Topo-Iberia CGPS network: A new 3D crustal velocity field in the Iberian Peninsula and Morocco based on eleven years (2008–2019)

doi:10.21203/rs.3.rs-1777869/v1

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Research Article

Topo-Iberia CGPS network: A new 3D crustal velocity field in the Iberian Peninsula and Morocco based on eleven years (2008–2019)

https://doi.org/10.21203/rs.3.rs-1777869/v1

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published 27 Jun, 2023

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Topo-Iberia network covering the Spanish part of the Iberian Peninsula and Morocco was established in 2008. After the first publication in 2015 of the horizontal velocity field based on the analysis of the first four activity years (2008–2012), a new 3D velocity field based on eleven years (2008–2019) is presented in this paper. Double-differencing technique with GAMIT software and precise point positioning (PPP) technique with GipsyX software are used for GPS processing obtaining loosely constrained solutions, and the methodology merging both solutions within a Kalman filter (GLOBK) is exposed. Position time series analysis carried out is described and results obtained by each processing strategy are compared. The combined velocity solution is presented in this paper as the new horizontal velocity field and the first vertical velocity field of Topo-Iberia CGPS network. A global view of Topo-Iberia stations quality for the processed period is also presented for the first time. The results are in good accordance with previous publications except in Betic Cordillera. Smallest and highest residual displacements with respect to Eurasia occur in northern Iberia and Morocco respectively. The results could confirm that a clockwise block rotation would have been occurring at present in the northern branch of the Gibraltar Arc, which present-day undergoing a northwest-southeast convergence rate of 3.6 mm/yr. A general low subsidence is observed in the Iberian Peninsula except for some isolated stations presenting uplift.

3D velocity field

GAMIT/GLOBK

GipsyX

GPS processing strategy

Iberia Morocco region

Topo-Iberia network

Topo-Iberia was a research project titled Geosciences in Iberia: Integrated studies of topography and 4-D evolution. 'Topo-Iberia' supported by the Spanish Government (Gallart 2006). Measurement of crustal deformation using Global Navigation Satellite System (GNSS)-based techniques was one of methodologies used, specifically Global Positioning System (GPS). As part of this project the Topo-Iberia network composed of 26 continuously operating GPS stations (CGPS), covering the Spanish part of the Iberian Peninsula (22) and Morocco (4), was established complementing existing networks and being fully operational in December 2008. The Spanish Geological Survey (IGME) implemented the Topo-Iberia Information System (SiTopo) where the data is stored.

Garate et al. (2015) presented a velocity field based on the analysis of the first four years of continuous GPS observations from Topo-Iberia network. Data analysis was made by three different groups using different scientific software packages and approaches: precise point positioning (PPP) technique using the GPS Inferred Positioning System, Orbit Analysis and Simulation Software (GIPSY/OASIS), developed by the Jet Propulsion Laboratory (JPL) (Zumberge et al. 1997); Bernesse software developed by the University of Bern (Dach et al. 2007); and GPS At MIT/Global Kalman filter (GAMIT/GLOBK) software, developed primarily by Massachusetts Institute of Technology (MIT) (Herring et al. 2010), using both software the so-called double differencing approach. Time series were also analyzed using different software. Every analysis group used a slightly different set of continuously operating reference stations (CORS) in order to align its solution to an International Terrestrial Reference Frame (ITRF). The final solution of each group was transformed to a common reference frame, and finally an average velocity field from the three solutions was calculated. With this study a contemporary crustal deformation velocity field for the Iberian Peninsula and Morocco was provided.

The project ended but the different groups or institutions in charge of the stations have made a great effort to keep them active, although some stations were dismantled. As a consequence having more than 11 years of data in some stations is currently possible, whose analysis would allow us to estimate the velocity field with greater precision. The previously published study on the Topo-Iberia network estimated an horizontal (2D) velocity field, and few are the studies that have estimated vertical deformation in the Iberian Peninsula, such as Serpelloni et al. (2013), Nguyen et al. (2016), Devoti et al. (2017) and Khazaradze et al. (2019). Therefore, the aim of this paper is processing all available data from Topo-Iberia CGPS network (Fig. 1) and offer a new 3D velocity field showing present-day deformation in Iberia plate and along their boundary zone with Nubia (Africa) plate in the western Mediterranean region. In addition, another purpose is to use different processing software reducing it to the minimum essential and using similar processing strategies as far as possible, although each software has its own characteristics inherent to the type of processing technique it uses. No comparison to do between software, nor combination between final results of different solutions is intended. Some reasons for applying different software are to check for possible systematic effects due to software or to avoid mistakes introduced during processing, such as faulty models or incorrect parameterizations, which are difficult to detect without a second analysis to compare with. In this way, among the software using double-differencing technique GAMIT is chosen and not Bernese, since together with GLOBK, being an integral part of the GAMIT package, no more is needed. Using PPP technique GipsyX version 1.7 (Bertiger et al. 2020) is chosen, and finally GLOBK is also used to analyze time series and fix the reference system. Combination procedure of the individual velocity solutions established by Herring et al. (2016) is followed in this work.

All available data from Topo-Iberia CGPS network cover the interval 2008–2019 at date of this study. Over time, some stations have been dismantled or have suffered incidents still unresolved, and as a consequence the extension of data spans varies significantly between stations (Fig. 2 left).

Blewitt and Lavallée (2002) established the relationship between the data span and the effect of annual signals in the estimation of velocities. The recommended standard minimum data span for velocity solutions intended for tectonic interpretation or reference frame is 2.5 years, and the velocity bias is minimum at integer-plus-half years. Although the available data span is long, these recommendations have been taken into account and the data span for each station has been tried to be integer-plus-half years. It has been achieved with the help of a previous data quality control carried out by using TEQC software (Estey and Meertens 1999). Thereby, the available span is shortened in front and behind as necessary eliminating as a priority the periods of malfunction (Fig. 3). This Figure also shows, for the first time, a global view of the quality of Topo-Iberia network station for the processed period based on the maximum number of complete observations recorded in 72122 RINEX (Receiver Independent Exchange) v. 2.11 format, indicated by a chromatic scale. Taking as quality reference the data quality information from IGS stations (IGS 2019), a station recording data at 30 second intervals during 24 hours will result in 20000 or more observations in case of GPS constellation. The average registered for each Topo-Iberia station is in range of 21640–24489 observations, being 23342 the average over the whole network, which reveals that the stations have shown better behavior than the IGS quality recommendations regarding this quality parameter. The number of sites as a function of the selected spans is shown in Fig. 2 (right) highlighting the largest number of sites over 9.5 years of observation. All the stations together form a dataset spanning from 2008-04-09 (Day Of Year 100) to 2019-10-29 (DOY 302), resulting in a total of 11.6 years. Details on available and processed data spans are shown in Table S1 of Supplementary Information 1 (SI_1).

