East Components Research Articles

Perspectives for Improvements on Real-Time GNSS Positioning with the Use of New Observables

The research aims to analyze Global Navigation Satellite System (GNSS) positioning solutions using the Precise Point Positioning (PPP) method in kinematic mode, in which the position is obtained epoch by epoch through data from only one GNSS receiver, precise ephemerides, and satellite clock corrections, both with high accuracy. In this context, the adopted methodology employs the open-source software RTKLIB, which, through its data post-processing capability, enables the evaluation of kinematic PPP performance by incorporating new observables such as L5 and E5a bands, crucial for enhancing positional accuracy and mitigating multipath effects. Additionally, for survey simulations, data from the UFPR and POVE stations of the Brazilian Network for Continuous Monitoring of GNSS (RBMC) were utilized. The selected stations are located in the Northern and Southern regions of Brazil. The GNSS data were processed with the same tracking duration for a 45-minute cold-start, aimed at observing solution convergence. Subsequently, the estimated outputs in RTKLIB were obtained based on station origins using coordinates provided by SIRGAS-CON. Moreover, by utilizing precise ephemerides data, it was possible to conclude that the addition of new observables for triple-frequency positioning led to an improvement in the accuracy of the obtained coordinates, particularly in the Vertical component. In this regard, the increase in accuracy in experiments using only triple-frequency data with a 15° elevation mask was approximately 25% at the UFPR station and about ~37% at the POVE station. Furthermore, it was observed that reducing the elevation mask from 15° to 10° had a positive impact on dual-frequency positioning at the UFPR station, resulting in gains of over 3% in the East component and around ~21% in the North component compared to values obtained with the 15° mask. Similarly, during triple-frequency positioning at the POVE station, gains exceedingly approximately 16% in the North component and around ~22% in the Vertical component were observed.

An improved Gaussian process for filling the missing data in GNSS position time series considering the influence of adjacent stations

Due to various unavoidable reasons or gross error elimination, missing data inevitably exist in global navigation satellite system (GNSS) position time series, which may result in many analysis methods not being applicable. Typically, interpolating the missing data is a crucial preprocessing step before analyzing the time series. The conventional methods for filling missing data do not consider the influence of adjacent stations. In this work, an improved Gaussian process (GP) approach is developed to fill the missing data of GNSS time series, in which the time series of adjacent stations are applied to construct impact factors, together with a comparison of the conventional GP and the commonly used cubic spline methods. For the simulation experiments, the root mean square error (RMSE), mean absolute error (MAE) and correlation coefficient (R) are adopted to evaluate the performance of the improved GP. The results show that the filled missing data of the improved GP are closer to the true values than those of the conventional GP and cubic spline methods, regardless of the missing percentages ranging from 5 to 30%, with an interval of 5%. Specifically, the mean relative RMSE and MAE improvements for the improved GP with respect to the conventional GP are 21.2%, 21.3% and 8.3% and 12.7%, 16.2% and 11.01% for the North (N), East (E) and Up (U) components, respectively. In the real experiment, eight GNSS stations are analyzed using improved GP, together with conventional GP and a cubic spline. The results indicate that the first three principal components (PCs) of the improved GP can perverse 98.3%, 99.8% and 77.0% of the total variance for the N, E and U components, respectively. This value is obviously higher than those of the conventional GP and cubic spline. Therefore, we can conclude that the improved GP can better fill in the missing data in GNSS position time series than the conventional GP and cubic spline because of the impacts of adjacent stations.

Azimuthal crustal variations and their implications on the seismic impulse response in the Valley of Mexico

AbstractPrevious studies have suggested prominent variations in the seismic wave behavior at the 5 s period when traveling across the Valley of Mexico, associating them with the crustal structure and contributing to the anomalous seismic wave patterns observed each time an earthquake hits Mexico City. This article confirms the variations observed at 0.2 Hz by analyzing the Green tensor diagonal retrieved from empirical Green functions (EGF) calculated using seismic noise data cross-correlations of the vertical and horizontal components. We observe time and phase shifts between the east and north EGF components and show that they can be explained by the crustal structure from the surface up to 20 km depth; we also observe that the time and phase shifts are more significant if the distance between the source and the station increases. Additionally, the article presents an updated version of the velocity model from receiver functions and dispersion curves (VMRFDC v2.0) for the crustal structure under the Valley of Mexico. To validate this model, we compare the EGFs with synthetic Green functions determined numerically. To do so, we adaptatively meshed this model using an iterative algorithm to numerically simulate the impulse response up to 0.5 Hz. Finally, the comparisons between noise and synthetic EGF showed that the VMRFDC v2.0 model explains the time shifts and phase differences at 0.2 Hz, previously observed by independent studies, suggesting it correctly characterizes the crustal structure anomalies beneath the Valley of Mexico.

