Multi-temporal InSAR for transport infrastructure monitoring: recent trends and challenges

Modern transport infrastructure is designed for a service life of 50–100 years (van Breugel, 2017). Over this timeframe, structures naturally degrade and thus experience a progressive reduction in structural performance. Design flaws, construction errors, traffic increases, adverse environmental conditions and both natural and anthropogenic disasters can further accelerate the deterioration processes involved, increasing the probability of catastrophic structural failure. In western countries, a major proportion of current transport infrastructure was built between the 1950s and the 1970s. As a result, thousands of assets have now exceeded their intended design lives. The number of structures requiring urgent rehabilitation increases every year and the prioritisation of maintenance activities is a constant challenge for asset managers (Alexakis et al., 2021; Briggs et al., 2017; Pregnolato, 2019) and a key aspect of infrastructure resilience (Achillopoulou et al., 2020).

Structural health monitoring (SHM) is a widely recognised method for evaluating the performance of structures in their operating environment, estimating their residual life and identifying potential damage precursors to ensure safe functionality over the asset's remaining service life (Chang et al., 2003). Traditionally, SHM systems involve a network of in situ sensors that can provide real-time measurements of structural conditions (Worden and Dulieu-Barton, 2004). Established SHM methods include the use of accelerometers, strain gauges and robotic total stations. However, despite the high reliability of the information gathered by such instruments, due to economical constraints and the difficulty in accessing some locations, only a limited number of infrastructure assets are currently equipped with SHM.

Space-borne synthetic aperture radar interferometry (InSAR) is a remote sensing imagery technology that can provide wide-area, low-cost measurements of surface displacements worldwide (Hanssen, 2001; Moreira et al., 2013; Rosen et al., 2000). InSAR systems can operate day and night, and in every weather condition. Due to the availability of historical archives of past satellite images, InSAR can be used retrospectively to study past deformation phenomena. Recent space-borne SAR missions have generated datasets with up to 1 m spatial resolution and 6 day revisit times (Bonano et al., 2013; Milillo et al., 2015). In several geoscience fields, InSAR is already a well-established monitoring technology and enables the study of geophysical processes in glaciology (Goldstein et al., 1993; Milillo et al., 2019a), landslides (Carnec et al., 1996; García-Davalillo et al., 2014), seismology (Dalla Via et al., 2012; Yun et al., 2015), tectonic motions (Bürgmann et al., 2006) and vulcanology (Milillo et al., 2015; Salzer et al., 2017).

Since the late 1990s, advanced signal processing algorithms have been used to analyse long temporal series of InSAR images, enabling surface deformations over time to be reconstructed (Ferretti et al., 2001; Lanari et al., 2004). Multi-temporal (MT) InSAR techniques are based on the identification of targets showing stable scattering behaviour within a series of radar images (Ferretti et al., 2000, 2001). These stable radar reflectors, called permanent scatterers (PSs), are usually associated with architectural elements, exposed rocks or metallic structures, making these techniques extremely effective in urban areas. Furthermore, MT-InSAR is capable of millimetre-scale deformation measurements (Ferretti et al., 2007), reaching an accuracy comparable to ground-based monitoring instruments.

Over the past 20 years, a wealth of literature has demonstrated the capability of MT-InSAR to detect deformations of buildings (Bianchini et al., 2015; Cavalagli et al., 2019; Cerchiello et al., 2017; Chen et al., 2021; Cigna et al., 2014a; Drougkas et al., 2020; Milillo et al., 2018; Peduto et al., 2017; Reale et al., 2019; Shimoni et al., 2017; Zhu et al., 2018), bridges (DePrekel et al., 2018; Milillo et al., 2019b; Selvakumaran et al., 2020), roadways (Infante et al., 2019; Macchiarulo et al., 2021a), railways (Chang et al., 2016) and dams (Di Martire et al., 2014; Milillo et al., 2016a, 2016b), highlighting the potential for this technology to provide measurements of assets that are not included in current monitoring schemes or are difficult to access for visual inspections and conventional SHM systems. With significant data availability and short revisit times, MT-InSAR is ideally suited to provide the inputs to improve damage assessment procedures (Giardina et al., 2019; Macchiarulo et al., 2021b) and decision support models to enable predictive maintenance planning of infrastructure systems (Hadjidemetriou et al., 2021), with the potential to enhance asset longevity and resiliency. MT-InSAR data could be used to develop early warning systems for the identification of potentially damaging structural deformations. If warning of an anomalous structural condition is given in advance, there is time to assess whether the observed deformations are concerning (possibly by taking additional survey measurements), undertake maintenance and, for example, divert traffic around a potentially dangerous structure, thus improving overall network resilience.

However, despite the high potential of this technology for SHM, several challenges arise when applying it in practice, thus limiting the operational use of MT-InSAR. These challenges include

• the availability and distribution of monitoring points for a specific structure

• decomposition of the deformation measurements with respect to the structure's reference system

• the magnitude and rate of maximum detectable movements

• the separation of noise from anomalous structural behaviours

• the assessment of measurement quality

• the accessibility of this technology to the civil engineering community.

The aim of this paper is to discuss the challenges currently limiting the practical use of MT-InSAR technology for transport infrastructure monitoring, to propose solutions for some of the identified issues and to highlight future research directions. Section 2 introduces InSAR, reviews the fundamentals of space-borne SAR sensors, and provides an overview of the technical aspects of the methodology, with a particular focus on MT-InSAR techniques (Section 2.1). Section 3 identifies and discusses the main challenges that need to be overcome for MT-InSAR to be adopted for mainstream structural monitoring usage. Applications to bridges and transport networks are discussed. Each challenge is addressed separately in a different subsection using the following structure: (a) the issue is firstly identified from the MT-InSAR perspective and technical limitations are defined; (b) the identified problem is analysed with a specific focus on the monitoring of bridges and transport networks; (c) possible solutions are suggested and promising research directions are highlighted. Finally, Section 4 summarises the findings and provides closing remarks.

Space-borne SAR is an active sensor that can extensively map areas around the globe by transmitting microwave pulses towards the Earth's surface and recording the backscattered returns. The sensor resolution depends on the wavelength and bandwidth of the transmitted signal. For a given acquisition mode, shorter wavelengths provide higher spatial resolutions. Current space-borne SAR sensors operate in three different wavelength bands: L-band (∼24 cm), C-band (∼5.6 cm) and X-band (∼3.1 cm). In SAR images, each pixel is characterised by a certain value of amplitude and phase. The amplitude quantifies the amount of backscattered energy detected by the sensor, and depends on the size, shape, roughness, orientation and dielectric properties of the targets located within the equivalent resolution cell. The phase refers to the signal propagation distance between the sensor and the resolution cell; it is expressed as an angle in the range of 0 to 2π.