Data from EPN CORS are also included in this analysis in order to tie the velocity solution into a global reference frame. A set of ten or more well-distributed sites with small uncertainties is enough to get a robust frame realization (Herring et al. 2018). The choice of these reference stations can have a non-negligible impact on the estimated positions and velocities and not all EPN stations are by definition suitable reference stations. To select the most optimal reference stations was used an interactive tool provided by EUREF (http://www.epncb.oma.be/_productsservices/ReferenceFrame/). Thirteen stations were selected between defined ones as recommended to be reference station for the given span: ALAC, ALME, BELL, CACE, CANT, CASC, HERS, MELI, RABT, SALA, VALE, VIGO, and YEBE. All of them, except BELL, CACE, CASC, and MELI are classificated as class C0 being the most stable and reliable stations in the EPN. These four stations are class C1 being still very stable. EUREF's station categorization is based on: size of the seasonal signals and scattering of the position time series; reliability of the velocity estimation; and stability of the station over its full history (EUREF 2021). The CORS set was completed with MAS1 and NOT1 stations belonging to IGS14 Core net, finally resulting in a total of fifteen reference stations (Fig. 1).

GPS data are processed using a three-step approach similar in general terms to the described by Dong et al. (1998) and Herring et al. (2018). In the first step daily loosely constrained estimates of station coordinates and their covariances are obtained from doubly differenced GPS phase observables (GAMIT) or from PPP using undifferenced observables from just a single GPS receiver (GipsyX). In the second step, time series (glred) in a consistent reference frame (IGb14) are generated by minimizing on each day for the selected CORS set (glorg). Outliers and offsets due to earthquakes or equipment changes, as well as periodic signals, are corrected to obtain clean time series. Also in this step the loosely constrained solutions from GAMIT and GipsyX are combined for each day generating subsequently their time series. In the third step all data are combined (globk) in a single solution applying generalized constraints (glorg) in position and velocity to define a uniform reference frame while estimating an overall translation and rotation of the network. Both second and third steps follow an iterative process. The first time series are stabilized only by the well-defined CORS, but the time series that best represents the final velocity solution is one that is stabilized with all of the sites in the solution. Thus, the first velocity solution obtained is used as a priori values in the next iteration and all sites used to stabilize. All the time series and velocity solutions are realized in a no-net-rotation (NNR) frame of the ITRF. Finally, positions, velocities, and uncertainties with respect to a fixed Eurasian and Nubian reference frame are estimated by fixing the set of CORS located on the stable part of the plates (glorg). Figure 4 depicts the process flow diagram of processing strategy described above.

Although each software uses different models or processing parameters, both use the same metadata and set of a priori station positions. General aspects of the processing models are exposed below. Details of GAMIT and GipsyX processing specifications and analysis parameters are given in Tables S2 and S3 (SI_1).

GAMIT strategy

Topo-Iberia stations (25) plus the additional CORS (15) are processed simultaneously in only one regional network (40) using GAMIT version 10.71 (Herring et al. 2018). Being the number of sites minor than ~ 50 in daily GAMIT processing, it is not necessary to use sub-networks for the processing to be more efficient and accurate. The regional solution uses 24-hour RINEX-formatted data sampled at 30 seconds being quality-checked with TEQC. Daily station positions and atmospheric delays are estimated from ionosphere-free linear combination GPS phase observables using double-differencing techniques to eliminate phase biases in the satellite and receiver clock oscillators. Satellite orbit parameters are fixed to the IGS final values and Earth Orientation Parameters (EOP) are interpolated from IERS Bulletin A (BASELINE mode in GAMIT). Second and third-order ionospheric corrections computed from Ionosphere Map Exchange (IONEX) files are applied. Ocean tidal loading effects are accounted for using the FES2014b model including corrections for center of mass motion. The ocean loading displacement coefficients for each of the sites are provided by Bos and Scherneck (2021), i.e., it is a list of values specific to a location and not a grid. Vienna Mapping Function (VMF1) grid (Boehm et al. 2006) is used for a priori hydrostatic and wet troposphere delay components and to model zenith delay variance. Integer phase ambiguities are resolved in a baseline-by-baseline mode. Constraints to a priori coordinates values are between 0.05 m for some reference sites chosen to enhance ambiguity resolution and 100 m for remaining sites, thus generating loosely constrained variance-covariance matrices and solutions by a weighted least squares algorithm. These GAMIT solutions are obtained in daily ASCII h-file format that are passed to GLOBK, where the final solution comes from.

The ambiguities are on average successfully resolved with 96.1% for wide-lane (WL) and 92.8% for narrow-lane (NL) (Fig. 5 top), which is an indicator of good quality of the solutions. In 95% of the daily solutions, greater than 90.9% of WL and greater than 85.3% of NL ambiguities are resolved. Another quality indicator of the daily GAMIT solutions is the square root of the chi-squared per degree of freedom \(\sqrt{\left({\chi }^{2}/f\right)}\), referred to as the normalized root-mean-square (NRMS). In practice with the default weighting scheme to account for temporal correlations, a good solution usually produces a NRMS of ~ 0.2 (Herring et al. 2018). It can also be seen in Fig. 5 that the values obtained are in range (0.16–0.19) being the average 0.18. The number of stations used in each daily GAMIT solution shown in Fig. 5 (bottom) evinces the variation of Topo-Iberia stations number over time, since the number of CORS is more or less fixed (15).

