The growing availability of SAR data offers a real-time deformation monitoring opportunity, but data utilization can be inefficient. Our study introduces a mathematical framework using recursive least-squares and the wrapped phase, allowing efficient updates when new data arrives. This method also incorporates prior knowledge about signal smoothness for non-linear displacement estimation. Compared to the batch solution, our recursive approach achieves parameter estimation without storing past measurements while respecting signal smoothness constraints.

@en

InSAR enables the estimation of spatio-temporal displacements, relative to a reference point and a reference epoch, here defined as the mother image. When dealing with time series, there are several options to treat the mother image in computing and plotting the temporal phase differences, producing distinctly different results, in terms of the estimated displacement parameters and their precision. Here we review the three approaches mostly encountered in literature, discuss the implications of the different approaches, and recommend the 'embracing mother' approach for standard InSAR analyses and visualizations.

@en

We introduce SARXarray and STMtools, two python libraries designed to support the exploitation of modern Interferometric Synthetic Aperture Radar (InSAR) data by enabling handling of larger-than memory datasets and the incorporation and fusion with relevant contextual information.The libraries are developed upon two innovative and well-established open-source Python libraries:Xarray [5] and Dask [6]. They are implemented as Xarray extensions. SARXarray is designed to manipulate and operate on larger-than-memory coregistered raster stacks such as Single-look Complex images (SLC) or interferograms, performing scatterer selection and producing STM objects. STMtools leverage the Space-Time Matrix (STM) concept [3,4] and provides functionalities to process STM and perform enrichment/data fusion with other data sources.Both libraries are built on the Xarray library, providing support for a wide range of data formats, and utilize Dask for parallel computation, making them scalable for distributed computation infrastructures. By enabling InSAR data analysis incorporating contextual information, the two libraries enhance the potential to uncover underlying mechanisms driving deformation phenomena.

@en

Ghana's coastline has been facing erosion and sedimentation phenomena for several decades, resulting in a serious threat to life and property considering that major urban settlements are located on the coast. In this region, there has been a lack of emphasis on comprehensive, large-scale investigations into coastal changes: prior research has predominantly centered on site-specific assessments. These studies have revealed alarming erosion rates, with reports indicating that nearly ten meters are lost annually. The use of high-resolution remotely sensed data can be a consistent support in regions where physical or economic obstacles interfere with collecting in situ information. In particular, the use of continuous all-weather SAR data may facilitate the evaluation of erosion and sedimentation phenomena in coastal areas. In this paper, we apply SAR data over a time period between 2017 and 2021. Sentinel-1 data are pre-processed using the Google Earth Engine platform, and a dedicated algorithm is then applied to identify and quantify erosion and sedimentation processes. Optical images are used as a reference for detecting the location of two areas where consistent sedimentation and erosion phenomena occurred in the considered four years. The results demonstrate that SAR backscattering variations over time offer a reliable method for monitoring coastal changes. This approach enables the identification of the type of phenomena occurring - sedimentation or erosion -, and allows for the quantification of their intensity and dimensions over time. The method can be worldwide applied once the appropriate thresholds are evaluated and help in predictive studies and environmental planning.

@en

We present the preliminary results of an InSAR analysis of peatland surface motion covering a large spatial and temporal extent. This work is the first large scale analysis of the Dutch Green Heart region, and is made possible using a novel distributed scatter (DS) InSAR processing method. This method is designed to handle breakages in the observed interferometric phase time series which occur due to temporal decorrelation, which we designate with the term loss-of-lock.

@en

The repeat period of SAR data and its side-looking characteristics make InSAR time series analysis useful for water level monitoring applications. The standard approach determines corresponding scatterers by focusing the study area on the multipath radar reflections that include the water level. This paper introduces an alternative approach to identifying such signals using two metrics: cosine similarity and temporal differential coherence. The results show that temporal differential coherence can detect phase variations similar to water level by constantly returning high values even when there is an offset, while cosine similarity yields low scores. Within an urban environment, this approach finds point scatterers corresponding to water level changes in or near water, such as permanent floating objects, bridges, and buildings adjacent to water, where the highest differential coherence value was acquired from a permanent floating restaurant in open water.

