The IRIDE constellation is an ambitious Italian space program that will support the national authorities in their analyses and monitoring activities, with a focus on Italian territory mapping. It will comprise a series of small satellite subconstellations exploiting a wide range of remote sensing technologies. This article analyses the NIMBUS X-Band synthetic aperture radar (SAR) IRIDE subconstellation, exploring potential orbital configurations beyond the more conventional and widespread dawn-dusk sun-synchronous orbit (SSO) one. In particular, starting from the mission target, we show that a 49° mid-inclination orbit (MIO) in a right-looking StripMap acquisition mode represents a highly effective choice for NIMBUS. We demonstrate that this configuration enhances the systematic coverage of the Italian territory with six nodal days of interferometric revisit time and high spatial resolution, thereby facilitating detailed observations of both natural phenomena and anthropic activities. In terms of differential SAR interferometry (DInSAR) performance, we prove that MIOs do not show significant limitations for what attains the critical baseline and geometric distortions. In addition, MIOs may lead to future advances in creating 3-D displacement maps because they allow for the recovery of the North-South deformation component that, conversely, cannot be precisely measured with DInSAR systems operating in SSO.

The Campi Flegrei caldera (southern Italy) is an active volcano whose last eruption occurred in 1538. This caldera is characterized by ground displacements (subsidence or uplift), typically identified with the term "bradyseism". Over the last two decades the Campi Flegrei caldera was affected by a phase of progressively increasing uplift and it was accompanied by increasing seismicity and geochemical anomalies. The ground displacement pattern is monitored through GNSS and Differential SAR Interferometry (DInSAR) analysis, the latter focused on the Sentinel-1 SAR data exploitation. According to the available measurements, the displacement pattern is mainly radial with a maximum uplift in the area corresponding to Rione Terra (Pozzuoli). However, we have also detected a geodetic anomaly, near the Mt. Olibano–Accademia area, where most of the recent seismicity of the caldera is concentrated, which become clearly recognizable starting from 2021 and further developed during 2022 and 2023.

In this work, we investigate potential orbital configurations of NIMBUS, one of the Synthetic Aperture Radar (SAR) components of the Italian constellation IRIDE, which will be completed by 2026 under the management of the European Space Agency (ESA), with the support of the Italian Space Agency (ASI). IRIDE is conceptualized as a "constellation of constellations", comprising multiple sub-constellations of satellites positioned in Low Earth Orbit (LEO) and equipped with various sensing technologies, including SAR and optical sensors with medium- and high-resolution capability, operating at different frequency ranges. Given both institutional and commercial users the constellation is expected to fulfill, this work introduces a methodology to compare different orbital configurations and finally identify the optimal orbital arrangement that maximizes the Italian national coverage within the shortest revisit time possible, considering both the capabilities and imaging performance of a SAR system planned for deployment in orbit.

We present in this study an enhancement to our previous work, in which an automated method, based on Convolutional Neural Networks (CNNs), has been developed for identifying co-seismic ground deformation patterns within the Differential SAR Interferometry (DInSAR) maps generated through the EPOSAR service of the European Plate Observing System (EPOS) Research Infrastructure. The implemented improvements have been achieved through two main lines of actions. Firstly, the generation of the synthetic dataset, used to train the developed CNN, has been enhanced; this concerns the improvement of the simulation of possible atmospheric disturbance within the DInSAR interferograms, and the introduction of a simulator of phase unwrapping errors. Secondly, the original CNN-based deformation pattern detector layout, performing a binary classification, has been modified to account for a multiclass deformation pattern classification. This allows us extending the capability of the system which, in addition to detect co-seismic deformation patterns, may also provide information on the earthquake source characteristics. The presented solution will be included in the EPOSAR DInSAR processing chain.

Phase unwrapping (PhU) is a challenging step in multi-temporal (MT) Differential SAR Interferometry (DInSAR) techniques that may have a significant impact on the accuracy of the retrieved displacements. In this paper, we present a simple solution to enhance a previously developed Compressive Sensing (CS)-based PhU approach, allowing us to improve its performance in particularly challenging surface displacement scenarios. The proposed method, without altering the technical framework of the CS-based original solution, specifically targets the refinement of the MT interferometric sequence selection process. In particular, starting from the pivotal role of the Delaunay triangulation in the SAR data acquisitions temporal/perpendicular baseline plane to identify the bulk multi-temporal DInSAR interferograms sequence, we easily enrich this sequence by properly adding highly coherent interferograms which have not been initially selected. The overall study is focused on multi-look L-band interferograms of the SAOCOM-1 constellation, relevant to the Stromboli Island (Italy), and a comparative analysis between the results obtained by applying the enhanced method and its original version is presented, showing the improved capability of the former.

We present in this work the results of an extensive, full resolution Parallel SBAS (P-SBAS) processing activity carried out on large multi-temporal SAR data archives of COSMO-SkyMed first (CSK) and second (CSG) generation SLC images, relevant to some of the main cities of the Italian territory, acquired from ascending and descending orbits since 2009. In particular, we first summarize the key points of the exploited, full resolution P-SBAS processing chain. Subsequently, we also describe the main algorithmic developments aimed to exploit large temporal sequences of CSK and CSG SLC data relevant to wide areas. Finally, we present several results highlighting, through some selected examples, that the use of high resolution SAR images, such as those of the CSK-CSG constellation, processed with techniques like the full resolution P-SBAS technique approach, may provide valued-added information that, properly integrated with in-situ measurements, can be very relevant for the assessment of the built-up environment health conditions, at the national scale.

