Global Navigation Satellite System Time Series Research Articles

Deep Learning CNN-GRU Method for GNSS Deformation Monitoring Prediction

Hydraulic structures are the key national infrastructures, whose safety and stability are crucial for socio-economic development. Global Navigation Satellite System (GNSS) technology, as a high-precision deformation monitoring method, is of great significance for the safety and stability of hydraulic structures. However, the GNSS time series exhibits characteristics such as high nonlinearity, spatiotemporal correlation, and noise interference, making it difficult to model for prediction. The Neural Networks (CNN) model has strong feature extraction capabilities and translation invariance. However, it remains sensitive to changes in the scale and position of the target and requires large amounts of data. The Gated Recurrent Units (GRU) model could improve the training effectiveness by introducing gate mechanisms, but its ability to model long-term dependencies is limited. This study proposes a combined model, using CNN to extract spatial features and GRU to capture temporal information, to achieve an accurate prediction. The experiment shows that the proposed CNN-GRU model has a better performance, with an improvement of approximately 45%, demonstrating higher accuracy and reliability in predictions for GNSS deformation monitoring. This provides a new feasible solution for the safety monitoring and early warning of hydraulic structures.

Selection of noise models for GNSS coordinate time series based on model averaging algorithm

In the field of global navigation satellite system (GNSS) time series noise analysis, appropriately modeling the noise components plays an important role in determining the velocity of GNSS sites and quantifying the uncertainty associated with the velocity estimation. Over the years, researchers have focused on only one optimal noise model, while other noise models that show similar performance to the optimal model have been ignored. We investigated whether these ignored noise models can be made use of to describe the noise in the GNSS time series after applying a model averaging algorithm. The experimental data were derived from 28 International GNSS Service (IGS) sites in the California region of the United States and 110 IGS sites worldwide. The results showed that for the GNSS time series of 28 IGS sites in the California, 79%, 68%, and 75% of the site components can be applied the model averaging algorithm in the east/north/up (E/N/U) directions, respectively. Based on it, the east direction showed the best performance, with 50% of the site components obtaining more conservative velocity uncertainty after applying the model averaging algorithm compared to the optimal noise model. For GNSS time series of 110 IGS stations worldwide, the model averaging algorithm demonstrates excellent performance in all the E/N/U directions. In the E/N/U directions, 86%, 94%, and 57% of the site components can apply the model averaging algorithm. Building upon this, 77%, 65%, and 62% of the site components achieve more conservative velocity uncertainty in the E/N/U directions compared to the optimal noise model. To fully validate the feasibility of the model averaging algorithm, we also tested GNSS time series of varying lengths and different thresholds of the model averaging algorithm. In summary, the model averaging algorithm performs exceptionally well in the noise analysis of GNSS time series. It helps prevent overly optimistic estimation results.

Extraction of periodic signals in Global Navigation Satellite System (GNSS) vertical coordinate time series using the adaptive ensemble empirical modal decomposition method

Abstract. Empirical modal decomposition (EMD) is an efficient tool for extracting a signal from stationary or non-stationary time series and is enhanced in stability and robustness by ensemble empirical mode decomposition (EEMD). Adaptive EEMD further improves computational efficiency through adaptability in the white noise amplitude and set average number. However, its effectiveness in the periodic signal extraction in Global Navigation Satellite System (GNSS) coordinate time series regarding the inevitable missing data and offset issues has not been comprehensively validated. In order to thoroughly investigate their impacts, we simulated 5 years of daily time series data with different missing data percentages or a different number of offsets and conducted them 300 times for each simulation. The results show that high accuracy could reach the overall random missing rate below 15 % and avoid consecutive misses exceeding 30 d. Meanwhile, offsets should be corrected in advance regardless of their magnitudes. The analysis of the vertical components of 13 stations within the Australian Global Sea Level Observing System (GLOSS) monitoring network demonstrates the advantage of adaptive EEMD in revealing the time-varying characteristics of periodic signals. From the perspectives of correlation coefficients (CCs), root mean square error (RMSE), power spectral density indices (κ) and signal-to-noise ratio (SNR), the means for adaptive EEMD are 0.36, 0.81, −0.18 and 0.48, respectively, while for least squares (LS), they are 0.27, 0.86, −0.50 and 0.23. Meanwhile, a significance test of the residuals further substantiates the effectiveness in periodic signal extraction, which shows that there is no annual signal remaining. Also, the longer the series, the higher the accuracy of the reasonable extracted periodic signal concluded via the significance test. Moreover, driving factors are more effectively facilitated by the time-varying periodic characteristics compared with the constant periodic signal derived by LS. Overall, the application of adaptive EEMD could achieve high accuracy in analyzing GNSS time series, but it should be based on properly dealing with missing data and offsets.