GipsyX strategy

Each of the 40 sites is separately processed using GipsyX version 1.7 (Bertiger et al. 2020) in precise point positioning (PPP) mode using ionosphere-free carrier phase and pseudorange observables. JPL’s final non-fiducial GNSS products (antenna models, ephemerides, clocks, and Earth rotation parameters) are used. Second-order ionospheric corrections are computed from JPL IONEX files except for 17 days computed from IGS IONEX due to non-availability of the first. Single receiver ambiguity resolution is performed using wide-lane phase biases (WLPB) method (Bertiger et al. 2010). Some models and processing parameters are common to those used in GAMIT. These similarities and also some differences are shown in Table 1. Station positions obtained in PPP processing, using fiducial-free strategy with a priori constraints of 10 m, are not tied to any specific terrestrial frame, but to satellite reference frame of the day defined by JPL. The stations are processed individually obtaining positions and covariance matrices in gdcov-file format. Those files that correspond to different sites but also to same day are joined to form an only gdcov-file per day, and subsequently it is translated to Solution Independent Exchange (SINEX) format file (IERS 2006). In the same way as GAMIT h-files, the daily SINEX files are passed to GLOBK to get the final solution. In both cases it is necessary to convert them into GLOBK binary h-files.

As part of the GipsyX ambiguity resolution process several statistics are generated, among others, number of double differences (DD) accepted and rejected for each test considered (duration, wide- and narrow-lane) (see Fig. 6). In this way, DD are rejected due to duration too short, and in the case of WL or NL due to bad DD, large sigma and low confidence. Ambiguities are successfully resolved with 99.8% for all RINEX, being 3832 the average number of DD that passed all tests.

The GAMIT h-files contain loosely constrained solution and full variance covariance matrix. The GipsyX-derived SINEX files come from separate PPP runs using fidual-free products, so there are not parameters linking position between stations, and therefore there is no covariance between their positions. In order to make these SINEX files loosely constrained and to complete the covariance matrix, the methodology exposed by Herring et al. (2015, 2016) is followed. A covariance matrix is added to the block diagonal covariance matrix in the SINEX files allowing the system to rotate and translate. This is accomplished with the GLOBK program htoglb adding 10 mas² in rotational variance and 1 m² in translation variance to covariance, at the same time converting the SINEX files into binary h-files. In this way, the minimum constraint solutions are loosen so that they can rotate and translate in GLOBK.

Table 1

Some models and processing parameters that differ and are common between GAMIT and GipsyX strategies. Details are given in Tables S2 and S3 (SI_1)
Processing Parameter	GAMIT	GipsyX
Strategy	Double-differencing (BASELINE mode)	Precise point positioning (single station PPP)
Data sampling	30 sec cleaning / 2 min analysis	Decimated to 5 min
Elevation angle cutoff	10°	7°
Orbits and clocks	IGS final orbits	JPL final (fidual-free) orbits and clocks
Atmospheric zenith delay and gradient estimates	Zenith wet delay parameterized by a piecewise-linear function with 2-hr intervals and process noise uncertainty constraint of 20 mm/√hr. One pair of gradients per day with a priori constraint of 30 mm at 10° elevation	Estimated every 5 min as a random-walk process noise of 3 mm/√h in zenith wet delay and 0.3 mm/√h in gradient
A priori atmospheric parameters	Meteorological data input from VMF1 with 50% relative humidity	Wet and dry nominal troposphere values from VMF1 for each station every 5 min
Second-order ionospheric corrections	IGS IONEX files (2nd and 3rd order)	JPL IONEX files
Ambiguity	Resolved in a baseline-by-baseline mode	Resolved using WLPB products from JPL
Phase elevation weighting	Site dependent constant and 1/sin (elevation angle) terms
Antenna corrections	Absolute antenna phase center variations based on IGS14 model for both satellite and ground antennas
Tropospheric mapping function	VMF1 dry and wet terms
Solid Earth tide	IERS 2010 convention (IERS 2010)
Earth pole tide	IERS 2010 convention
EOP	IERS Bulletin A
Ocean tidal loading	FES2014b model with center of mass correction (list values)
Atmospheric nontidal loading	Not applied
Atmospheric tidal loading	Not applied

Combined strategy

As exposed above, different models or processing parameters are used in GAMIT and GipsyX (basic and modeled observables, data sampling and weighting, etc.). As a consequence, the noise models of both analyzes are different, which also results in different standard deviations of the position estimates. In order for the individual final solutions to be comparable, their covariance matrices are rescaled to weight the solutions equally. The scale factors are determined such that the average values of the χ²/ƒ of the fits to the coordinate differences at the reference frame stations are near unity (Herring et al. 2016). With the chosen GAMIT processing mode (BASELINE) and default reweighting scheme of autcln program, the error budget is pretty conservative and the mean NRMS values obtained in time series are ~ 0.6–0.8. Since ultimately everything boils down to a problem of relative weight of one solution with respect to the other one, instead of rescaling both as in Herring et al. (2016), GAMIT solution is used as it is (unscaled) and only the GipsyX one is rescaled. In addition, to get the appropriate scaling value, the relation between sigmas in the time series of both solutions is studied (Fig. 7), therefore this scaling step is done after standard GipsyX/GLOBK processing is completed. Analyzing the histograms in the Fig. 7, it is determined that GipsyX position estimates have standard deviation ~ 1.9 times smaller than GAMIT values, therefore the GipsyX sigmas would have to be multiplied by 1.9 to match GAMIT’s. This sigma factor corresponds to a scale factor of 3.6, since it is necessary to square before applying it, i.e., the GipsyX h-files are downweighted by 3.6 in covariance (a factor of 1.9 in uncertainty). A sigma factor ~ 2 between GAMIT and Gipsy solutions also was determined in the study realized by Floyd et al. (2020). Once the GipsyX h-files are processed with GLOBK applying the scale factor (GipsyX rescaled), their sigmas are approximately in alignment with GAMIT/GLOBK solution as shown in the histograms.

For individual processing, scale factors for GAMIT and GipsyX solutions are fixed to 1 and 3.6 respectively. When the results of both strategies are combined or, what is the same, two solutions for the same network of sites are combined, these factors are doubled so that solutions from individual strategies and their combination (Combined strategy) have similar standard deviations for the position estimates (Herring et al. 2016; Floyd MA and Herring TA personal communication 2022).