Over the past 30 years it has been widely demonstrated the effectiveness of the Differential Synthetic Aperture Radar Interferometry (DInSAR) technique to retrieve surface deformation information relevant to tectonically active areas. However, this technique exhibits some limitations due the presence of possible decorrelation effects, phase unwrapping errors, and artefacts due to the temporal/spatial variability of the atmospheric conditions between the SAR acquisition pairs exploited to generate the interferograms and the corresponding deformation maps or time series. A challenging situation may arise when an earthquake event occurs and a co-seismic DInSAR deformation map is generated to quickly support risk management operations. In this scenario, having an automatic process reducing the uncertainties of the retrieved, DInSAR-based, surface deformation information could highly improve the quality of the products made available to the scientific community and of the service provided to the national disaster recovery authorities. We present in this work a solution, based on standard CNN architectures embedded in the DInSAR processing chain of the EPOSAR service, developed within the European Plate Observing System (EPOS) Research Infrastructure, to automatically identify co-seismic ground deformation patterns.

We present in this work some advances of the Differential SAR Interferometry (DInSAR) technique referred to as Parallel Small BAseline Subset (P-SBAS) approach, allowing us to effectively process the recently available L-band SAR images acquired by the Argentinian SAOCOM-1 constellation. This activity has been carried out within the DInSAR-3M project, co-funded by the Italian Space Agency, which is aimed to develop technical solutions for the joint exploitation of multi-frequency (X-, C- and L- band) and multi-platform (spaceborne and airborne) DInSAR measurements. The main goal is the generation of surface deformation time series and corresponding mean displacement velocity maps, spatially and temporally dense, for the multi-scale analysis of natural and anthropogenic phenomena.The assessment of the developed advances has been carried out by processing several SAOCOM-1 SAR datasets acquired over Italy between 2019 and 2022.

In this paper, we present an innovative Phase Unwrapping (PhU) procedure for Multi Temporal DInSAR techniques, based on the Extended Minimum Cost Flow technique schema. The developed algorithm benefits from the Compressive Sensing (CS) theory. In particular, the procedure consists of the cascade of three steps. At first, the set of spatially connected arcs between close pixels is identified by selecting the points to be unwrapped and linking them through the Delaunay algorithm; in the second step, the temporal PhU of all the arcs is carried out by using the CS approach and an L1-norm estimator. In the last step, the algorithm uses the unwrapped arcs to perform spatial PhU of each interferogram using MCF technique. To assess the performance of the developed approach, we analyze the area related to Stromboli volcano (Italy) by processing the dataset acquired by Sentinel-1 constellation over descending orbit from 2016 to 2021.

We present in this work a solution to identify Phase Unwrapping (PhU) errors in redundant sequences of small baseline Differential SAR Inteferometry (DInSAR) interferograms like those exploited by the Small Baseline Subset (SBAS) approach, which allows the retrieval of displacement time series. In particular, the temporal information is exploited through the temporal coherence parameter, which represents a point-like quality indicator of the PhU solutions within advanced DInSAR methods like the above mentioned SBAS technique. First of all we show that this parameter needs to be carefully considered because it may lose sensitivity when the number of images of the exploited dataset increases. Subsequently, we explore a different use of the temporal coherence, moving from a single valued parameter to a time-dependent function. This permits to regain sensitivity and to reduce the number of interferograms eligible to be corrected. The last part of the work is devoted to present a case study where the proposed solution allows the identification of PhU errors.

In this work, we present an advanced implementation of the full resolution Parallel Small BAseline Subset (P-SBAS) DInSAR processing chain, aimed to effectively and automatically generate DInSAR products (displacement time series and corresponding velocity maps) related to single buildings and infrastructures over the whole Italian territory. The proposed full resolution P-SBAS pipeline exploits innovative hardware and software parallel technologies based on GPUs, which are able to efficiently process large amounts of full resolution DInSAR data stacks in reasonable time frames and with high scalability. The presented results, achieved by processing very large archives of full resolution X-band first and second generation COSMO-SkyMed data and C-band Sentinel-1 images, demonstrate the effectiveness of the proposed solution in terms of computing time and computational efficiency.

We present in this work the first results of the project referred to as DInSAR-3M, which is aimed to generate surface deformation time series and mean velocity maps, spatially and temporally dense, for the multi-scale analysis of natural and anthropogenic phenomena. The project objective will be pursued through the use of the advanced Differential SAR Interferometry (DInSAR) technique referred to as Parallel Small BAseline Subset (P-SBAS) approach and the development of a solution for the integration of multi-frequency (X-, C- and L- band) and multi-platform DInSAR measurements. In the following, we present the first results focused on the interferometric exploitation of the recently available L-band SAR images acquired by the Argentinian SAOCOM constellation.

