The main objective of this paper is to develop and evaluate a pragmatic approach to obtain an InSAR stochastic model for reduced InSAR datasets. This goal is achieved by calculation of the stochastic parameters per InSAR stack, propagating the noise structure to reduced datasets. The propagation of full covariance matrices when using a reduced dataset in space and time is avoided, using the derived analytical functions. This way, a computationally efficient approximation of the exact covariance matrix is obtained for reduced datasets. ... Read more

This paper describes several geodetic studies that consolidate the reliability and precision of monitoring subsidence due to hydrocarbon production: the deployment of Integrated Geodetic Reference Stations (IGRS); the application of high resolution InSAR; the comparison of different GNSS processing methodologies; the implementation of an efficient InSAR stochastic model, and the framework of integrated geodetic processing (levelling, GNSS, InSAR). The advances that have been made are applicable for any other subsidence monitoring project. ... Read more

Temporal decorrelation is one of the main error sources in satellite radar interferometry. As the range of physical mechanisms causing temporal decorrelation is wide, there is no single analytical method to model this effect. Recent studies report seasonally varying coherence behavior over pasture areas, which cannot be described by the current analytical models of temporal decorrelation. To acknowledge this periodicity, we introduce a new analytical model. Here, the hypothetical movements of elementary scatterers within resolution cells are modeled as a periodic stochastic process with non-stationary increments. The proposed model is a function of the temporal baseline and the date of the master image of each interferogram. The parameters of the proposed decorrelation model have been estimated and validated for a case study in the Netherlands ... Read more

The Rhine-Meuse-Scheldt delta is shaped by natural and manmade landscapes. Over many polder areas, soils are drained to be used as pastures. Around 30% of the pastures are situated on peat soils, of which many are located in the western part of the Netherlands, known as the ‘Green Heart’. Peat is composed of organic materials that oxidize and emit greenhouse gases when exposed to air as a consequence of the draining. Oxidation of peat soils results in volume reduction and subsequent subsidence. As a result, the groundwater level rises relative to the surface. Consequently, the soil needs to be dewatered to keep it sufficiently dry for farming, resulting in more oxidation, and therefore more subsidence. This process is bound to continue until the peat soils have disappeared completely. The societal cost of land subsidence due to peat soils are estimated to be 5200 million euro for urban areas and 200 million euro for peatland pastures, for a period until 2050. ... Read more

During the last decades, time-series interferometric synthetic aperture radar (InSAR) has been emerged as a powerful technique to measure various surface deformation phenomena of the earth. The multivariate statistics of interferometric phase stacks plays an important role in the performance of different InSAR methodologies and also in the final quality description of InSAR derived products. The multivariate phase statistics are ideally described by a joint probability distribution function (PDF) of interferometric phases, whose closed-form evaluation in a generic form is very complicated and is not found in the literature. Focusing on the first two statistical moments, the stack phase statistics can be effectively described by a full (co)variance matrix. Although a closed-form expression of interferometric phase variances has been derived in literature for single-looked pixels, there is no such an expression for neither the variances of the multilooked pixels nor the covariances among interferometric phases. This paper presents two different approaches for evaluation of the full covariance matrix: one based on the numerical Monte-Carlo integration and the other based on an analytical approximation using nonlinear error propagation. We first, clarify on the noise components that are the subject of statistical models of this paper. Then, the complex statistics in SAR stacks and the phase statistics in a single interferogram are reviewed, followed by the phase statistics in InSAR stacks in terms of second statistical moments. The Monte-Carlo approach and the derivation of an analytical closed-form evaluation of InSAR second-order phase statistics are then introduced in details. Finally, the two proposed methods are validated against each other. ... Read more

This contribution proposes a new approach for the analysis and preparation of geodetic data for the use in geophysical modeling. The approach resolves the problem of non-uniformity in the datasets obtained by different measurement techniques. The approach is based on two main steps: uniformization of the data using a standardized data format, and the application of the CUPiDO conversion tool to construct double-difference observations. Both steps are described in detail. By using double-difference observations, the effect of different reference points and geodetic datums is eliminated, thereby making the outcomes of the CUPiDO tool well suited for an integrated inversion to estimate a model. The CUPiDO tool will be made publicly available. ... Read more

