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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The Permanent Scatterers Interferometric SAR technique (PSInSAR) is a method that accurately estimates the near vertical terrain deformation rates, of the order of ∼1 mm year^{-1}, overcoming the physical and technical restrictions of classic InSAR. In this paper the method is strengthened by creating a robust processing chain, incorporating PSInSAR analysis together with algorithmic adaptations for Permanent Scatterer Candidates (PSCs) and Permanent Scatterers (PSs) selection. The processing chain, called PerSePHONE, was applied and validated in the geophysically active area of the Gulf of Corinth. The analysis indicated a clear subsidence trend in the north-eastern part of the gulf, with the maximum deformation of ∼2.5 mm year^{-1} occurring in the region north of the Gulf of Alkyonides. The validity of the results was assessed against geophysical/geological and geodetic studies conducted in the area, which include continuous seismic profiling data and GPS height measurements. All these observations converge to the same deformation pattern as the one derived by the PSInSAR technique.

The classic InSAR technique has offered numerous examples for the reliable measurement of ground deformation [^{-1}. Thus, this technique is ideal for measuring small-scale ground deformation due to displacements in active fault zones [

A crucial requirement for this method is the availability of stable targets, which present a dominant reflection component in the radar signal while their scattering characteristics remain unchanged in time. These targets are called Permanent Scatterers (PS) and can be used to remove the above mentioned undesirable components [

The Gulf of Corinth study area is illustrated in ^{-1} [

The image data used in the present PSInSAR study were acquired from the ERS-1 and ERS-2 satellites, kindly provided by the European Space Agency (ESA). Scene selection was based on three criteria: the first relating to the time span of the scenes, which was selected to be long enough to incorporate a sufficient number of images, but not exceeding a maximum of seven years, in order to avoid temporal decorrelation. The second criterion was the absence of intense non-linear phenomena during the studied period, such as earthquakes, to meet the requirement for linear deformation rates. According to the third criterion, the data set used was characterized by uniform distributions of interferometric baselines and acquisition dates of the scenes (i.e. avoid time gaps, such as the 2002 ERS-2 failure). On the basis of these three criteria a full data set consisted of twenty ERS scenes, with a time span of 6½ years, from June 19^{th}, 1995 to October 16^{th}, 2001 (^{th} June 1995 (orbit No. 20536) was selected to be the common master scene.

Some necessary pre-processing steps were applied to the raw SAR data. These related to image focusing, image cropping and compensating for zero Doppler centroid. An important step at this stage was the radiometric normalization of the amplitude images in order to achieve enhanced cross-correlation statistics for image registration.

A customized version of the Centre National d'Etudes Spatiales (CNES) DIAPASON software [

The PerSePHONE (

In PSInSAR technique the so called Dispersion Index (DI) is a useful indicator for the selection of the initial set of PSCs. It was obtained from the SAR amplitude images indicating a target's amplitude dispersion over time. Small values of DI indicated a possible stable target termed as PSC [

The interferometric phase of each target j in each interferogram i contains the following phase components [_{topo_res} contains the correction for the actual target height in relation to the used DEM, v contains the deformation velocity of the radar target and E contains the effect of other components, namely non linear atmospheric disturbances, noise due to temporal and spatial decorrelation and non linear target movement.

The equation must be applied to tiles of small dimensions which will allow the estimation of the APS and the orbital errors by a 2-D linear phase approximation. Therefore the term α in each target j, in each interferogram i, in each tile t can be estimated as:
_{ξ}, p_{η} denote the slope values along the azimuth (ξ) and the slant range (η) respectively and c denotes the constant values of the 2-D linear phase approximation.

Consequently the next step was to divide the area of interest into tiles. The test area was divided into 800 tiles each having dimensions of 500 pixels in azimuth and 100 pixels in range, covering an area of ∼4 km^{2}. About 200,000 targets having DI<0.33 were identified from all tiles as a first selection of PSCs, denoted as PSCs^{(1)}. Proceeding to subsequent algorithm iterations this set was reduced to PSC^{(n)}, with the index n indicating the number of the iteration.

The calculation of the APS and the orbital errors (term α of _{topo} of ^{(i)} set. The criterion for identifying the non converging PSCs was the standard deviation of the correction values at each advanced iteration step of the unknowns (velocities and DEM errors). This procedure was repeated until either the algorithm converged or the number of PSCs^{(n)} in a specific tile became lower than a minimum threshold which was set to 40. Finally, the non-linear atmospheric disturbances of low frequency were isolated from the phase residuals (term E of

The outcome of this iterative procedure is the estimation of the APSs in 74 tiles that emerged from 4425 PSCs, having a density of ∼15 PSCs per km^{2}. This value is rather limited in comparison with other research scenarios conducted in highly populated urban areas as in [^{2}. Note though, that some tiles (especially in urban and peri-urban areas) with a larger number of initial PSCs^{(n)} were represented at the end of the iterative processing by a final density of up to 58 PSCs per km^{2} which was considered a satisfactory outcome.