In a recent publication, Ansariet al.(2021) claimed (see, in particular, the Discussion and Recommendation Section in their article) that the advanced differential SAR interferometry (InSAR) algorithms for surface deformation retrieval, based on the small baseline approach, are affected by systematic biases in the generated InSAR products. Therefore, to avoid such biases, they recommended a strategy primarily focused on excluding “the short temporal baseline interferograms and using long baselines to decrease the overall phase errors.” In particular, among various techniques, Ansariet al.(2021) identified the solution presented by Manuntaet al.(2019) as a small baseline advanced InSAR processing approach where the presence of the above-mentioned biases (referred to as a fading signal) compromises the accuracy of the retrieved InSAR deformation products. We show that the claim of Ansariet al.(2021) is not correct (at least) for what concerns the mentioned approach discussed by Manuntaet al.(2019). In particular, by processing the Sentinel-1 dataset relevant to the same area in Sicily (southern Italy) investigated by Ansariet al.(2021), we demonstrate that the generated InSAR products do not show any significant bias.

In this work, we present a new method based on the compressive sensing (CS) theory to correct phase unwrapping (PhU) errors in the multitemporal sequence of interferograms exploited by advanced differential interferometric synthetic aperture radar (DInSAR) techniques to generate deformation time series. The developed algorithm estimates the PhU errors by using a modified$L_{1}$-norm estimator applied to the interferometric network built in the temporal/spatial baseline plane. Indeed, in order to search the minimum$L_{1}$-norm sparse solution, we apply the iterative reweighted least-squares method with an improved weight function that takes account of the baseline characteristics of the interferometric pairs. Moreover, we also introduce a quality function to identify those solutions that have no physical meaning. Although the proposed approach can be applied to different multitemporal DInSAR approaches, our analysis is tailored to the full-resolution small baseline subset (SBAS) processing chain that we properly modify to implement the proposed CS-based algorithm. To assess the performance of the developed technique, we carry out an extended experimental analysis based on simulated and real SAR data. In particular, we process two wide SAR datasets acquired by Sentinel-1 and COSMO-SkyMed constellations over central Italy between 2011 and 2019. The achieved experimental results clearly demonstrate the effectiveness of the developed approach in retrieving PhU errors and generating displacement time series related to strongly nonlinear deformation phenomena. Indeed, the developed CS-based technique significantly increases the number of detected coherent points and improves the accuracy of the retrieved deformation time series.

In this work, we present the ground deformation analysis of the Italian Peninsula carried out via the Sentinel-1 (S-1) Parallel Small BAseline Subset (P-SBAS) approach. In particular, we generate surface deformation time-series and the corresponding mean deformation velocity maps by considering the overall archive of S-1 data acquired from both ascending and descending orbits during the March 2015 - December 2018 period. Moreover, we perform a large-scale comparison of the retrieved results with the deformation measurements of the available GPS stations deployed on the Italian territory and provided by the Nevada Geodetic Laboratory at the University of Nevada, Reno, USA (UNR-NGL). Finally, we properly combine the ascending and descending deformation time-series in order to compute the vertical and east-west components of the retrieved surface displacements. The achieved results demonstrate the capability of the P-SBAS processing chain to efficiently process large S-1 datasets to investigate ground deformation dynamics of large portions of the Earth surface.

We present the implementation of a global archive of Differential Synthetic Aperture Radar Interferometry (DInSAR) co-seismic deformation maps. The archive has been generated by automatically processing all the Copernicus Sentinel-1 data spanning about 300 significant (at least Mw > 5.5) earthquakes all over the Earth. An empirical relation between magnitude and epicenter depth was considered to limit the study to those earthquakes that can likely induce ground deformation. DInSAR processing has been carried out within a Cloud-Computing (CC) environment, specifically the Amazon Web Services, to benefit of high processing capacity. The generated DInSAR results are then made freely and openly available to the Solid Earth scientific community through the European Planet Observing System (EPOS) Research Infrastructure.

We present an automatic pipeline implemented within the Amazon Web Services (AWS) Cloud Computing platform for the interferometric processing of large Sentinel-1 (S1) multi-temporal SAR datasets, aimed at analyzing Earth surface deformation phenomena at wide spatial scale. The developed processing chain is based on the advanced DInSAR approach referred to as Small BAseline Subset (SBAS) technique, which allows producing, with centimeter to millimeter accuracy, surface deformation time series and the corresponding mean velocity maps from a temporal sequence of SAR images. The implemented solution addresses the aspects relevant to i) S1 input data archiving; ii) interferometric processing of S1 data sequences, performed in parallel on the AWS computing nodes through both multi-node and multi-core programming techniques; iii) storage of the generated interferometric products. The experimental results are focused on a national scale DInSAR analysis performed over the whole Italian territory by processing 18 S1 slices acquired from descending orbits between March 2015 and April 2017, corresponding to 2612 S1 acquisitions. Our analysis clearly shows that an effective integration of advanced remote sensing methods and new ICT technologies can successfully contribute to deeply investigate the Earth System processes and to address new challenges within the Big Data EO scenario.

We present an unsupervised and automatic system for volcano deformation monitoring via the Copernicus Sentinel-1 data. The system relies on the Parallel Small BAseline Subset (P-SBAS) approach, permitting us to generate updated displacement time series at every new Sentinel-1 acquisition over a selected area of interest in a fast and accurate way. The service is currently operative to monitor the main active Italian volcanoes in the framework of cooperation with the Italian Department of Civil Protection. The system is potentially extendable to every area on the Earth, thus making it suitable for surface displacement monitoring of a large variety of phenomena. Finally, the obtained results are made available to the scientific community through the EPOS Research Infrastructure.