SAR satellites move along near-polar orbits and, depending on the satellite's flight direction, they can observe the Earth's surface from south to north (ascending pass) or north to south (descending pass). Space-borne SAR systems have a side-looking imaging geometry, meaning that the sensor is looking sideways with respect to the flight direction (Figure 1). The satellite viewing direction is defined as the line of sight (LoS), and has an inclination (⁠$θ$⁠) of 20–50° relative to the vertical, or nadir. Depending on the SAR acquisition mode, the swath width can vary from 30 km to 500 km (Moreira et al., 2013). The satellite position over the same area at two distinct times is never identical, and the spatial distance between two acquisition spots is defined as the interferometric baseline. The projection of the interferometric baseline along the direction perpendicular to the satellite LoS is the perpendicular baseline. Finally, the interferometric revisit time of a satellite determines the minimum time interval (or temporal baseline) required to overpass the same area for generating an interferogram. Currently, SAR satellites have a temporal baseline of 1 day (e.g. the COSMO-SkyMed constellation when multiple satellites in the constellation are used), 3 days (e.g. TerraSAR-X and PAZ) or 6 days (e.g. Sentinel-1A/B).

Since the early 1990s, multiple SAR satellites have been orbiting the Earth, providing observation data with different frequencies and resolutions. Figure 2 provides an overview of past, present and upcoming satellite SAR missions and, for each sensor, the minimum revisit time and spatial resolution are specified. Some of these satellites are no longer operative, such as ERS and Envisat, but have provided valuable archives of data that are still used for studying past deformation phenomena. Active SAR missions include COSMO-SkyMed, TerraSAR-X, RADARSAT-2, Sentinel-1 and ALOS-2. This second generation of space-borne SAR sensors are capable of metre-scale spatial resolutions and revisit times of the order of a few days, providing near-real-time monitoring capability (Bonano et al., 2013; Milillo et al., 2015). Finally, recently launched satellites, such as ICEYE and Capella (Ignatenko et al., 2021; Stringham et al., 2019), or upcoming missions, like HRWS (Gebert et al., 2006), will soon be able to provide data with sub-metre spatial resolution and hourly frequency, with the potential to reach real-time monitoring capability.

InSAR exploits the phase information of a pair of SAR images separated in time to detect changes within the observed area (Gabriel et al., 1989; Massonnet and Feigl, 1998). In InSAR techniques, an interferogram is generated by cross-multiplying two SAR images of the same area on a pixel-by-pixel basis. The phase $Φ$ is proportional to the two-way travel distance between the radar and the target (⁠$2r$⁠) and the wavelength (⁠$λ$⁠) of the signal:

A variation in the phase indicates possible target movements between the two acquisitions (Hanssen, 2001). The phase variation (⁠$ΔΦ$⁠) can be written as:

where $Δr$ is the change in distance travelled by the signal as a consequence of the target movement (Figure 3). However, the interferometric phase $ΔΦ$ not only captures the target movements (⁠$ΔΦdefo$⁠), but also captures some additional contributions, such as the flat earth terrain $ΔΦearth$⁠, the topography $ΔΦtopo$⁠, the atmospheric delay $ΔΦatm$ and some noise $ΔΦnoise$⁠:

The terms $ΔΦearth$ and $ΔΦtopo$ are associated with the observation of a different Earth's curvature and a different local topography between two acquisitions of the same area at two distinct times. This is a consequence of the slightly different position assumed by a satellite with respect to its nominal orbit when it overpasses the same geographic region. The atmospheric phase term $ΔΦatm$ corresponds to a signal delay produced by different atmospheric conditions, mainly associated with water vapour content, at two distinct acquisition times. The term $ΔΦnoise$ captures possible noise caused by spatial and temporal decorrelations of the radar signal, co-registration errors, orbital errors, soil moisture and residual errors associated with incorrect compensation of the other phase terms. To determine the target displacement, the additional phase terms in Equation 3 need to be estimated and removed. While $ΔΦearth$ and $ΔΦtopo$ can be removed by using orbital data and a digital elevation model (DEM) of the area of interest, when only one interferogram is used it is difficult to quantify the atmospheric delay and possible decorrelations of the radar signal. While some methods can be used to mitigate tropospheric (Jolivet et al., 2011) and ionospheric (Gomba et al., 2015) components within single-interferogram approaches, they have been limitedly applied to geophysical phenomena, with rare applications to infrastructure monitoring. In contrast, multi-interferogram methods (i.e. Multi Temporal (MT)-InSAR techniques) enable all the unwanted contributions in Equation 3 to be estimated. The capability of MT-InSAR to reach sub-centimetre accuracy depends on the quality of the data and the joint use of processing parameters and methodologies. The phase of each InSAR image pixel is accurate to a fraction of the radar wavelength (Equation 2), which is of the order of centimetres. Thus, MT-InSAR techniques can theoretically achieve millimetre-scale accuracy on a single deformation measurement.

MT-InSAR is a collection of powerful signal processing techniques that can be used to analyse multiple InSAR images of the same area acquired at different times to measure the displacement over time of point-like targets (Ferretti et al., 2000, 2001). In contrast to other InSAR approaches, MT-InSAR only processes a subset of image pixels, thus resolving the limitations of previous InSAR methods, such as geometrical and temporal decorrelation and atmospheric inhomogeneities. The pixels selected have very distinctive backscattering characteristics. These pixels correspond to highly reflective targets with a stable backscattering over time to the radar and, for this reason are known as Permanent Scatterers (PSs).

During MT-InSAR analysis, PSs are geolocated in three-dimensional (3D) space and their coordinates and elevation can be determined with metre precision. If a sufficient number of PSs are identified across a series of InSAR images, these points can be used to reconstruct a highly accurate approximation of the actual displacement field. PSs form a ‘natural geodetic network’ (Perissin, 2008), conceptually similar to a network of GNSS (Global Navigation Satellite Systems) stations. This results in a much denser source of measurements than conventional geodetic methods, without any need for installation or maintenance of instrumentation. Field experiments have verified the accuracy of MT-InSAR measurements, confirming the capability of MT-InSAR to reach millimetre-scale accuracy (Ferretti et al., 2007; Rucci et al., 2012). The outcomes of MT-InSAR analysis usually consist of a geospatial dataset containing the PSs identified during the processing and, for each point, the geographic coordinates, elevation, displacement time-series and average velocity are provided. Each point also comes with an index of quality defined as the temporal coherence. All deformation measurements obtained through MT-InSAR analysis are relative to a reference point selected during processing. This reference point is usually selected in a location of known high coherence that is relatively stable in terms of displacement. Since any displacement of the reference point will subsequently affect the displacement measurements of the other PSs, measurements should always be interpreted relative to each other.

Due to their geometric configurations and dielectric properties (Perissin and Ferretti, 2007), bridges, buildings, monuments, metallic objects and exposed rocks are ideal targets for MT-InSAR analysis. Targets that are subjected to significant change (e.g. vegetation) or provide weak reflections (e.g. water basins) do not generate PSs. In urban areas, there can be thousands to tens of thousands of PSs available per square kilometre (Milillo et al., 2018; Perissin and Rocca, 2006), while in extra-urban areas, PSs can still be abundant for viaducts, roadways and railways. These targets are characterised by a very strong reflection and their signal prevails over weaker scatterers that may be present within the same pixel, such as vegetation or water.

Each SAR satellite always overpasses the same area at the same local coordinated universal time (or UTC). Consequently, multiple InSAR images of the same area acquired on different days can capture the seasonal variation of local environmental parameters without being affected by daily temperature and humidity gradients. Thus, thermal expansion effects can be modelled and estimated during MT-InSAR analysis (Fornaro et al., 2013; Gernhardt et al., 2010; Monserrat et al., 2011).