Bundle Adjustment of Aerial Linear Pushbroom Hyperspectral Images with Sub-Pixel Accuracy

AbstractLinear pushbroom (LP) cameras are often used in airborne hyperspectral imaging (HSI). Orthoimages are generated for HSI analyses but these require accurate camera orientations from bundle adjustment. However, the limited image overlap leads to an over-parameterization in the bundle adjustment with six degrees of freedom per image exposure, i.e., LP image line. Feature-based matching based on salient key points in small image neighborhoods cannot be readily applied to LP image lines, since each LP image line is only a single pixel wide in one of the image dimensions. A naive mosaicing of consecutive LP image lines leads to unacceptably large errors owing to the relative camera motion within these mosaics, even for a stabilized camera. Thus, a new method that allows the use of established methods for feature-based matching from aerial LP image lines is presented, and observations are retrieved and used in the bundle adjustment. The examination of the spatial misregistration between spectral bands in HSI cameras, i.e., the chromatic aberration, is also examined. The method assumes a stabilized camera system with a processed global navigation satellite system aided inertial navigation system solution. The bundle adjustment is done by estimating trajectory corrections in time intervals and retrieving discrete trajectory estimates from cubic spline interpolation. An experiment was conducted to demonstrate the method. The chromatic aberration is shown to be of sub-pixel level in the LP HSI camera, and the resulting planimetric accuracy (normalized median absolute deviation) from the bundle adjustment is $$\sim 1/4$$ ∼ 1 / 4 of the ground sampling distance in each of the north and east components. The accurate estimates from the bundle adjustment are shown to be suitable for high-quality orthoimage generation.

Comprehensive Analysis on GPS Carrier Phase under Various Cutoff Elevation Angles and Its Impact on Station Coordinates’ Repeatability

When processing the carrier phase, the global navigation satellite system (GNSS) grants the highest precision for geodetic measurements. The analysis centers (ACs) from the International GNSS Service (IGS) provide different data such as precise clock data, precise orbits, reference frame, ionosphere and troposphere data, as well as other geodetic products. Each individual AC has its own strategy for delivering the abovementioned products, with one of the key elements being the cutoff elevation angle. Typically, this angle is arbitrarily chosen using generic values without studying the impact of this choice on the obtained results, in particular when very precise positions are considered. This article addresses this issue. To this end, the article has two key sections, and the first is to evaluate the impact of using the two different cutoff elevation angles that are most widely used: (a) 3 degrees cutoff and (b) 10 degrees cutoff elevation angle. This analysis is completed in two major parts: (i) the analysis of the root mean square (RMS) for the carrier phase and (ii) the analysis of the station position in terms of repeatability. The second key section of the paper is a comprehensive carrier phase analysis conducted by adopting a new approach using a mean of the 25-point average RMS (A-RMS) and the single-point RMS and using an ionosphere-free linear combination. By using the ratio between the 25-point average RMS and the single-point RMS we can define the type of scatter that dominates the phase solution. The analyzed data span a one-year period. The tested GNSS stations belong to the EUREF Permanent Network (EPN) and the International GNSS Service (IGS). These comprise 55 GNSS stations, of which only 23 GNSS stations had more than 95% data availability for the entire year. The RMS and A-RMS are analyzed in conjunction with the precipitable water vapor (PWV), which shows clear signs of temporal correlation. Of the 23 GNSS stations, three stations show an increase of around 50% of the phase RMS when using a 3° cutoff elevation angle, and only four stations have a difference of 5% between the phase RMS when using both cutoff elevation angles. When using the A-RMS, there is an average improvement of 37% of the phase scatter for the 10° cutoff elevation angle, whereas for the 3° cutoff elevation angle, the improvement is around 33%. Based on studying this ratio, four stations indicate that the scatter is dominated by the stronger-than-usual dominance of long-period variations, whereas the others show short-term noise. In terms of station position repeatability, the weighted root mean square (WRMS) is used as an indicator, and the results between the differences of using a 3° and 10° cutoff elevation angle strategy show a difference of −0.16 mm for the North component, −0.21 mm for the East component and a value of −0.75 mm for the Up component, indicating the importance of using optimal cutoff angles.

