GSeisRT: A Continental BDS/GNSS Point Positioning Engine for Wide-Area Seismic Monitoring in Real Time

Jianghui Geng; Kunlun Zhang; Shaoming Xin; Jiang Guo; David Mencin; Tan Wang; Sebastian Riquelme; Elisabetta D'Anastasio; Muhammad Al Kautsar

doi:10.1016/j.eng.2024.03.012

Engineering ›› 2025, Vol. 47 ›› Issue (4) :62 -75. DOI: 10.1016/j.eng.2024.03.012

Research Precise Positioning and Geoinformation Science—Article

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GSeisRT: A Continental BDS/GNSS Point Positioning Engine for Wide-Area Seismic Monitoring in Real Time

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Abstract

Precise coseismic displacements in earthquake/tsunamic early warning are necessary to characterize earthquakes in real time in order to enable decision-makers to issue alerts for public safety. Real-time global navigation satellite systems (GNSSs) have been a valuable tool in monitoring seismic motions, allowing permanent displacement computation to be unambiguously achieved. As a valuable tool presented to the seismic community, the GSeisRT software developed by Wuhan University (China) can realize multi-GNSS precise point positioning with ambiguity resolution (PPP-AR) and achieve centimeter-level to sub-centimeter-level precision in real time. While the stable maintenance of a global precise point positioning (PPP) service is challenging, this software is capable of estimating satellite clocks and phase biases in real time using a regional GNSS network. This capability makes GSeisRT especially suitable for proprietary GNSS networks and, more importantly, the highest possible positioning precision and reliability can be obtained. According to real-time results from the Network of the Americas, the mean root mean square (RMS) errors of kinematic PPP-AR over a 24 h span are as low as 1.2, 1.3, and 3.0 cm in the east, north, and up components, respectively. Within the few minutes that span a typical seismic event, a horizontal displacement precision of 4 mm can be achieved. The positioning precision of the GSeisRT regional PPP/PPP-AR is 30%–40% higher than that of the global PPP/PPP-AR. Since 2019, GSeisRT has successfully recorded the static, dynamic, and peak ground displacements for the 2020 Oaxaca, Mexico moment magnitude (Mw) 7.4 event; the 2020 Lone Pine, California Mw 5.8 event; and the 2021 Qinghai, China Mw 7.3 event in real time. The resulting immediate magnitude estimates have an error of around 0.1 only. The GSeisRT software is open to the scientific community and has been applied by the China Earthquake Networks Center, the EarthScope Consortium of the United States, the National Seismological Center of Chile, Institute of Geological and Nuclear Sciences Limited (GNS Science Te P $\bar{u}$ Ao) of New Zealand, and the Geospatial Information Agency of Indonesia.

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Keywords

Real-time / Precise point positioning / Multi global navigation satellite system / Seismic monitoring / Rapid earthquake response

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Jianghui Geng, Kunlun Zhang, Shaoming Xin, Jiang Guo, David Mencin, Tan Wang, Sebastian Riquelme, Elisabetta D'Anastasio, Muhammad Al Kautsar. GSeisRT: A Continental BDS/GNSS Point Positioning Engine for Wide-Area Seismic Monitoring in Real Time. Engineering, 2025, 47(4): 62-75 DOI:10.1016/j.eng.2024.03.012

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1. Introduction

Global navigation satellite system (GNSS) precise point positioning (PPP) has been increasingly applied to seismic monitoring [1], [2]. Coseismic displacements can be directly computed using a high-rate GNSS and leveraged for rapid and accurate magnitude determination, moment tensor calculation, and finite fault modeling, aiming at earthquake/tsunami early warning (EEW/TEW), especially for large events [3], [4], [5], [6], [7], [8]. PPP is essentially a global positioning technique using a single GNSS receiver and is quite suitable for seismic monitoring. While daily GNSS positioning precision can easily achieve the millimeter level, high-rate or kinematic positioning can benefit from the addition of Galileo and the BeiDou System (BDS), and thus be improved significantly in terms of displacement resolution [9], [10], [11]. Xu et al. [12] reported that a high-rate Global Positioning System (GPS) could reach millimeter-level precision over the few minutes spanning a typical earthquake duration [13]. Compared with GPS-only solutions, the precision of a high-rate multi-GNSS is generally higher by 30%–60%; more specifically, the root mean square (RMS) errors for horizontal components against truth benchmarks can be as low as a few millimeters, even in the case of a 24 h span [14], [15], [16]. In addition, integer ambiguity resolution can further improve the positioning precision in vibration detection, especially for the east component [17].

However, real-time PPP is still challenging in the case of time-critical high-precision seismic monitoring in the real world. From a technical perspective, real-time GNSS should have the capability to identify millimeter-level deformations in wide areas of up to the continental scale [18]. Large earthquake events often take place along long faults and devastate huge areas; for example, the 2002 Denali earthquake was associated with a surface rupture of about 340 km [19]. However, real-time scenarios are normally associated with relatively poor quality of satellite orbits and clocks, compared with post-processing products [20], [21], [22]. Even worse, global-network-derived satellite clock and phase bias products suffer from a more complicated error budget in comparison with a case with short baselines [23]. On the other hand, from an operational perspective, real-time GNSS is typically structured in a server/client manner, and thus is vulnerable once the server/client connection is down or interrupted. High-precision GNSS positioning requires correction streams (i.e., satellite orbits, clocks, and biases) computed by the server end using a remote or even global reference network. Any pronounced latency or discontinuity of the correction stream—which is almost inevitable, due to the global connections across disparate sources—degrades the timeliness of real-time positioning.