For the specific case of transport infrastructure, the suitability of MT-InSAR for monitoring deformations of bridges, roadways and railways has been investigated in several studies. Some researchers have used historical InSAR images to evaluate retroactively the structural condition of collapsed bridges, showing the potential of this technology for detecting precursor signs of structural failures (Milillo et al., 2019b; Selvakumaran et al., 2018; Sousa and Bastos, 2013). Others have used MT-InSAR to reconstruct the thermal expansion of reinforced concrete or metallic arch bridges (Huang et al., 2018; Lazecky et al., 2016; Qin et al., 2018; Zhao et al., 2017) and compared MT-InSAR deformations with 3D finite-element models of bridge thermal behaviours (Cusson et al., 2018, 2020). Finally, in a few recent studies, MT-InSAR data have been used in combination with in situ sensors, showing the potential of this technology for complementing traditional in situ instruments (Alani et al., 2020; Hoppe et al., 2019; Selvakumaran et al., 2020).

While recent studies have highlighted the potential of MT-InSAR for monitoring infrastructure assets, several limitations still need to be overcome in order to implement MT-InSAR on an operational basis. In this section, the major challenges facing MT-InSAR as a structural monitoring tool are discussed and possible solutions and promising research directions are highlighted.

In contrast to ground-based monitoring instruments that yield deformation measurements at strategic points on a structure, MT-InSAR is an ‘opportunistic deformation measurement method’ (Crosetto et al., 2016; Hanssen, 2005) where the PS location is not known before performing the MT-InSAR analysis. Instead, the availability of PSs within an imaged area depends on several factors, as follows.

The number of PSs is limited because they can only be identified in targets that show stable reflective properties over time. Due to their physical nature, bridges, railways and roadways usually satisfy this condition and can generate a high number of PSs. However, in some circumstances, the ability of infrastructure assets to provide stable backscattering over time can be compromised, leading to either a complete or partial loss of PSs. An example is a structure that is covered by snow for some parts of the year. In such scenarios, few – if any – PSs may be available, thereby limiting the monitoring capabilities of MT-InSAR technology. If flooding or snow coverage only occurs for a limited period of time, images affected by these events can be discarded during processing. However, depending on the duration of these events, this might result in large temporal gaps of deformation evolution, and could limit the potential to study seasonal thermal expansion of assets or may introduce unwrapping errors and phase ambiguities in the displacement time-series (Section 3.5). Another example of limited PSs is for structures undergoing maintenance, such as street re-pavement, construction or demolition works. Due to the absence of repeatable targets, these structures may experience a complete or partial loss of PSs. However, this problem can be overcome by using processing methods that deal with temporary or partially coherent targets, such as the Quasi-PS InSAR technique (Perissin and Wang, 2011). Such techniques extend the capability of conventional MT-InSAR and can be used to estimate the deformation of targets that remain stable over a limited time (i.e. Quasi-PSs), thus increasing the spatial density of monitoring points. In several circumstances, the number of PSs can be limited but, in urban areas, several strong reflectors are naturally available. For these strong reflectors, the main lobe and the secondary lobes of the backscattered radiation can be visible in the radar image, risking compromising the association of a pixel to the corresponding target. Side lobes need to be suppressed during processing (Perissin and Rocca, 2006). Similarly, there is ongoing effort in the field to resolve issues associated with radar interference (Reigber and Ferro-Famil, 2005; Zhou et al., 2007).

Another crucial point is the distribution and dimensions of measurable targets with respect to the sensor spatial resolution. For InSAR images with low resolution, it is likely that multiple targets are contained within the same cell, leading to the identification of a relative low number of PSs. This might prove critical in monitoring structures with a small spatial footprint (e.g. short bridges) and may prevent the acquisition of the minimum number of monitoring points required for damage assessment procedures (Giardina et al., 2019; Macchiarulo et al., 2021b). Consequently, during the development of a monitoring plan, the radar band needs to be selected carefully, based on the study area under consideration, the extent of the structure and the required accuracy. Due to their shorter wavelength, X-band SAR sensors can achieve a finer spatial resolution (up to 30 cm (Prats-Iraola et al., 2012)) than C-band or L-band satellites. They can thus generate a higher number of PSs for short bridges and can even capture discrete measurements for different parts of the structure. As an example, Figure 4 compares the PS density associated with medium-resolution C-band satellites (Figure 4(a)) and high-resolution X-band satellites (Figure 4(b)) for the same motorway junction in Rome, Italy. Figure 5(b) shows the estimated longitudes and elevations of PSs identified on a motorway viaduct in Genoa, Italy. The PSs were obtained by processing the same dataset used by Milillo et al. (2019b), which consisted of 130 COSMO-SkyMed ascending images from 2011 to 2018. Thanks to the high resolution of the COSMO-SkyMed data, the estimated PS elevations (Figure 5(b)) captured the three lanes of the asset (Figure 5(a)). However, as a higher resolution is usually connected to a smaller swath, a larger number of frames is needed to observe the same area when compared with lower resolution satellites (Peduto et al., 2015). If PSs are scarce with high-resolution data, MT-InSAR results could be used to optimally identify which assets should have ground-based monitoring systems installed. An alternative solution would be to install corner reflectors on the structures that did not generate sufficient PSs (Ferretti et al., 2007; Selvakumaran et al., 2020). Corner reflectors are cheaper than in situ monitoring instruments and could be installed in strategic locations on the structure to produce sufficient reflection to be picked up as PSs during processing. However, in the case of damage, alignment errors during installation or layers of dust, the visibility of corner reflectors to a satellite could be compromised (Selvakumaran et al., 2021).

Finally, PSs are usually not evenly distributed – thus, some regions of a structure may be rich in PSs while other regions may have a complete absence of monitoring points. For example, Qin et al. (2018) observed a higher number of PSs on bridge piers and a lower amount of PSs on bridge spans, while Hoppe et al. (2016) noticed gaps in PSs corresponding to traffic lanes. Reasons for the unequal distribution of PSs include (a) the loss of permanent targets due to intense traffic and asphalt radiation bouncing away from the sensor or being absorbed, (b) geometrical distortions caused by the oblique viewing geometry of satellites (see Section 3.2) and (c) diverse backscattering mechanisms associated with different materials and/or geometrical shapes of different components of the structure (Perissin and Ferretti, 2007). Prior to developing a monitoring plan, a virtual SAR simulator (Auer et al., 2009) with the characteristics of the available sensors can be utilised to evaluate the likely availability and distribution of PSs on a structure. Simulation results could prove useful for (a) evaluating the suitability of MT-InSAR technology for monitoring specific structures, (b) selecting the best source of data in terms of both the number of and the distribution of monitoring points and (c) identifying locations that would require either corner reflectors or in situ instruments to be installed for adequate monitoring.

As already mentioned, SAR is a side-looking imaging sensor and the 3D space observed by the satellite is then projected into a planar image in radar coordinates (i.e. slant range and azimuth). Consequently, the acquired images can be affected by geometric distortions of the terrain (Hanssen, 2001). Typical distortion effects are shadowing, foreshortening and layover. These effects can be observed when the visibility of the terrain to the radar sensor is compromised as a result of the orientation of the satellite look direction with respect to the local incidence angle.