Determining the tectonic velocity of some continuously operating reference stations (CORS) in Vietnam 2019-2022 using precise point positioning method

We use precise point positioning (PPP) technique to process the Global Navigation Satellite Systems (GNSS) data of 10 continuously operating reference stations (CORS) in Vietnam during the period 2019-2022. PPP processing results show that the time series of the North, East and Up components of CORS fluctuate with a period of approximately 1 year. After modelling this variation using a sine function with a fixed period of 351.6 days, we calculate the mean displacement velocity of the CORSs according to the North, East and Up components as follows: (-9.2, +29.5, -4.6) mm/year. The general movement direction of all CORSs is East-Southeast. In which the North, East and Up components of 3 big cities Ha Noi, Da Nang and Ho Chi Minh city are (-9.1, +32.7, +1.0) mm/year, (-9.1, +30.5, -6.0) mm/year and (-7.9, +28.4, -1.9) mm/year, respectively. Compared with the period 2016-2018, the velocities of the tectonic plate change less than 4 mm/year in the horizontal component, and 8 mm/year in the Up component. We have processed three more International GNSS Service (IGS) stations in Thailand (CUSV) and China (HKSL and KMNM) for testing. Our results are consistent with JPL at 1 mm/year in the horizontal and 2 mm/year in the Up component.

A dusty protocluster surrounding the binary galaxy HerBS-70 at z = 2.3

ABSTRACT We report on deep SCUBA-2 observations at 850 $\mu$m and NOrthern Extended Millimetre Array (NOEMA) spectroscopic measurements at 2 mm of the environment surrounding the luminous, massive (M* ≈ 2 × 1011 M⊙) Herschel-selected source HerBS-70. This source was revealed by previous NOEMA observations to be a binary system of dusty star-forming galaxies at z = 2.3, with the east component (HerBS-70E) hosting an active galactic nucleus. The SCUBA-2 observations detected, in addition to the binary system, 21 sources at >3.5σ over an area of ∼25 square comoving Mpc with a sensitivity of 1σ850 = 0.75 mJy. The surface density of continuum sources around HerBS-70 is three times higher than for field galaxies. The NOEMA spectroscopic measurements confirm the protocluster membership of three of the nine brightest sources through their CO(4–3) line emission, yielding a volume density 36 times higher than for field galaxies. All five confirmed sub-mm galaxies in the HerBS-70 system have relatively short gas depletion times (80−500 Myr), indicating the onset of quenching for this protocluster core due to the depletion of gas. The dark matter halo mass of the HerBS-70 system is estimated around 5 × 1013 M⊙, with a projected current-day mass of 1015 M⊙, similar to the local Virgo and Coma clusters. These observations support the claim that DSFGs, in particular the ones with observed multiplicity, can trace cosmic overdensities.

Orbit and clock products for quad-system satellites with undifferenced ambiguity fixing approach