At present, most off-the-shelf real-time PPP engines are designed to ingest external or even third-party satellite products, which are usually subject to global networks streaming fiducial observations [24], [25]. As a result, a latency of up to several tens of seconds, or even repeated loss of satellite product streams, is observed in practice. One situation is the failure of computing satellite clocks by the server end, which is mostly attributed to frequent disconnection from a number of reference stations. This problem can be quite common for non-commercial real-time GNSS services aiming at public welfare, such as rapid geohazard response. Another situation is the relatively slow aggregation process of global data streams into the server end for satellite product computation. The disparate infrastructure for Internet connections from contributing institutions complicates this data gathering in real time.

In this study, we establish a more self-contained real-time PPP engine, named PRIDE GSeisRT, which is dedicated to seismic monitoring. In particular, GSeisRT ingests continental-scale network observations to compute satellite clock and phase bias products in real time, which are then disseminated to local stations to capture ground motions at a millimeter-level displacement resolution. GSeisRT is especially advantageous when applied to continental or national GNSS networks operated and governed by an official institution. This is because the reference network for satellite products and the local network data for seismic motions can be streamed from the same source, greatly facilitating data management and reducing both the latency and discontinuities of data connections. In this way, the critical timeliness for a rapid earthquake response can be satisfied as much as possible. It should be noted that GSeisRT does not estimate satellite orbits; instead, it fetches them from a third party, such as the International GNSS Service (IGS) [26], since a regional network cannot be used to estimate reliable orbits. Fortunately, IGS-predicted satellite orbit products cover the upcoming 24 h and are minimally affected by malfunction at the server end or product streaming. Current ultra-rapid orbits can achieve centimeter-level accuracy, which is sufficient to meet the accuracy demands of the GSeisRT server [27].

Since 2019, GSeisRT has been applied to a number of earthquake-prone areas in collaboration with EarthScope of the United States, which operates the Network of the Americas (NOTA, 980 stations); the China Earthquake Networks Center, which operates the Crustal Movement Observation Network of China (CMONOC, 260 stations); the National Seismological Center of the University of Chile (CSN, 50 stations); Institute of Geological and Nuclear Sciences Limited of New Zealand (GNS, 53 stations, 37 of which are operated on behalf of Toitū Te Whenua Land Information New Zealand); and the Geospatial Information Agency of Indonesia (Badan Informasi Geospasial BIG; 386 stations). This article is organized as follows: The next section introduces the GNSS satellite product estimation and PPP with ambiguity resolution (PPP-AR) in GSeisRT. Then, details about real-time data and experiments are described, before relevant results for all the above networks are displayed and analyzed. Finally, conclusions are drawn.

2. Methods

The GNSS observation equation from satellite

j

to receiver

i

on frequency

q

can be written as follows:

(1)

\{\begin{matrix} λ_{q} φ_{i, q}^{j} = ρ_{i}^{j} + c (t_{i} - t^{j}) + m_{i}^{j} T_{i} - g_{q}^{2} I_{i}^{j} + λ_{q} N_{i, q}^{j} \\ P_{i, q}^{j} = ρ_{i}^{j} + c (t_{i} - t^{j}) + m_{i}^{j} T_{i} + g_{q}^{2} I_{i}^{j} \end{matrix}

where

φ_{i, q}^{j}

and

P_{i, q}^{j}

are the carrier-phase and pseudorange observations of frequency value

f_{q}

, respectively;

λ_{q}

(q = 1, 2 \dots)

is the wavelength of the corresponding signal;

ρ_{i}^{j}

is the geometric distance from satellite

j

to receiver

i

;

c

is the speed of light in a vacuum;

t_{i}

and

t^{j}

are the receiver and satellite clock errors, respectively;

m_{i}^{j}

is the mapping function to project the zenith tropospheric delay

T_{i}

onto the line-of-sight direction;

g_{q} = \frac{f_{1}}{f_{q}}

is a scaling factor for the ionospheric delay

I_{i}^{j}

f_{1}

and

f_{q}

are the frequency values of the corresponding signals; and

N_{i, q}^{j}

is the ambiguity term. It should be noted that hardware delays, multipath effects, and measurement noise terms are all ignored for brevity.

The dual-frequency ionosphere-free linear combination is used in GSeisRT:

(2)

\{\begin{matrix} \begin{matrix} L_{i, 0}^{j} = \frac{g_{2}^{2}}{g_{2}^{2} - 1} λ_{1} φ_{i, 1}^{j} - \frac{1}{g_{2}^{2} - 1} λ_{2} φ_{i, 2}^{j} = ρ_{i}^{j} + c (t_{i} - t^{j}) + m_{i}^{j} T_{i} + λ_{1} N_{i, 0}^{j} \end{matrix} \\ \begin{matrix} P_{i, 0}^{j} = \frac{g_{2}^{2}}{g_{2}^{2} - 1} P_{i, 1}^{j} - \frac{1}{g_{2}^{2} - 1} P_{i, 2}^{j} = ρ_{i}^{j} + c (t_{i} - t^{j}) + m_{i}^{j} T_{i} \end{matrix} \end{matrix}

where “0” denotes the ionosphere-free combination and “

L

” denotes the carrier-phase observation in meters.