Shadowing occurs in areas that are hidden from radar illumination. As a consequence, structures located behind very tall buildings or mountain slopes steeper than the satellite look angle will not be visible to the satellite. This also means that PSs can be abundant for structural surfaces facing towards the satellite while the surfaces facing away may be fully or partially obscured. This is shown for two bridges in Figure 6.

Foreshortening can be observed for structures located on moderately steep mountainous slopes facing towards the satellite or for raised structures where the radar signal reaches different parts of the target simultaneously (such as the roof and wall of a building). As a result, the structure is compressed in the image, with the risk that few if any PSs are available.

Layover occurs for bridges located on slopes facing the satellite and with a steepness in excess of the radar look angle, or for very tall buildings. As a consequence, the structure appears tilted in the resulting image, making it difficult to correctly associate PSs.

Finally, since the flight path of satellites is almost parallel to the north–south (N–S) direction, structures with a N–S alignment and characterised by specular reflections may not be visible to the satellite. This is illustrated in Figure 7, where a segment of the E25 motorway in the Liguria region, Italy, is shown in both optical (Figure 7(a)) and radar (Figure 7(b)) images. In Figure 7(b), the edges and guardrails of the motorway mostly appear as bright pixels because they are very reflective. In contrast, the pixels associated with the road pavement tend to generate weaker returns and thus appear darker in the image. Such amplitude information has been recently used for the assessment of road pavement conditions (Meyer et al., 2020). Furthermore, depending on the orientation of the motorway with respect to the satellite's LoS direction, some parts of the infrastructure appear brighter than others and, consequently, may generate more PSs. Figure 7(b) also shows an example of layover: the bright pixels in the lower left-hand corner of the radar image correspond to the mountain peaks located in the top left-hand corner of the optical image (Figure 7(a)).

The use of datasets from both ascending and descending orbits and/or the integration of data from multiple sensors can mitigate these problems. If opposite viewing directions are used, surfaces and targets in shadow in one image may be visible in the opposing direction. Utilising multiple looking directions with different inclinations can improve coverage and sensitivity to displacement on slopes. Prior to the development of a monitoring plan, a simulator taking a high-resolution digital surface model (DSM) and satellite incidence angles as inputs could be used to identify which sensor minimises these effects and consequently predict which locations are likely to be affected by distortions (Cigna et al., 2014b).

Another aspect that can interfere with structural monitoring is double- or multi-bouncing reflections (Balz et al., 2009; Franceschetti et al., 2002). Double-bouncing arises when the radar signal backscattered by the structure interacts with the ground before being reflected back to the radar, while triple-bouncing is when the radar signal undergoes a further reflection back onto the structure. Double- or triple-bouncing echoes can also occur for bridges over water, where the water acts almost like a mirror to the radar, and with superstructures such as arch bridges (Balz et al., 2009; Cusson et al., 2012; Qin et al., 2018). Figure 8 shows an example of the double-bouncing effect observed in radar images of Pertusillo dam, Italy. In contrast to Figure 8(a) where only a single reflection of the dam crown can be observed, the radar image shown in Figure 8(b) recorded multiple reflections of the crown due to a change in the seasonal water level (Milillo et al., 2016b). Furthermore, the basement of the dam is not visible in the images as it is in shadow. Double-bounce and triple-bounce signals are only virtual effects and should be excluded when estimating deformation (Qin et al., 2018).

Associating PSs with their corresponding structures is another critical aspect of the MT-InSAR technique. The PSs identified during processing usually correspond to different reflecting targets (e.g. bridges, buildings, railways and roadways) located within the area observed by the satellite. To evaluate the performance of a specific structure, the relevant PSs need to be identified and assigned to the target.

During MT-InSAR analysis, PSs are geolocated in 3D space and are thus provided with 3D coordinates (latitude, longitude and elevation). Geospatial tools such as Google Earth or a geographic information system (GIS) can be used to visualise the location of PS data over optical satellite images or base maps, and thus relate deformation to corresponding targets. However, as a consequence of geometric distortions and double-bouncing effects (see Section 3.2), a possible bias in PS geolocalisations, inaccurate height estimations or the presence of multiple targets within the same pixel, PS points can be misassigned and consequently the deformation phenomena misinterpreted.

In several studies, PS data have been analysed in combination with geospatial catalogues of building and infrastructure assets in order to identify points falling within the footprint of structures of interest. While this simple approach usually works well, PSs close to the edges of the structure footprint might not be captured due to the side-looking geometry of SAR sensors or possible localisation errors. This risks losing meaningful information about the behaviour of the structure. Every satellite has a geolocation accuracy that characterises how likely PSs not belonging to a particular structure might be included in the analysis of said structure. Furthermore, due to the possible presence of multiple scatterers within the same pixel, deformation measurements related to targets located within or on a structure, such as traffic lights on roads, could be captured and assigned to the structure. Figure 9 shows an example of geolocation errors observed for PSs extracted on roadways and bridges. Figure 10 shows COSMO-SkyMed MT-InSAR data for a motorway viaduct in the Liguria region, Italy, where some of the PSs assigned to the asset actually correspond to an overhead road sign.

For the analysis of raised structures such as bridges, some researchers have used a filter on PS heights to separate PSs belonging to a structure from PSs located on adjacent ground (Giardina et al., 2019; Huang et al., 2018; Peduto et al., 2017; Qin et al., 2018). For example, Qin et al. (2018) interpolated PS heights to extract the points located on a reinforced concrete bridge and discarded all PSs with an elevation more than three standard deviations from the interpolated curve. However, filtering or fitting PS heights is less suitable for analysing assets with a complex shape (e.g. roadway junctions) or linear structures located at the same ground level (e.g. roads and railways). Hoppe et al. (2019) and Milillo et al. (2019b) used optical images and/or light detection and ranging (lidar) data to improve the alignment of PSs on bridges and correctly identify the points belonging to the assets. In several studies, a buffer around the structure's perimeter was defined to isolate the PSs belonging to a given structure from the entire MT-InSAR dataset (Chang and Hanssen, 2015b; Chang et al., 2016; Delgado Blasco et al., 2019; Ge et al., 2009; Giardina et al., 2019; Infante et al., 2019; Macchiarulo et al., 2021a, 2021b; Peduto et al., 2017). For example, Peduto et al. (2017) used a buffer larger than the structure's footprint to compensate for a possible loss of PSs near the edges of the structure. In this case, a PS geolocation precision of 1.5 m was estimated, and PSs located on the building's roof and falling within a 2 m wide buffer around the building perimeter were assigned to the structure. In this specific application, the additional PSs included in the analysis were mostly correct, with only a few invalid PSs (mainly belonging to lamp posts) introduced. Nevertheless, the suitability of this approach needs to be carefully assessed, especially when analysing roadway junctions or bridges located in dense urban areas where PSs from surrounding structures can be easily introduced.