Considerations for vertical component

Precision of the GNSS vertical component is in general about 2–3 times lower than for the horizontal component due to various reasons, among them, geometry and distribution of satellites, phenomena such as ocean loading, atmospheric delays, etc. In order to improve the accuracy some changes have been made to the default GAMIT configuration. Default mapping function used for modeling and estimation of the atmospheric delay is Global Mapping Function (GMF) from fitting numerical weather model (NWM) data over 20 years, sufficient for all but the most accurate studies of heights and for meteorological studies (Herring et al. 2018). Instead, the VMF1 model has been used, a more accurate reconstruction of the NWM data. Since having the most accurate value of pressure, from local measurements of surface pressure, for the a priori zenith hydrostatic delay (ZHD) has not been possible, the next most accurate source has been chosen, the VMF1 grid. In addition, zenith delays have been estimated every 2 hours, although there is little increase in accuracy of station heights and it greatly increases processing time. Regarding ocean tide loading, the model with the best possible accuracy at the date of the study has been used, the FES2014b model. Default GipsyX configuration was also changed with regard to VMF1 and FES2014b models.

Time series analysis

The loose solutions previously obtained, binary h-files rescaled or not depending on the case, are considered individually by glred to generate position time series of each station, day-to-day repeatability, throughout the span considered in an adequate framework.

Prior to any velocity estimation, it is necessary to estimate and subtract non-secular (no tectonic) motions that can affect the stations, which by definition of the ITRF framework must be linear. The raw time series are analyzed in order to estimate and remove outliers, periodic terms, and discontinuities in an iterative process briefly described below. This is realized using the GLOBK program tsfit, command-line tool for fitting time series and generating statistics, and the interactive Matlab-based program tsview (Herring 2003) since in long and continuous time series the point-by-point visual inspection is impractical. Files generated with tsfit/tsview containing outliers, discontinuities, and periodic signals are inputs of GLOBK to get a combined solution and extract positions and velocities more refined. Raw and cleaned time series of Topo-Iberia CGPS stations are shown in Figures S2-S14 (SI_1).

Outliers

Outliers are detected and eliminated by two automatic procedures, max-sigma and n-sigma. Any position estimate whose uncertainty is greater than 2, 2, and 3 cm in East, North, and Up respectively is removed (max-sigma), as well as the points that exceeded 2-sigma values after detrending the data. Although the final result corresponds to this n-sigma criterion, the analysis has also been carried out with 3-sigma criterion in order to verify and compare the results, which should be quite similar. Small values of this criterion allows for more precise results but also can lead to all data being deleted, and even more so if there are non-secular motions not detected correctly. Taking into account only the information known from station metadata, a preliminary analysis is carried out with both n-sigma criteria revealing notable discrepancies in horizontal velocity at some Topo-Iberia stations (Fig. 8 top). The results shown correspond to GAMIT/GLOBK, but also occur with GipsyX and Combined strategies. Stations showing the most discrepancies are ALJI, LIJA, LOJA, and TAZA. These relative differences are due to the fact that with 2-sigma criterion some data segments are considered outliers, resulting in different velocity directions that the one obtained with 3-sigma criterion. Although these stations could have time series with acceptable statistical values, a further analysis is required. In a second analysis, some data segments have been excluded that could be related to malfunctions due to battery problems in winter periods than were already detected in other Topo-Iberia stations (García-Armenteros 2020), but the cause is unknown in most of them. An example can be seen in Figs. 9a,b where a data segment that has been deleted in Figs. 9c,d is shown, and it can be verified after its deletion how the resulting velocities are similar with both criteria. After the second analysis, the major velocity discrepancies disappear or are reduced (Fig. 8 bottom).

Discontinuities

A discontinuity can occur due to events such as earthquakes, hardware or antenna changes, and other causes of unknown origin in the surroundings of the station producing abrupt and permanent changes in position. In the preliminary analysis only the offsets due to known equipment changes were taken into account, and once these were corrected, other offsets could be detected and corrected by adding breaks. Some of these breaks correct obvious jumps to the naked eye, and in other cases correct small offsets (amplitude of some mm) improving the linearity in some velocity component and reducing the time series statistics. For example, comparing Figs. 9e,f it can be seen that when 2-sigma criterion is used, a data segment in 2008 is automatically deleted as it is considered an outlier, causing the discrepancy in the horizontal velocity direction shown above in Fig. 8 (top). In Figs. 9g,h an offset break has been added after a small gap correcting the loss of the data segment and the velocity discrepancy between both n-sigma criteria.

Periodic signals

Periodic signals can affect the three components of GPS time series being their frequency spectrum dominated by annual and semi-annual periods (seasonal signals). When the data were selected for processing, the effect of these signals in the estimation of velocities (Blewitt and Lavallée 2002) was taken into account selecting data spans of integer-plus-half years and longer than 4.5 years. Although the velocity bias could be minimum, annual and semi-annual periods (sine and cosine terms) are estimated from time series with tsfit/tsview. Further seasonal signals constitute a source of noise for velocity estimation, therefore the elimination of these signals facilitates detecting anomalous data segments and smaller offsets (amplitude of some mm) masked in the time series noise.

A comparison has been realized between the velocity estimates with and without taking into account annual and semi-annual terms in time series, and the results obtained with GAMIT/GLOBK are shown in Fig. 10. Except for a few stations, it is observed that the variation in velocity is minimal, particularly in periods greater than 8.5 years. Table 2 summarizes the statistics of the differences obtained between both solutions for the three strategies showing similar and low values. This low affectation of estimating the seasonal signals was expected according to the length of data spans and the precautions taken in its selection. Furthermore, whether or not to take this estimation into account does not affect the velocity uncertainties. The prominent east velocity variation at ALJI station (Fig. 10) is studied in detail in Fig. 11. The annual frequency has been the most detected (top right) being its amplitude in east component of ~ 1.5 mm, five times greater than in north component. When seasonal signals are estimated and removed (bottom left), the annual frequency is almost completely removed resulting in the mentioned velocity variation in the east component.