A machine learning approach for slow slip event detection using GNSS time-series

Extracting tectonic transient displacements on the Earth’s surface from Global Navigation Satellite System (GNSS) time series remains a challenge, because GNSS station displacements depend on multiple processes occurring simultaneously, along with noise that obscures low-magnitude transient signals. We present a novel method for automatic detection of slow slip events (SSEs) in time series of a GNSS network by training a supervised machine learning (ML) model for classification. The proposed methodology detects both temporally and spatially the signatures of SSEs or regional transients within a GNSS network. The time series of a GNSS network were transformed into grayscale images, from which descriptors, including Bag of Visual Words (BoW) and Extended Local Binary Patterns (ELBP), were extracted. These descriptors served as input features for two distinct ML models: Support Vector Machines (SVM) and Artificial Neural Networks (NN). To train and test the ML classification model, two 3-year synthetic datasets were generated, one with GNSS networks featuring slow slip events (SSEs) of varying location, duration, onset time, and magnitude, and the other without SSEs, resulting in positive and negative sets, respectively. For each GNSS network, an image was created by combining the east and north components of the time series, which have been previously detrended and common mode error filtered. Each image is further divided into sub-images corresponding to 60 days time windows, in order to temporarily detect the existence of a transient. For training and testing, the datasets were separated into 75% for training and 25% for testing, each with 50% positive and 50% negative cases. In the final step, we analyze the positively classified images, representing the time windows in which the classifier detected transients. Within each of these windows, we identify the network’s time series with the highest velocity, indicating the stations and geographic area where the detected transients occurred. The test results demonstrate that both ML models achieved high performance using both ELBP and BoW descriptors as features. Finally, our ML models were validated on a real dataset with a transient signal recorded before the 2014 Iquique earthquake in Chile, and they effectively detected this anomalous signal. The proposed method can effectively detect transient signals related to SSEs with high accuracy, sensitivity, and specificity in both the test and instrumentally recorded datasets.

Joint Bayesian Modeling of Velocity Break Points, Noise Characteristics, and Their Uncertainties in GNSS Time Series: Far‐Field Velocity Anomalies Concurrent With Magmatic Activity in Iceland

AbstractEstimating the timing of velocity changes (break points) in Global Navigation Satellite System (GNSS) coordinate time series is required for understanding various Earth processes and how they may couple with each other. We jointly estimate break points, noise parameters and their uncertainties in GNSS time series using Bayesian interference. Synthetic data experiments demonstrate that time‐correlated noise can cause spurious estimates of break points for small velocity change and suggest the lower limits of velocity change for reliable estimates. A case study at the Krafla volcanic system shows increased rift‐perpendicular movementof 7.6–9.8 mm/yr, preceding by 23–77 days the 2014 Bárðarbunga rifting episode that occurred ∼120 km to the south (maximum likelihood estimates). These far‐field velocity anomalies occur in the same period as enhanced near‐field seismicity and deformation before the dike intrusion at Bárðarbunga, possibly indicating the coupling between the two volcanic systems through a deep partial melt zone.

Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis

Singular spectrum analysis is widely used in geodetic time series analysis. However, when extracting time-varying periodic signals from a large number of Global Navigation Satellite System (GNSS) time series, the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient. To improve the efficiency and accuracy of singular spectrum analysis, this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix. The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series, and the extraction efficiency of a single time series is six times that of singular spectrum analysis. The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.

Function Model Based on Nonlinear Transient Rheology of Rocks: An Analysis of Decadal GNSS Time Series After the 2011 Tohoku‐oki Earthquake

AbstractThe postseismic Global Navigation Satellite System (GNSS) time series after the 2011 Tohoku‐oki earthquake is often empirically explained by one or more logarithmic and exponential decay functions. However, a function model with these decay functions struggles to illuminate various deformation mechanisms. Here, we propose a new function model incorporating laboratory‐derived constitutive laws (power‐law flow and velocity‐strengthening friction) utilized in mechanical postseismic models of the last decade. We demonstrated that our function model accurately predicts the decade‐long time series of inland GNSS stations, including coastal areas where significant postseismic uplift continues now. Moreover, it decomposes them into displacements due to viscoelastic relaxation and afterslip, similar to results produced by previous stress‐dependent postseismic models of the 2011 Tohoku‐oki earthquake. This physics‐based function model is an effective tool to ease the process of forecasting long‐term GNSS time series by dividing them into two dominant mechanisms at the plate interface and the surrounding viscoelastic mantle.

