Determination of a GNSS-based velocity field of the African continent
This study provides for the entire continent of Africa the position/ velocity solution precisely expressed with reference frame IGSR3
GNSS-based velocity fields are a key tool to assess the boundaries around major deforming areas, to explain the main patterns of surface motion and deformation, to analytically review existing kinematics models and finally, to study the underlying tectonic activities. Determination of a velocity field for Africa is of great importance in the determination of the African Reference Frame; this is essential for better understanding the African plate tectonics. Therefore, this study focusses on the determination of the African velocity fields using continuously operated GNSS stations. We processed and analyzed 11 years of data obtained from a total number of 145 GNSS site using GFZ’s EPOS.P8 software. The result shows that Africa moves in the North-East direction. The station coordinates derived with PPP show averaged RMS values of 2.9 mm, 9.9 mm and 8.5 mm for the north, east and up components with respect to the estimated trajectory models. Horizontal velocities at sites located on stable Nubia plate fit a single plate model with residual motion below 1 mm/year of RMS. We confirm significant southeast motion in Morocco and Zambia with residual velocities of 1.4 mm/year and 0.9 mm/ year, respectively. We estimate the Euler Poles for Nubia and Somalia with 48.59ı N, –78.64°E, 0.264°/Myr and 60.38°N, –83.33°E, 0.272°/Myr, respectively. Vertical velocities range from –2 to + 2 mm/year, close to their uncertainties, with no distinct geographic pattern. The study also provides continental-wide position and velocity field solution for Africa, and can also be considered as a contribution to the upcoming AFREF, the African Geodetic Reference Frame.
The African Continent comprises of several cratons, stable blocks of old crust with deep roots in the subcontinental lithospheric mantle, and less stable terranes, which converged together to form the African Plate during the assembly of the supercontinent Pangea about 250 million years ago (Begg et al. 2009). The cratons include the Kalahari Craton, Congo Craton, Tanzania Craton, and West African Craton (see Fig. 1). The cratons were widely separated in the past, but brought together during the Pan-African orogeny and stayed together when Gondwana split up. The cratons are joined by orogeny belts, regions of highly deformed rock where the tectonic plates have engaged (Saria et al.2013). The African plate that moved relatively slowly for the last 150 Ma (LithgowBertelloni and Silveri 1998; Torsvik et al. 2010) is an interesting plate for studying intraplate magmatism. It contains various intraplate volcanic segments that are remote from the African plate boundaries. Such segment is the NE-SW oriented Cameroon Volcanic Line which bisects the angle where the coast of Africa makes a 90° bend from the western coast along the south of the West African craton and the southern coast along west of the Congo craton (see Fig. 1). It is characterized by moderate magnitude earthquakes and active volcanism (Aka et al. 2004; Milelli et al. 2012). Moreso, the East African Rift System (EARS), is a place where the Earth’s tectonic forces create new plates by splitting apart old ones. In other words, it is a fracture in the Earth’s surface that widens over time. The Nubian Plate makes up most of Africa, while the smaller plate that is pulling away is named Somalian Plate. These two plates are moving away from each other and also away from the Arabian plate to the north (Chu and Gordon 1999). The point where these three plates meet is the triple-junction at the Afar region of Ethiopia. However, all the rifting in East Africa is not confined to the Horn of Africa; it further extends to south into Kenya, Tanzania and Great Lakes region of Africa. The East African Rift system reaching from the Afar in the northern Ethiopia to Mozambique in the south shows spreading rates of up to 5 mm/year (Saria et al. 2013).
The dynamics of the tectonic plate activities of the Earth are the major causes for ground motion. Beginning from the mid-1980s, the Global Navigation Satellite Systems (GNSS) have been effectively used in determining plate tectonic movement and other geodynamic phenomena. Over the last years, the monitoring of station coordinates located on the Earth’s surface has become a great interest. Determination of velocity fields produces the means of analysing intra- and inter-plate geodynamic interactivities and other crustal disturbances (Holden et al. 2017; Kierulf et al. 2021). Saria et al. (2013) carried out some geodynamic studies for Africa from the combined GPS and DORIS space geodetic solutions, and observed that the velocity on the stable Nubia fits to a single rigid plate model with a WRMS of 0.6 mm/year, that is consistent with the current uncertainty of geodetic measurements in the region. Investigation of GNSS-based monitoring of continental-wide variations in Africa (Nubia) and Arabia plate shows that there is little variation in rates of motion along the boundary, ranging from 5.4 ± 1 mm/year in the eastern Mediterranean to 4.5 ± 1 mm/year near Gibraltar (McClusky et al. 2003), hence, this study tends to focus on the determination of velocity field for Africa. This introduction is followed by Sect. 2 the methodology and processing strategies. Section 3 presents the results, and Sect. 4 conclusions and recommendations.