@en

In the view of climate change, understanding and managing effects on coastal areas and adjacent cities is essential. Permanent Laser Scanning (PLS) is a successful technique to not only observe notably sandy coasts incidentally or once every year, but (nearly) continuously over extended periods of time. The collected point cloud observations form a 4D point cloud data set representing the evolution of the coast provide the opportunity to assess change processes at high level of detail. For an exemplary location in Noordwijk, The Netherlands, three years of hourly point clouds were acquired on a 1 km long section of a typical Dutch urban sandy beach. Often, the so-called level of detection is used to assess point cloud differences from two epochs. To explicitly incorporate the temporal dimension of the height estimates from the point cloud data set, we revisit statistical testing theory. We apply multiple hypothesis testing on elevation time series in order to identify different coastal processes, like aeolian sand transport or bulldozer works. We then estimate the minimal detectable bias for different alternative hypotheses, to quantify the minimal elevation change that can be estimated from the PLS observations over a certain period of time. Additionally, we analyse potential error sources and influences on the elevation estimations and provide orders of magnitudes and possible ways to deal with them. Finally we conclude that elevation time series from a long term PLS data set are a suitable input to identify aeolian sand transport with the help of multiple hypothesis testing. In our example case, slopes of 0.032 m/day and sudden changes of 0.031 m can be identified with statistical power of 80% and with 95% significance in 24-h time series on the upper beach. In the intertidal area the presented method allows to classify daily elevation time series over one month according to the dominating model (sudden change or linear trend) in either eroding or accreting behaviour.

@en

We introduce the term loss-of-lock to describe a specific form of coherence loss that results in the breakage of a synthetic aperture radar interferometric (InSAR) time series. Loss-of-lock creates a specific pattern in the coherence matrix of a multilooked distributed scatterer (DS) by which it may be detected. Along with identification, we introduce a new DS processing methodology that is designed to mitigate the effects of loss-of-lock by introducing contextual data to assist in the time-series processing. This methodology is of particular relevance to regions that suffer from severe temporal decorrelation, such as northern peatlands. We apply our new method to two subsiding cultivated peatland regions in The Netherlands which previously proved impossible to monitor using DS InSAR techniques. Our results show a very good agreement with in situ validation data as well as spatial correlation between regions and the natural terrain.

@en

InSAR enables the estimation of displacements of (objects on) the earth's surface. To provide reliable estimates, both a stochastic and mathematical model are required. However, the intrinsic problem of InSAR is that both are unknown. Here we derive the Variance-Covariance Matrix (VCM) for double differenced phase observations for an arc, i.e., the phase difference between two points relative to a reference epoch. Using the Normalized Amplitude Dispersion we subdivide the time series in multiple partitions. The method results in a more realistic stochastic model, and consequently more realistic and reliable displacement parameters. The stochastic model also allows to make statements on the precision and reliability of the estimated parameters.

@en

We present SPAMS: Simple Parameterization for the Motion of Soils, a model to describe the motion of deformable soils in the Vadose zone, mainly peat and clay, herein called shallow soft soils. The SPAMS model estimates the reversible and irreversible vertical component of surface displacement to within sub-centimetre RMSE, using only four parameters: three scaling factors and an integration time. Requiring only meteorological data as an input, its lightweight nature and simple implementation make it a powerful tool when used as a first approximation in inverse problems like those encountered in remote sensing. It has been validated against in-situ data from five test sites in The Netherlands with different Holocene soil strata.