2.1. Satellite clock determination using the inter-epoch differenced carrier phase

Satellite clocks are normally estimated using undifferenced observations. While this approach works well with respect to a global network, re-initializations of satellite clock estimates lasting a few hours would take place repeatedly in the case of a regional network, since satellites cannot be tracked continuously. The satellite clocks in the initialization phase have low precision and cannot ensure a millimeter-level displacement detection. Even worse, a satellite would pass a regional network for a few hours at most, leaving insufficient time for the clock estimates to converge to high precision. Moreover, undifferenced network analysis requires a huge number of ambiguities to be estimated simultaneously, which is a computationally intensive task [28]. As a result, the sampling rate of real-time satellite clock products at present is only 5–10 s to alleviate the pressure on computational resources.

GSeisRT therefore implements the approach presented in Ref. [28], where inter-epoch differenced carrier-phase observations without ambiguities are used in addition to an undifferenced pseudorange to estimate high-rate satellite clocks; that is:

(3)

\{\begin{matrix} Δ L_{i, 0}^{j} (k) = c {Δ t}_{i} (k) - c Δ t^{j} (k) + Δ m_{i}^{j} (k) T_{i} (k) \\ P_{i, 0}^{j} (k) = ρ_{i}^{j} (k) + c t_{i} (k) - c t^{j} (k) + m_{i}^{j} (k) T_{i} (k) \\ t^{j} (k) = t^{j} (0) + \sum_{n = 1}^{k} Δ t^{j} (n) \end{matrix}

where

k

denotes the epoch index,

Δ

denotes an inter-epoch differencing operation,

Δ t^{j} (k)

is the satellite clock variation of epoch

k

relative to epoch

(k - 1)

t^{j} (0)

is an absolute clock estimate at epoch “0,” and n denotes the index of summation, ranging from 1 to k. Thus, the satellite clock at epoch

k

(i.e.,

t^{j} (k)

) is achieved by adding the clock variations across epochs 1–

k

t^{j} (0)

. It is worth mentioning that

t^{j} (0)

is governed merely by the pseudorange in Eq. (3) and might consequently be compromised in terms of precision. Fortunately, the

t^{j} (0)

estimates can be stabilized (i.e., achieve convergence) within a few tens of minutes after satellite

j

’s rise with respect to a regional network, and the resultant clock estimates

t^{j} (k)

for satellite

j

can then immediately contribute to PPP. In this case, the typical initialization period for satellite clock determination can be reduced from several hours in the undifferenced processing mode to a few tens of minutes in the inter-epoch differencing mode. In addition, the satellite clock determination based on Eq. (3) is much faster than that based on the undifferenced carrier phase, and we are able to estimate 1 Hz clock products in this case [28].

2.2. Satellite observable-specific phase bias determination

Phase biases are necessary to enable PPP-AR. GSeisRT first estimates wide-lane and narrow-lane uncalibrated phase delays (UPDs) for GPS, Galileo, and BDS using a reference network by fixing known satellite orbits and clocks [29]; it then converts them into observable-specific phase bias (phase OSBs). We use the Melbourne–Wübbena combination [30], [31]

(4)

λ_{w} N_{i, w}^{j} = \frac{g_{2}}{g_{2} - 1} λ_{1} φ_{i, 1}^{j} - \frac{1}{g_{2} - 1} λ_{2} φ_{i, 2}^{j} - (\frac{g_{2}}{g_{2} + 1} P_{i, 1}^{j} + \frac{1}{g_{2} + 1} P_{i, 2}^{j})

to compute wide-lane ambiguities

N_{i, w}^{j}

, where λ_w represents the wavelength of wide-lane combination observations; and wide-lane UPDs (

b_{i, w}^{j}

) are derived from

(5)

b_{i, w}^{j} = Frac (N_{i, w}^{j})

where

F r a c (\cdot)

is a function to extract the fractional part of ambiguity estimates. It should be noted that the UPD for a reference station can be assigned an arbitrary value (e.g., 0) to identify pseudo-absolute satellite UPDs, as denoted by

b_{w}^{j}

With

b_{i, w}^{j}

, GSeisRT is able to fix

N_{i, w}^{j}

to integers denoted as

{\hat{N}}_{i, w}^{j}

. Then, the corresponding narrow-lane ambiguity can be computed using the following equation:

(6)

N_{i, n}^{j} = \frac{g_{2} + 1}{g_{2}} N_{i, 0}^{j} - \frac{1}{g_{2} - 1} {\hat{N}}_{i, w}^{j}

Similar to Eq. (5), narrow-lane UPDs can be computed as follows:

(7)

b_{i, n}^{j} = F r a c (N_{i, n}^{j})

and the satellite narrow-lane UPDs are

b_{n}^{j}

. Normally, a number of reference stations are needed to achieve high-precision UPD estimates; GSeisRT empirically sets this number to 10.

