Conference Agenda

Mine operational safety is one aspect of the operational continuity of a mining area. One aspect of concern in mining operations is land subsidence in the mining area. Observations regarding land subsidence have shown progress with the use of radar-based satellite data such as synthetic aperture radar (SAR). The use of SAR data is one of the concerns with superior visibility and shorter revisit times. In the mining industry, the use of InSAR can focus on the impact of land subsidence due to underground mining. subsidence can have a significant impact on the environment, infrastructure and the surrounding area, increasing the need for accurate and continuous monitoring. In addition, the implication of the short visit time on the satellite allows more data to be collected from a time series observation. This prompted us to develop an InSAR-based time-series analysis method that is able to extract more reliable information. The development of time-series methods is also increasingly diverse by maximizing the potential of distributed scatterers (DS) as a companion to persistent scatterers (PS). DS contribution can be used with PS in analyzing deformation changes in the observation time series. In addition, the development of DS and PS combinations in observation points requires an efficient and reliable method to extract post-process deformation.

In this study, we used the imrpovmed combined scatterers with optimized point scatters (ICOPS) method to analyze soil surface changes using time series InSAR. The ICOPS is the development of the InsAR time-series method based on a combination of PS/DS with additional post-process to improve quality and reliability. The increase in spatial coverage is achieved by exploiting distributed scatterrs (DS) as a complement to persistent scatterres. In the process, distributed scatterers candidate (DSC) is generated by evaluating homogeneous pixels based on the FaSHPS method, which provides reliable results with the advantages of clustered pixels. To obtain a quality DSS that can be combined with PS, we evaluate the consistency of the available data based on spatial and temporal coherence. Coherence provides information on the stability of the phase within the observation period which is an important element in measurement. After the DS and PS are obtained, the unwrap process is carried out using the minimum cost flow (MCF) method on the DInSAR data stack. The time series is measured using the Singular Variable Decomposition (SVD) method as a solution to solving problems in surface deformation. In that process, topography correction and atmospheric estimation were also carried out on the results of that phase.

Our study highlights the use of machine learning and statistical methods to optimize post-processing. PS/DS process measurement points are used as an optimization database to determine optimal measurement points with minimal intervention. The support vector regression (SVR) method is used to determine the optimal measurement point based on the characteristics of the time series. Finally, hotspot optimization analysis is performed to produce cluster maps, minimize interference from uncorrelated points, and generate deformation cluster maps. Then, we are trying to measure surface deformation changes in the mining area in Musan, North Korea. The data used comes from the Sentinel-1 SAR C-band satellite with a data collection period from 2017-2022. Our findings can provide information on the advantages of ICOPS which can increase spatial coverage compared to other traditional PS methods by more than 20%. for the subsidence rate, the rate of land subsidence is approximate ~ 10cm/year in the 2017-2022 time range. The cumulative subsidence at the end of the observation was 145 cm and 127 cm for mine sites 1 and 2, respectively. Based on the annual subsidence rate, there is a change in the rate of decline, especially in 2021-2022, compared to the previous period. We explore changes in the annual rate of subsidence compared to digital elevation model data for reference. As for the analysis of the mechanism of land surface change, we evaluate it including geological conditions and the distribution of faults in the Musan mining area.

Overall, the ICOPS method has proven to be a valuable tool for analyzing InSAR time series subsidence analysis at the Musan Mine in North Korea. The improved accuracy and reliability of the method enabled a more detailed and comprehensive understanding of the dynamic processes occurring in the study area. In addition, the ability to detect temporal variations and trends in surface deformation has provided valuable insights for the monitoring and management of mining area in North Korea. Thus, the results obtained in this research can inspire the development of time-series InSAR methods, especially in post-processing data. The combination of machine learning is one of the breakthroughs that can provide improvements and new insights in better understanding deformations. Although some challenges that arise such as the condition of the dataset in training or setting operational parameters are a concern. Development in further research can maximize the potential of this machine learning-based post-process in order to obtain more reliable final results in InSAR time-series analysis.

InSAR monitoring of ground displacement requires a correction for the phase differences due to topographic height. In the early days of the technology this was commonly enabled using three-pass InSAR approaches, however once open access digital elevation model (DEM) datasets such as SRTM became widely available these became the standard way to mitigate elevation signals in deformation measurements.