@en

The estimation of displacement vectors for (objects on) the Earth's surface using satellite InSAR requires geometric transformations of the observables based on orbital viewing geometries. Usually, there are insufficient viewing geometries available for full 3-D reconstruction, leading to nonunique solutions. Currently, there is no standardized approach to deal with this problem, resulting in products that are based on haphazard and/or oversimplified assumptions with biased estimates and reduced interpretability. Here, we show that a clear definition of - and subsequent adherence to - enabling conditions guarantees the validity and quality of displacement vector estimates leading to standardized interferometric products with improved interpretability. We introduce the concept of the null line as a key metric for InSAR geometry and bias estimation, assess its impact and orientation for all positions on Earth, and propose a novel reference system that is inherently unbiased. We evaluate current operational practice, leading to a taxonomy of frequently encountered misconceptions and to recommendations for InSAR product generation and interpretation. We also propose new subscript notation to uniquely distinguish different projection and decomposition products. Our propositions contribute to further standardization of InSAR product definition, improved map annotation, and robust interpretability.

@en

The observed phase in time series of interferometric synthetic aperture radar (InSAR) products is a superposition of various components. Differential topography, line-of-sight displacements, and differential atmospheric delays are the main contributions and need to be disentangled to derive accurate digital elevation model (DEM), deformation, or atmospherical products from InSAR. However, isolating the atmospheric component has been proven difficult as it is spatiotemporally highly dynamic and a superposition of two atmospheric states. Here, we propose an approach to parameterize the stochastic properties of the single-epoch atmospheric delay field as a way to define the atmospheric signal. We found that the atmospheric signal of a time series of interferograms can be characterized by structure functions, which can be used to isolate the single-epoch structure functions. Due to the scaling properties of the atmospheric signal, it is then possible to construct a parametric function per SAR acquisition, using two isotropic and three anisotropic parameters. In particular, the isotropic parameters for the short-distance variation and long-distance variation in atmospheric delay can be used to characterize the atmospheric signal. For a test set of 151 Sentinel-1 acquisitions, this results in an atmospheric energy range of about 10 for short-distance scales and about 50 for long-distance scales. Our parameterization demonstrates that we can describe the spatiotemporal variability of InSAR atmospheric delays, which provides a measure for atmospheric noise for individual epochs in deformation time series based on distance and azimuth.

@en

Multi-epoch interferometric synthetic aperture radar (InSAR) is a highly effective technique for monitoring deformation in urban areas. However, interpreting InSAR deformation can be challenging due to various factors, including inherent geometric imaging distortion, the intricate structure and deformation properties of targets in urban scenes, and the multiple scattering of microwave signals between objects in urban scenes. This paper discusses the challenges involved in interpreting time-series InSAR deformation: (1) Precisely identifying the location of deformation signals and linking them to their corresponding objects, i.e., determining where the deformation signal occurs, (2) understanding the mechanisms and factors that cause the detected deformation signals, i.e., determining what the deformation signal represents, (3) establishing the connection among the detected deformation signals, the deformation events, and the scattering mechanisms. We suggest a parametric framework to improve the accurate interpretation of InSAR deformation. This framework includes several factors, including kinematic characteristics (deformation rate, cumulative deformation, deformation gradient, and deformation model), geometric parameters (position, size, structure, orientation, and roughness), semantic information (land cover type, terrain morphology, texture, and auxiliary information on natural and anthropogenic disturbance) and physical properties (scattering mechanism, penetrability, extensibility, conductivity, and thermal conductivity). Our approach aims to enhance the representation of coherent points for a better understanding of InSAR deformation. This paper offers a comprehensive overview of the advancements achieved in extracting parameters of InSAR coherent points and interpreting deformation based on geometric parameters, semantic information, and physical properties. High-precision 3D positioning is crucial for InSAR fine monitoring in urban areas. It helps determine the source of deformation signals and facilitates the analysis of deformation mechanisms. Semantic information, such as 3D models, high-resolution optical images, laser point cloud data, and land use data, can aid in interpreting InSAR deformation. By combining InSAR deformation data with a deep learning approach, there is an opportunity to interpret deformations effectively. In urban environments, the scattering mechanism of ground objects is complex. Multiple scattering signals can provide effective observations of deformation and information about the target’s size. However, combining the scattering mechanism of synthetic aperture radar signals to carry out parameter inversion and deformation mechanism interpretation of urban target terrain remains a challenge. The framework, which considers the geometric parameters, semantic information, and physical attributes of InSAR coherent points, will be crucial for deformation interpretation and mechanism cognition. This framework will enable fine deformation monitoring, intelligent recognition, and application in future urban scenes.