Table 2

Statistics of differences in North, East, and Up velocity component estimates with and without taking into account seasonal signals for each strategy
Strategy	ΔV_N (mm/yr)		ΔV_E (mm/yr)		ΔV_U (mm/yr)
Strategy	RMS	Mean	RMS	Mean	RMS	Mean
GAMIT	0.05	0.00	0.08	0.01	0.08	-0.01
GipsyX	0.06	0.01	0.06	0.01	0.08	0.00
Combined	0.06	0.00	0.08	0.01	0.05	0.00

Noise model

In this work the noise in GPS position time series is assumed to be a combination of white noise plus random-walk (RW) noise. The long-period temporally correlated noise is accounted for using realistic-sigma algorithm or First-Order Gauss–Markov Extrapolation (FOGMEX) (Herring et al. 2015; Floyd and Herring 2020) to determine a RW noise term and add it to the error model used by GLOBK. The FOGMEX algorithm is an option implemented in tsfit and previously proposed and referred to as the RealSigma option by Herring (2003). RW values are generated for each site by analysis of the position residuals from fitting their time series. A minimum RW process noise value of 0.05 mm²/yr is imposed in each station. The RW median values obtained in north, east and up components were 0.06, 0.06 and 0.09 mm²/yr respectively from Combined strategy. Similar values were obtained from GAMIT and GipsyX except in up component, which were 0.12 and 0.11 mm²/yr respectively. Maximum horizontal random-walk (HRW) process noise value was obtained at TIOU station (0.3 mm²/yr), therefore, there have been no stations with high process noise values that could contaminate nearby stations. The RW process noise values obtained are incorporated into the Kalman filter (GLOBK) after the last iteration of the process flow (Fig. 4) to estimate the final velocities and get more realistic uncertainties.

A comparison between globk velocity solutions applying and without applying the FOGMEX algorithm was realized to quantify their impact on the velocity uncertainties. Table 3 shows that increase in uncertainties is similar in the three strategies.

Table 3

Statistics of differences in velocity uncertainties (1σ) applying and without applying FOGMEX algorithm for each strategy
Strategy	Δσ_N (mm/yr)		Δσ_E (mm/yr)		Δσ_U (mm/yr)
Strategy	RMS	Mean	RMS	Mean	RMS	Mean
GAMIT	0.08	0.07	0.07	0.07	0.10	0.08
GipsyX	0.07	0.06	0.07	0.07	0.09	0.08
Combined	0.06	0.06	0.07	0.07	0.08	0.07

Comparison of time series

Once finished the GPS data processing exposed above, estimates of velocity field in IGb14 reference frame based on the final position time series analysis of data from 2008-04-09 to 2019-10-29 (11.6 years) were generated. Statistics of these final time series generated by GAMIT, GipsyX and Combined strategies are summarized in Table 4 and Fig. 12. The median horizontal RMS scatters are less than or equal 0.88 mm for all strategies, being 0.53 mm the lowest value for GipsyX east component and not higher than 0.64 mm for the rest strategies in north and east components. The median up RMS scatters are less than or equal 2.06 mm, being the lowest value for Combined strategy. The means in north and east components are in range of 0.61–0.74 mm indicating a good repeatability. In general, statistics are similar in the three strategies and the differences between them are of the order of a tenth of a mm.

Table 4

Statistics of RMS scatters of position residuals in the final fitting the time series for each strategy
Strategy	North (mm)		East (mm)		Up (mm)
Strategy	Median	Mean	Median	Mean	Median	Mean
GAMIT	0.64	0.74	0.61	0.70	1.89	2.09
GipsyX	0.60	0.66	0.53	0.61	2.06	2.18
Combined	0.61	0.67	0.58	0.64	1.81	1.95

Comparison of velocity solutions

A previous comparison between GAMIT and GipsyX solutions without applying the realistic-sigma algorithm has been realized to check their degree of matching. In Fig. 13 (top) some discrepancies in direction of velocity vectors are observed, more visible at NOT1 and southern stations with higher velocity. In principle it could be interpreted that there is a little dextrorsum rotation in GipsyX velocity solution with respect to GAMIT one, except at NOT1 station being sinistrorsum rotation. However, it has been found that these discrepancies are related to the effect resulting from the estimation of translation on each velocity solution. Furthermore the translations are not expected to be the same because of different orbital modeling. In the standard GAMIT processing (BASELINE mode) the h-files are converted into GLOBK binary h-files by using htoglb with the default option, i.e., applying a rotational and translational deconstraints. If translation is then estimated in glorg, it is not necessary to explicit it in globk since doing so will have little effect. In the analysis carried out, a combination of GAMIT and GipsyX was intended, therefore to facilitate subsequent combination of h-files, automatic deconstraints are not applied for GAMIT solution. In this case, if the estimation of translation is intended, it is necessary to explicit it in globk, and the result will be similar to standard GAMIT processing. On the other hand, the GipsyX SINEX files do not contain EOP information and were converted applying a rotational and translational deconstraints, so the explicit estimation of EOP and translation will have no effect when doing a GipsyX-only solution. In the Combined solution, the estimation of translation will have an effect when there are GipsyX and GAMIT h-files on the same day (Floyd MA and Herring TA personal communication 2022). In order to ensure that GAMIT and GipsyX solutions are in conditions as similar as possible for comparison purposes only, it would be necessary not to explicit translation in GAMIT solution (Fig. 13 bottom). It is observed how the velocity solutions match in a remarkable way considering that both come from independent processing.

A comparison of mean and root-mean-square of the differences between the final velocity estimates obtained by the three different strategies is shown in Table 5. FOGMEX algorithm is applied in these final velocity solutions. The agreement between the velocity estimates from each strategy is very good overall, with RMS of differences < 0.21 mm/yr in horizontal component and < 0.33 mm/yr in height component. The comparison of velocity estimates from GAMIT and GipsyX solutions shows that match at the level of 0.16 mm/yr in north and east components, and 0.33 mm/yr in height. These values are very similar to those resulting from comparing Combined and GipsyX solutions, but when Combined and GAMIT are compared, the RMS of differences reduces to 0.07 mm/yr in horizontal and up component.

Table 5

Statistics of differences in North, East, and Up velocity components between the final velocity solutions (Strategy 1 minus Strategy 2)
Strategy 1	Strategy 2	ΔV_N (mm/yr)		ΔV_E (mm/yr)		ΔV_U (mm/yr)
Strategy 1	Strategy 2	RMS	Mean	RMS	Mean	RMS	Mean
Combined	GAMIT	0.05	0.02	0.05	0.01	0.07	-0.03
Combined	GipsyX	0.10	-0.01	0.14	-0.03	0.32	0.03
GAMIT	GipsyX	0.14	-0.03	0.16	-0.04	0.33	0.06

Final horizontal velocity solutions in IGb14 and Eurasian-fixed reference frames are shown in Fig. 14. Combined solution hides most of the vectors due to their great matching in IGb14 frame. However, it tends to take an intermediate position between the other velocity solutions in Eurasian frame, although closer to the GAMIT one, as shown the statistics in Table 5. The RMS of realistic horizontal velocity uncertainties (1σ) is 0.11 mm/yr for the three strategies. The Combined horizontal velocity solution is considered in this paper as the new horizontal CGPS velocity field of Topo-Iberia network based on eleven years (2008–2019). Residual velocities with respect to a Eurasian-fixed reference frame are shown in Table 6, and the velocities for all stations used in this analysis in different reference frames are provided in Tables S4–S6 (SI_1).

