSS station time series to the loading displacements is demonstrated by multiple studies, mainly for the non-tidal atmospheric loading (NTAL) and non-tidal ocean loading (NTOL). But the impact of the loading displacements is beyond the coordinate time series, including and not limited to geocenter motion, Earth Orientation Parameters, satellite orbits, etc. We extensively evaluate the impact on and the improvements of the reference frame products from reprocessed 25 years of GPS and GLONASS network solution with a consistent application of non-tidal loading and Continental Water Storage Loading (CWSL) displacement at the observational level. We also discussed the differences of correcting for the loading displacements at the observation level and correction at the product level on GNSS station coordinates and Geocenter motions, we elaborate the advantage of the inclusion of correction at the observational level.</p><p> </p><p>Significant improvements are found in estimated coordinate time series, almost 90% of the station shows improved WRMS in North and Up directions and over 75% in East. CWSL dominates the contribution in the North direction. The annual Geocenter variations (over 80% of the x and y components) can be explained by the loading displacement. A small and consistent reduction of orbit disclosure is found among all 32 GPS satellites and most of the GLONASS satellites (23 out of 25) after the inclusion of all the loading displacements.  All the improvements demonstrate the urgent need for the adoption of loading displacements in the global GNSS analysis.</p>

Detecting earthquakes in GNSS station coordinate time series using machine learning algorithms

<p>Earthquakes are natural hazards that occur suddenly and without much notice. The most established method of detecting earthquakes is to use a network of seismometers. Nowadays, station positions of the global navigation satellite system (GNSS) can be determined with a high accuracy of a few centimetres or even millimetres. This high accuracy, together with the dense global coverage, makes it possible to also use GNSS station networks to investigate geophysical phenomena such as earthquakes. Absolute ground movements caused by earthquakes are reflected in the GNSS station coordinate time series and can be characterised using statistical methods or machine learning techniques.</p><p>In this work, we have used thousands of time series of GNSS station positions distributed all over the world to detect and classify earthquakes. We apply a variety of machine learning algorithms that enable large-scale processing of the time series in order to identify spatio-temporal patterns. Several machine learning algorithms, including Random Forest, Nearest Neighbours, and Multi-Layer Perceptron, are compared against each other, as well as against classical statistical methods, based on their performance on detecting earthquakes from the station coordinate time series.</p>