@en

The dramatic improvement in access to satellite imagery and data processing tools makes it possible to observe deformations of the Earth's surface in near real time. Remote sensing imagery is a powerful, reliable, and spatially dense source of information that can be used to understand the Earth and its surface manifestations as well as to mitigate natural hazards.This book provides a comprehensive analysis of the methodological approaches developed to measure surface displacements using synthetic aperture radar (SAR) or optical images, and their applications in monitoring major geophysical phenomena. The first part presents the foundations of radar interferometry (lnSAR) and image correlation as well as the latest developments. The second part reviews the applications of these methods to geophysical phenomena and anthropogenic activities causing deformations of the Earth's surface.@en

Phase unwrapping, also known as ambiguity resolution, is an underdetermined problem in which assumptions must be made to obtain a result in SAR interferometry (InSAR) time series analysis. This problem is particularly acute for distributed scatterer InSAR, in which noise levels can be so large that they are comparable in magnitude to the signal of investigation. In addition, deformation rates can be highly nonlinear and orders of magnitude larger than neighboring point scatterers, which may be part of a more stable object. The combination of these factors has often proven too challenging for the conventional InSAR processing methods to successfully monitor these regions. We present a methodology which allows for additional environmental information to be integrated into the phase unwrapping procedure, thereby alleviating the problems described above. We show how problematic epochs that cause errors in the temporal phase unwrapping process can be anticipated by the machine learning algorithms which can create categorical predictions about the relative ambiguity level based on the readily available meteorological data. These predictions significantly assist in the interpretation of large changes in the wrapped interferometric phase and enable the monitoring of environments not previously possible using standard minimum gradient phase unwrapping techniques.

@en

Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an earthquake's faulting mechanism. This inverse problem requires a numerical forward model that is both accurate and fast, as typical inverse procedures require many evaluations. The Weakly-enforced Slip Method (WSM) was developed to meet these needs, but it was not before applied in an inverse problem setting. Consequently, it was unknown what affects particular properties of the WSM, notably its inherent continuity, have on the inversion process. Here we show that the WSM can accurately recover slip distributions in a Bayesian-inference setting, provided that data points in the vicinity of the fault are removed. In a representative scenario, an element size of 1 km was found to be sufficiently fine to generate a posterior probability distribution that is close to the theoretical optimum. For rupturing faults a masking zone of 10 km sufficed to avoid numerical disturbances that would otherwise be induced by the discretization error. These results demonstrate that the WSM is a viable forward method for earthquake inversion problems. While our synthesized scenario is basic for reasons of validation, our results are expected to generalize to the wider gamut of scenarios that finite element methods are able to capture. This has the potential to bring modeling flexibility to a field that is often forced to impose model restrictions in a concession to computability.