Once both wide-lane and narrow-lane UPDs are obtained, the phase OSBs can be generated using the following [32]:

(8)

[\begin{matrix} b_{1}^{j} \\ b_{2}^{j} \end{matrix}] = [\begin{matrix} - \frac{1}{c g_{1}} & \frac{g_{1} + 1}{c g_{1}} \\ - \frac{g_{1}}{c} & \frac{g_{1} + 1}{c} \end{matrix}] [\begin{matrix} {λ_{w} b}_{w}^{j} + \frac{g_{1} d_{1}^{j} + d_{2}^{j}}{g_{1} + 1} \\ λ_{n} b_{n}^{j} \end{matrix}]

where the phase OSBs

b_{1}^{j}

and

b_{2}^{j}

have the unit of nanoseconds following the Radio Technology Committee of Marine (RTCM) standard. The code OSBs

d_{1}^{j}

and

d_{2}^{j}

are presumed to be already known in the unit of length and are thus directly corrected from

{λ_{w} b}_{w}^{j}

. GSeisRT computes phase OSBs at each epoch on account of their temporal instabilities in real-time scenarios. Of particular note, GSeisRT is also capable of resolving multifrequency ambiguities; for the relevant phase OSB determination, interested readers can refer to Ref. [16].

2.3. PPP-AR

The OSB products can be directly corrected from raw pseudorange and carrier-phase observations to recover the integer property of undifferenced ambiguities in PPP. However, in real-time practice, the phase OSB products for some satellites might be missing from time to time, due in part to an insufficient number of reference stations (i.e., less than 10). The aftermath is that such epochs must be discarded in order to avoid inconsistency in calibrating OSBs on the raw observations, even though ambiguity-float solutions can still be achieved at these epochs. Instead, GSeisRT chooses to reconstruct UPDs from OSBs and then calibrate UPDs on PPP ambiguities without affecting the raw observation processing. In this manner, ambiguity-float solutions can still be maintained in the main filter, even if phase OSBs are missing for some epochs.

Similar to the UPD determination, PPP-AR is divided into two phases: wide-lane and narrow-lane ambiguity fixing. First, wide-lane ambiguity resolution is attempted using the Melbourne–Wübbena combination and wide-lane UPDs. A rounding operation is usually adopted to identify the integer candidates. Once the wide-lane ambiguities are fixed successfully, the narrow-lane ambiguities can be recovered using Eq. (6), and their integer-cycle resolution can be attempted by correcting for narrow-lane UPDs [33].

GSeisRT employs two strategies to resolve narrow-lane ambiguities. One strategy is the least-square ambiguity decorrelation adjustment (LAMBDA) method [34]. Real-valued ambiguities and their variance-covariance matrix are conveyed into LAMBDA to search for the best integer candidates. The other strategy is the best integer equivariant (BIE) method [35], which is optimal in the aspect of the minimum mean squared error [36]. Once the integer candidates are obtained, ambiguity-fixed solutions can be computed by adding integer constraints as properly weighted pseudo-observations.

3. The structure of GSeisRT

GSeisRT has two versions, GSeisRT-Lite and GSeisRT-Pro, to satisfy different user requirements (Fig. 1). GSeisRT-Lite, which is actually the client end only, performs real-time PPP. It targets those users that cannot support satellite clock and phase bias estimations due to network scale limitations (e.g., all stations within earthquake-prone areas). Conversely, GSeisRT-Pro is the full version of GSeisRT; it is capable of estimating satellite clocks and phase biases and delivering them to clients to carry out real-time PPP. GSeisRT-Pro is suitable for users that have a large enough network extent to enable satellite clock determination. Regarding the required size of such a regional network, in our experiments, both the NOTA network and the CMONOC network spanning several thousand kilometers supported the deployment of GSeisRT server processing. Although a regional network of any extent can theoretically warrant GSeisRT server processing, there should be reference stations outside earthquake-prone areas.

Fig. 1 shows that GSeisRT consists of the server and the client ends. A data caster is needed to manage real-time streams through the Networked Transport of RTCM via Internet Protocol (NTRIP) [37]. The server end includes the real-time precise satellite clock and phase bias determination. The satellite clocks also contribute to estimating satellite phase biases. These satellite products, along with the IGS-predicted satellite orbits, are then encoded in an RTCM state space representation (SSR) format and sent to the caster.

The GSeisRT client takes on the role of real-time PPP. It acquires the SSR streams from a dedicated caster established by the GSeisRT server end or a third party such as the IGS, and then decodes them into satellite orbits, clocks, and phase biases. Users should run one client for each station, and all clients are independent.

4. Real-time data

GSeisRT has been applied to NOTA, CMONOC, CSN, GNS, and BIG. For brevity, we mainly focus on the real-time PPP/PPP-AR experiments carried out using GSeisRT-Pro from April 30 to May 9 in 2023, based on NOTA’s 600 representative stations, although summarized results from other networks will also be shown briefly. We did not process all 980 stations, because some were down, and the computational resources were limited. Fig. 2 shows the 90 stations ingested into the GSeisRT server end (blue solid triangles) as well as another 603 for the client end (red solid circles). The stations for the server end should be far from earthquake-prone areas. Details about the data-processing strategies are provided in Table 1 [38], [39], [40]. Some stations (about 10%) only have GPS, rather than multi-GNSS, data. It should be noted that some stations’ real-time data might be missing during our experiment due to network downtime. We thus only collected the results for stations with complete real-time GNSS data.