GNSS Data Collection and Processing
The GNSS data set used in this study includes 11 years of observations (2009– 2019) from GNSS sites where data are openly available (see Fig. 1). A total number of 145 GNSS sites were used and the data were obtained from TrigNet1 a network of continuously operating system base stations that are located in South Africa, from the UNAVCO archive2 and the AFREF archive.3 There are other GNSS network stations in Africa that are operating but unfortunately, could not be included due to data restriction. All openly available GNSS data used in this paper were processed; stations less than 3 years of observations were skipped. This is slightly above 2.5 years which is the minimum amount of time required to average out seasonal signals unrelated to the long term motions of interest in order to obtain a good velocity estimate (Blewitt and Lavallée 2002). There has been a rapid increase of GNSS stations in the years from 2004 to 2019 (see Fig. 2).
We analyse the GNSS data in PPP mode using the GFZ’s EPOS.P8 software, based on GFZ repro3 solution (Männel et al. 2020). Precise point positioning (PPP) method is a robust method that focused on the processing of measurements from stand-alone GNSS receivers to compute high accurate positions (Zumberge et al. 1997), and has become cost effective in achieving centimeterlevel accuracy. GNSS orbit modelling, satellite clocks and Earth Rotation Parameters (ERP) from GFZ repro3 were introduced apriori (Männel et al. 2021). We processed zero-differenced GPS observations using ionospherefree linear combination with a 5 min sampling rate, to estimate daily station coordinates and tropospheric delays with 1 h ZTD and 24 h troposphere gradients. Phase ambiguities were not re-solved but estimated. We applied models following the IERS 2010 Conventions (Petit and Luzum 2010) and repro3 setup.4 As the orbit products are provided in the repro3- specific reference frame, our coordinates are determined in this IGSR3 frame (Rebischung 2021). To ensure consistency, GNSS phase center corrections given in igsR3_2077.atx were applied.
These daily solutions were used to generate position time series, which we closely inspected to identify outliers, offsets, or discontinuities. Coordinate and data conversion were done based on the GeodeZYX toolbox (Sakic et al. 2019). Subsequently, we used the Sari software (Santamaría- Góm 2019), to model site positions as the sum of (1) linear term representing secular displacement (2) offsets caused by earthquakes, and other effects, mostly equipment changes and (3) periodic components. The model equation for each of the component (east, north, up) is given below
where a is the coordinate (initial position at reference epoch), b is the linear velocity (trend), c are the discontinuities, d and e are the annual amplitudes, t is the time epoch, GI is the binary operator equal to zero, if t is less than zero or equal to 1, if t is greater or equal to zero, respectively. Sites, especially those with frequent offsets, including, PRE1, PRE2, HRAO (all in South Africa), NAZR, DAFT (all in Ethiopia) showed too many outliers and offsets and were therefore excluded from the final solution.
Results and discussion
Raw Time Series, FUNC (Madeira Island, Portugal) and LSMH (Ladysmith, South African)
From the raw coordinate time series, in the north and east components of the two stations, a linear trend is observed with a pronounced positive slope which shows north-east motion of 27± 0.3 mm/ year. Moreover, it can be observed that the height (up) component is quite noisier than the horizontal components which are due to observation geometry. In order to model the station trajectories, we used Eq. (1) to estimate the linear trend, annual signals and discontinuities. The estimated linear trend and the residual coordinates are shown in Fig. 3 and Table 1.