Where these off-the-shelf DEMs were limited by low spatial resolution, or measurement errors, many processing chains further introduced height correction steps. These commonly involve a joint inversion of phase signals for displacement and a height error term proportional to perpendicular baseline. This provides an updated elevation model at the spatial resolution of the SAR data, and a resulting decrease in noise within interferograms and time series measurements.

However, these approaches typically assume a fixed height error for the duration of a data stack, and are therefore not always applicable for environments where topography changes over time. This is a particular issue when monitoring active mine sites and Tailings Storage Facilities (TSFs). In addition to the elevation decreases of tens or even hundreds of metres in actively worked parts of a pit, mine sites also have waste piles and/or stockpiles which change height over time and TSF operations frequently involve periodic wall raises of multiple metres.

These elevation changes inevitably cause loss of coherence while they are taking place, but in many cases this happens over a short period of time and in a limited area, and coherence is subsequently regained. Resuming measurements across these areas is desirable for monitoring, however in the periods after a change occurs the small number of available SAR image pairs does not provide an optimal spread of baselines for an updated regression. This is further complicated by the strong likelihood of areas having co-located subsidence, due to consolidation of the fill material.

This work uses case studies from active mines and TSFs to highlight some of the challenges of monitoring sites with evolving elevations It then reviews available datasets and methods with which this can be mitigated, to provide accurate and reliable operational monitoring for these applications.

National Grid Energy Transmissions (NGET), which owns and maintains the high-voltage electricity transmission network in England and Wales, conducts invasive analysis annually to monitor the towers most at risk of movement. Moreover, the NGET inspection teams perform annual line walking activities and monthly substation inspections during which they visually assess the presence of asset motion. These interventions are crucial to avoid issues which may cause expensive assets replacements or reconstruction. It costs NGET over £6 million per year to monitor only 1% of their most at risk assets.

Synthetic Aperture Radar Interferometry (InSAR) is an accurate Earth observation method to monitor an asset’s stability at a much lower cost and without the need to have physical access to the assets. This technique uses SAR satellite datasets e.g., Sentinel-1 which is freely available from the European Space Agency (ESA). Persistent Scatterer InSAR (PSI) is a novel technique to select strong, stable scatterers that remain coherent for the entire time series of radar acquisitions (Ferretti et al. 2001). In this study, we first applied conventional PSI analysis using SARPROZ software (Perissin et al.,2011) across three NGET areas of interest which each included 80 km of overhead lines (OHLs) and some underground cables and overground substations. To monitor an asset’s stability using the PSI technique, it must be possible to identify at least one data point that can be accurately and definitively assigned to the asset itself. Some assets, depending on their characteristics (e.g. size, orientation, roughness and material) and their scattering behavior are ‘natural reflectors’ providing a strong and coherent back scattered signal that can be used for PSI asset motion analyses, but not all. One of the results of this study was an insight into the high % of towers that are not ‘natural reflectors’ and a study of how this issue could be solved by the installation of corner reflectors.

Corner reflectors (CRs) can be used to enhance the backscattered signal from the target where the signal is not strong and coherent enough to be selected as a Persistent Scatterer (PS) point (Cigna et al., 206 and Kelevitz et al., 2022). Therefore, in the next phase, we focused on designing and installing a number of CRs both on National Grid pylons, and a test site at Cranfield University, to assess their ability to make NGET assets, in particular tower monitorable when using PSI derived from free and open-source Sentinel-1 imagery. This project also set out to determine what the minimum distance between two installed CRs would need to be to still get two separate signals and therefore two distinct asset motion measurements from one single asset. We designed the CRs for these experiments to be clearly visible in images for a typical UK rural landscape away from woodland. Assuming a low vegetated background and a signal to noise ratio (SNR) equals to 10, five trihedral CRs with an inner side length of 70 cm were manufactured. In the installation phase, the CRs were fixed rigidly to a support and pointed towards the Sentinel-1 selected tracks using the local incidence angle and azimuth angle.