The geolocation accuracy depends on the satellite SAR sensor and the quality of the DEM used during MT-InSAR analysis (Section 2). For satellites with a large orbital tube, such as COSMO-SkyMed, the geolocalisation can be highly accurate, while PS geolocation is much more difficult for satellites with tight orbital tubes like Sentinel (Milillo et al., 2019b). DEMs provide a 3D representation of the terrain and are used during MT-InSAR analysis to estimate and remove the topographic phase (⁠$ΔΦtopo$⁠) from Equation 3. However, depending on the DEM accuracy, the elevation information contained in the DEM can be affected by errors, leading to the risk that $ΔΦtopo$ is not properly estimated. The difference between the estimated and the real topographic phase is called the residual topographic error (⁠$Δh$⁠). This error can affect the rest of the processing, introducing offsets in the PS coordinates, elevations and deformations. To reduce the level of uncertainty in the deformation measurements, geolocation errors need to be minimised. Jung et al. (2019) observed that $Δh$ can be estimated as suggested by Perissin and Rocca (2006) or Zhao et al. (2017), and then projected onto the east–west and north–west planes to determine latitude and longitude errors:

where $θ$ and $ϕ$ are the inclination of the satellite look direction and the azimuth angle, respectively (Figure 1).

DSMs, which provide a 3D representation of the Earth's surface with the inclusion of bridges and other manmade structures, can be used to detect shifts in PS heights (Chang and Hanssen, 2014). In addition to the use of DSMs, PS localisation can be calibrated by installing an artificial reflector at a specific location and measuring its position using GNSS (Nahli et al., 2020; Yang et al., 2016). Finally, to correct residual geolocalisation errors and improve the localisation accuracy of PSs, PS data could be compared with point clouds measured using lidar (Chang et al., 2020; Montazeri et al., 2018).

Further errors can manifest when incorrectly associating PSs to specific structural elements. This can be critical when local deformation analyses need to be performed or when interpreting the deformations of structures comprised of multiple construction materials or with a complex shape. While artificial corner reflectors could overcome this problem, their use is not always feasible or practical. Three-dimensional urban models obtained from aerial photos or laser technology could be extremely useful to locate the deformation of assets with a complex shape such as arch bridges or roadway junctions. In a recent study, Selvakumaran et al. (2021) showed that PS data analysed in combination with building information modelling (BIM) enabled the visualisation of monitoring data with 3D asset models. To understand which parts of the structure are likely to generate PSs and under what conditions, ray tracing techniques (Auer et al., 2009) can be used in a virtual SAR environment to simulate how different structural shapes and materials influence backscattering.

Another crucial aspect affecting InSAR accuracy is that measurements are restricted to a 1D viewing geometry or LoS. This corresponds to the direction connecting the sensor to the target on the ground, and only a projection of the displacements along the LoS direction is reconstructed during MT-InSAR analysis. Apart from rare cases in which the targets move with a velocity parallel to the satellite look direction, a series of InSAR images from a single viewing geometry cannot fully capture the magnitude and direction of the real deformation and, for most cases, the LoS displacements underestimate the real motion (Hu et al., 2014). This concept is illustrated in Figure 11, which shows a target moving along a direction close to the vertical (Figure 11(a)) and a target with a dominant horizontal motion (Figure 11(b)). In Figures 11(a) and 11(b), the target is observed from both ascending and descending acquisition geometries. It can be observed that the magnitude of the measured deformation (⁠$Δr$⁠) varies according to the satellite acquisition geometry (i.e. ascending or descending) and the direction of the actual movement (⁠$Δractual$⁠). In addition, if the actual motion is mainly horizontal (Figure 11(b)), the two acquisition geometries will measure movements with opposite directions. For example, in Figure 11(b) the displacement measured from an ascending viewing geometry would suggest that the target is moving away from the satellite while, in the descending configuration, movement towards the satellite is detected. Therefore, the level of underestimation increases with the angle between the motion direction and the satellite LoS. For extreme cases where the displacement vector is perpendicular to the LoS direction, the measured displacement is zero, which naturally carries the risk of missing real deformation. Furthermore, since InSAR satellites move along near-polar orbits, this technology is insensitive to N–S movements.

The analysis and interpretation of deformations based on MT-InSAR should be supported by careful consideration of the expected motion, topography and characteristics of the structure under evaluation. Because of the low incidence angle of SAR look directions, MT-InSAR is mostly sensitive to vertical movements. Fuhrmann and Garthwaite (2019) observed that, in some studies, LoS deformations have been interpreted as vertical displacements without discussing the implications of possible horizontal movements (Del Soldato et al., 2016; Solari et al., 2016; Stramondo et al., 2008; Teatini et al., 2005). Prior knowledge of expected motion can be used to make an assumption regarding the direction of the 3D deformation. For example, in areas subjected to uplift, subsidence or tunnelling-induced settlements, motion mainly occurs in the vertical direction and horizontal displacements can be neglected. In these specific scenarios, a common approach is to assume that no horizontal displacements have occurred (Giardina et al., 2019; Milillo et al., 2018; Osmanoğlu et al., 2011; Perissin et al., 2012; Solano-Rojas et al., 2020; Yan et al., 2012) and to estimate the displacement vertical projection (⁠$Δrv$⁠) by dividing the MT-InSAR LoS measurements by the cosine of the radar incidence angle $θ$⁠:

However, if the implications of this assumption are not addressed carefully, depending on the magnitude of the horizontal deformations, the steepness of the local topography and the incidence angle of the satellite looking direction, estimations may result in large errors (Fuhrmann and Garthwaite, 2019). The validity of neglecting the horizontal component should also depend on the structure under analysis. For example, this approximation may be reasonable for studying the tunnelling-induced settlement of stiff buildings (Giardina et al., 2019) or the deformation of roadways in subsiding areas, while bridges are typically subjected to strong thermal effects that may result in large horizontal movements.

To overcome the limitation of 1D LoS measurements, InSAR images from opposite viewing geometries (i.e. ascending or descending) can be used to derive the vertical (up–down) and horizontal (east–west) components of deformation (Milillo et al., 2016b; Wright et al., 2004). This approach involves independent processing of the ascending and descending datasets covering the same location acquired within the same time period to retrieve LoS deformation measurements for each viewing geometry. Then, a co-projection of ascending and descending displacement vectors can be used to resolve the displacement field in the east–west–up–down plane:

where $ΔrDesc$ and $ΔrAsc$ are the ascending and descending cumulative displacements, respectively.

Figure 12 shows an example of the decomposition of LoS displacements from ascending and descending acquisition geometry into up–down and east–west components. PS points identified in the ascending and descending datasets are not necessarily the same and might also be affected by geolocation offsets (Gernhardt et al., 2011). Consequently, to integrate datasets from different viewing geometries, pixels in each dataset need to be interpolated in both time and space. However, when this multi-geometry approach is applied to the analysis of bridges, some problems can arise. Satellites with ascending and descending orbits overpass the same area at different times of the day a few days apart from each other. Consequently, due to the different temperatures and/or environmental conditions of the acquired ascending and descending images, bridges can show different thermal behaviours, making reconstruction of the total movement difficult (Hoppe et al., 2016; Selvakumaran et al., 2020). Furthermore, ascending and descending datasets are not always able to provide measurements for a common area. This might be especially prevalent in mountainous regions where geometric distortions (e.g. shadowing, foreshortening and layover) are very likely, or in urban areas where nearby raised structures (e.g. bridges and tall buildings) can lead to a lack of monitoring points (Section 3.2). Finally, for structures characterised by strong deformations along the N–S direction, two viewing geometries are simply not enough to capture N–S displacements. The possibility of estimating the N–S displacement component and reconstructing a 3D displacement field may be crucial for evaluating the health of bridge structures. However, for bridges orientated along the N–S direction, crucial data are missing.