In this work we present a cloud-computing based strategy for generating surface displacement time series and mean deformation velocity maps of very large areas by exploiting Sentinel-1 (S1) data. Our approach relies on the simultaneous exploitation of a fast access to the S1 data archives, High Performance Computing resources and external geodetic data.The presented pipeline is based on an advanced cloud-computing implementation of the differential SAR interferometry (DInSAR) Parallel Small BAseline Subset (P-SBAS) processing chain, which allows the fully unsupervised processing of huge Interferometric Wide Swath (IWS) Sentinel-1 data volumes.In particular, for what concerns the S1 data archives, we benefited from the NASA's Alaska Satellite Facility (ASF) Distributed Active Archive Center (DAAC), which stores and distributes S1 SAR data from Amazon Web Service (AWS) for advancing Earth science research. The ASF-DAAC allowed us to reach a very high performance level in terms of downloading time and system reliability. Moreover, we exploited the geodetic measurements provided from the Magnet + Global GPS Network Map of the Nevada Geodetic Laboratory at the University of Nevada, Reno, USA (UNR-NGL), which supply GPS measurements daily updated and continuosly available. The GPS measurements were used to account for regional trends and to better discriminate the low (tectonic) and high (local) frequency deformation patterns.The presented solution is highly scalable and has been migrated to the Amazon Web Service (AWS) environment. It runs out along an automatic routine to generate the mean deformation velocity maps of the vertical and horizontal (East-West) displacement components of the whole investigated area.The developed pipeline has been tested on ascending and descending Sentinel-1 archives acquired over a large area of Southern California (US), which extends over about 150,000 square kilometers.

The Differential Synthetic Aperture Radar Interferometry (DInSAR) remote sensing technique permits to investigate the temporal behaviour of the detected displacements through the generation of the deformation time-series. In this scenario the Phase Unwrapping (PhU) is a crucial point where several errors could occur since the problem is intrinsically ill-posed. In this paper we present a technique to correct unavoidable PhU errors and limit their impact in the final deformation time-series. The proposed approach works pixel-by-pixel and is based on the combination of an L1-norm inversion for the identification of the possible PhU errors and a genetic algorithm (GA) for the search of the best fitting solution. We include the technique in the Small Baseline Subset (SBAS) DInSAR processing chain to correct the results of the Extended Minimum Cost Flow algorithm, but in principle it can be used as a correction step after a generic PhU procedure used in SBAS. Results from MonteCarlo simulations are shown in this paper while real data cases will be presented at the conference.

We present an unsupervised tool for the automatic generation of co-seismic displacement maps by using satellite Differential Synthetic Aperture Radar Interferometry (DInSAR) technique. The tool relies on the use of Sentinel-1 SLC Interferometric Wide Swath (IWS) data and main earthquake information, the latter retrieved from on-line global catalogs. In particular, the tool collects location, depth and magnitude of a seismic event and immediately triggers the data download and the interferometric process over the area affected by the earthquake. The generated DInSAR results (mainly interferograms and displacement maps) are then made available to the Solid Earth scientific community through the EPOS Research Infrastructure. Moreover, the implemented system is also used to serve the Italian Department of Civil Protection in case of main seismic events in Italy. Finally, due to the Sentinel-1 characteristics, the obtained results can contribute to the generation of a global database of DInSAR co-seismic displacement maps.

We investigate the deformation of Mt. Etna volcano (Italy) by exploiting the DInSAR technique referred to as the Small BAseline Subset (SBAS) algorithm. In particular, we take advantage of the multi-sensor data processing capability of the SBAS algorithm which allows us to generate Mt. Etna mean deformation velocity maps and the corresponding time series in the last twenty-five years. To achieve this task, we exploit different set of SAR data collected by ERS-1/2, ENVISAT, COSMO-SkyMed and Sentinel-1 radar sensors in the 1992-2018 time interval. We, also, show the deformation pattern induced by the recent seismo-volcanic crisis occurring from 24 to 27 December 2018. The main results show that the East-West displacement map highlights the most significant entities, whose maximum values exceed 30 cm towards the West and 40 towards the East on the summit of the volcano. In this scenario, the measurements permit to model the geometry and characteristics of the causative deformation sources; preliminary results suggest the presence of two different sources: a shallow dyke feeding the eruptive activity at summit craters and a major strike-slip fault/s on the southeastern flank nucleating the 26thmainshock.

We present an advanced differential synthetic aperture radar (SAR) interferometry (DInSAR) processing chain, based on the Parallel Small BAseline Subset (P-SBAS) technique, for the efficient generation of deformation time series from Sentinel-1 (S-1) interferometric wide (IW) swath SAR data sets. We first discuss an effective solution for the generation of high-quality interferograms, which properly accounts for the peculiarities of the terrain observation with progressive scans (TOPS) acquisition mode used to collect S-1 IW SAR data. These data characteristics are also properly accounted within the developed processing chain, taking full advantage from the burst partitioning. Indeed, such data structure represents a key element in the proposed P-SBAS implementation of the S-1 IW processing chain, whose migration into a cloud computing (CC) environment is also envisaged. An extensive experimental analysis, which allows us to assess the quality of the obtained interferometric products, is presented. To do this, we apply the developed S-1 IW P-SBAS processing chain to the overall archive acquired from descending orbits during the March 2015-April 2017 time span over the whole Italian territory, consisting in 2740 S-1 slices. In particular, the quality of the final results is assessed through a large-scale comparison with the GPS measurements relevant to nearly 500 stations. The mean standard deviation value of the differences between the DInSAR and the GPS time series (projected in the radar line of sight) is less than 0.5 cm, thus confirming the effectiveness of the implemented solution. Finally, a discussion about the performance achieved by migrating the developed processing chain within the Amazon Web Services CC environment is addressed, highlighting that a two-year data set relevant to a standard S-1 IW slice can be reliably processed in about 30 h.The presented results demonstrate the capability of the implemented P-SBAS approach to efficiently and effectively process large S-1 IW data sets relevant to extended portions of the earth surface, paving the way to the systematic generation of advanced DInSAR products to monitor ground displacements at a very wide spatial scale.