Table 6

Velocities with 1σ realistic uncertainties of Topo-Iberia CGPS stations in a Eurasian-fixed reference frame. V_E is the east component, V_N the north component, V_Hz the horizontal magnitude, V_U the up component, and Az the azimuth. Results for all stations, plus an ASCII text file for direct use in GMT, are provided in Tables S4–S6 (SI_1) and Supplementary Information 2 (SI_2)
#	ID	V_E ± 1σ		V_N ± 1σ		V_Hz ± 1σ		V_U ± 1σ		Az
#	ID	(mm/yr)		(mm/yr)		(mm/yr)		(mm/yr)		(°N)
1	ALJI	-2.86	0.13	0.89	0.12	3.00	0.13	-0.47	0.31	287.29
2	AREZ	-0.85	0.09	0.11	0.09	0.86	0.09	-0.01	0.16	277.37
3	ASIN	0.02	0.12	-0.12	0.12	0.12	0.12	-0.20	0.25	170.54
4	BENI	-3.95	0.15	0.34	0.16	3.96	0.15	0.62	0.49	274.92
5	CABU	-0.09	0.09	0.36	0.09	0.37	0.09	-0.31	0.15	345.96
6	CAST	-1.68	0.12	0.24	0.10	1.70	0.12	-0.53	0.16	278.13
7	CIER	0.12	0.09	0.05	0.09	0.13	0.09	0.33	0.14	67.38
8	EPCU	-1.04	0.09	-0.19	0.09	1.06	0.09	-0.69	0.19	259.65
9	ERRA	-3.86	0.11	1.76	0.11	4.24	0.11	0.04	0.30	294.51
10	FUEN	-0.07	0.11	-0.19	0.11	0.20	0.11	-0.06	0.24	200.22
11	LIJA	-2.54	0.16	0.11	0.18	2.54	0.16	-0.87	0.44	272.48
12	LNDA	-0.06	0.15	0.26	0.17	0.27	0.17	0.58	0.36	347.01
13	LOBE	-0.14	0.11	0.13	0.11	0.19	0.11	-0.27	0.25	312.88
14	LOJA	-1.95	0.12	-1.52	0.15	2.47	0.13	-0.80	0.26	232.06
15	MAIL	-0.51	0.10	0.33	0.10	0.61	0.10	-0.24	0.17	302.91
16	NEVA	-1.49	0.08	-0.75	0.08	1.67	0.08	0.18	0.16	243.28
17	PALM	-2.54	0.09	-1.27	0.09	2.84	0.09	-0.17	0.16	243.43
18	PILA	-0.80	0.08	1.15	0.08	1.40	0.08	-0.76	0.14	325.18
19	REIN	0.06	0.10	0.13	0.10	0.14	0.10	-0.28	0.16	24.78
20	RUBI	-0.72	0.09	-0.11	0.10	0.73	0.09	-0.17	0.23	261.31
21	TAZA	-4.39	0.21	2.25	0.14	4.93	0.20	0.01	0.31	297.14
22	TGIL	-0.83	0.10	-0.42	0.12	0.93	0.10	-0.66	0.39	243.16
23	TIOU	-3.39	0.22	1.49	0.27	3.70	0.23	-1.56	0.77	293.73
24	TRIA	-0.23	0.11	0.30	0.11	0.38	0.11	-0.43	0.20	322.52
25	UCMT	0.52	0.12	-0.14	0.11	0.54	0.12	-0.11	0.18	105.07

Final vertical velocities depicted in Fig. 15 confirm that values from GAMIT and Combined strategies are quite similar as indicated by the RMS of their differences (0.07 mm/yr in Table 5). In contrast, in values from GipsyX strategy not only are there more differences in magnitude compared to the other ones, but presents opposite results in 25% of cases. Vertical velocities are in general low, being their RMS of 0.64 mm/yr for GAMIT and Combined strategies, and 0.70 mm/yr for GipsyX one. The RMS of realistic uncertainties are, in the same order, 0.23, 0.25, and 0.24 mm/yr. The uncertainties are shown in Fig. 16 and evince a clear decreasing trend as the processed data span increases in a similar way for the three strategies, coinciding their linear regression lines. The highest uncertainty detaching in the graph corresponds to TIOU station with a data span of 8.5 years. 50% of Topo-Iberia stations have over 9.5 years of data span and, according to the graph, it would correspond to an uncertainty of ~ 0.2 mm/yr, which is quite acceptable considering the low vertical velocities estimated.

Combined vertical velocity solution is shown in Fig. 17 as the first vertical CGPS velocity field of Topo-Iberia network. A generalized subsidence is observed, except in a few cases as BENI and LNDA stations showing an uplift of 0.6 ± 0.5 and 0.6 ± 0.4 mm/yr respectively. Coincidentally, processed data spans from both stations are the shortest, 4.5 years (Fig. 15), and possibly a longer data span would be needed to get lower uncertainty and verify the uplift. Furthermore, BENI station was dismantled, which added to the lack of information about what would have happened in its surroundings, does not allow its velocities to be offered in this work with total confidence.