Integer Ambiguity Resolution (IAR) can significantly improve the accuracy of GNSS Precise Orbit Determination (POD). Traditionally, the IAR in POD is achieved at the Double Differenced (DD) level. In this contribution, we develop an Un-Differenced (UD) IAR method for Global Positioning System (GPS)+ BeiDou Navigation Satellite System (BDS) + Galileo navigation satellite system (Galileo)+ Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) quad-system POD by calibrating UD ambiguities in the raw carrier phase and generating the so-called carrier range. Based on this method, we generate the UD ambiguity-fixed orbit and clock products for the Wuhan Innovation Application Center (IAC) of the International GNSS Monitoring and Assessment System (iGMAS). One-year observations in 2020 from 150 stations are employed to investigate performance of orbit and clock products. Notably, the UD Ambiguity Resolution (AR) yields more resolved integer ambiguities than the traditional DD AR, scaling up to 9%, attributable to its avoidance of station baseline formation. Benefiting from the removal of ambiguity parameters, the computational efficiency of parameter estimation undergoes a substantial 70% improvement. Compared with the float solution, the orbit consistencies of UD AR solution achieve the accuracy of 1.9, 5.2, 2.8, 2.1, and 2.7 cm for GPS, BeiDou-2 Navigation Satellite System (BDS-2), BeiDou-3 Navigation Satellite System (BDS-3), Galileo, and GLONASS satellites respectively, reflecting enhancements of 40%, 24%, 54%, 34%, and 42%. Moreover, the standard deviations of Satellite Laser Ranging (SLR) residuals are spanning 2.5–3.5 cm, underscoring a comparable accuracy to the DD AR solution, with discrepancies below 5%. A notable advantage of UD AR lies in its capability to produce the Integer Recovered Clock (IRC), facilitating Precise Point Positioning (PPP) AR without requiring additional Uncalibrated Phase Delay (UPD) products. To assess the performance of quad-system kinematic PPP based on IRC, a network comprising 120 stations is utilized. In comparison to the float solution, the IRC-based PPP AR accelerates convergence time by 31% and enhance positioning accuracy in the east component by 54%.

The Effect of Vehicles Attitude Angle Error on Magnetic Compass Heading Estimation

The three-component magnetic sensor is used to measure the heading of the vehicle. Under working, the magnetic sensor be rotated to the horizontal plane according to the attitude angle of the vehicle, and then the heading estimation is performed. However, the vehicle’s attitude angle measurement errors affect the accuracy of the magnetic sensor measurement’s east and north components and then lead to a false heading result. Based on the relation of magnetic field measurement error and magnetic heading error, the effect model of geomagnetic measurement error on magnetic heading error is derived in this paper. Finally, the characteristics of attitude angle errors on magnetic heading are verified by experiments, and the results show that particular angles can avoid the magnetic compass’s effect by the vehicle’s attitude angle error.

Analysing the impact of SWOT observation errors on marine gravity recovery

SUMMARY The wide-swath altimeter satellite Surface Water and Ocean Topography (SWOT) will provide high spatiotemporal resolution sea surface heights (SSHs), which is crucial for studying the impact of observation errors on marine gravity recovery. This study uses simulated SWOT data to derive deflection of the vertical (DOV) and gravity anomalies in the northern South China Sea. We quantified the impact of SWOT errors on DOV and gravity anomalies, and analysed the contributions from different directions of geoid gradient. The results show that the geoid gradient in the cross-track direction significantly improves gravity field recovery by enhancing the precision of east component of DOV. For one-cycle SWOT observations, phase errors emerge as the most impactful error affecting both DOV and gravity anomalies, followed by random errors. 2-D Gaussian filtering and the tilt correction proposed in this study could effectively mitigate their impact. Using the corrected data for DOV computation, the precision in the east and north components improves by 75.32 and 46.80 per cent, respectively, while enhancing the accuracy of the gravity field by 70.23 per cent. For 17-cycle data, phase errors and random errors remain the predominant factors affecting DOV and gravity anomalies, but their impact diminishes with an increase in SWOT observations. Our results indicate that marine gravity accuracy improves by approximately 70 per cent compared to a single cycle. Whether for single-cycle or multicycle data, the impact of phase errors is roughly twice that of random errors. These data processing strategies can serve as valuable references for wide-swath altimeter data processing, aiming to advance the precision and resolution of marine gravity field recovery.

Estimating Winter Arctic Sea Ice Motion Based on Random Forest Models

Sea ice motion (SIM) plays a crucial role in setting the distribution of the ice cover in the Arctic. Limited by images’ spatial resolution and tracking algorithms, challenges exist in obtaining coastal sea ice motion (SIM) based on passive microwave satellite sensors. In this study, we developed a method based on random forest (RF) models to obtain Arctic SIM in winter by incorporating wind field and coastal geographic location information. These random forest models were trained using Synthetic Aperture Radar (SAR) SIM data. Our results show good consistency with SIM data retrieved from satellite imagery and buoy observations. With respect to the SAR data, compared with SIM estimated with RF model training using reanalysis surface wind, the results by additional coastal information input had a lower root mean square error (RMSE) and a higher correlation coefficient by 31% and 14% relative improvement, respectively. The latter SIM result also showed a better performance for magnitude, especially within 100 km of the coastline in the north of the Canadian Arctic Archipelago. In addition, the influence of coastline on SIM is quantified through variable importance calculation, at 22% and 28% importance of all RF variables for east and north SIM components, respectively. These results indicate the great potential of RF models for estimating SIM over the whole Arctic Ocean in winter.