In this work we present a fully parallel SBAS-DInSAR processing chain for the effective and massive generation of Sentinel-1 (S-1) Interferometric Wide Swath (IWS) deformation time-series. The pursued strategy to develop such a parallel processing chain fully benefits from the data acquisition characteristics of the TOPS mode, consisting of a series of bursts that can be considered as separate images to be independently processed. Such a data structure fosters the intrinsic parallelization of the S-1 IWS interferometric data processing, which can automatically be carried out through the exploitation of high-performance distributed computing infrastructures, and of efficient algorithms for tackling the huge data flow provided by the S-1 constellation. In order to demonstrate the capability of the presented S-1 P-SBAS processing chain to deal with the huge amount of data acquired by the S-1 constellation, we process a very extended dataset acquired over Italy from which we compute the mean velocity maps and corresponding deformation time-series.

In this work we implement a completely automatic interferometric processing chain, based on the well-known advanced DInSAR algorithm referred to as Parallel Small BAseline Subset (P-SBAS), for the generation of Sentinel-l (S-1) Interferometric Wide Swath (IWS) deformation mean velocity maps and time-series of very wide areas, implemented within the Amazon Web Services (AWS) Elastic Cloud Compute environment. Our processing chain consists of the initial data query to the S-1 archive that we created on the AWS S3 storage, then the data transfer to the AWS computing nodes, the data processing and, finally, the transfer of the obtained interferometric results back to the original S3 storage. In order to demonstrate the capability of the implemented Cloud-based processing chain to deal with massive amount of data, we focus our analysis on the whole Italian territory by processing all the available data acquired both from ascending and descending orbits within the October 2014 - March 2017 time interval. As final result we combine the retrieved LOS displacements in order to compute the mean velocity maps and time-series of the vertical and East-West surface deformation components.

In this work we present an advanced interferometric processing chain, which is based on the DInSAR algorithm referred to as Parallel Small BAseline Subset (P-SBAS) approach, for the massive processing of SENTINEL-1 (S1) Interferometric Wide Swath (IWS) data. The P-SBAS S1 processing chain produces surface deformation time series, and the relevant mean velocity maps, in automatic and systematic way by efficiently exploiting Cloud Computing infrastructures, thus allowing us to perform DInSAR analyses at very large scale in reduced time frames. As experimental results, the overall mean deformation velocity map relevant to the Central and Southern Italy zone (from Lazio to Sicily), generated by processing in parallel about 300 S1 acquisitions within the Amazon Web Services Cloud Computing platform, is presented. Moreover, the displacement time series of some pixels located in volcanic deforming areas such as the Campi Flegrei Caldera (Napoli Bay area) and the Mt. Etna (Sicily) are shown.

In this work we present an efficient interferometric processing chain, based on the advanced DInSAR algorithm referred to as Parallel Small BAseline Subset (P-SBAS), for the generation of Sentinel-1A (S1A) Interferometric Wide Swath deformation time-series, which is able to exploit distributed computing architectures. The presented S1A P-SBAS processing chain has been successfully implemented within the ESA Geohazard Exploitation Platform to provide an on-demand automatic service for the unsupervised generation of P-SBAS displacement time-series. To give an idea of the effectiveness of the presented S1A processing chain, as a preliminary result we show a 12-days interferometric analysis at continental scale, carried out by exploiting 150 S1A interferometric pairs acquired over Europe for an overall covered area of about 7,500,000 km2.

In the present radar remote sensing scenario, the huge availability of SAR data acquired by a number of satellite constellations is a key point for investigating Earth's surface at large scale. In particular, techniques as Differential SAR Interferometry (DInSAR) could strongly benefit from such data availability for measuring ground displacement at global scale. However, to efficiently and effectively exploit such amount of Big DInSAR Data, the development of new algorithms and techniques as well as the use of appropriate High Performance Computing infrastructure is becoming mandatory. In this work we present a number of case studies based on the recently proposed Parallel Small BAseline Subset (P-SBAS) DInSAR algorithm, that allows generating surface displacement maps in automatic and unsupervised way, aimed at providing effective solutions to the increased DInSAR data volume processing.

This work is aimed at describing the development of an efficient interferometric processing chain, based on the well-known advanced Differential Interferometric Synthetic Aperture Radar (DInSAR) algorithm referred to as Small BAseline Subset (SBAS) technique, for the generation of Sentinel-1A (S1-A) Interferometric Wide Swath (IWS) deformation time-series. Due to the TOPS mode characterizing the IWS acquisitions, the existing SBAS processing chains was properly adapted with new procedures for efficiently handling the S1-A data. The developed SBAS-DInSAR chain has been tested on both S1-A and TOPS RadarSAT-2 interferometric dataset, clearly demonstrating the capability of the developed SBAS-DInSAR processing chain to effectively investigate land subsidence phenomena affecting large areas.