Wavelet-like denoising of GNSS data through machine learning. Application to the time series of the Campi Flegrei volcanic area (Southern Italy)

The 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.

A Temporal and Spatial Denoising Method for Intelligent Settlement Sensing System

Global Navigation Satellite System (GNSS) has the ability to provide timely structural settlement information and been widely installed on the critical infrastructures. However, the inevitable noise negatively affects the accurate assessment, measurement and evaluation of the status. Although some methods have been developed in previous studies, fully mining the temporal and spatial correlations is still necessary to further analyze. Therefore, we propose a new denoising method based on truncated high-order singular value decomposition to reduce the noise in multivariate GNSS signals. Using synthetic signals and real-world GNSS signals, the proposed method is evaluated by comparison with some benchmark models. The results show that the proposed method can effectively reduce both white noise (WN) and flicker noise (FN). Moreover, experiments on the signal-noise ratio (SNR) from 1 to 10 demonstrate that the proposed method can achieve stable performances for GNSS time series denoising. The organization of GNSS signals as the high-dimensional tensor has been proved to be an effective analytical tool to mine the complicated spatial and temporal correlations.

Geodetic evidence of land subsidence in Cirebon, Indonesia

The subsidence phenomena occur in numerous cities in Indonesia (Jakarta, Bandung, and Semarang) and have been observed over the last few decades using geodetic techniques such as interferometric synthetic aperture radar (InSAR) and the Global Navigation Satellite System (GNSS). Three variables are considered the leading causes of substantial subsidence in those cities: urban development, excessive groundwater removal, and geological context. Considering these considerations, we assess surface displacement in the surrounding area of Cirebon, Indonesia, which has similar background circumstances. We used 43 Sentinel-1A images covering from 2014 to 2021 and processed them using the small baseline subset (SBAS) method obtaining 78 interferograms for time series analysis. A weighted correction from two weather models was used to correct tropospheric errors. The results from the InSAR time series were compared with the continuous GNSS time series (2010–2021) processed using GAMIT/GLOBK GNSS processing softwares. Cirebon experienced a slow land subsidence rate with an average magnitude of -2.6 mm/yr. Furthermore, we underline that more significant subsidence rates were found in several locations. Conic-shaped subsidence with a diameter of around 1 km was observed in a highly inhabited area, with a maximum rate of up to -17 mm/yr near the cone’s center. We also found more prominent land subsidence along the coastline with magnitudes up to -25 mm/yr. Surface lowering with a magnitude of up to -32 mm/yr also affects power plant regions close to Cirebon city. Meanwhile, the fastest subsidence rate was observed over the salt evaporation field area of about -50 mm/yr. We attribute the natural and anthropogenic factors to causing the subsidence in this area.

GNSS_Vel_95CI.py: A Python Module for Calculating the Uncertainty of GNSS-Derived Site Velocity

GNSS_Vel_95CI.py is an open-source Python-3 module for calculating the 95% confidence interval (95% CI) for the site velocity derived from global navigation satellite systems (GNSS) daily positions, which are often affected by time-correlated noises. The detailed methodology for calculating the 95% CI is documented in a recent article (Wang 2022) and initially programmed in Fortran. However, few young researchers (e.g., graduate students) are familiar with Fortran now. In an effort to support a broader user community, we have realized the method in the Python programming language, which has been commonly taught in current college curriculums. Through the use of this module, researchers and engineers can focus on the applications of GNSS time series, rather than on coding and data processing. In particular, the module has the option to output the autocorrelation function (ACF) and the GNSS time-series decomposition results: the linear, nonlinear, seasonal, and residual components, which allow students and researchers having little coding experience to conduct advanced GNSS time-series analysis. The module is versatile, easy to install through the pip installer and GitHub, and simple to use. An example Python program is provided to illustrate the use of this module.