As shown in Fig. 3, FUNC and LSMH move with 17–18 mm/year towards north. The east component shows a similar trend for both stations with a velocity of 15– 17 mm/year. We compared the velocity results computed using PPP solutions with the velocity results computed using UNAVCO plate motion calculator with respect to GSRM2.1 (Kreemer et al. 2014) (see Table 2), though there is a difference of 1.0–1.6 mm/year and 0.9–1.3 mm/year in the north and east direction, respectively, their difference is insignificant. For the vertical component their velocities are 0.6±0.2 mm/year and 0.4±0.2 mm/year, respectively. This slight motion could be from vertical uplift movements caused by atmo- spheric pressure variation and mass loading redistribution of non-tidal ocean loading and soil moisture (El-Fiky et al. 1997). The up component shows yearly variations with deterministic model (shown in red) containing harmonics, based on the leastsquares approach. We notice in the up components, periodic surface deformations of about 25 mm, which are not apparent in the north and east components. These surface deformations are believed to be due to a large influence of non-tidal loading especially hydrological loading (Männel et al. 2019; Liu et al. 2017). We compared our velocity estimates against the ITRF2014 and found only minor discrepancies of 1–0 mm/year and 0 to –0.1 mm/year in the North and the East direction, respectively.
Figure 4 shows detrended data of the two selected stations FUNC and LSMH. The Root Mean Squares (RMS) of the residuals, i.e. the observed minus the computed, are 4.4 mm, 8.1 mm, 8.6 mm and 2.2 mm, 6.7 mm, 7.4 mm for the north, east and up components, respectively. We observe in Table 1 that the RMS in the north component is smaller than that of the east components in both stations, and highest in the up components. This is related to (1) observation geometry and (2) that the ambiguities are not fixed (float solution), which is causing a larger RMS in the east component. In addition, considering both stations, we observed that the RMS of station FUNC is higher in all the components than that of station LSMH, which shows that station LSMH is more stable to that of the station FUNC. This is most probably related to the station monuments as FUNC is located at the terrace of an old building whereas station LSMH is located on a concrete block.
Figure 5 shows the horizontal velocity fields for the whole Africa. We grouped the horizontal and vertical velocity field estimates into different groups A, B, C, D and E as indicated in Figs. 5 and 6, according to their velocity pattern. From our observations, the estimated horizontal geodetic veloci- ties show completely the same pattern, thus indicating that African plate moves as rigid plate in north east direction with respect to the IGSR3 reference frame with velocity field of each group and their corresponding root mean square given Table 3.
The mean horizontal velocity for the overall block in north east direction is 27 ± 0.3 mm/year with average root mean square residuals for north, east and up components of 2.9 mm, 9.9 mm and 8.5 mm respectively. Looking at B (Tanzania) and E (Benin Republic), we observe that their horizontal velocities are the same which shows that the two blocks are moving in north east direction at the same rate. In addition, for group C (Kenya, Rwanda and Uganda) and group D (Ethiopia), their velocities stand out with a slight local velocity difference with respect to IGSR3 due to their location on the great valley rift (stratovolcano), as previous studies have shown that the African continent is undergoing continuous rifting along the East African Rift System (Ring 2014; Gaina et al. 2013). Considering group A (South Africa), stations KOKS (Kokstad), DRBN (Durban), STAN (Stanger) and GREY (Greytown), located in the KwaZulu Natal province exhibit different but significant vertical displacement of velocity values of +1.5 ± 0.2 mm/year, +1.7 ± 0.3 mm/year, +1.8 ± 0.3 mm/year and +1.6 ± 0.3 mm/year, respectively. Stations KOKS, DRBN and STAN all in Kwa-Zulu Natal show uplift, which could be due to seismically active zones (one lesser, one greater in linear extent) across the continent ocean boundary at high angle (Hartnady 1990). In group B (Tanzania), we observed a significant change which probably indicates an uplift vertical displacement of velocity field approximately ranging from –2 to +2 mm/ year; in agreement with Saria et al. (2013). As anticipated, uncertainties expeditiously decrease with time series length.