5. Results

5.1. Latency for different SSR streams

We compare the latency between the IGS SSR and the GSeisRT SSR under normal computing and network environments, which are listed in Table 2. Such latencies are mainly due to network transmission delays. The configurations for the SSR are listed in Table 3. Fig. 3 illustrates the SSR latencies for three products from December 3 to 10, 2023, as a typical example. The light green, light blue, and dark blue dots denote the respective latencies of GSeisRT, Wuhan University (WHU), and Centre National d'Études Spatiales (CNES) SSRs. It can be seen that the latencies in the receiving SSR at the client end are generally stable within a week. For the GSeisRT SSR, the mean latency is around 6.36 s, mainly thanks to a “local” configuration of data streaming under the management of EarthScope within North America. There are still outlier dots located above 10 s, which are attributed to the occasional network downtime at a certain number of epochs. There are also some scattered dots at the boundary of the day, which are attributed to scheduled tasks set on the GSeisRT SSR server, leading to periodic fluctuations in the computational load. In the case of the IGS SSR products, the mean latencies for WHU and CNES are up to 20.20 and 19.89 s, respectively, three times longer than the GSeisRT latency. This can be imputed to the data-streaming configurations aimed at global users by the IGS. A long latency means that SSR users must predict satellite clocks and phase biases to match the epoch of the observations to be processed, which will degrade the positioning precision, as the inconsistency between the SSR products and the GNSS observations is compromised. The longer the latency, the worse the positioning precision. In this sense, the “local” setting of data streaming by GSeisRT is more favorable for time-critical seismic monitoring.

In the real-time positioning experiments in the remainder of this article, however, we precisely match the time tags of SSR products and user observations without predicting satellite clocks or phase biases. In this manner, we can evaluate the true precisions of different SSR products for a fair comparison.

5.2. Real-time multi-GNSS satellite clock and phase bias

Fig. 4 shows the standard deviations of the GSeisRT GPS/BDS/GLONASS/Galileo satellite clocks on April 30, 2023. The quadric difference approach is used to evaluate the satellite clock product [41]. The Wuhan University Multi-GNSS experiment (WUM) final satellite clock products are used as a reference. It can be seen that almost all the standard deviations are less than 0.20 ns, and the mean values are all around 0.10 ns, both of which are comparable to the typical statistics of real-time IGS clocks [20]. Over the entire experiment period (from April 30 to May 9, 2023), the GPS, GLONASS, Galileo, and BDS satellite clock standard deviations against the WUM final products are 0.09, 0.08, 0.10, and 0.10 ns, respectively. It is worth mentioning that the rise and fall of satellites with respect to a regional network result in poor clock estimates at low elevations. To be specific, when the elevation of a satellite is low (e.g., less than 10°), few stations are able to observe the satellite; moreover, its observation quality is not as good as that at a high elevation due to more pronounced multipath effects and atmospheric delays. As a result, the satellite clock estimate

t^{j} (0)

in Eq. (3) during its initialization phase can be biased by up to a few nanoseconds. Fortunately, such clock biases can be absorbed by carrier-phase ambiguities in PPP without impairing the positioning precision.

Fig. 5 shows the GPS/Galileo/BDS wide-lane and narrow-lane phase biases or UPDs on April 30, 2023. The maximum and minimum standard deviations of the phase bias variations across all satellites are plotted within each panel. Due to the unique signal modulation (frequency division multiple access (FDMA)) and the existence of inter-frequency phase biases (IFPBs) [42], GSeisRT does not estimate GLONASS satellite phase biases. For wide-lane phase biases, the maximum standard deviation is not greater than 0.10 cycles. The mean standard deviations for all GNSS are less than 0.03 cycles, showing good temporal stability. In contrast, the maximum standard deviation of narrow-lane phase biases can be up to 0.134 cycles, and the mean for all GNSS reaches 0.06 cycles, which manifests larger temporal instability compared with wide-lane phase biases. Real-time narrow-lane phase biases usually experience a convergence phase due to satellite rise with respect to a regional network [43]. During this period, satellite elevations are low, and their observations are down-weighted, impairing the precision of phase bias estimates. In addition, BDS has worse phase bias estimates than GPS and Galileo, since fewer NOTA stations have BDS data.

5.3. Real-time PPP and PPP-AR

To quantify the precision of GSeisRT kinematic positions, we computed their RMS errors against the precise NOTA coordinates provided by EarthScope. For CMONOC and CSN, which are also processed using GSeisRT-Pro, we used the coordinates provided by the Nevada Geodetic Laboratory or computed daily static positions as truth benchmarks. For completeness, the CMONOC stations used for the satellite clock and phase bias determination are from the north–eastern, south–eastern, and north–western parts of China, while those for CSN are from Argentinean national GNSS network [44].

Fig. 6 shows the GSeisRT positioning results of two typical stations, P358 and P049, for April 30, 2023. P358 has multi-GNSS (GPS/BDS/GLONASS/Galileo), while P049 has only GPS observations. In the case of real-time PPP solutions (red curves), the RMS errors in the horizontal components for both stations are less than 2 cm, and the horizontal RMS of P358 is even below 1 cm, which is illustrated by the slimmer time series of P358 compared with P049. Over the whole day, discernible fluctuations are present in the red curves, especially for the GPS-only station, P049. In contrast, after ambiguity resolution (blue curves), the time series of the positioning errors are more stable, which is clearer in the case of station P049. Both stations’ RMS errors in the horizontal components drop by 30%–70% in contrast to the ambiguity-float solutions, and P358 still has lower noise than P049. The bottom panels of Fig. 6 show that station P358 has more than 25 satellites, on average, at each epoch, while P049 has only 8.7, which explains the advantages of multi-GNSS in terms of positioning precision [23].