The final deformation rates and precise DEM errors for each target inside a tile were then calculated. This was performed by maximizing the targets' Phase Coherence (PC), which refers to the phase stability of the targets, after removing the calculated APS from each tile [^{-1} and DEM errors of [-10, 10] m was assumed.

The last processing step was the identification of the PSs inside each tile. The Maximum PC (MPC), referring to each target, was the criterion for keeping only those that show high phase stability in time. The total number of the derived PSs was 154 and they are mapped in

Since the identified PS density per tile was rather low due to land cover incoherence and atmospheric disturbances, it was considered reasonable to continue with a surface interpolation of the observed deformation, estimating the general gradient of the velocity field in the study area, while filtering out any local anomalies. For this a thin-plate smoothing spline [_{s}=0.05, was used to best fit the returned PS velocities. As the smoothing parameter p varies from 0 to 1, the smoothing spline varies, from the least-squares approximation to the data by a linear polynomial when p is 0, to the thin-plate spline interpolant to the data when p is 1. This highlighted the general subsidence trend located in the northeast of the Gulf of Corinth study area, while the maximum deformation occurred in the region north of the Gulf of Alkyonides (∼2.5 mm year^{-1}), as it became clearly visible from

Marine geological and geophysical studies conducted in the Gulf of Corinth validate the above results. In [^{-1} (essentially 0.7-1 mm year^{-1}) of the northern margin of the Gulf of Corinth during the last 250 kyears was estimated, based on the continuous subsidence of at least four oblique prograding sequences obtained by seismic profiling in the area of Eratini. This subsidence rate is in very good agreement with the average deformation rate of ∼1 mm year^{-1} estimated from the PSInSAR study herein. Furthermore, in [

An alternative approach for validating the derived PSInSAR measurements was the use of GPS height measurements collected and analyzed in the broader area of the Gulf of Corinth. These GPS campaigns were conducted by the Laboratory of Higher Geodesy of the National Technical University of Athens and the Institute of Earth Physics of Paris and lasted for approximately 13 years, starting from February 1989 till March 2002 [^{2}) of the interpolation, a measure of the reliability of the linear relationship between height measurement and time. Consequently, only points with R^{2} greater than 0.7 were kept. This simple procedure resulted in maintaining 25 points along the study area. A thin-plate smoothing spline surface was fitted to these GPS observations, using the same parametric values as for the PSInSAR surface above. A direct comparison of the two methods is presented in

In this paper the so-called PerSePHONE PSInSAR technique developed at the Institute for Space Applications and Remote Sensing of the National Observatory of Athens was implemented for systematically measuring for the first time the ground deformation velocities at the Gulf of Corinth area, over a six year period. A number of algorithmic adaptations were implemented, mainly concerning the PSC selection procedure through applying a histogram equalization technique, and the PSC iterative algorithm convergence criteria using the standard deviation of the correction values.

The Gulf of Corinth was a challenging case study for PS processing due to signal incoherence, induced by dense vegetation, high cloud coverage, frequent rainfall and lack of rocky areas and urban settlements. This analysis though, identified regions with an adequate number of PSs, providing the capability for PSInSAR processing. The stable PS targets emerged after applying strict criteria and for this reason the resulted deformation rates are considered to be accurate readings. This was confirmed by the agreement between the subsidence trend returned by the PS interpolated surface and the displacement rates reported in the relevant geophysical/geological and geodetic (GPS) studies conducted in the same area, highlighting the validity and the accuracy of the developed PSInSAR methodology.

Apart from the derived and validated deformation trend of the area, another innovative outcome of the systematic observation of the Gulf of Corinth is the identification of the exact position of potential Permanent Scatterers, information previously unpublished. This will be of paramount importance for the scientific community when selecting the location of future GPS stations, aiming at consistent observation of the region.

We are grateful to the European Space Agency (ESA) for providing the ERS data, in the frame of ESA-GREECE AO project 1489OD/11-2003/72.

Structural map of the Gulf of Corinth [

Normal baselines versus the acquisition dates of the scenes. The figure labels correspond to the ERS orbit number of each scene.

Block diagram illustrating the PerSePHONE algorithm processing steps.

(a) Bilinear PS interpolated surface and the corresponding PSs. (b) Deformation surface derived from GPS measurements. White dots correspond to PS measurement points while red dots to GPS locations.