During the last decades, time-series interferometric synthetic aperture radar (InSAR) has emerged as a powerful technique to measure various surface deformation phenomena of the earth. Early generations of time-series InSAR methodologies, i.e. Persistent Scatterer Interferometry (PSI), focused on point targets, which are mainly man-made features with a high density in urban areas and associated infrastructure. Later, methodologies were introduced aiming to extract information from other targets known as distributed scatterers (DS), which are associated with ground resolution cells occurring mainly in rural areas. Unfortunately, the underlying properties and assumptions behind various DS-phase estimation methodologies are sometimes subjective and incomparable, which hampers the objective application of the different methods. Moreover, for some terrain types, such as agricultural terrain or pastures, the feasibility of DS-methodologies is not straightforward. In view of these challenges, the two main objectives of this study are (i) to formulate and implement the estimation methodology of DS-pixels in a standard geodetic framework and to compare it with other existing methods, and (ii) to assess the feasibility of exploiting distributed scatterers for deformation monitoring over agricultural and pasture areas. We review state-of-the-art time-series InSAR methodologies with special attention to processing aspects related to distributed scatterers. From an estimation theory perspective, the key processing step to extract information from DS-pixels is the equivalent single-master (ESM) phase estimation. To situate this estimation in a geodetic framework, a mathematical model is proposed in the form of a Gauss-Markov model. To evaluate the stochastic part of the model, a numerical Monte-Carlo methodology as well as an analytical approach are introduced. Regarding the functional part, the ESM-phase estimation is formulated in the form of a hybrid linear system of observation-equations with both real-value and integer unknowns. The solution of the proposed model is given by the integer least-squares (ILS) estimator. The properties of such an estimator for ESM-phase estimation are described and demonstrated using synthetic and real datasets. Furthermore, to provide a theoretical comparison between the proposed ILS estimator and other existing ESM-phase estimators, a unified mathematical model in the form of a system of observation equations is proposed. Evaluating all the existing DS-methods shows that, although they all provide specific solutions, their fundamental difference is in how they assign weights to the interferometric observations. The feasibility of exploiting PS, DS, and their combination over agricultural and rural landscapes is assessed via a case study on a subsidence area near city of Veendam, the Netherlands, based on the coherence behavior of different types of land use. It is shown that, under the condition of using the entire time-series, agricultural and pasture areas show only limited improvement in point density compared to the results of PSonly processing. This is due to the seasonal behavior of the temporal coherence, which causes an almost complete drop in coherence during summer periods, mainly as a result of tillage, crop growth and harvesting. To model this periodicity, a new analytical model is introduced. In this model, the hypothetical movements of elementary scatterers within DS resolution cells are modeled as a stochastic process with non-stationary but periodic increments. The parameters of this model are estimated for pasture areas, and are subsequently used to assess the feasibility of exploiting DS-pixels in agricultural areas by different satellite missions. The results confirm that, assuming a three-year stack of data, the information content in DS-pixels from current C-band and X-band missions is not enough for the successful utilization of their entire time-series. However by using intermittent series, e.g., by processing individual coherent periods, the results indicate that DS-pixels can be exploited: based on the proposed decorrelation model, the short repeat times of Sentinel-1 (6 or 12 days) results in a sufficient number of coherent interferograms over each winter period, enabling DS exploitation even over agricultural and pasture areas. ... Read more

Deformation estimates from Interferometric Synthetic
Aperture Radar (InSAR) are relative: they form a ‘free’
network referred to an arbitrary datum, e.g. by assuming a reference
point in the image to be stable. However, some applications
require ‘absolute’ InSAR estimates, i.e. expressed in
a well-defined terrestrial reference frame, e.g. to compare
InSAR results with those of other techniques. We propose a
methodology based on collocated InSAR and Global Navigation
Satellite System (GNSS) measurements, achieved by
rigidly attaching phase-stable millimetre-precision compact
active radar transponders to GNSS antennas. We demonstrate
this concept through a simulated example and practical case
studies in the Netherlands ... Read more

InSAR deformation estimates form a 'free network' referred to an arbitrary datum, e.g. by assuming a reference point in the image to be stable. Consequently, the estimates of any measurement point in the image are dependent of these postulations on reference point stability, and the estimates cannot be compared with datasets of other types of measurement (e.g. historical levelling data or sea-level changes). Yet, some applications require 'absolute' InSAR estimates, i.e. expressed in a well-defined terrestrial reference frame (TRF). We achieve this using collocated InSAR and GNSS measurements, achieved by rigidly attaching phase-stable millimetre-precision compact active transponders to permanent GNSS antennas. The InSAR deformation estimates at these transponders are then estimated in a TRF using the GNSS measurements. Consequently, deformation estimates at all other scatterers are now also defined in the same TRF. ... Read more