Impacts of Local Green's Functions on Modeling Atmospheric Loading Effects for GNSS Reference Stations

AbstractThe Green's function approach is well‐established and widely used for modeling the surface mass loading displacements. Global mean Green's functions (MGFs) are commonly applied without considering local variations of the crustal structure. Derived from the modified layered Earth structure, the local Green's functions (LGFs) are theoretically beneficial to generate more accurate deformation, since they consider interior information of the local crust. This paper analyzed the differences among MGFs from Gutenberg–Bullen A model and two sets of LGFs derived from modified PREM Earth models consolidating with two crust models TEA12 and CRUST1.0, hereafter called PREMTEA and PREMCRU, respectively. Utilizing MGFs and two sets of LGFs, we modeled the corresponding 3D atmospheric loading displacements for 984 ITRF2014 stations and compared them with the ITRF2014 residuals. The results show that LGFs from PREMTEA and PREMCRU perform well in further promoting scatter reduction for ∼72%, ∼56%, and ∼85% of stations for the Up, East and North components, respectively. The improvements for the North components are significant (up to 3.6%). In particular, stations in the east coastal areas of North America and the west edge of Greenland exhibit further promoting scatter reduction for the East components (up to ∼2.5%), while those located in west coastline of North America show better performance for the North components. Nevertheless, there are significant anomalies in northern Europe for PREMCRU, the mutation margin of which should be carefully considered when using a resolution higher than 1°. In the area around station MORP (358.31°W, 55.21°N, sited at coastline of Britain), we suggest using PREMTEA model.

A reduced-condition-number algorithm for single-frequency precise point positioning based on regularized Kalman filter

Single-frequency receivers are low cost and portable, thus being widely applied in engineering; the extended Kalman filter (EKF) is commonly used to perform single-frequency precise point positioning (SF-PPP). However, the positioning performance of SF-PPP is seriously influenced by various errors. Due to the large process noise and initial variance of the estimated parameters, the weight matrix of state parameters will be ill-conditioned, and since the noise of the pseudo-range is much higher than that of the carrier phase, the weight matrix of observations presents as ill-conditioned. Additionally, the condition number of the normal matrix will jump on the conditions of cycle slip, new emerging satellites, and signal outages. To reduce the condition number of the normal matrix, the regularized Kalman filter (RKF) algorithm is proposed, with additional support for the maximum variance matrix and singular value decomposition, thereby improving the accuracy and stability of SF-PPP. Through static and dynamic experiments, it is found that the proposed method can reduce both the ill-conditioning of the weight matrices of the observations and the state parameters. The condition number of the normal matrix is <500 per epoch, and the convergence time is shortened by >40%. Compared with the SF-PPP using EKF, centimeter-level static positioning accuracies of 1.13, 0.73, and 2.92 cm and decimeter-level kinematic positioning accuracies of 12.5, 10.8, and 27.3 cm in the east, north, and vertical components, respectively, using RKF; this yielded 38.3, 29.8, and 45.2% and 39.6, 41.9, and 21.3% improvement in the static and kinematic scenarios, respectively.

Machine learning approach for GNSS geodetic velocity estimation

This study aimed to investigate the performance of machine learning (ML) algorithms in determining horizontal velocity at specific points using the current Global Navigation Satellite System (GNSS) velocity field. To achieve this objective, the analysis utilized the most comprehensive velocity field available for Turkey, where 70% of the GNSS velocities was allocated for training the ML algorithms, while the remaining 30% was used for testing. Contrary to the previous research, the significance of considering the tectonic structure within the study area was emphasized at this point. To determine the tectonic structure of the horizontal velocity field in the region, a preliminary clustering procedure was conducted. Subsequently, distinct ML algorithms were trained using velocity fields associated with different tectonic plates. Moreover, to investigate the impact of the tectonic domain, the entire velocity field was also tested using ML algorithms without considering the tectonic structure. Four different ML algorithms, namely, Gradient Boosting Machines (GBM), LightGBM, Random Forest (RF), and eXtreme Gradient Boosting Machines (XGBoost), were employed to estimate the horizontal velocities (east and north components). The findings imply that incorporating the tectonic structure improved the performance of machine learning predictions, as indicated by the GBM algorithm's decreased root-mean-square error values. In addition, when the tectonic structure was taken into account, the accuracy assessment values for the RF and XGBoost algorithms in the east component decreased significantly. In terms of predicting GNSS velocities, the RF algorithm exhibited the lowest root-mean-square error values compared to other algorithms. The horizontal velocity differences between averages of the reference velocity field and the RF velocity estimates are maximum 0.4 mm/yr.

