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.