@en

Peat areas in the Netherlands are expected to exhibit extremely dynamic vertical motion, including both reversible and irreversible components. Yet the exact behaviour as a function of time is unknown, and is spatially very variable. This results in a poorly known estimation of greenhouse gas emissions and impact to existing infrastructure, and consequently limited ability to design and deploy mitigating or adaptive measures. In situ measurements are inefficient to capture this dynamic spatio-temporal variability. To monitor wide areas, InSAR has the necessary coverage, resolution, and high temporal sampling, but is very sensitive to noise due to temporal decorrelation of vegetated areas, which in combination with the high temporal dynamics exacerbates the success rate of the phase ambiguity estimation. Moreover, motion measured with InSAR is inherently relative to a reference point which is typically not stable in time. Thus even if InSAR would yield sufficiently coherent results, interpretation is notoriously difficult. To address these problems, an Integrated Geodetic Reference Station (IGRS) was installed in a peat area. It includes SAR reflectors mechanically coupled to a GNSS antenna. Arcs from the IGRS to natural scatterers can therefore be connected to ETRS89. The resulting arcs are thus single-differences of elevation with respect to a reference epoch. In order to reduce noise, and subsequently increase the success rate of ambiguity resolution, we define Elementary Usage Polygons (EUPs), which are expected to move homogeneously. This is achieved by constraining each EUP to have only one subsurface type and one land usage, which allows for the definition of an expected functional model of the vertical movement. Using the expected functional model in combination with the GNSS measurements on the IGRS we can constrain the unwrapping on the arcs between the IGRS and nearby EUPs in order to improve the success rate of the unwrapping. By making use of elevation model data from 2020, the elevation of the reference epoch can be constrained. The single-difference arcs showing elevation change with respect to the reference epoch are transformed into elevations with respect to NAP, allowing for an absolute elevation time series from InSAR observations in the vegetated rapid-moving peat areas of the Netherlands.@en

Compact and low-cost radar transponders are an attractive alternative to corner reflectors (CRs) for interferometric synthetic aperture radar (InSAR) deformation monitoring, datum connection, and geodetic data integration. Recently, such transponders have become commercially available for C-band sensors, which poses relevant questions on their characteristics in terms of radiometric, geometric, and phase stability. Especially for extended time series and for high-precision geodetic applications, the impact of secular or seasonal effects, such as variations in temperature and humidity, has yet to be proven. In this article, we address these challenges using a multitude of short baseline experiments with four transponders and six CRs deployed at test sites in The Netherlands and Slovakia. Combined together, we analyzed 980 transponder measurements in Sentinel-1 time series to a maximum extent of 21 months. We find an average radar cross section (RCS) of over 42 dBm2 within a range of up to 15° of elevation misalignment, which is comparable to a triangular trihedral CR with a leg length of 2.0 m. Its RCS shows the temporal variations of 0.3-0.7 dBm2 (standard deviation), which is partially correlated with surface temperature changes. The precision of the InSAR phase double differences over short baselines between a transponder and a stable reference CRs is found to be 0.5-1.2 mm (one sigma). We observe a correlation with surface temperature, leading to seasonal variations of up to ±3 mm, which should be modeled and corrected for in high-precision InSAR applications. For precise SAR positioning, we observe antenna-specific constant internal electronic delays of 1.2-2.1 m in slant range, i.e., within the range resolution of the Sentinel-1 interferometric wide (IW) product, with a temporal variability of less than 20 cm. Comparing similar transponders from the same series, we observe distinct differences in performance. Our main conclusion is that these characteristics are favorable for a wide range of geodetic applications. For particular demanding applications, individual calibration of single devices is strongly recommended.

@en

In the planning stage of new infrastructure or when designing renovation of existing infrastructure, information about existing slope movements or settlements is essential to make informed design decisions. Interferometric
Synthetic Aperture Radar (InSAR) techniques can be of value to identify these risks in an early stage of a project. InSAR can offer insight into the surface movements of an area from historic archives using satellite-based SAR
data. Furthermore, InSAR observations can help identify zones with displacements larger than the average of an area, and be used to plan future soil investigation more effectively. Thanks to their high temporal and spatial resolution, InSAR observations can also complement in situ conventional monitoring during the construction and operational stage. Despite these possibilities, the use of InSAR is not yet standard practice in geotechnical projects
and no formal guidelines are currently available to inform engineers, planners and infrastructure stakeholder on the use of InSAR-based monitoring within geotechnical design codes. Here we provide an operational framework for the practical integration of InSAR monitoring into current geotechnical design codes, such as Eurocode-7, for all project stages. The proposed framework is then demonstrated for the planning stage of a highway renovation project, focusing on an area potentially subjected to landslides where no conventional monitoring
data was available at this stage. We concluded that the proposed framework is a practical and operational
tool that can be used by planners and engineers in the whole lifecycle of an infrastructure project.@en