A flexible method for BDS-3 multi-frequency phase observable-specific biases estimation and its PPP analysis with different ambiguity resolution strategies

With the rapid progress of Global Navigation Satellite Systems (GNSS), integer ambiguity resolution has gradually become one of the key factors that affecting Precise Point Positioning (PPP) to achieve high-precision positioning results and fast convergence. Fortunately, the proposal of observable-specific code/phase biases (OSB) has greatly alleviated this problem tremendously. Different from obtaining OSB by dual-frequency linear combinations, this research proposed BeiDou Navigation Satellite System (BDS) OSB estimation method from raw observations. This method allows for more flexible estimation in a global network, without the need to compose the complex linear combinations when involving multi-frequency measurements processing. The BDS-3 observation data collected from 112 stations over one month (October 2022), containing B1C/B1I/B2a/B2b/B3I frequencies, were used for five-frequency phase OSBs estimation. Subsequently, static and kinematic PPP were executed utilizing two different ambiguity resolution strategies to corroborate the efficacy of this method. The results revealed that the BDS-3 five-frequency phase OSBs possessed good monthly stability, with standard deviation less than 0.3 cycle. High position accuracy was achieved in the static mode by fixing the ambiguity directly, with root mean square (RMS) of 3.0, 4.8 and 9.9 mm. Meanwhile, the ambiguity fixed rate was maintained at a high level around 96 % in multi-frequency tests. Simultaneously, the kinematic mode also presented the centimeter-level dynamic positioning results and the positioning accuracy improved by 55, 31 and 17 % in the East, North and Up components, respectively. Compared to the float solutions, the adoption of multi-frequency OSBs significantly accelerated the convergence speed by 55 % on average.

Performance evaluation of HY-2 series satellites in marine gravity field recovery

China has successfully launched four Haiyang-2 (HY-2) series altimetry satellites. HY-2A has attracted significant attention in gravity field recovery, but the performance of other HY-2 series satellites, including HY-2B/C/D, is seldom discussed. This study evaluated the performance of all the HY-2 series satellites in recovering marine gravity field. First, the crossover discrepancies in sea surface height of the four satellites, HY-2A, HY-2B, HY-2C, and HY-2D, were analyzed to assess their altimetry stability. It was found that HY-2B had the best altimetry quality, followed by HY-2D. Subsequently, different combinations of altimetry data were used to calculate vertical deflections and gravity anomalies in the South China Sea (112°E−119°E, 12°N-20°N). The results showed that combining data from HY-2B, HY-2C, and HY-2D improved the inversion accuracy of gravity anomalies by 0.3 mGal compared to using HY-2A data alone. HY-2C and HY-2D contributed to enhancing the accuracy of the east component of vertical deflections.

Noise analysis of irregularly sampled VLBI position time series using maximum likelihood estimation

