Human infrastructures located in karst environments may be affected by severe ground instability problems . In particular, the occurrence and activity of sinkholes in carbonate and evaporite karst terrains is one of the main causes of subsidence-related damage and accidents on conventional railways . Deflections in the railway track caused by dissolution-induced settlement can compromise safety on transportation infrastructure . The implementation of monitoring and early-warning systems on potentially problematic railway stretches may constitute an effective mitigation measure, mainly aimed at preventing accidents. Differential Synthetic Aperture Radar Interferometry (DInSAR) may be postulated as a useful subsidence monitoring technique for railways. Most of the reported Interferometric Synthetic Aperture Radar (InSAR) applications to the monitoring of high-speed railways (HSR) have been developed in China and Taiwan. In these countries, railway and highway infrastructure are experiencing rapid development and they traverse numerous areas affected by ground instability phenomena . The instability processes that produce most problems on Chinese railways, and are the main targets of InSAR analyses, are related to groundwater abstraction and permafrost . For a railway built upon permafrost, documented temporal variations of deformation in relation to rainfall and air temperature, and measured higher strain in topographically lower areas, where water accumulation increases the impact of thawing and freezing. Further, the activity of sinkholes has been monitored using DInSAR in different geological settings of Germany , Israel , Italy , Jordan , Spain (, , ) and USA (, ).

Here, we present DInSAR displacement profiles that reveal previously undetected active subsidence on sections of different railways in the surroundings of Zaragoza, Ebro Valley evaporite karst, NE Spain (Fig. ). The Cenozoic bedrock in the analysed area of the Ebro Valley consists of subhorizontally lying halite- and glauberite-bearing evaporites of the Zaragoza Formation (Fig. ). Subsurface dissolution results in the development of numerous sinkholes affecting both the evaporitic bedrock and the alluvial cover and references therein. Active subsidence associated with these sinkholes causes costly damage to man-made structures e.g.. The dissolution-induced ground deformation can be studied quantitatively using InSAR techniques as illustrated by previous works cf.,.

We have analysed two railway stretches. One of them includes two parallel railways, a conventional one and the Madrid–Barcelona high-speed line. Here, 1850 m and 1900 m long sections are built on embankments and in excavated trenches, respectively. The latter are flanked by cuttings that expose subsidence structures. The other stretch with active subsidence includes a 4000 m long section of the conventional Castejón–Zaragoza railway (Fig. ). Both railway corridors traverse large sinkholes previously documented in geomorphological maps . Some of these sinkholes were defined as being active on the basis of surficial signs of settlement and on the occurrence of collapses within them. For example, on 1 March 2003, a collapse sinkhole with 5 m diameter formed beneath the high-speed railway a few months before its inauguration . We also observed obvious deformation in a poorly maintained subsidiary railroad of the Castejón–Zaragoza line, coinciding with the location of a sinkhole mapped on the basis of geomorphic criteria (Fig. ). However, so far the precise area affected by active subsidence has not been identified, nor has its settlement rates been measured. The data obtained by DInSAR analyses represents a step forward in the sinkhole risk analysis for avoiding accidents such as the derailment of a freight train caused by a collapse sinkhole in the conventional Madrid–Barcelona railway on 11 September 1991 (at km 360.7; ) (Fig. ). In this work we integrate DInSAR deformation data with different subsidence evidence (geomorphic, deformed sediments, damaged man-made structures). The convergence of the different lines of evidence is used to support the utility of DInSAR for monitoring railways affected by dissolution-induced subsidence.

Archived data from two orbital SAR (Synthetic Aperture Radar) missions have been used to produce the InSAR deformation maps analysed in this work. One of the data sets includes C-band data of 29 ENVISAT ASAR images acquired at 22:00 on ascending orbits from 2 May 2003 to 17 September 2010 (track 58, frame 829). The other data set comprises L-band data of 13 ALOS PALSAR images acquired at 22:30 in ascending mode and HH polarization, and it covers a period from 12 February 2007 to 7 April 2010 (track 665, frame 820).