Machine Learning Models Applied to a GNSS Sensor Network for Automated Bridge Anomaly Detection

Structural health monitoring (SHM) based on global navigation satellite systems (GNSS) is an interesting solution to provide absolute positions at different locations of a structure in a global reference frame. In particular, low-cost GNSS stations for large-scale bridge monitoring have gained increasing attention these last years because recent experiments showed the ability to achieve a subcentimeter accuracy for continuous monitoring with adequate combinations of antennas and receivers. Technical solutions now allow displacement monitoring of long bridges with a cost-effective deployment of GNSS sensing networks. In particular, the redundancy of observations within the GNSS network with various levels of correlations between the GNSS time series makes such monitoring solution a good candidate for anomaly detection based on machine learning models, using several predictive models for each sensor (based on environmental conditions, or other sensors as input data). This strategy is investigated in this paper based on GNSS time series, and an anomaly indicator is proposed to detect and locate anomalous structural behavior. The proposed concepts are applied to a cable-stayed bridge for illustration, and the comparison between multiple tools highlights recurrent neural networks (RNN) as an effective regression tool. Coupling this tool with the proposed anomaly detection strategy enables one to identify and localize both real and simulated anomalies in the considered data set.

Water-Vapour Monitoring from Ground-Based GNSS Observations in Northwestern Argentina

The Central Andes in northwestern Argentina are characterized by steep topographic and climatic gradients. The humid foreland areas at 1 km asl elevation rapidly rise to over 5 km in the eastern Cordillera, and they form an orographic rainfall barrier on the eastern windward side. This topographic setting combined with seasonal moisture transport through the South American monsoon system leads to intense rainstorms with cascading effects such as landsliding and flooding. In order to better quantify the dynamics of water vapour transport, we use high-temporal-resolution global navigation satellite system (GNSS) remote sensing techniques. We are particularly interested in better understanding the dynamics of high-magnitude storms with high water vapour amounts that have destructive effects on human infrastructure. We used an existing GNSS station network with 12 years of time series data, and we installed two new ground stations along the climatic gradient and collected GNSS time series data for three years. For several stations we calculated the GNSS signal delay gradient to determine water vapour transport direction. Our statistical analysis combines in situ rainfall measurements and ERA5 reanalysis data to reveal the water vapour transport mechanism for the study area. The results show a strong relationship between altitude and the water vapour content, as well as between the transportation pathways and the topography.

Iteration empirical mode decomposition method for filling the missing data of GNSS position time series

The Global Navigation Satellite System (GNSS) can provide the daily position time series for the geodesy and geophysical studies. However, due to various unpredictable factors, such as receiver failure or bad observation conditions, missing data inevitably exist in GNSS position time series. Most traditional time series analysis methods require the time series should be completed. Therefore, filling the missing data is a valuable step before analyzing the GNSS time series. In this study, a new method named Iteration Empirical Mode Decomposition (Iteration EMD) is proposed to fill the missing data in GNSS position time series. The simulation experiments are performed by randomly removing different missing percentages of the synthetic time series, with the added different types noise. The results show that Iteration EMD approach performs well regardless of high or low missing percentage. When the missing percentage increases from 5 % to 30 % with a step of 5 %, all the Root Mean Square Errors (RMSE) and Mean Absolute Errors (MAE) of Iteration EMD are smaller than Interpolation EMD. The relative improvements at different percentages of Iteration EMD relative to Interpolation EMD are significant, especially for the high missing percentage. The real GNSS position time series of eight stations were selected to further evaluate the performance of Iteration EMD with an average missing percentage 8.15 %. Principal Component Analysis (PCA) was performed on the filled time series, which is used to assess the interpolation performance of Iteration EMD and Interpolation EMD. The results show that Iteration EMD can preserve variance 75.9 % with the first three Principal Components (PC), more than 66.5% of interpolation EMD. Therefore, we can conclude that Iteration EMD is an efficient interpolation method for GNSS position time series, which can make full use of available information in existing time series to fill the missing data.

Modelling and prediction of GNSS time series using GBDT, LSTM and SVM machine learning approaches

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.

Quantitative Evaluation of Environmental Loading Products and Thermal Expansion Effect for Correcting GNSS Vertical Coordinate Time Series in Taiwan