Some of these problems can be mitigated through the use of multi-geometry/multi-aperture and multi-sensor methods. These methods allow one to combine satellite data acquired from different viewing geometries, frequencies and incidence angles, while simultaneously allowing for the integration of external data sources such as global positioning system or precise levelling (Cuenca et al., 2011a; Fuhrmann et al., 2015; Hu et al., 2014). In contrast to the simple multi-geometry approach – which can only provide deformation measurements in 2D space – a combination of these methods can be used to reconstruct 3D deformations from LoS MT-InSAR measurements. For instance, LoS measurements from different SAR sensors and acquisition geometries can be analysed using the Markov chain–Monte Carlo (MCMC) approach to estimate 3D deformations of analysed assets (Milillo et al., 2016a, 2019b). This approach is useful when an underlying model of the observed deformation is available (Milillo et al., 2016a) or for calculating uncertainties in the 3D displacement field (Milillo et al., 2019b). Furthermore, the use of data from different satellite sensors can increase the range of viewing geometries, potentially providing measurements for structures or regions of structures otherwise in shadow. As an example, Figure 13 shows a schematic illustration of the 3D deformation of key structural elements of Morandi Bridge in Italy. The 3D deformation rates were reconstructed by analysing Sentinel and COSMO-SkyMed MT-InSAR LoS measurements from 2015 to 2018 with the MCMC approach (Milillo et al., 2019b).

The maximum measurable deformation rate depends on the radar wavelength (⁠$λ$⁠) and the satellite interferometric revisit time (⁠$ΔT$⁠) (Kampes, 2006; van Leijen, 2014):

where $ΔΦdefo$ is the deformation phase introduced in Equation 3, $αp$ corresponds to the model used to describe the actual deformation rate (which is a function of $ΔT$⁠), $Dp$ is the deformation parameter and $P$ is the number of models adopted.

Due to the periodic nature of the radar phase, MT-InSAR observations are ambiguous in phase; that is, the measurements are wrapped in the interval $−π$ to $+π$⁠. For two adjacent pixels and two acquisitions separated in time, if the differential deformation phase exceeds $−π$ or $+π$ the deformation cannot be estimated unambiguously. The problem of resolving such phase ambiguity is called phase unwrapping. Without careful consideration of this technological limitation, large and/or fast structural deformations cannot be detected. MT unwrapping approaches can be used to resolve such phase ambiguity. However, these methods are usually limited by the assumption of a phase model (Ferretti et al., 2000). For example, for a linear phase model, Equation 8 can be written as:

where $D1$ is the average displacement rate observed between the first and last InSAR acquisitions. As the maximum deformation that can, in theory, be estimated over repeat interval $ΔT$ is $λ/4$⁠, for a linear deformation model, the maximum deformation rate is (Kampes, 2006; van Leijen, 2014):

When a linear phase model is used (Equation 9), Crosetto et al. (2016) and van Leijen (2014) observed that, for Envisat, TerraSAR-X, Sentinel-1 and ALOS, the maximum deformation rates measurable along the satellite LoS were 14.7 cm/year, 25.7 cm/year, 42.6 cm/year and 46.8 cm/year, respectively. If more complex deformations or higher displacement rates are anticipated, the deformation phase may be modelled through an arbitrary higher order of polynomials, such as quadratic (e.g. $4π/λ(ΔT2D2)$⁠) or cubic (e.g. $4π/λ(ΔT3D3)$⁠). Table 1 shows the maximum deformation rates that can be measured for selected SAR sensors when a linear, a quadratic or a cubic deformation model is used. It is worth noting that the values shown in Table 1 are only theoretical; in practice, the actual deformation rate also depends on noise in the data and the unwrapping technique used during processing. While longer wavelengths enable larger displacements to be retrieved, they also provide a lower resolution and a higher phase noise.

Some MT-InSAR methods adopt a non-linear deformation model (Bakon et al., 2014; Ferretti et al., 2000). These methods enable the observation of a maximum deformation of $λ/2$ over a repeat interval $ΔT$⁠, enabling higher deformation rates to be estimated. However, depending on the low-pass filter adopted during processing, methods using a non-linear deformation model could incorrectly estimate the atmospheric phase term $ΔΦatm$⁠, thus leading to an incorrect estimation of deformations. To minimise errors caused by an incorrect estimation of $ΔΦatm$⁠, there is the need to adopt revisit times as short as possible. Consequently, non-linear methods are more suitable for near-real-time analysis. In this regard, future constellation concepts propose an optimal revisit time of 6 h for atmospheric mitigation during MT-InSAR analysis (Rosen et al., 2019; Zebker and Rosen, 2020). If no prior knowledge exists about the physical model describing the actual deformation field or deformations larger than the theoretical limits are anticipated, such as when assets are located in mining regions (Colesanti et al., 2005), MT-InSAR measurements could be complemented with in situ measurements or integrated with amplitude-based SAR techniques (Casu et al., 2011; Crosetto et al., 2016). For such techniques, the amplitude information of two or multiple SAR images is used to determine the pixel offset at the same positions, providing a 2D estimate of deformation.

Other methods that do not require the assumption of a displacement model during processing are small-baseline techniques (Berardino et al., 2002; Lanari et al., 2004). In these methods, the interferograms in a given series of InSAR images are divided into multiple subsets with small temporal baseline $ΔT$⁠. Then, the interferograms within each subset are unwrapped in space before time-series analysis is performed. However, Ansari et al. (2020) and Usai (2003) observed that small-baseline methods are likely to introduce systematic biases in the deformation phase, risking overestimation of the actual displacement. In the scientific community, discussions on the topic are currently ongoing, thus highlighting the challenging nature of the problem (De Luca et al., 2021; Milillo et al., 2020).

Temporal sampling of deformations is limited by the satellite revisit time. Since most current SAR satellites yield data every 6–24 days, MT-InSAR can effectively monitor slow deformation phenomena, evolving over months or years. Consequently, this technology is appropriate for long-term monitoring of aging assets (Macchiarulo et al., 2021a; Milillo et al., 2019b), where it could provide data at a higher frequency than visual inspections. Similarly, it could be used for assessing the impact of residual settlements on existing structures in post-tunnelling scenarios (Giardina et al., 2019; Macchiarulo et al., 2021b). In its current form, MT-InSAR cannot be used for real-time monitoring and is thus not suitable for monitoring infrastructure response during fast-deformation phenomena or catastrophic events such as typhoons, monsoon events and earthquakes. Recent satellite developments suggest that data with a higher temporal resolution could become available relatively soon. Constellations of satellites, like the COSMO-SkyMed constellation or RADARSAT constellation mission, may be used to achieve shorter repeats, while private agencies could be able to reach daily or hourly imaging capabilities by the end of 2021, with the possibility of providing commercial data for MT-InSAR applications in intervals of 4–6 h (Ignatenko et al., 2021; Stringham et al., 2019).