This paper presents the integration of the advanced Differential SAR Interferometry (DInSAR) algorithm referred to as Parallel Small BAseline Subset (P-SBAS) within the ESA's Grid Processing on Demand (G-POD) environment in the framework of ESA Geohazards Exploitation Platform (GEP). The aim of this activity is to set up a scientific service that allows, in unsupervised manner, the generation of SBAS-DInSAR products, such as surface mean deformation velocity map and the corresponding time series. In particular, such a web tool is aimed at efficiently exploit the huge ESA's SAR data archives (ERS and ENVISAT), giving a support to scientific users, especially those non-expert of SAR data processing, for interferometric analysis in a short time frame.

In this work we propose a numerical optimization procedure constrained by field and SBAS-DInSAR measurements, as an alternative to standard forward Finite Elements (FE) models, to deeply analyze slope instabilities. The performed optimization procedure is based on the minimization of the difference between SBAS-DInSAR data and the results of the FE model, in terms of the displacement rate. As case study to evaluate the performances of the proposed procedure, we select the Ivancich landslide, located in the eastern part of the Assisi municipality (central Italy), and affected by an active slow-moving landslide since its first urbanization process. In this case, we focused on the Newtonian approach by considering a creeping flow approximation, suitable to simulate the kinematic trend of the investigated site. In addition, a set of 39 SAR images, acquired by COSMO-SkyMed constellation between 2009 and 2012, was exploited to generate deformation time series.

The work is focused on the exploitation of the results of a DInSAR analysis applied to ERS-ENVISAT and CSM data. The derived data are adopted to implement a multilevel analysis approach to investigate built-up areas at wide and local scales. The adopted analysis is aimed at performing: a territorial analysis to evaluate the distribution of large-scale deformation processes; an aggregated analysis applied at settlement scale to identify critical areas by providing building classification maps; a single structure damage assessment, using semi-quantitative and quantitative models to evaluate the stability of a structure and the potential damage scenarios.

The aim of this paper is to demonstrate the applicability of sparse representation to filter out the noise from SAR interferograms. More specifically, we consider an innovative approach for interferometric phase denoising, based on K-SVD technique applied to SAR interferograms, for estimating the noise-free underlying structure of the phase information. To examine the effectiveness of th is approach, the method has been successfully tested both on simulated and real interferograms. In the latter case, the proposed approach has been evaluated using ENVISAT SAR data acquired over the area of Napoli (Italy). The good results achieved applying the proposed method demonstrate its effectiveness for denoising SAR interferograms.

The current Remote Sensing scenario is characterized by the availability of huge archives of SAR data that are going to increase with the advent of Sentinel-1 satellites. The effective exploitation of this large amount of data requires both adequate computing resources as well as advanced algorithms able to properly exploit such facilities. In this work we discuss the migration of the DInSAR technique referred to as Parallel Small BAseline Subset (P-SBAS), which is used for Earth's surface deformation investigation, to the Amazon Web Services (AWS) public Cloud Computing environment. An experimental analysis aimed at evaluating the P-SBAS scalable performances that are achieved within the Cloud environment is presented. The achieved results show very good parallel performances and allow us to identify the major bottlenecks that can hamper such behavior when the amount of data to process highly increases. Accordingly, we present an advanced P-SBAS implementation that is designed to overcome the identified bottlenecks. The experimental analysis is carried out by processing both Envisat and COSMO-SkyMed datasets and by exploiting both a High Performance Computing cluster as well as AWS public Cloud.

The effective exploitation of the available huge SAR data archives in reasonable time-frames has motivated the development of P-SBAS, a parallel computing solution for the SBAS (Small BAseline Subset) processing chain. Hence, P-SBAS parallel solution represents a valuable tool for the analysis of the complex phenomena characterizing the surface deformation dynamics of Earth large areas, since it permits to exploit the parallelism offered by the modern computational platforms. In this paper, the performance of the parallel algorithm P-SBAS is investigated. The quantitative evaluation of the computational efficiency of the implemented parallel prototype in terms of achieved speedup is addressed to demonstrate the effectiveness of the proposed approach. An experimental analysis has been carried out on real data by employing a computational platform comprising 32 processors. In particular, the performance analysis has been conducted by exploiting different SAR datasets pertinent to different sensors (Envisat and Cosmo Sky-Med) and the factors limiting the inherent scalability are discussed.

In this work we present a detailed analysis of the co-seismic deformation signals associated with the 2012 Emilia (Northern Italy) seismic crises through spaceborne Differential Synthetic Aperture Radar (SAR) Interferometry. In particular, we provide a general picture of the ground deformation fields relevant to the Ml 5.9 and Ml 5.8 main shocks, by generating four co-seismic displacement maps from X-band COSMO-SkyMed and C-band RADARSAT-1/2 SAR data, collected by descending orbits over the investigated area. Subsequently, we perform an analytical modelling of the seismic events by exploiting the RADARSAT-2 displacement map through a finite dislocation fault, in order to get more information about the earthquake source locations and their geometries.