Euler Pole parameter estimation
We generated a rigid plate model by estimating plate rota- tions (Euler poles). Hence, we group the stations according to their location (Fig. 5), while testing the rigid plate assumption. We estimate the rotation rate vector for the Nubian and the Somalian plate and tested the significance relative to the IGSR3 interpretation using sites outside the deformation zones along the plate boundaries, and by excluding nearby redundant sites (Fig. 7). Stations NAZR, DABT and HERM were removed after outlier detection. Previous reports of Nubian and Somalian plate uses fewer sites, so we define a new subset of sites with a larger and better geographic distribution (Saria et al. 2013). The angular velocity of the Nubian plate with respect to IGSR3 (Table 4 and Fig. 7) is close to the recent estimate of Altamimi et al. (2017). The uncertainty associated with this new angular rotation of Nubia with respect to IGSR3 so far is the smallest, most likely because the solution presented in this study is based on a larger number of GNSS sites and longer observation time span.
Nevertheless, a significant limitation is the lack of dense, homogeneous continuous GNSS network over most of the Africa. With respect to stable part of Nubia, the residual velocities as given in Fig. 7, shows regions with significant deformation. It is expected that in the eastern part of the East African Rift, larger residuals are observed as this region contains various microplates (Wedmore et al. 2021). We also observed a deviation from the plate rigidity in stations RABT, IFR1, TETN in Morocco and MONG in Zambia with their residual velocities tended towards SSE at average velocities 1.4 mm/year and 0.9 mm/year respectively.
For the Somalian plate, we selected 55 GNSS stations to estimate site velocities as shown in (Fig. 1). We observed that stations in the volcanically active island Reunion (Fig. 7) have velocities that are agreeing with the rigid Somalian and could therefore be used to define its kinematics. Stations NEGE and ROBE (Ethiopia), located 15 km from the rift, and MTDK (Tanzania), located 100 km from the Tanzania Rift, are also agreeing with rigid Somalian.
In this study, we processed data of 145 stations from 2009 to 2019 with GFZ EPOS.P8 solution in PPP mode. These data sets were taken from a geodetic network precisely designed and surveyed to measure tectonic motion through the South African network, UNAVCO and AFREF. The resulting coordinates were used to determine the horizontal and vertical velocity fields with respect to IGSR3. The linear trends in the coordinate time series were estimated by fitting a trend to the data and estimate its velocity coefficients using the leastsquares principle. We observed that Africa is moving in north-east motion with respect to IGSR3 with the overall horizontal average velocity field of 27 ± 0.3 mm/year and with vertical uplift in Tanzania with velocity field ranging from −2 to +2 mm/year; other regions show no significant changes. Moreover, the present availability of geodetic sites in Africa is not even and the intra-plate deformation at regional or local scales with the current networks may not be detectable.
This study provides for the entire continent of Africa the position/velocity solution precisely expressed with reference frame IGSR3, and hence it will serve as a base in the contribution to the computation of the velocity field of Africa in the determination of the upcoming African Reference Frame AFREF and also gives a better understanding of the African plate tectonics, that appears to be lacking in earlier studies of the AFREF reports. Though much effort has been made on GNSS site distribution in Africa, most part of the African continent still remains undersampled. Effort to augment the geodetic infrastructure is under way, through link academic research projects, AFREF or in the level of surveying applications. Hence, the objective of this new data will help in the establishment and maintenance of a unified geodetic reference network for Africa which will serve as a fundamental basis for national reference networks that will fully be consistent and homogeneous with the global reference frame of the International Reference Frame (ITRF).
The authors would like to thank and express their gratitude to the South African Network (TrigNet), UNAVCO, AFREF, and IGS (Johnson et al. 2017) for making their GNSS data available.
Availability of data and materials
The data used to support the findings of this study are available on their website cited as footnote.
Conflict of interest The authors declare that they have no conflicts of interest.
Authors’ contributions Saturday Ehisemhen Usifoh downloaded the data, processed, analysed and wrote the manuscript. BM, PS, DJ, and HS verified the feasibility of the method, checked the processing, the analysis, the interpretation, and the discussion of the results. All authors joined in revising the manuscript and figures modification.
Code availability Not applicable.
Ethics approval and consent to participate Not applicable.
Consent for publication Not applicable.
Funding Not applicable.
1 http://data.unavco.org/archive/gnss/ rinex/obs: Date access 9th June, 2020.
2 http://afredata.org: Date access 25th August, 2020.
3 ftp://ftp.trigent.co.za: Date access 13th September, 2020.
4 acc.igs.org/repro3/repro3.html: Date access: 15th January, 2021.
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