To remove the $2π$ ambiguity and produce a continuous signal during MT-InSAR analysis, several phase unwrapping techniques have been developed (Costantini et al., 2012; Cuenca et al., 2011b; Hooper and Zebker, 2007; Luo et al., 2019; Wu et al., 2018). These techniques mostly use residual or least-squares methods to unwrap the differential phase in both space and time. However, no universally accepted solutions have been found yet, and unwrapping errors remain a major source of uncertainty in MT-InSAR data. Unwrapping errors are often manually removed during post-processing. If they are not identified and resolved, the dataset will contain anomalies and will not align with other monitoring instruments, increasing the risk of misinterpreting the real deformation response. Unwrapping errors can be recognised when the displacement difference between two subsequent acquisitions is equal to, or close to, half a wavelength. For example, Figure 14 shows two unwrapping errors in the time domain for a PS detected on a Los Angeles highway after processing Sentinel data between 2016 and 2019 (Macchiarulo et al., 2021a).

Another possible source of error is the criteria used to estimate the reliability of deformation measurements. The quality of MT-InSAR data is quantified in terms of its temporal coherence $ξPS$⁠:

where $N$ is the number of InSAR images used during processing and $ΔΦn$ and $ΔΨn$ are the measured and modelled interferometric phase of the nth InSAR image, respectively. The temporal coherence can vary between 0 and 1, and is inversely proportional to the signal-to-noise ratio. Thus, the higher the coherence, the more accurate and reliable subsequent displacement estimates will be, according to the phase model adopted.

To minimise the level of noise in measurements and identify only highly reliable scatterers, PSs are usually selected by applying a coherence threshold. At present, no common agreement exists about the optimal coherence threshold. In some studies, all PSs with a coherence greater than 0.6 or 0.7 are selected (Ma et al., 2019; Milillo et al., 2019b; Selvakumaran et al., 2020) while, in others, more conservative values such as 0.8 or 0.9 are adopted (Cusson et al., 2018; Giardina et al., 2019; Macchiarulo et al., 2021b; Sousa and Bastos, 2013). It is worth noting that high threshold values not only reduce the probability of false alarm rates but also reduce the number of PSs selected (Figure 15); consequently, the risk of losing valuable information increases. If the coherence threshold is too low, noisy points will be introduced into the analysis and the structural deformation could consequently be misinterpreted. Thus, to successfully exploit MT-InSAR technology, an optimal balance between the number of monitoring points and the reliability of estimates needs to be found.

Theoretically, the higher the coherence (⁠$ξPS$⁠), the lower the dispersion (⁠$σdisp$⁠) of the estimated measurements (Colesanti et al., 2003):

The number of images used during processing (⁠$N$⁠) and the wavelength of the satellite SAR sensor (⁠$λ$⁠) also impact measurement uncertainty. For example, Colesanti et al. (2003) observed that for, C-band satellites (e.g. ERS/Envisat and Sentinel), $ξPS$ values of 0.8, 0.9, 0.95 and 0.975 correspond to $σdisp$ values of 3, 2, 1.44 and 1 mm, respectively. Based on these coherence values, theoretical $σdisp$ values for X-band, C-band and L-band satellites are shown in Table 2. Similarly, the standard deviation of velocity (⁠$σΔv2$⁠) decreases for shorter wavelengths and as $N$ increases. For a linear phase model:

where $σT$ is the variance of the temporal baseline $ΔT$ and $σΦ$ is the variance of the phase noise, which is a function of the temporal coherence ( $σΦ≈−2lnξPS1/2$⁠). Equations 12 and 13 suggest that, depending on the number of images adopted during processing and the wavelength of the satellite SAR sensor, different coherence thresholds could be adopted. According to Perissin and Wang (2011), when the number of images available is small (e.g. N < 25), a minimum temporal coherence of 0.9 should be used; while images are more abundant (e.g. N > 60), the coherence threshold can be decreased to 0.7. However, such values were proposed on the basis of theoretical modelling (Colesanti et al., 2003) and only apply to C-band SAR satellites with a large orbital tube, such as ERS and Envisat. To the authors’ knowledge, no studies show the impact of setting different coherence thresholds for real scenarios and for SAR satellites with different characteristics.

The efficacy of a coherence selection method further depends on the accuracy of the deformation model used during the processing (Colesanti et al., 2003). Most MT-InSAR methods use a linear deformation model. Consequently, in areas characterised by highly non-linear movements, a coherence drop is observed due to the lack of conformity between the actual deformation and the adopted model. In these scenarios, low coherence values may be interpreted as noise in the data and can lead to some PSs being incorrectly classified as unreliable and discarded, or the estimated deformations may underestimate the actual displacement. Naturally, this has significant implications for infrastructure monitoring, where cracking, material deterioration and damage processes are frequently described by non-linear trends (Chang et al., 2003). Some MT-InSAR algorithms enable the use of a non-linear deformation model (Bakon et al., 2014; Ferretti et al., 2000). However, these methods are usually computational demanding and thus unsuitable for regional analysis.

Bridges, buildings and transport infrastructure usually remain highly coherent over a time-series of InSAR images. However, in the presence of snow coverage, traffic (Milillo et al., 2020), maintenance, construction or demolition works (Section 3.1), these targets may lose coherence and behave as Quasi-PSs. In addition to the use of techniques dealing with this specific problem (Perissin and Wang, 2011), a recent study by Refice et al. (2020) explored the possibility of using parameters other than coherence to discriminate non-linear deformations or partially coherent targets from a subset of PSs with very low coherence. In that study, fuzzy entropy – a parameter completely independent from the model adopted during processing – was used to characterise InSAR time-series on both simulated and real data. Despite the promising results, the need for a very long series of images (⁠$N>180$⁠) to achieve stable results may be the limiting factor for this approach and more studies are needed to assess its robustness.

Specialised processing skills remain a barrier preventing the widespread adoption of MT-InSAR data within the civil engineering industry. Estimating deformations from long temporal series of InSAR images involves a number of non-intuitive steps, which can be challenging for non-specialists. Results of MT-InSAR analysis rely heavily on the assumptions made and the parameters chosen during processing. Chang and Hanssen (2015a) observed that, depending on the employed processing criterion and threshold values used, very different outcomes could be obtained for the same area (Chen et al., 2012; Xie et al., 2010) or for the same dataset (Sousa et al., 2011). Over recent years, several software packages reproducing the core steps of MT-InSAR analysis have been developed. These user-friendly programs are designed for a wide range of different applications and provide highly flexible environments. However, users with insufficient experience could easily adopt false assumptions or inappropriate input parameters without fully understanding their influence, thus compromising the results.

The development of user-ready products can minimise these problems, keeping the use of MT-InSAR data accurate and easy at the same time. Open-source MT-InSAR datasets processed by radar experts are starting to become available (Costantini et al., 2017; Crosetto et al., 2020; Raspini et al., 2018), making MT-InSAR-derived measurements more accessible to stakeholders. To facilitate user-friendliness, data should be provided in a format that is easily accessible through standard GIS platforms and with detailed metadata.