We exploit advanced Differential SAR Interferometry (DInSAR) techniques for enhanced analyses of slope instability phenomena. In particular, we focus on the Ivancich urban area, in the worldwide known historic town of Assisi, Central Italy, affected by a deep-seated, slow moving active landslide for which geological and geotechnical data are also available. Furthermore over the landslide site, large datasets of SAR acquisitions collected in the last two decades by the C-band ERS-1/2 and ENVISAT SAR sensors, and by the X-band radars of the COSMO-SkyMed constellation are available. In our study, we applied the advanced DInSAR technique referred to as Small BAseline Subset (SBAS), benefiting from its ability to generate deformation time series at full spatial resolution from multi-sensor SAR data, that allowed us to characterize the temporal and spatial pattern of ground deformations induced by the landslide. Furthermore, we experimented an innovative approach for landslide modeling, based on the integration of DInSAR measurements with conventional geological and geotechnical data used in landslide studies.

We have investigated the recent deformation affecting the Messina Strait area in South Italy, across the Calabria and the Sicilia Regions. Messina Strait is an extensional tectonic feature that separates peninsular Italy from Sicily, and it is also one of the most seismically active and deforming area of the Mediterranean. It is located between the Neogene Tyrrhenian backarc basin, developed in the hanging wall of the Apennines, and the Mesozoic-Paleogene Ionian basin, which is the foreland and the area of propagation of the Neogene to present Apennines accretionary prism. We have exploited Synthetic Aperture Radar (SAR) data along the time period between 2002 and 2010 by applying the advanced Differential Interferometric Synthetic Aperture Radar (DInSAR) technique referred to as Small BAseline Subset (SBAS) algorithm. GPS data relative to permanent stations within the study area have been also used.

This paper proposes a parallel model for the Differential Interferometry Synthetic Aperture Radar approach referred to as Small BAseline Subset (SBAS) algorithm. This new computational model has been designed to be specifically exploited within the emerging cloud computing environments. An experimental analysis, involving two different case studies, has been carried out to demonstrate the effectiveness of the methodology. The major novelty of the proposed Parallel SBAS (P-SBAS) model consists in the capability of processing large SAR data sets in reasonable time-frames. This key feature may be of great impact not only for hazard monitoring and risk mitigation activities but also for data sharing and knowledge spreading within the scientific community.

We focused on the joint exploitation of satellite and ground-based technologies in order to understand the kinematic behavior of landslides and subsidence phenomena relevant to different test sites in Europe. In this context, we efficiently exploited C-band and X-band satellite and ground-based SAR data for the investigation of the temporal and spatial pattern of ground deformations caused by natural and human-induced hazards. The present work has been conducted within the FP7-EU DORIS project.

We carry out a quantitative assessment of the accuracy of the advanced Differential SAR Interferometry (DInSAR) approach referred to as Small BAseline Subset (SBAS) in mapping deformation phenomena affecting active volcanic areas, by exploiting SAR data acquired by the “first” and “second” generation SAR sensors, and by comparing the achieved results with independent geodetic measurements, the latter assumed as reference. In particular, we analyze the impact that the different wavelengths and looking geometries may have in the SBAS-DInSAR measurement retrieval depending on the radar system. To this aim, we consider SAR images acquired by the ERS-1/2 and ENVISAT (C-band) as well as COSMO-SkyMed (X-band) sensors (i.e., by the “first” and “second” generation SAR sensors, respectively) over the Campi Flegrei caldera (Southern Italy) and the in-situ displacement measurements provided by the continuous GPS stations deployed in the area. The performed comparative analysis reveals a general good agreement between DInSAR and geodetic data; it also shows that the single displacement measurements have a sub-centimetric accuracy with a standard deviation of about 0.5 cm.

We investigate the capability improvement of the advanced differential interferometric synthetic aperture radar (DInSAR) techniques to map deformation phenomena affecting urban areas by exploiting multitemporal SAR data acquired by the new X-band sensors with respect to those of the previous C-band systems. In particular, we perform a comparative analysis of the deformation time-series retrieved by applying the full-resolution Small BAseline Subset DInSAR technique to selected sequences of SAR data acquired by the ENVISAT and RADARSAT-1 sensors (both operating at C-band) and by the X-band radar systems onboard the SAR sensors of the COSMO-SkyMed (CSK) constellation. This study, focused on the city of Napoli (Italy), allows us to quantify the dramatic increase of the DInSAR coherent pixel density achieved by exploiting the high-resolution X-band CSK SAR images (a few meters), resulting in an improvement factor of about 320% and 550%, with respect to the RADARSAT-1 and ENVISAT products, respectively. This improvement permits us to analyze nearly all the structures located within the investigated urbanized area and, in many cases, also portions of the same building. The improved coherent pixel spatial densities, combined with the reduced revisit times of the new X-band SAR missions, allow us to significantly increase the effectiveness of the advanced DInSAR methodologies, further extending the role of those Earth Observation data in the development of monitoring scenarios.

We present some of the main advances on long term deformation time series analysis achieved thanks to the 10 years of operation of ENVISAT ASAR sensor. This is done by considering a number of selected case studies, which are mostly based on the use of the Small BAseline Subset (SBAS) technique. In particular, we show how we benefit from the ENVISAT data availability to extend the ERS time series, thus allowing us to obtain almost 20 years of deformation history. Moreover, we demonstrate how the multi-mode capability of ENVISAT permits improving the temporal sampling in SBAS time series. Finally, we introduce a novel technique, tested on ENVISAT data, to generate displacement time series in areas affected by large deformation phenomena.