Although the statistics in Fig. 6 agree with the established results in the open literature, caution is necessary: multi-GNSS versus GPS-only might not be the only factor explaining why station P358 has lower noise than P049, since the two stations have differing observation environments and instruments. A more rigorous experiment would be to run two parallel PPP computations at station P358, where one ingests multi-GNSS data and the other GPS-only, as designed by Ref. [9]. However, such an experimental design was difficult to consider in the operational real-time processing for NOTA’s 600 stations. Despite this issue, we believe that aggregating statistics from a good number of stations will be more convincing than Fig. 6.

Moreover, we investigate the convergence time of GSeisRT PPP and the time to first fix (TTFF) of PPP-AR by dividing the data into hourly pieces in real-time experiments. It is notable that a full convergence or successful fix in this study is achieved only when the horizontal and vertical components remain at an error of less than 10 and 15 cm, respectively, for 10 min. Fig. 7 illustrates the convergence performance at three typical stations. These three stations are from different regional GNSS networks—CMONOC, NOTA, and CSN. It can be seen that the positioning with more satellites exhibits improved precision at the beginning of the processing and thus shows accelerated convergence. The PPP at P622 achieves convergence within about 10 min, and the solution of PPP-AR only needs about 5 min to achieve a successful fix. PPP-AR at stations AHAQ and CURR can achieve a successful fix within less than 20 min. In addition, a significant improvement is found in the east component after ambiguity resolution. However, there are some outlier epochs due to incorrect ambiguity resolution during the convergence phases. PPP without ambiguity resolution can usually provide a more continuous and smooth time series relative to PPP-AR, especially in the case of incorrect ambiguity resolution. Table 4 exhibits the mean convergence time of the PPP and TTFF of PPP-AR with respect to the satellite number. It can be seen that introducing both ambiguity resolution and more satellites accelerates the convergence significantly. The mean convergence time of the PPP and TTFF of real-time PPP-AR are 16.4 and 11.1 min, respectively.

Table 5 shows the mean RMS errors for the east, north, and up components of NOTA’s 82 GPS-only and 521 multi-GNSS (i.e., any two or more of GPS/BDS/GLONASS/Galileo) stations over all days, and Fig. 8 shows the distribution of the RMS errors at all of NOTA’s stations. Overall, PPP-AR shows smaller RMS errors irrespective of the number of satellites. On average, the mean RMS errors over all stations are reduced from 2.2, 1.7, and 3.4 cm to 1.2, 1.3, and 3.0 cm for the east, north, and up components, respectively, suggesting improvements of 45%, 24%, and 12%. The mean RMS errors for GPS-only PPP-AR in the three coordinate components are 1.4, 1.4, and 3.2 cm. Regarding multi-GNSS stations, the mean RMS errors for PPP-AR reach 1.2, 1.3, and 2.9 cm, showing an appreciable improvement of 14%, 7%, and 9%, respectively, compared with GPS-only stations. These statistics reinforce the fact that more satellites result in improved satellite geometry and more redundant observations.

In addition to RMS error, absolute point accuracy is an important indicator, as it reflects positioning reliability. Table 6 presents the mean point errors at the 50% and 95% percentile for the east, north, and up components of 82 GPS-only and 521 multi-GNSS stations in the NOTA network, spanning all days. The results indicate that, at the 50% percentile, multi-GNSS outperforms GPS-only in PPP, suggesting improvements of 27% and 14% for the east and up components, respectively. However, there is little difference for PPP-AR. At the 95% percentile, regardless of ambiguity resolution, multi-GNSS always exhibits significant enhancements over GPS-only, demonstrating more stable and reliable positions. Overall, with ambiguity resolution, GSeisRT can provide reliable positioning services with 95% of three-dimensional (3D) absolute errors smaller than 2.2, 2.4, and 5.5 cm over all stations.

Fig. 9 shows the distribution of the RMS errors of all stations in the east, north, and up components for PPP and PPP-AR. The statistics for CMONOC and CSN are also plotted for comparison. Regarding the ambiguity-float solutions (red open bars) for NOTA, about 50% of horizontal RMS errors are less than 2 cm, while 40% are less than 3 cm for the vertical. Once ambiguity fixing is enabled (blue solid bars), the two percentages improve to 80% and 60%, respectively. It is clear that the bars close to zero become much taller for the PPP-AR solutions compared with their PPP counterparts, especially for the horizontal components. A comparable performance can be achieved in the case of CMONOC, where the horizontal RMS errors below 2 cm account for 80% and the vertical below 3 cm account for 45% after PPP-AR. CSN’s performance seems worse compared with those of NOTA and CMONOC, largely due to its real-time data quality, but slight amelioration can still be perceived, achieved by ambiguity fixing. Overall, ambiguity fixing enabled within continental networks leads to appreciable improvements of up to 45% in terms of positioning precision.