We mounted three CRs at the Cranfield University site, on 15th Dec 2022 in an open grassy area south-west of the runway in an L shaped formation (60 m along track and 20 m across-track), each with a 100% clear view to the Sentinel 1 satellites. We compared the amplitude time series of the pixel in which each CR was located in the three images taken before CR installation with four images taken after installation. Before doing the amplitude time series analysis, we co-registered all Sentinel-1 SLC images track 81 descending with respect to the first image after the first CR installation and georeferenced the images using a high-resolution LiDAR DEM, and finally manually corrected georeferencing using a visible feature in the SAR image. The result of this analysis confirms that the installed CRs have a strong back scattering signal towards the satellite in comparison to the background before the installation which matches with what we expected. We then proceeded to reduce the distances between the CR’s in the North-South (along track) and East-West (across track) directions, with two experiments- 30 m along track and 10 m Across-track on 9 Jan 2023 and 5 m and 10 m in across track on 21 Jan 2023 (table 1). The results showed that as long as the spacing is more than approximately 30 m (N-S) or 7 m (E-W) then the reflectors should be visible in the amplitude images as distinct targets. As the targets merge, it is probably possible to detect that more than one reflector is present, but this may require more than a simple visual inspection to be confident of the result. To better distinguish the signal of the two overlapping CRs in the amplitude image after installation, we applied amplitude time series analysis for all the pixels in the large bright area. The time series analysis confirmed a jump of amplitude after the CR installation for the pixels belongs to the CRs. Moreover, we applied an RGB colour composite analysis using the images before and after each installation which helped to distinguish the pixels corresponding to the installed CRs. Figure 1a) shows the RGB color composite analysis for the third CR installation using the image after the first installation (20221216, I1) as red, the image after the second installation (20230109, I2) as green and the image after the third installation (20230121, I3) as blue. Figure 1.b) shows the amplitude image on 20230121 after the third installation and figure 1.c-d) shows the amplitude time series for the pixels belonging to the three launched CR at the third experiment.

The second test site was the National Grid Deeside Innovation Center, there we installed one CR on Tower 1 on 2nd Nov 2022 on the southernmost leg with a 100% clear (unobstructed by the body or arms of the tower or any other nearby object) view to the Sentinel 1 satellite with descending direction (track 52). The visual inspection of the amplitude images before and after installation shows no obvious change, therefore we analyzed the amplitude time series of the pixel in which the CR was located. We compared the three images taken before CR installation with the four images taken after installation. The result of this analysis clearly shows that there is a jump in amplitude of the reflected signal from the pixel in which the CR is located after installation. The signal of the CR in the amplitude image is not as significant or visually obvious as the CRs installed at Cranfield. This is likely due to the power of background clutter at Deeside which is higher than the Cranfield site which has a grassy field as it’s background. Having located our first CR in the optimal position on a tower with a 100% clear view the team wanted to test a much more challenging CR location. The second test CR was installed on Tower 2 on 7th Dec 2022 on the west facing leg with a 0% clear (fully obstructed by the body and arms of the tower) view to the Sentinel 1 satellites. As anticipated due to the obstruction caused by the tower body there was no amplitude increase post CR installation that was either visible to the naked eye or visible in amplitude time series analysis.

We plan to apply PSI analysis using SARPROZ software and Sentinlel-1 images (track 52) over the Deeside test side to investigate whether CR installation on the tower leads to select any PS pixel at the tower location. In the next phase of this study, we plan to improve the impact of the tower’s CR experiments on the amplitude enhancement and phase stability using a new design. The radar cross-section (effectively the signal strength in the image) depends on the reflector size to the power 4, so increasing the side length to 1 m (relative to 70 cm) quadruples the cross-section. Reflectors larger than 1 m can be built, but they become increasingly difficult to manufacture to the required tolerances and more cumbersome to use operationally. Therefore, in our potential new design, we will assess how practical it would be to install a bigger CR or an array of small CRs on the tower.

Acknowledgments:

This project was an Alpha phase project led by National Grid Energy Transmission and funded through the Strategic Innovation Fund by Ofgem working in partnership with Innovate UK. The Strategic Innovation Fund (SIF) is designed to drive the innovation needed to transform UK gas and electricity networks for a low-carbon future.

References:

Cigna,F., et al. "25 years of satellite InSAR monitoring of ground instability and coastal geohazards in the archaeological site of Capo Colonna Italy" Proc. SPIE vol. 10003 pp. 100030Q Oct. 2016.