Comparison with previous publications

Garate et al. (2015) presented the Topo-Iberia CGPS network velocity field based on the analysis of the first four activity years (2008–2012). Subsequently Galindo-Zaldivar et al. (2015) and Gonzalez-Castillo et al. (2015) carried out studies located in the Betic Cordillera (southern Spain) extending the data span to five years (2008–2013), although reducing the number of Topo-Iberia stations used to 5 and 4 respectively. All of them realized the velocity solution in ETRF08, however the new velocity solution presented in this paper is realized in IGb14, as well as respect to a fixed Eurasian and Nubian reference frames. In order to be able to compare the different fields, the ETRF08 velocity solution is rotated and translated into the reference frame of the new velocity one by using velrot v.1.01 program. Number of stations used by Galindo-Zaldivar et al. (2015) and Gonzalez-Castillo et al. (2015) is small, and taking into account that the velocities they present coincide with those of Garate et al. (2015), it has been decided to transform only the latter. The resulting average RMS of the fit based on 33 common stations is 0.39 mm/yr, indicating a good adjustment. The new velocity solution is also compared with the velocity field presented by Koulali et al. (2011), study on the deformation along the Africa–Eurasia plate boundary zone in the western Mediterranean region, although in this case there are no Topo-Iberia stations in common. In this case the RMS fit based on 11 common stations is 0.22 mm/yr, also indicating a good adjustment. At present, these plates converge in this region at a rate of 4.9 mm/yr according to the GSRM v2.1 plate motion model (Kreemer et al. 2014).

The new horizontal CGPS velocity solution is in general in good accordance with velocities published by Garate et al. (2015). The smallest residual displacements with respect to Eurasia are observed in northern Iberia. Their current displacement values range from 0.1 mm/yr at ASIN in the northeast to 1.1 mm/yr at EPCU in the central zone (Table 6 and Fig. 18 left). The stations with highest displacements are those deployed in Morocco and located on the Nubia plate, showing in general northwestward displacements ranging from 3.7 to 4.9 mm/yr. The main differences are visible in the Betic Cordillera, specifically at ALJI, LIJA, LOJA, and NEVA stations (Fig. 18 bottom left), located in the Betic-Rif deformation zone controlled by slab retreat and Alboran Domain collision (Mancilla et al. 2015).

Most of the displacements in central and eastern Betics are westward, with a variable southwestward component. AREZ and TGIL stations keep the westward and southwestward displacements respectively presented in previous studies, but their current velocities are even reduced by 76% in case of TGIL, both being below 0.9 mm/yr. PILA station (1.4 mm/yr) shows northwestward displacement in the eastern Betics where part of the shortening between Nubia and Eurasia plates is accommodated (Borque et al. 2019). NEVA station (1.7 mm/yr) continues showing a displacement roughly parallel to the nearby GRAN and the farthest CAAL station as in Galindo-Zaldivar et al. (2015), coinciding exactly with the azimuth of PALM station (2.8 mm/yr), but currently the stations as a whole show a higher southwestward component instead of purely westward motion. LOJA station (2.5 mm/yr), in addition to presenting a reduction in velocity as NEVA and PALM stations, also presents a higher southwestward component being integrated into both stations and together with CABR and MOTR stations of velocity field of Koulali et al. (2011).

Displacements in the western Betic Cordillera show a westward motion as prior published results (Garate et al. 2015; Gonzalez-Castillo et al. 2015). It can be considered that at LIJA station (2.5 mm/yr) there are no evident changes in motion due to its current uncertainty showing a westward displacement as ROND and LEBR stations. Between the displacements of Topo-Iberia stations in the western Betic, a maximum is reached at ALJI station (3 mm/yr) showing present-day a west-northwestward instead of the westward motion parallel to LIJA station. The new displacement at ALJI station, compared with the velocity field of Koulali et al. (2011), is in harmony with ALGC and UCAD stations, being even more evident with respect to Nubian-fixed reference frame (Fig. 18 bottom right). This new direction could confirm more clearly that a clockwise block rotation would have been occurring at present in the northern branch of the Gibraltar Arc (Gonzalez-Castillo et al. 2015), tectonic belt connecting Betic and Rif Cordilleras surrounding the Alboran Sea and present-day undergoing a northwest-southeast convergence rate established in this paper of 3.6 ± 0.1 mm/yr. The displacements as a whole also are in agreement with the tectonic model involving roll-back in the western Alboran Sea and indentation in the central and eastern areas proposed by Galindo-Zaldivar et al. (2022).

It might be thought that the origin of the discrepancies described above could be related to different criteria followed by the authors in the time series analyses, but the case of NEVA station is remarkable since it has not been necessary to intervene in its time series, and instead, it presents a new direction of displacement. NEVA time series have been very stable with the different criteria used, keeping the result constant, without information gaps in its metadata and without unknown strange behaviors during its long activity period (10.5 years). Therefore, the new southwest displacement at LOJA station, more or less parallel to NEVA and PALM stations, can be found coherent. In addition, the data span of LOJA and ALJI stations analyzed in this work has been extended from 4 to 9.5 years, allowing a more precise determination of their present-day displacements.

With respect to the vertical velocity field, in addition to the higher uncertainties associated with this component, it must be taken into account that the results presented by different publications usually come from methodologies differing in, among others, processing software, noise model or stations defining the reference system. As a consequence the vertical velocity estimates presented tend to have quite a few differences. All of this makes a detailed comparison of velocity at each station less conclusive than whether or not there is agreement between regions of subsidence or uplift. On the other hand, the density of Topo-Iberia network and CORS used in this study, although covering the study area, does not allow establishing rates of subsidence or uplift with confidence for the entire Iberian Peninsula and Morocco. However, as in previous publications, a general subsidence is observed in the Iberian Peninsula except for some isolated stations (Fig. 19). The fastest subsidence velocities (0.6 mm/yr averaged) are located in southern Iberian Peninsula and approaching zero close to the southern Pyrenees in agreement with Serpelloni et al. (2013), although they establish subsidence rates ~ 2 mm/yr higher than this work. They did not use Topo-Iberia stations and, although present a dense spatial distribution of stations, only covered the central and southeastern regions. Velocity rates close to zero in the Pyrenees also coincide with those presented by Nguyen et al. (2016), where there are four stations in common and the estimated velocity coincides in two of them (LNDA and FUEN), which could confirm the uplift at LNDA station.

After the first publication in 2015 of the horizontal velocity field in the Iberian Peninsula and Morocco in the framework of the Topo-Iberia project, a new 3D velocity field based on eleven years is presented in this paper. Data available up to 2019 are used, with 50% of Topo-Iberia stations having over 9.5 years of data.

A quality control is carried out on the entire network, with which the optimal data spans to process are determined trying to get them of integer-plus-half years and longer than 4.5 years. In addition, a global view of the quality of Topo-Iberia network stations for the processed period, based on the maximum number of complete observations recorded, is presented for the first time. The results, with an average over the whole network of 23340 observations, show that the Topo-Iberia stations meet the IGS recommendations regarding this quality parameter for the processed period.