We explored the driving factors of nonlinear signals in vertical coordinate sequences of stations in a Taiwan global navigation satellite system (GNSS) network, including atmospheric loading (ATML), hydrological loading (HYDL), and non-tidal ocean loading (NTOL) effects. At the same time, we used the finite element analysis software MIDAS to quantify the vertical displacements of different types of monuments due to the thermal expansion effect, including deep drilled braced (DDB) and short drilled braced (SDB). By quantitatively comparing the correction results of GNSS time series with different single mass loading models, we found that there was little difference in the correction of different environmental loading products. We compared different combinations of each loading product to correct the GNSS time series, and finally selected the best combination suitable for Taiwan GNSS network, that is, ATML (GFZ_ECMWF IB) + HYDL (IMLS_MERRA2) + NTOL (IMLS_MPIOM06). We found that the spatial and temporal models of ATML and NTOL are very similar, with non-tidal atmospheric loading and non-tidal ocean loading working together, a pattern that may be related to tropical cyclones. Both models also showed good correction effect on GNSS stations in the western plain of Taiwan, but with limited correction effect in the eastern part of Taiwan. This may be due to the influence of the subtropical monsoon climate in Taiwan and the barrier of the central mountain range, resulting in obvious differences between eastern and western Taiwan. The hydrological loading was found to act in the opposite way to the thermal expansion effect in the temporal domain, indicating that some displacements in hydrological loading may cancel out displacements caused by the thermal expansion effect. This aspect of displacement is not included in the hydrological loading model but should be considered when accurately estimating the temporal and spatial variation of water storage capacity in Taiwan using GNSS observed displacements.

Sea Level Rise Estimation on the Pacific Coast from Southern California to Vancouver Island

Previous studies have estimated the sea level rise (SLR) at various locations on the west coast of the USA and Vancouver Island in Canada. Here, we construct an entire SLR profile from Vancouver Island in the Pacific Northwest to San Diego in Southern California. First, we process global navigation satellite system (GNSS) measurements at 405 stations blanketing the whole coast to generate a profile of vertical land motion (VLM) known to bias century-long tide gauge (TG) measurements recording relative SLR (RSLR). We are then able to estimate the absolute SLR (ASLR) by correcting the SLR with the VLM. Our study emphasizes the relationship between the various tectonic movements (i.e., the Cascadia subduction zone, the San Andreas strike-slip fault system) along the Pacific coast which renders it difficult to accurately estimate the SLR. That is why we precisely model the stochastic noise of both GNSS and tide gauge time series using a combination of various models and information criterions (ICs). We also use the latest altimetry products and sea surface height (SSH) to compare it with ASLR at the same location as the TGs. This study supports previous analysis that the power law + white noise and generalized Gauss–Markov + white noise models are the best stochastic noise models for the GNSS time series. The new coastal profile confirms the large variability of VLM estimates in the Pacific Northwest around the Cascadia subduction zone in agreement with previous studies, and a similar result when the San Andreas fault comes onshore in Central California (San Francisco Bay). Negative RSLR values are mostly located in the Pacific Northwest (Vancouver Island and Olympic Peninsula). We also observe a much bigger variation (about 90–150%) of the ASLR in the Pacific Northwest which is predominantly due to glacial isostatic adjustment (GIA). Moreover, the comparison between the ASLR and the SSH estimates shows similarities in the center of the studied area (South Washington, Oregon planes, and some parts of Southern California) where the tectonic activity does not significantly influence the TG measurements. Finally, the twentieth-century satellite geocentric ocean height rates show a global mean of 1.5 to 1.9 mm/yr. Our estimates based on ASLR and SSH are within this interval.

Bayesian modelling of piecewise trends and discontinuities to improve the estimation of coastal vertical land motion

One of the major sources of uncertainty affecting vertical land motion (VLM) estimations are discontinuities and trend changes. Trend changes are most commonly caused by seismic deformation, but can also stem from long-term (decadal to multidecadal) surface loading changes or from local origins. Although these issues have been extensively addressed for Global Navigation Satellite System (GNSS) data, there is limited knowledge of how such events can be directly detected and mitigated in VLM, derived from altimetry and tide-gauge differences (SATTG). In this study, we present a novel Bayesian approach to automatically and simultaneously detect such events, together with the statistics commonly estimated to characterize motion signatures. Next to GNSS time series, for the first time, we directly estimate discontinuities and trend changes in VLM data inferred from SATTG. We show that, compared to estimating a single linear trend, accounting for such variable velocities significantly increases the agreement of SATTG with GNSS values (on average by 0.36 mm/year) at 339 globally distributed station pairs. The Bayesian change point detection is applied to 606 SATTG and 381 GNSS time series. Observed VLM, which is identified as linear (i.e. where no significant trend changes are detected), has a substantially higher consistency with large-scale VLM effects of glacial isostatic adjustment (GIA) and contemporary mass redistribution (CMR). The standard deviation of SATTG (and GNSS) trend differences with respect to GIA+CMR trends is by 38% (and 48%) lower for time series with constant velocity compared to variable velocities. Given that in more than a third of the SATTG time series variable velocities are detected, the results underpin the importance to account for such features, in particular to avoid extrapolation biases of coastal VLM and its influence on relative sea-level-change determination. The Bayesian approach uncovers the potential for a better characterization of SATTG VLM changes on much longer periods and is widely applicable to other geophysical time series.