Ferretti,A., Prati,C., and Rocca,F., "Permanent scatterers in SAR interferometry," in IEEE Transactions on Geoscience and Remote Sensing, vol. 39, no. 1, pp. 8-20, Jan. 2001, doi: 10.1109/36.898661.

Kelevitz,K., Wright,T.W., Hooper,A.H., and Selvakumaran,S., “Novel Corner-Reflector Array Application in Essential Infrastructure Monitoring,” in IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1-18, 2022, Art no. 4708518, doi: 10.1109/TGRS.2022.3196699.

Perissin,D., Wang, Z., Wang, T., "The SARPROZ InSAR tool for urban subsidence/manmade structure stability monitoring in China", Proc. of ISRSE 2011, Sidney, Australia, 10-15 April 2011.

Surface displacement-related geohazards are ubiquitous in the alpine region. Time series of spaceborne SAR data are routinely used to assess ground motion with large spatial coverage. Yet, there are also many cases for which terrestrial radar systems are better suited or even simply required to obtain surface displacement measurements: these cases include (1) north- or south-facing slopes for which the line of sight of current space-based SAR systems flying in interferometric orbit tubes is roughly perpendicular to the preferred direction of ground motion, so that displacement measurements from space are not possible for these areas, (2) slopes that are in radar shadow for current space-based SAR geometries, (3) fast-moving landslides that require much shorter interferometric intervals (down to hours or minutes), and (4) cases where higher spatial resolution or higher frequencies (e.g. Ku-band) with higher sensitivity to line-of-sight movements are required.

Existing terrestrial (quasi-)stationary radar systems [1,2] have been used for many years to partially fill this observation gap.

However, the real aperture of these terrestrial radar systems, or the typically very limited synthetic apertures of a few meters, mean that these systems have an approximately constant angular resolution in the azimuth direction. Thus, the spatial azimuth resolution decreases with increasing distance. These terrestrial radar systems typically operate in Ku- or X-band [3-5] to provide adequate azimuth resolution.

Monitoring a mountainside from a moving car or UAV, and thus using a much longer synthetic aperture, allows the use of lower frequencies, such as the L-band, with good spatial resolution (at meter level). If aperture synthesis is used from a car or UAV at higher frequencies (e.g. Ku-band) with correspondingly smaller radar antennas, the azimuth resolution can still be significantly improved (on the order of one or more decimeters) compared to the azimuth resolution of (quasi-) stationary radar systems (order of 10m and more) at longer ranges of several kilometers.

In [6-8], we have demonstrated mobile mapping of surface displacements using our compact repeat-pass L-band interferometric SAR system, including its application to measure ground motion of a fast-moving landslide in Brienz (CH) [8]. More recently, we have added a Ku-band SAR system (a Gamma Portable Radar Interferometer (GPRI) equipped with horn antennas [9]) to our car-borne InSAR measurement configuration.

In Fig. 1 (see pdf attachment), on the left, the car-borne mobile mapping measurement setup is shown at Guttannen, Switzerland. It includes the Gamma L-band SAR and the modified GPRI at Ku-band mounted on a car together with a Honeywell HGuide n580 INS/GNSS system and an ad-hoc GNSS reference station (see also [9] for a more detailed technical description and close-up views). This configuration allows to acquire SAR data at both frequencies simultaneously. The repeat-pass SAR measurements are taken while driving along roads.

In terms of temporal decorrelation, frequency diversity is of advantage, particularly, for mountain slopes with varying land cover (including rocks and vegetation) and motion processes with different velocities and scales.

In this contribution, we will present recent and current results from car-borne mobile mapping campaigns at different sites in the Swiss Alps acquired with our dual-frequency car-borne SAR setup (Gamma L-band SAR and a modified GPRI at Ku-band). Here, in the abstract, we give two examples of interferometric data sets obtained during these campaigns: in Fig. 1 (see pdf attachment), middle and right, an example of repeat-pass interferometric phase and coherence obtained with the L-band system is shown. In Fig. 2 (see pdf attachement), another example from another recent time series is shown including simultaneously acquired L-band and Ku-band repeat-pass SAR imagery obtained with the car. A steep rock phase has been imaged. Short-term (4 minutes) and long-term (4 months) coherence at both frequencies are shown. The 4-month interferometric pair includes a winter (2022-02-15) and a summer (2022-06-14) acquisition and effectively highlights the complementary properties of L-band versus Ku-band regarding temporal decorrelation in the presence of changing environmental conditions (partial snow/ice cover in winter and different vegetation stage).