In the GPS data processing, different software is used with the intention of having different analyzes with which to compare and avoid possible errors introduced during processing, while maintaining the premise of reducing the software to the minimum necessary. Thus, GAMIT applying a double-difference network processing strategy and GipsyX applying a precise point positioning strategy are used. GLOBK is used to analyze time series and fix the reference system, as well as to combine the individual solutions in the Combined strategy. In order to the individual solutions to be comparable, the methodology exposed by Herring et al. (2016) is followed, but in this paper only GipsyX solution, and not GAMIT one, is rescaled by a factor of 3.6 obtained from the relation between sigmas in time series of both solutions. Velocity solutions are not combined or operated, but the two independent loosely constrained solutions from GAMIT and GipsyX are merged within a Kalman filter (GLOBK).

It is shown that the discrepancies between GAMIT and GipsyX horizontal velocity solutions are related to the effect resulting by the estimation of translation on each solution, since it has no effect when doing a GipsyX-only solution due to the SINEXs creation method and the lack EOP information in their headers.

Position time series analysis is realized with two n-sigma criteria, 2- and 3-sigma, in order to verify and compare results. In this way, some anomalies are detected and corrected in stations that in principle presented time series with acceptable statistical values. Periodic signals are estimated and it is shown that their effect is minimal in periods greater than 8.5 years, although estimating them is advisable as shown in the case of ALJI station. FOGMEX algorithm is applied to get realistic uncertainties and there are no stations with high process noise values, obtaining the maximum horizontal random-walk process noise (0.3 mm²/yr) at TIOU station.

The means of RMS scatters of position in north and east components in the time series for the three strategies are in range of 0.61–0.74 mm, and in the up component is in range of 1.95–2.09 mm indicating a good repeatability.

The agreement between the velocity estimates from each strategy is very good overall, being the RMS of their differences < 0.21 mm/yr in horizontal component, and < 0.33 mm/yr in height. The RMS of the differences reduces to 0.07 mm/yr in horizontal and up components when Combined and GAMIT solutions are compared.

Combined horizontal velocity solution is considered in this paper as the new horizontal CGPS velocity field of Topo-Iberia network based on eleven years (2008–2019). The RMS of their realistic uncertainties (1σ) is low, 0.11 mm/yr. The new velocity field is in good accordance with results of previous publications on Topo-Iberia network, except for some discrepancies in Betic Cordillera. Smallest residual displacements with respect to Eurasia occur in northern Iberia ranging from 0.1 to 1.1 mm/yr. Highest displacements are observed in Morocco showing in general a northwestward component ranging from 3.7 to 4.9 mm/yr. The new horizontal velocities in Betics are lower than those established in previous publications. Furthermore, in the central sector of the Betic Cordillera, the stations present a higher southwestward component instead of purely westward motion. The main discrepancies in western Betic Cordillera is observed at ALJI station, where a maximum is reached (3 mm/yr), showing present-day a west-northwestward instead of westward motion. The results could confirm that a clockwise block rotation would have been occurring at present in the northern branch of the Gibraltar Arc, which present-day undergoing a northwest-southeast convergence rate of 3.6 ± 0.1 mm/yr. The displacements as a whole also are in agreement with the tectonic model involving roll-back in the western Alboran Sea and indentation in the central and eastern areas proposed by Galindo-Zaldivar et al. (2022).

Combined vertical velocity solution is presented in this paper as the first vertical CGPS velocity field of Topo-Iberia network. Vertical velocities obtained are in general low, their RMS is 0.64 mm/yr and the RMS of their realistic uncertainties is 0.25 mm/yr. As in previous publications, a general subsidence is observed in the Iberian Peninsula except for some isolated stations such as LNDA station. Fastest subsidence velocities (0.6 mm/yr averaged) are located in southern Iberian Peninsula and approaching zero close to the southern Pyrenees. Considering the limitations of vertical component estimation, although some changes were made to GAMIT and GipsyX default configuration to improve their accuracy, the results offered increase the information on subsidence or uplift regions, since there are very few studies on vertical velocity in the Iberian Peninsula and Morocco.

Acknowledgements I would like to express my most sincere gratitude to Michael A. Floyd and Thomas A. Herring from MIT for their help and answer all my questions despite their busy schedules. Likewise, I would like to thank Mario Sánchez Gómez for his advice in this work, as well as my colleagues at CEACTEMA, Pedro A. Ruiz and Juan Jiménez for their support in software license management. I am grateful to the EPN, MIT, and JPL for providing open GNSS data, and especially to the IGME and colleagues of Topo-Iberia team for their efforts in network maintenance.

Funding This research was supported in part by University of Jaén and Spanish Ministry of Economy, Industry and Competitiveness (PTA2015-11507-I MINECO).

Competing interest The author declares no competing interests.

Data availability GNSS data provided by EPN can be accessed from https://epncb.eu/ftp/obs/ and https://epncb.eu/_networkdata/stationlist.php. Data provided by IGME is non-public access. GNSS products used with GipsyX provided by JPL are available at https://sideshow.jpl.nasa.gov/pub/JPL_GPS_Products/Final/. VMF1 files for GAMIT are available at ftp://everest.mit.edu/pub/GRIDS/, and for GipsyX at https://vmf.geo.tuwien.ac.at/trop_products/GRID/2.5x2/VMF1/STD_OP/. Maps were created by using Generic Mapping Tools software version 5.4.5 (Wessel et al. 2013), graphs by using Gnuplot version 5.2 (http://www.gnuplot.info/) and figures edited by using Inkscape version 0.92.4 (https://inkscape.org). Additional data and resources used in this work are indicated in the main body.

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published 27 Jun, 2023

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Topo-Iberia CGPS network: A new 3D crustal velocity field in the Iberian Peninsula and Morocco based on eleven years (2008–2019)

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Abstract

Figures

Introduction

Gps Data

Data Processing Strategy

GAMIT strategy

GipsyX strategy

Combined strategy

Considerations for vertical component

Time series analysis

Outliers

Discontinuities

Periodic signals

Noise model

Analysis Of Final Results And Discussion

Comparison of time series

Comparison of velocity solutions

Comparison with previous publications

Summary And Conclusions

Declarations

References

Additional Declarations

Supplementary Files

Status:

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