The SAR images were processed using the Stable Point Network (SPN) technique . Preprocessing was carried out using the DIAPASON interferometric algorithm . This algorithm incorporates the persistent scatterer and distributed scatterer approaches based on full-resolution and medium-resolution data, respectively. The topographic component of the interferometric phase was removed using the Spanish photogrammetric elevation model “GISOleícola” with a spatial resolution of 20 m.

The ENVISAT-ASAR-derived displacement rate map was produced at full resolution from a total of 61 interferograms. The persistent scatterers (PSs) were selected, establishing a coherence threshold of 0.46 on the basis of the SAR amplitude selection criterion. The average line of sight (LOS) displacement rate and the LOS displacement time series of each PS were derived from the Single Look Complex (SLC) ASAR images. Displacement rate values > 2 mmyr-1 were considered as non-stable points as it is usually defined for ENVISAT C-band data . The ALOS-PALSAR-derived displacement rate map was produced at a ground resolution of about 25m×25m and a coherence threshold of 0.40 was established. In this case, displacement rates > 4 mmyr-1 were considered as indicative of surface deformation. This threshold is consistent with values used by other authors . Additional technical information on SAR data sets and DInSAR deformation profiles is listed in Table 1.

Railways served as good reflection features for ALOS and ENVISAT sensors, providing a relatively high density of measurement points, especially in the ALOS-derived map. Two profiles of LOS displacement rates have been constructed along the railway corridors using the InSAR maps (Fig. ). We analysed ALOS and ENVISAT data in each profile and selected the best results to be presented in this work: ALOS measurements in the Castejón–Zaragoza railway line, and ENVISAT PS points in the Madrid–Zaragoza profile (Fig. ).

The displacement rates measured in the SW and NE portions of the analysed Madrid–Zaragoza railway section, as high as -6.6 mmyr-1 (negative values indicate subsidence), may be related to compaction of the embankments, as the direct correlation between subsidence rates and embankment height suggests (Fig. , Profile 1). LOS displacement rates indicate rapid settlement (> 4 mmyr-1) in the NE sector of the analysed stretch, coinciding with the location of a buried depression of unknown origin, filled a few decades ago and identified with aerial photographs. Here, subsidence is most probably related to compaction of anthropogenic deposits, which may exceed 10 m including the embankment. However, further investigations would be required to rule out the potential contribution of dissolution-induced subsidence (e.g. trenching, geophysics, vertical extensometers).

The negative LOS displacement values measured in the sector where the path of the railway has been excavated in Quaternary alluvium can be attributed to dissolution-induced subsidence. There is a significant number of points with LOS displacement rates below -2 mmyr-1 between 1500 and 2700 m in Profile 1. In this sector, the railways run across subdued sinkholes recognized in old aerial photographs and expressed in cuttings as deformed Quaternary alluvium . The sinkhole cluster comprises a large diffuse-edged depression and several smaller subcircular sinkholes (Fig. ). In addition to the DInSAR deformation data, several lines of evidence consistently indicate active subsidence in some sectors of the sinkhole cluster: enclosed depressions, severe cracking on buildings, conspicuous sags and wide fissures on roads and small collapse sinkholes, including the 2003 event. An excavation carried out at the SW edge of the large depression for the foundation of a bridge exposed tilted Quaternary deposits dipping toward the depression centre (Fig. ). Two sedimentary packages were distinguished. The lower one corresponds to pre-sinkhole terrace gravel deposits with an apparent NE dip of 14–17∘. The upper one corresponds to natural sinkhole fill deposits that pinch out towards the SW (sinkhole edge). The dip of these sediments progressively attenuates upwards (cumulative wedge-out), suggesting synsedimentary subsidence.

The high density of measurement points derived from the ALOS data along the Castejón–Zaragoza railway provides valuable information on the activity of three previously inventoried sinkholes traversed by the infrastructure. A clear subsidence zone, with negative LOS displacement rates as high as -9.7 mmyr-1, coincides with a sinkhole of about 300 m in diameter previously classified as being active (Figs.  and , Profile 2). Here, ground motion values show a consistent pattern with increasing subsidence rates towards the centre of the sinkhole (Fig. ). The LOS displacement values measured in the other two sinkholes, previously described as inactive , suggest ground stability or very slow subsidence (< 2 mmyr-1).