These interferometric measurement campaigns are ongoing. The main goal is to experimentally evaluate the interferometric measurements particularly in terms of the temporal decorrelation with different land-cover and temporal measurement intervals at both frequencies and for typical cases of slope stability mapping in the Alps. The final presentation will therefore also include updated results including the latest measures further extending the time series. The focus of the analysis and discussion is laid on aspects relevant to develop operational deformation applications based on such car-based (or also drone-based) systems at different frequencies.

References

[1] Caduff, R., Schlunegger, F., Kos, A. and Wiesmann, A. (2015): “A review of terrestrial radar interferometry for measuring surface change in the geosciences,” Earth Surface Processes and Landforms, vol. 40, no. 2, pp. 208–228.

[2] Monserrat, O., Crosetto, M., and Luzi, G. (2014): “A review of ground-based SAR interferometry for deformation measurement,” ISPRS Journal of Photogrammetry and Remote Sensing, vol. 93, pp.40–48, 2014.

[3] Werner, C., Strozzi, T., Wiesmann, A., and Wegmuller, U. (2008): “A real-aperture radar for ground-based differential interferometry,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., pp. 210–213.

[4] Luzi, G., Pieraccini, M., Mecatti, D., Noferini, L., Guidi, G., Moia, F., and Atzeni, C. (2004): “Ground-based radar interferometry for landslides monitoring: atmospheric and instrumental decorrelation sources on experimental data,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 11, pp. 2454–2466, Nov. 2004.

[5] Leva, D. Nico, G., Tarchi, D., Fortuny-Guasch, J., and Sieber, A. (2003): “Temporal analysis of a landslide by means of a ground-based SAR interferometer,” IEEE Trans. Geosci. Remote Sens., vol. 41, no. 4, pp. 745–752.

[6] Frey, O., Werner, C. L. and Coscione, R. (2019), Car-borne and UAV-borne mobile mapping of surface displacements with a compact repeat-pass interferometric SAR system at L-band, in 'Proc. IEEE Int. Geosci. Remote Sens. Symp.', pp. 274-277.

[7] Frey, O. and Werner, C. L. (2021), UAV-borne repeat-pass SAR interferometry and SAR tomography with a compact L-band SAR system, in 'Proc. Europ. Conf. Synthetic Aperture Radar, EUSAR', VDE, pp. 181-184.

[8] Frey, O., Werner, C. L., Manconi, A. and Coscione, R. (2021), Measurement of surface displacements with a UAV-borne/car-borne L-band DInSAR system: system performance and use cases, in 'Proc. IEEE Int. Geosci. Remote Sens. Symp.', IEEE, pp. 628-631.

[9] Frey, O., Werner, C. and Caduff, R. (2022), Dual-frequency car-borne DInSAR at L-band and Ku-band for mobile mapping of surface displacements, in 'Proc. of EUSAR 2022 - 14th European Conference on Synthetic Aperture Radar', VDE, pp. 489-492.

The effectiveness of the advanced Differential Synthetic Aperture Radar (DInSAR) techniques [1], [2] to analyze ground surface displacements over large areas of the Earth, with limited costs and sub-centimetric accuracy, has largely promoted their wide exploitation among various scientific and operational frameworks. Indeed, thanks to the availability of long sequences of satellite SAR data, acquired over an area of interest and co-registered with respect to a reference image geometry, the DInSAR techniques allow detecting and monitoring ground displacements associated to different hazard phenomena through the generation of spatially and, whenever possible, temporally dense deformation time series. Originally devoted to regional scale deformation analyses in natural hazard contexts (e.g., volcanic eruptions, seismic events, landslides, subsidence), in the recent years the advanced DInSAR techniques have successfully broadened their application fields, thanks to the achievable large pixel density, the sub-centimetric accuracy of the related DInSAR products (velocity maps and deformation time series), as well as the possibility to perform back analyses on the phenomena under investigation. Moreover, the widespread accessibility of large archives of SAR images acquired by advanced satellite systems characterized by different operational modes (Stripmap, TOPSAR, ScanSAR), bandwidths (L-, C-, and X-band) and spatial-temporal resolutions has even more fostered the development of advanced DInSAR techniques for high spatial resolution applications.