To obtain a complete assessment of the real-time GNSS displacement noise on various periods, we computed the displacement “wander,” which is the RMS of the displacements between any two epochs of positions distanced at a particular time interval [45]. This is an alternative to quantify the noise level over a range of periods. More specifically, the drift

D (τ)

for an interval

τ

is computed as follows:

(9)

D (τ) = \sqrt{\frac{\sum_{n (τ)} {(x (k + τ) - x (k))}^{2}}{n (τ)}}

where

n (τ)

denotes the number of data pairs with an interval

τ

, and

x (k)

denotes the displacement at epoch

k

Accordingly, Fig. 10 shows the mean displacement wander over all GPS-only and multi-GNSS stations in NOTA on all days. Since ground motion induced by significant earthquakes can last up to several minutes, the displacement wanders are computed for the time intervals of 1 s to 1 h only. It can be seen from both panels of Fig. 10 that—regardless of whether ambiguity fixing is enabled or not—the wanders of multi-GNSS solutions in horizontal components are always 1–3 mm smaller than those of GPS-only solutions over all periods from 1 s to 1 h, and are 3–5 mm smaller for the vertical, agreeing with the results presented by Geng et al. [9]. More specifically, over the periods shorter than 100 s, all coordinate components have comparable displacement wanders, irrespective of ambiguity fixing: GPS-only solutions have wanders of about 5–6 mm in the horizontal components and 12 mm in the vertical, while these are about 3–4 and 8 mm for the multi-GNSS solutions. This finding means that ambiguity fixing does not in fact significantly improve the displacement precision over short periods. In contrast, over periods longer than 2000 s, the PPP-AR solutions have smaller displacement wanders than their PPP counterparts. The improvement is up to 7 mm at a period of 3600 s in the case of GPS-only solutions, but declines to 3 mm when multi-GNSS observations are used. However, the fact that ambiguity fixing contributes more to improving displacement resolution over long periods is still significant, as some slow ground motions such as very early postseismic deformations and storm surge loading events can potentially be more identifiable in real time [46], [47].

5.4. A comparison between the IGS and GSeisRT SSR in driving GSeisRT

We used the IGS-CNES SSR, a global real-time product, to drive six GSeisRT clients (i.e., P030, P118, P122, P358, P682, and P707) and undertook a comparison with the GSeisRT SSR. Fig. 11 thus shows the results of a representative station P030 in NOTA for April 30, 2023 where both PPP (red curves) and PPP-AR (blue curves) solutions are plotted. The bottom panels show that both SSR products are able to ensure that about 22 satellites are processed on average. However, the GSeisRT SSR products lead to higher positioning precision than the IGS SSR: the horizontal positioning RMS errors are reduced by about 50% for ambiguity-float solutions versus up to 70% for ambiguity-fixed solutions. Although this advantageous result might be attributed in part to the software consistency between the GSeisRT server and client ends, we believe that the higher sampling rate (i.e., 1 against 5 s), the steadier server/client communication, and the regional adaptability of the GSeisRT SSR products also play important roles in explaining the better result of GSeisRT. Moreover, both SSRs are able to enable ambiguity fixing. While the GSeisRT SSR achieves an RMS error reduction of about 62%, 11%, and 25% for the east, north, and up components, respectively, PPP-AR based on the CNES SSR seems unstable, although marginal precision improvements can be recognized. This result reveals that globally applicable satellite phase biases cannot easily and steadily reach high precision and reliability in real time at the moment.

Table 7 further shows the mean positioning RMS errors at all six stations on all days based on the IGS-CNES SSR and GSeisRT SSR products. Overall, the global SSR products represented by IGS-CNES enable more satellites to contribute to positioning than the regional SSR products provided by GSeisRT. This is because the low-elevation satellites with respect to NOTA have been removed from GSeisRT. However, regardless of whether ambiguities are fixed to integers or not, the GSeisRT SSR always leads to RMS errors that are 30%–45% and over 40% smaller than those of IGS-CNES SSR in the horizontal and vertical components, respectively. Although such an inferiority of the IGS-CNES SSR is mostly related to the streaming instability imputed to its global applicability, we should emphasize that a regional self-contained real-time high-precision GNSS service is preferable for time-critical applications such as seismic monitoring.

6. Earthquake events captured by GSeisRT in real time

In the years of real-time operation on NOTA and CMONOC since 2019, several seismic events have been successfully captured by GSeisRT, including the June 23, 2020 Oaxaca, Mexico moment magnitude (Mw) 7.4 event; the June 24, 2020 Lone Pine, California Mw 5.8 event; and the May 21, 2021 Maduo, Qinghai Mw 7.3 event. The first GNSS stations to record the ground motions produced by each of these events were OXUM station of NOTA, P466 station of NOTA, and QHMD station of CMONOC, respectively. We used the epicenters published by the United States Geological Survey (USGS) to calculate their epicentral distances of 58, 17, and 40 km. Following Melgar et al. [48], we further identified the peak ground displacements (PGDs) from the three stations’ displacement recordings to compute the earthquake magnitudes using a scaling law [4].