The presented data illustrate that DInSAR offers promising potential for monitoring railways that are affected by sinkhole activity and dissolution-induced subsidence. This postulate is supported by two relevant aspects of our investigation. (1) There is a good spatial correlation between the deformation values measured by DInSAR and unambiguous field evidence of active subsidence associated with sinkholes. (2) We obtained good results using InSAR data derived from a regional investigation see. Detailed analyses focused on railway tracks or on specific sections of the infrastructure should provide higher density and more accurate deformation data than in the profiles presented in this paper.

Railways are linear features that are commonly positioned on relatively flat surfaces that act as adequate reflectors for the spaceborne SAR systems, providing spatially dense and temporarily stable coherent scatterers . illustrate the strong backscattering of railways in ALOS PALSAR and ENVISAT ASAR amplitude images, compared with the surrounding features. The density of natural reflection points depends on the land cover, the number of images used in the InSAR analysis, the adopted processing parameters and algorithm type, the selected coherence threshold and the spatial resolution of radar imagery . In our case, ENVISAT displacement points cover a larger area in the Madrid–Zaragoza profiles (NW–SE orientation) than the ALOS displacement data. On the contrary, ALOS data provided the best distribution of measured points along the Castejón–Zaragoza stretch (NE–SW orientation). Apparently, this difference could be attributed to the relative orientation of the railway tracks with respect to the flight path of sensors. However, both the ENVISAT and ALOS data correspond to ascending paths and, consequently, the differences observed between the two DInSAR displacement rate maps cannot be related to the course of the satellites. and have obtained deformation sequences covering long time spans analysing PSs along railways. measured numerous minor and locally distributed displacements that were not detected by levelling. obtained a higher density of PSs with ALOS PALSAR data than with ENVISAT ASAR data. This was probably due to the longer wavelength of the former and the higher critical baseline applied to generate the ALOS interferograms of the small baseline subset (SBAS) method . This resulted in higher coherence, especially in zones with high deformation gradients and in man-made features such as the railway embankment. inferred that the difference in the distribution of PSs derived from L- and C-band data are controlled by their different scattering mechanisms. In the PALSAR results, the railway embankment was more easily detected because of its resolution (10 m). Man-made linear features were dominated by the dihedral scattering and resulted in a high density of PS points in the PALSAR results. For ENVISAT data, despite the strong backscattering of the railway, motion was not detected using the PS method, probably due to the noise caused by the scattering mechanism of instable land surfaces.

DInSAR techniques allowed the detection of previously unknown settlement in several stretches of two major railway lines of NE Spain. The area in the outskirts of Zaragoza is severely affected by evaporite karst subsidence. This deformation was detected thanks to medium-resolution surface velocity maps generated through the analysis of archived data of the ENVISAT and ALOS SAR missions. The results show that DInSAR methods allow deformation of railways to be identified and monitored, that may otherwise compromise both serviceability and safety.

DInSAR velocity maps coupled with detailed geomorphological maps may help in the identification and characterization of the railway stretches affected by active deformation that may require site-specific monitoring. These stretches may be controlled by using real-time advanced ground-based monitoring techniques such as motorized total station systems that measure prisms attached directly to the structure, time-domain reflectometry (TDR) coaxial cable sensors cf., or GB-InSAR cf.,. DInSAR also could be an alternative to these expensive techniques where catastrophic collapse can be ruled out and the ground deformation does not show dangerous subsidence rates (according to the admissible deformation of the railway track). Site-specific investigations combining more adequate and higher-resolution SAR data with ground references (e.g. corner reflectors, GPS benchmarks) may provide a very precise monitoring system. PS detection in linear infrastructures is improving substantially by using high-resolution data (e.g. CosmoSkyMed, TerraSAR-X) . High-resolution imagery can provide a point density 10 times higher than medium-resolution data . found dense PSs in highways and railways using high-resolution TerraSAR-X data due to the presence of numerous stable objects distributed along the infrastructure, such as lamps, stones or fences. Future studies in our study area should focus on the monitoring of deformation using TerraSAR-X and COSMO-SkyMed data coupled with other ground-based measurements.