Detection of Slow Slip Events Using Wavelet Analysis of GNSS Recordings

ABSTRACT At many places, tectonic tremor is observed in relation to slow slip and can be used as a proxy to study slow slip events of moderate magnitude in which surface deformation is hidden in Global Navigation Satellite System (GNSS) noise. However, in subduction zones in which no clear relationship between tremor and slow slip occurrence is observed, these methods cannot be applied, and we need other methods to be able to better detect and quantify slow slip. Wavelets methods such as the Discrete Wavelet Transform and the Maximal Overlap Discrete Wavelet Transform (MODWT) are mathematical tools for analyzing time series simultaneously in the time and the frequency domains by observing how weighted differences of a time series vary from one period to the next. In this article, we use wavelet methods to analyze GNSS time series and seismic recordings of slow slip events in Cascadia. We use detrended GNSS data, apply the MODWT transform, and stack the wavelet details over several nearby GNSS stations. As an independent check on the timing of slow slip events, we also compute the cumulative number of tremor in the vicinity of the GNSS stations, detrend this signal, and apply the MODWT transform. In both the time series, we can then see simultaneous waveforms where timing corresponds to the timing of slow slip events. We assume that there is a slow slip event whenever there is a positive peak followed by a negative peak in the wavelet signal. We verify that there is a good agreement between slow slip events detected with only GNSS data and slow slip events detected with only tremor data for northern Cascadia. The wavelet-based detection method effectively detects events of magnitude higher than 6, as determined by independent event catalogs (e.g., Michel et al., 2019). As a demonstration of using the wavelet analysis in a region without significant tremor, we also analyze GNSS data from New Zealand and detect slow slip events that are spatially and temporally close to those detected previously by other studies.

Two-Decade GNSS Observation Processing and Analysis with the New IGS Repro3 Criteria: Implications for the Refinement of Velocity Field and Deformation Field in Continental China

Extensive observation collection, unified and rigorous data processing, and accurate construction of the station motion model are the three essential elements for the accuracy and reliability of the Global Navigation Satellite System (GNSS) velocity field. GNSS data reprocessing not only can weaken the influence of untrue nonlinear site signals caused by imperfect models but also can eliminate the displacement offset caused by frame transformation, solution strategy, and model change. Based on the new repro3 criteria of the International GNSS Service (IGS), we process rigorously GNSS observations of continental China from the period 2000 to 2020 to refine GNSS station secular velocities and analyze the present-day crustal deformation in continental China. The main contributions of this work included the followings. Firstly, the repro3 algorithm and model are used to uniformly and rigorously process the two-decade GNSS historical observations to obtain more reliable GNSS coordinate time series with mm-level precision. Combined with the historical records of major earthquakes in continental China, we build a GNSS time series model considering nonlinear factors (velocity, offset, period, co-seismic/post-seismic deformation) to extract GNSS horizontal velocity field whose root mean square (RMS) mean is 0.1 mm/a. Secondly, the GNSS horizontal grid velocity field in continental China is interpolated using the gpsgridder method (the minimum radius is set to 16, and the Poisson’s ratio is set to 0.5). Estimation and analysis of the crustal strain rate solution lead to the conclusion that the strain degree in West China (the high strain region is mainly located in the Qinghai Tibet Plateau and Tianshan Mountains) is much more intense than that in the east (the main strain rate is less than 5 nstrain/year). In addition, most strong earthquakes in the Chinese mainland occurred on active blocks and their boundary faults with large changes in the GNSS velocity field and strain field. Then, an improved K-means++ clustering analysis method is proposed to divide active blocks using GNSS horizontal velocity field. Furthermore, different relative motion models of different blocks are constructed using the block division results. Among them, the Eurasian block has the lowest accuracy (the RMS of residual velocity in the east and north directions are 5.60 and 9.65 mm/a, respectively), and the China block 7 has the highest accuracy (the RMS mean of relative velocity in the east and north directions are 2.60 and 2.65 mm/a, respectively). More observations (2260+ sites), longer time (20 years), and updated criteria (Repro3) are to finely obtain the GNSS velocity field in continental China, and depict crustal deformation and active block with the gpsgridder and improved K-means++ methods.