Fig. 12 shows the coseismic displacements in the east, north, and up components at the three GNSS stations in the left panels and the resulting PGD magnitudes in the right panels as a function of time after the earthquake origin time. The dashed vertical lines in the left panels denote the origin time, and those in the right panels denote the epoch when the final PGDs were obtained. As expected, GSeisRT was able to measure permanent displacements, which is the most outstanding advantage over inertial seismic sensors. From the right panels, PGDs of 17, 9, and 32 s are obtained after the onset of the three events, and the earthquake magnitudes converge to 7.31, 5.73, and 7.17, which are quite close to the USGS estimates, with minor errors of around 0.1.

7. Discussion

All the results presented above are based on the GSeisRT-Pro version, where a server end is established to compute regional satellite clocks and phase biases. This version requires users to have a large enough network extending beyond earthquake-prone areas to ensure stable reference stations during seismic events. Obviously, this precondition cannot be satisfied by all users, such as the GNS and BIG GNSS networks. Therefore, GSeisRT provides a light version, GSeisRT-Lite, which is actually the client end, to facilitate users’ implementation of real-time PPP-AR using IGS SSR products. At the moment, only the IGS-CNES and IGS-WHU analysis centers provide phase bias products (Table 3) [49], [50].

We applied the two SSR products to the GNS and BIG stations, collected real-time positioning results, and computed the RMS errors similar to Fig. 9 over all days. Fig. 13 thus shows the distribution of positioning RMS errors at all stations in the three coordinate components for PPP-AR. Overall, the WHU SSR leads to smaller RMS errors than the CNES SSR. More specifically, the GNS RMS errors based on the WHU SSR are roughly 50%, 57%, and 33% smaller than those based on the CNES SSR, while these percentages are 23%, 18%, and 12% for the BIG network. Moreover, the GNS solutions with horizontal RMS errors of less than 2 cm account for about 80% based on WHU SSR. In contrast, this percentage declines to less than 10% in the case of CNES SSR. Again, we believe that the better performance of WHU SSR is partly due to the high compatibility of the GNSS software packages developed at WHU.

In addition, GSeisRT can realize the real-time integration of collocated GNSS/accelerometer data. We have embedded this function into an instrument called SMAG2000 [51], [52]. Accelerometer data have a higher sampling rate (e.g., > 100 Hz) and lower noise compared with high-rate GNSS. GNSS/accelerometer data fusion can achieve even higher displacement precision over a broad frequency band [53].

8. Conclusions and outlook

This study introduced a continental GNSS point positioning engine, GSeisRT, for wide-area seismic monitoring in real time. GSeisRT comprises a server end and a client end. The server end is capable of generating satellite clock and phase bias streams using a regional GNSS network, while the client end realizes multi-GNSS PPP/PPP-AR to capture ground motions with centimeter- to sub-centimeter-level precision in real time.

Based on real-time experiments over 603 NOTA stations, the GSeisRT SSR has 2–3 times shorter latency than the IGS SSR, thereby better satisfying the time-critical requirements of seismic monitoring. The mean positioning precisions of PPP-AR over a 24 h span can reach 1.2, 1.3, and 3.0 cm in the east, north, and up components, respectively. For a 100 s period, which would span a typical seismic event, a displacement precision of about 4 and 8 mm can be achieved in the horizontal and vertical components, respectively, when multi-GNSS observations are applied. Moreover, the positioning precision based on the GSeisRT regional SSR products are 30%–40% higher than that based on the IGS global SSR products.

Since 2019, GSeisRT installed for NOTA and CMONOC has successfully captured the full displacement waveforms in a number of seismic events. We can then compute the earthquake magnitudes with an error of around 0.1 for Mw 5.8–7.4 events immediately after the PGDs are obtained. The GSeisRT software is free and open to the scientific community.

CRediT authorship contribution statement

Jianghui Geng: Conceptualization, Project administration, Methodology, and Software; Kunlun Zhang and Shaoming Xin: Writing original draft, Data curation, Investigation, and Validation; Jiang Guo: Resources; David Mencin, Tan Wang, Sebastian Riquelme, Elisabetta D'Anastasio, and Muhammad Al Kautsar: Writing review and editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is funded by National Science Foundation of China (42025401) and National Key Research and Development Program of China (2022YFB3903800). We thank CMONOC, NOTA, and the Chilean GNSS Network for the real-time data. We thank the collaboration with China Earthquake Administration, EarthScope, CSN, GNS, and BIG. We thank the IGS for its high-quality satellite products and casters to stream our products. We acknowledge the New Zealand GeoNet Programme and its sponsors Earthquake Commission (EQC), GNS Science, Land Information New Zealand (LINZ), National Emergency Management Agency (NEMA), and the Ministry of Business, Innovation and Employment (MBIE) for providing data used in this study.

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Abstract

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1. Introduction

2. Methods

2.1. Satellite clock determination using the inter-epoch differenced carrier phase

2.2. Satellite observable-specific phase bias determination

2.3. PPP-AR

3. The structure of GSeisRT

4. Real-time data

5. Results

5.1. Latency for different SSR streams

5.2. Real-time multi-GNSS satellite clock and phase bias

5.3. Real-time PPP and PPP-AR

5.4. A comparison between the IGS and GSeisRT SSR in driving GSeisRT

6. Earthquake events captured by GSeisRT in real time

7. Discussion

8. Conclusions and outlook

CRediT authorship contribution statement

Declaration of competing interest

Acknowledgments

References

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