Here we focus on the Small BAseline Subset (SBAS) DInSAR technique [3]-[4] and its parallel algorithmic solution referred to as Parallel SBAS approach [5][6], which are suitable to provide systematic, regional- to- continental scale displacement measurements in different hazard scenarios related to both natural and built-up environments. One key point of the P-SBAS approach, which fostered its wide exploitation in a bulk of scientific and operational applications, is its capability to perform long-term DInSAR analyses at different spatial resolutions (for regional and local scale investigations), particularly suitable when dealing with localized deformation phenomena, as those affecting critical infrastructures and single buildings. In particular, we can exploit the full resolution P-SBAS approach [7], which allows to perform long term advanced DInSAR analyses related to extended urban areas, by generating deformation time series at the full spatial resolution of the exploited SAR sensors [8].

In this framework, the best performance achieved by the full resolution P-SBAS technique in terms of detection and monitoring capabilities of localized displacements related to infrastructures and single buildings in extended urban areas may be reached when dealing with very high resolution SAR images, as those collected by the X-band (about 3 cm wavelength) SAR sensors.

To accomplish this aim, we can fully benefit from the huge archives of the X-band data collected since 2009 along the overall Italian territory by the sensors of the Italian COSMO-SkyMed (CSK) constellation, operated through the Stripmap mode (with about 3 m x 3 m spatial resolution), which allows to monitor the surface deformations affecting the built-up environment with a very high spatial and temporal measurement density. Moreover, with the recent launches in 2019 and 2022 of the two satellites of the COSMO-SkyMed Second Generation (CSG) constellation (which will be further extended with other two satellites in the next years), it is also possible to maintain the operational consistency with the current CSK programme, with enhanced capabilities in terms of data product quality and functionalities, thus allowing to guarantee the continuity in the monitoring activities of deformation phenomena related to built-up environment.

Accordingly, in this work we first show the results of an extensive full resolution P-SBAS processing which exploits huge archives of CSK/CSG SAR images acquired from ascending and descending orbits since 2009, in order to identify potentially critical health conditions of transport infrastructures and buildings located in a large number of important cities of the Italian territory. To do this, we both exploit advanced DInSAR processing methods based on up-to-date parallel strategies, as well as modern HPC e-infrastructures to efficiently manage and process large full resolution interferometric data stacks and possibly extract value-added information from the generated P-SBAS products. Concerning the second point, the exploitation of intrinsically parallel hardware and software solutions based on multi-core GPUs result to be particularly effective to generate in short time frames full resolution P-SBAS deformation time series of an extended area, since GPUs guarantee high efficiency in terms of velocity, computational load and scalability performance.

To perform a national scale full resolution ground deformation analysis, we have also to tackle some algorithmic improvements on the full resolution P-SBAS processing chain, in order to deal with very extended SLC images deriving from a dedicated “merging” operation applied to consecutive CSK/CSG SLC images related to the same data acquisitions along a specific orbit trajectory. This is accomplished by properly taking into account possible phase offsets between adjacent “slices” of the same CSK/CSG data, which are compensated for retrieving high quality SLC data relevant to very extended (in azimuth direction) strips and, accordingly, accurate national-scale full resolution DInSAR deformation time series.

At the conference time, we will present some results achieved by applying the implemented full resolution P-SBAS processing chain to some CSK/CSG SLC data stacks acquired from ascending/descending orbits, relevant to the main Italian cities. For brevity, we here show the full resolution P-SBAS results generated from a stack of CSK/CSG SLC data acquired from ascending orbits during the 2011-2021 time span over the city of Rome (Fig. 1).

As a further analysis, we plan to show the first results achieved by processing L-band SAR data acquired by the new twin sensors of the Argentinian SAOCOM-1 constellation of CONAE. As this system was recently launched and started acquiring in the interferometric mode over the Italian territory in 2020, by the conference time the L-band data collected over the main Italian cities should reach a number large enough to carry out advanced full resolution P-SBAS analyses. In particular, we will investigate the possibilities offered by the L-band data to overcome some of the typical limitations of X-band SAR systems, such as the impact of phase unwrapping errors, and to maintain high coherence for a long time interval.