Identification of the optimal noise model for space geodetic time series is crucial for various studies in geodynamics and geodesy. However, the position time series of Very Long Baseline Interferometry (VLBI) are typically irregularly sampled. There is no clear evidence from previous studies to support that the Maximum Likelihood Estimate (MLE) method can allow for stable and reliable noise estimates for irregularly sampled data. To address this issue, we first conducted simulation studies. Results indicate that when the number of data points in the VLBI position time series reaches 300, reliable noise estimations result can be obtained using the MLE. We also found that the higher proportion of white noise a station has, the less influences the data gaps would be on noise estimations. Second, we apply the MLE to investigate the noise properties in the 32 VLBI position time series. About 12 (37.5%) stations exhibit pure white noise, and 15 (46.9%) stations display a combination of white noise and flicker noise. For these stations, the median amplitudes of white noise in the East, North, and Up components are 3.9, 4.6, and 11.9 mm, respectively. Moreover, white and flicker noise amplitudes show a latitude-dependent pattern, with stations located in the southern hemisphere and low latitudes (0-30°N) in the northern hemisphere exhibiting higher noise amplitudes. The remaining approximately 5 stations (15.6%) have the optimal noise model of power law noise with the mean spectral index of −0.32, −0.36, and −0.53 for the East, North, and Up components, respectively. Simply assuming pure white noise can significantly affect velocity uncertainty estimates when compared to using a noise model that includes colored noise. The velocity uncertainty will be underestimated by a factor of 2.9 on average. The effects of a small proportion of colored noise in VLBI data on velocity uncertainty estimation can be ignored only when the time series length exceeds 32.6 years. Additionally, the choice of different noise model can lead to a maximum difference of 0.84 mm for the annual signal of the Up component.

2.5D Time Series of Postseismic Deformation Following the 2018 Mw 7.5 Palu Earthquake Using Sentinel-1 InSAR

The observed Displacement of Line of Sight (LOS) InSAR can only measure the displacement towards and away from the satellite sensor, making it difficult to provide an intuitive depiction of the deformation source. In the previous studies, research on the characteristics of postseismic deformation mechanisms was conduct by InSAR but only in the vertical component. Therefore, our study attempts to complement this deformation picture by considering both the horizontal and vertical components. It is hoped that this will provide a more comprehensive understanding of the postseismic deformation mechanism of the 2018 Palu earthquake. In this study, we attempted to estimate the 2.5-D surface deformation resulting from the 2018 Palu Earthquake using Sentinel-1 data. The data was then modeled using exponential and logarithmic functions to understand the characteristics of the postseismic deformation mechanism. The 2.5-D surface deformation exhibited variations in horizontal and vertical motions. The East-West (EW) displacement values showed a maximum value of -66.19 mm in the east direction, while the maximum value in the west direction is 75.23 mm. On the other hand, for the Up-Down (UD) displacement, there was a maximum subsidence of -73.40 mm and a maximum uplift of 67.28 mm. To study the characteristics of the transient postseismic deformation, observations were made at 14 points. Postseismic deformation was observed at all locations in the study area. During the period 2018-2021, the time series of the north and east components of the postseismic transients were analyzed using logarithmic and exponential functions. The modeling results showed that the Root Mean Square Error (RMSE) value for the exponential model is 81.80 mm, while for the logarithmic model is 81.38 mm. Therefore, the logarithmic model demonstrated a better fit, indicating that the postseismic deformation mechanism is influenced by afterslip.

Optimal distribution of VLBI transmitters in the Galileo space segment for frame ties

Equipping Galileo satellites with a VLBI transmitter (VT) will allow to observe satellites next to quasars with Very Long Baseline Interferometry (VLBI) radio telescopes. This concept will facilitate the direct estimation of the satellite orbits in the celestial reference frame. Moreover, these observations along with usual Galileo observations can be used to transfer the space tie between the VT and the antenna on the Galileo satellite to the Earth surface realizing the frame tie at the geodetic site with VLBI radio telescope and Galileo antenna. In this study, we assess the accuracy of that frame tie by simulating the estimation of station coordinates from VLBI observations to Galileo satellites next to quasars. We find that at least two or three satellites need to be equipped with a VT with the best results if all satellites with a VT are placed in the same plane. Concerning the ratio between satellite and quasar observations within a schedule, the results suggest that the optimal ratio is around 30% to 40% satellite observations out of the total number of observations in order to have enough observations for the estimation of the station coordinates but still enough quasar observations to ensure a sufficient sky-coverage for the estimation of troposphere parameters. The best scenario with two satellites yields repeatabilities for the east and north components between 7.5 and 10 mm, and for the up component between 9.5 and 12 mm. In case there is a third satellite with a VLBI transmitter in the same plane, the repeatabilities are reduced by up to 2 mm for the horizontal components and up to 3 to 4 mm for the up component. Rotating the schedules over the constellation repeat cycle of Galileo of 10 days reveals that there are differences between the individual days, but there are no days with a significantly worse precision of the estimated station coordinates.Graphical

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.