In recent years, new algorithms have been proposed to retrieve maximum available information in synthetic aperture radar (SAR) interferometric stacks with focus on distributed scatterers. The key step in these algorithms is to optimally estimate single-master (SM) wrapped phases for each pixel from all possible interferometric combinations, preserving useful information and filtering noise. In this paper, we propose a new method for SM-phase estimation based on the integer least squares principle. We model the SM-phase estimation problem in a linear form by introducing additional integer ambiguities and use a bootstrap estimator for joint estimation of SM-phases and the integer unknowns. In addition, a full error propagation scheme is introduced in order to evaluate the precision of the final SM-phase estimates. The main advantages of the proposed method are the flexibility to be applied on any (connected) subset of interferograms and the quality description via the provision of a full covariance matrix of the estimates. Results from both synthetic experiments and a case study over the Torfajökull volcano in Iceland demonstrate that the proposed method can efficiently filter noise from wrapped multibaseline interferometric stacks, resulting in doubling the number of detected coherent pixels with respect to conventional persistent scatterer interferometry. ... Read more

The landslide activity in the area of Bolshoy Sochi (Big Sochi) situated at the Black Sea coast of the Great Caucasus has been studied using the StaMPS PS-InSAR method. We incorporated three sets of radar images from the satellites with different wavelengths ALOS, Envisat and Terra-SAR-X from both ascending and descending tracks which cover the time period from January 2007 to September 2012. Comparative investigation of surface displacements obtained from all the data sets is presented. Areas where high surface displacement rates have been located on the base of the satellite data coincide well with zones of high landslide activity according to ground observations. We constructed time series for the two landslides: in the Baranovka and Mamaika villages where considerable surface movements had been observed during the time of acquisitions. Analysis of the time series made it possible to determine periods of activity and relative stability of the landslides and compare them with ground observations. ... Read more

The geodetic quality of a low-cost commercial off-the-shelf InSAR transponder has been empirically assessed, both under controlled conditions and operationally for landslide monitoring. Comparison of 113 transponder-InSAR observations with independent validation measurements (levelling or GPS) yields a transponder precision range of 1.8-4.6 mm after outlier removal for double-difference (spatial and temporal) phase measurements in the satellite line of sight for Envisat and ERS-2, making it a compact and lightweight alternative to a corner reflector for C-band InSAR. ... Read more

Algorithms have been proposed in the recent years in order to retrieve all information available in interferometric stacks of SAR acquisitions with focus on distributed scatterers. One of the key steps in these algorithms - called phase triangulation, phase linking or phase multi-linking - is to optimally estimate filtered wrapped interferometric phases from all possible interferometric combinations preserving useful information and filtering noise. The advantages of these methods compared to conventional approaches are that the algorithm can be applied before phase unwrapping, and that it considers all possible interferograms. In this contribution we propose a new algorithm for phase triangulation based on the integer least squares (ILS) method. We model the phase triangulation problem as a system of linear observation equations. After computing the full covariance matrix of interferometric phases using a Monte-Carlo method, we use ILS to estimate the unknowns. The advantages of our method are that it is capable of considering the mutual correlation between all interferograms, and additionally provides as a output the precision of the estimates. Simulation results show that the proposed method works effectively and can optimally filter noise from interferometric stacks before unwrapping. ... Read more

Artificially introduced persistent scatterers (PS) are often desirable, and sometimes even crucial, when monitoring deformation using InSAR especially in non-urbanised areas. The use of active radar transponders as viable 'artificial PS' is demonstrated via two field experiments: a validation test in a controlled calibration environment, and their operational use for monitoring landslides. In the latter case, the added value of having collocated InSAR-GNSS measurements is also presented. ... Read more

One of the limitations of InSAR is that it is only capa-ble of measuring a 3D projection of a real deformation vector on the radar line of sight. Therefore it is not possi-ble to retrieve the full displacement vector from a single InSAR measurement. The optimal solution for this limi-tation is a combination of InSAR measurements from dif-ferent imaging geometries. However, this solution is not applicable in areas where InSAR data are available in one particular geometry only. In this paper, a new approach will be discussed for 3D decomposition of InSAR defor-mation measurements for the case of subsidence. We use the hypothesis of a physical relation between horizontal displacement and vertical deformation. Using this hy-pothesis, we propose an iterative strategy for 3D decom-position of InSAR subsidence measurements. The pro-posed approach is tested on the PSI results of a complex subsidence field in Friesland, the Netherlands. Finally, the results are validated by comparison with available lev-eling data. ... Read more