To guide users with no radar experience through the processing, the practical impact of different assumptions and parameters should be investigated. There is therefore a need for more comparative and systematic studies that compare different processing methods and assess the sensitivity of results to input parameter settings and circumstances. This could help to identify the most appropriate approach for specific structural monitoring applications, with the further possibility of standardising the procedure.

Finally, while consolidated knowledge and experience in MT-InSAR technology may be crucial to secure reliable results, deep knowledge of the processes governing structural deformation is fundamental to correct interpretation of MT-InSAR measurements for structural monitoring applications. The next generation of civil engineers should be trained in this remote sensing technique, while collaborations between radar scientists and civil engineers should be encouraged and communication strengthened.

MT-InSAR has the potential to be a cost-effective tool for transport infrastructure monitoring, enabling infrastructure managers to move from reactive to proactive maintenance, preserving functionality while increasing network resilience. MT-InSAR can provide highly accurate deformation point measurements over wide areas at fine spatial resolution, enabling the observation of both individual assets and whole networks. These measurements could be used to estimate structural performance indicators or provide the inputs for prediction procedures, with the potential to provide asset managers with the data they need to make risk-related lifecycle decisions (e.g. maintenance scheduling) to maximise asset utility efficiently and increase network resilience. As this technology operates remotely, it is environmentally friendly and safer than ground-based monitoring. It could complement and extend upon in situ monitoring, thus simplifying logistics and reducing costs. Thanks to the availability of historical archives of SAR images, MT-InSAR enables the study of past structural failures and construction incidents for which monitoring data is not available, with the potential to provide new insights into failure mechanisms.

However, despite numerous studies demonstrating the potential of MT-InSAR technology for structural monitoring, several challenges still need to be addressed. In this paper, the major current challenges were analysed from a structural monitoring perspective. The following conclusions were drawn from this work.

• Due to the ‘opportunistic’ nature of MT-InSAR techniques, the locations and distribution of monitoring points are known only after completion of the MT-InSAR analysis. Consequently, the availability of PSs for a specific structure cannot be guaranteed. In addition, due to, for example, snow coverage and maintenance activities, the pixels related to a structure can lose coherence within the series of InSAR images, causing complete or partial loss of PSs. For structures characterised by a lack of PSs, corner reflectors could be used to reproduce artificial scatterers and ‘supply’ monitoring points. Ray tracing techniques could be used to create a virtual SAR environment with the characteristics of available SAR sensors. This environment could then be used to predict the capability of the structure to generate PSs based on its material properties and in relation to existing SAR satellites. Finally, Quasi-PS InSAR techniques could be used to deal with partially coherent targets.

• Radar images provide 2D representations of the real world. For raised structures, steep topography or in urban areas, some geometric distortions can be observed. In addition, scattering interactions between a structure and nearby surfaces can be recorded in InSAR images, producing geometrical artefacts. The use of MT-InSAR data from multiple satellites and acquisition geometries can improve the chance of observing structures in shadow, while simulations can be used to predict geometrical distortions and artefacts before undertaking processing.

• Correctly associating monitoring points to the corresponding structure or to a specific part of that structure can be complicated by the aforementioned artefacts and distortions, possible geolocation offsets, the presence of additional targets on the structure (e.g. traffic lights and road signs) and the complex shape of some structures (e.g. arch bridges and roadway junctions). DSMs and lidar-based point clouds can be used during the post-processing phase to improve the geolocation accuracies of PSs and identify unwanted targets on the structure. High-resolution data can capture deformations for different parts of the structure and building information modelling (BIM) can be used to interpret measured deformations in relation to different structural components.

• To study the deformation of transport infrastructure, 1D LoS measurements obtained from MT-InSAR analysis need to be converted into 3D space, and possibly projected onto the structural reference system. However, due to the 1D nature of the sensor viewing geometry, deformations derived from a single acquisition geometry cannot fully capture the magnitude and direction of the actual displacement field. In addition, for the extreme case of movements occurring along a direction orthogonal to a satellite LoS, deformations cannot be measured. Consequently, without correct understanding or interpretation of LoS measurements, the actual deformation of a structure could be underestimated. While the simple projection of measurements from a single acquisition geometry could lead to large underestimations, the integration of MT-InSAR measurements with other monitoring data (e.g. GNSS) or the combined use of MT-InSAR data from multiple viewing geometries and sensors can help estimate 2D or 3D deformations more accurately.

• The magnitude of the maximum detectable deformation is limited by the cyclic nature of the phase and is thus connected to the sensor wavelength, while the detectable deformation rate is limited by the satellite revisit time. Consequently, large and/or fast structural deformations may not be detected or may be incorrectly reconstructed in time/space, leading to unwrapping errors. Despite repeated efforts by the radar science community to resolve this technical limitation, the issue persists. More robust processing algorithms able to detect and resolve phase ambiguity are needed.

• The criteria used to assess the reliability of MT-InSAR measurements is another important limitation of the technology. There is the need for a quality estimator independent from the deformation model adopted during processing.

• Finally, to exploit the full potential of MT-InSAR for structural monitoring purposes, both the technology and products developed should be made more accessible to the civil engineering community. If the barrier to entry is lowered sufficiently, widespread industry adoption could ensue. To facilitate this, there needs to be more avenues to nurture cooperation between radar experts and the civil engineering community.

Valentina Macchiarulo was supported by a PhD scholarship granted by Sue and Roger Whorrod and the Alumni programme of the University of Bath. This publication is also part of project number OCENW.XS5.114 of the research programme Open Competition Domain Science – XS, which is financed by the Dutch Research Council (NWO).

$D1$

deformation parameter for linear phase model

$Dmax$

maximum deformation rate

$Dp$

deformation parameter

$N$

number of images

$P$

number of models

$2r$

two-way travel distance between radar and target

t₀

time of first acquisition or reference time

t₁

time of second acquisition

$αp$

model used to describe actual deformation rate

$Δh$

residual topographic error

$Δr$

line of sight displacement (or measured deformation)

$Δractual$

actual displacement of target

$ΔrAsc$

line of sight displacement measured from ascending acquisition geometry

$ΔrDesc$

line of sight displacement measured from descending acquisition geometry

$ΔrEast$

displacement in east–west plane

$ΔrUp$

displacement in up–down plane

$Δrv$

displacement vertical projection

$ΔT$

satellite interferometric revisit time (or temporal baseline)

$Φ$

phase

$ΔΦ$

phase variation (or interferometric phase)

$ΔΦdefo$

phase variation due to target movement

$ΔΦearth$⁠, $ΔΦtopo$⁠, $ΔΦatm$⁠, $ΔΦnoise$

phase variation due to flat earth terrain, topography, atmospheric delay and noise, respectively

$ΔΦn$⁠, $ΔΨn$

measured and modelled interferometric phase of nth InSAR image

$θ$

satellite look angle

$λ$

wavelength

$σdisp$

dispersion of measured displacement

$σT$

variance of temporal baseline $ΔT$

$σΔv2$

standard deviation of velocity

$σΦ$

variance of phase noise

 $ξPS$

temporal coherence

$ϕ$

azimuth angle