We investigate the capability improvement of the DInSAR techniques to map deformation phenomena affecting urban areas, by performing a comparative analysis of the deformation time series retrieved by applying the full resolution Small BAseline Subset (SBAS) DInSAR technique to selected sequences of SAR data acquired by the ENVISAT, RADARSAT-1 and COSMO-SkyMed (CSK) SAR data. The presented study, focused on the city of Napoli (Italy), allows us to quantify the dramatic increase of the DInSAR coherent pixel density achieved by exploiting the high resolution X-Band CSK SAR images with respect to the RADARSAT-1 and ENVISAT products, respectively; this permits us to analyze nearly all the structures located within the investigated urbanized area and, in many cases, also portions of a same building.

We perform a quantitative assessment of the accuracy of Differential SAR Interferometry (DInSAR) time series in volcanic areas, retrieved through “first” and “second generation” SAR data. In particular, we analyze the impact that the wavelengths and looking geometries may have in the DInSAR measurement retrieval depending on the radar system. To this aim, we focus on the DInSAR algorithm referred to as Small BAseline Subset (SBAS) to generate mean deformation velocity maps and corresponding time series starting from sequences of SAR images. Moreover, we consider collections of SAR data acquired by the ERS-1/2 and ENVISAT (C-band), and COSMO-SkyMed (Xband) sensors over the volcanic area of the Campi Flegrei caldera, Southern Italy. We invert these SAR data sequences through the SBAS-DInSAR technique, thus obtaining C- and X- band deformation time series that we compare to continuous GPS measurements, the latter assumed as reference. The achieved results provide, in addition to a clear picture of the surface deformation phenomena already occurred and occurring in the selected case study, relevant indications for the analysis of the SBAS-DInSAR time series accuracies in volcanic areas passing from the first to second generation SAR sensors.

We propose an innovative Phase Unwrapping (PhU) approach to unwrap a sequence of full-resolution multi-temporal differential interferograms through a Region Growing (RG) strategy. The algorithm is designed to handle noisy interferograms to carry out effective phase unwrapping process concurrently of large single-look differential interferograms. The key idea of our algorithm is to exploit a set of well unwrapped pixels (seed points) by applying existing multi-temporal differential technique and propagate the solution to successfully unwrap the neighbouring wrapped pixels (candidate points). To this aim, phase unwrapping of the candidate point network is effectively performed exploiting the Extended Minimum Cost Flow (EMCF) algorithm applied to a Constrained Delaunay Triangulation. The proposed algorithm has been applied to a set of 116 ERS-1/2 and ENVSAT SAR images acquired over the city of Rome (Italy) in 1992-2010. The achieved results demonstrate the effectiveness of the innovative proposed PhU approach.

We present an efficient space-time phase unwrapping (PhU) algorithm allowing us to analyze sequences of multitemporal full resolution differential Synthetic Aperture Radar (SAR) interferograms for the generation of deformation time-series. The core of the proposed technique is represented by the extended minimum cost flow (EMCF) PhU algorithm. Our method is based on a joint analysis of the spatial and temporal relationships among a set of properly selected multitemporal differential interferograms. More specifically, the key idea is to split the complex MCF network problem into that of simpler sub-networks. Accordingly, we start by identifying and solving a primary network that involves a proper selection of coherent pixels of the computed interferograms, representing the backbone structure of the overall network. Subsequently, this result is applied for constraining the solution of the sub-networks connected to the primary one, involving the entire set of analyzed pixels. This task is achieved by solving a constrained optimization problem based on the computation of a Constrained Delaunay Triangulation in the Azimuth/Range domain. The experimental results, achieved by applying the proposed approach to a dataset consisting of European Remote Sensing (ERS) SAR data acquired, from June 1992 to August 2007 over the Napoli (Italy) bay area, confirm the effectiveness of the proposed PhU approach..

We analyze the temporal evolution of the deformation affecting the Yellowstone (Wyoming, U.S) complex volcanic system in the 1992-2010 time period. This work represents, at our knowledge, the first attempt at retrieving through differential synthetic aperture radar (DInSAR) techniques long-term deformation time-series at the Yellowstone Caldera. This is due to the presence of severe temporal decorrelation noise in the differential interferograms, which limit the overall performances of the DInSAR technique, especially with respect to phase unwrapping (PhU) operations. Accordingly, to increase the number of the investigated points in low coherent zones, we complement PhU operations with a space-time region growing method. The presented results, obtained by applying the Small Baseline Subset (SBAS) DInSAR technique to a data set composed of 21 ERS and 22 ENVISAT SAR images, clearly demonstrate the validity of the proposed method.

We present an efficient space-time phase unwrapping (PhU) algorithm that allows us to process sequences of multitemporal full resolution differential synthetic aperture radar (SAR) interferograms for the generation of deformation time-series. The core of the proposed technique, dealing with sparse data grids, is represented by the extended minimum cost flow (MCF) (EMCF) PhU algorithm that was originally developed for the analysis of sequences of multilook interferograms. In particular, our method relies on the joint analysis of the spatial and temporal relationships among a set of properly selected multitemporal differential interferograms, which are compatible with the Small BAseline subset (SBAS) deformation time-series technique. The key point of the approach is the idea to split the complex MCF network problem, representing the overall PhU operation, into that of simpler subnetworks. More precisely, we start by identifying and solving a primary network that involves a proper selection of coherent pixels of the computed interferograms, representing the backbone structure of the overall network. Subsequently, this result is applied for constraining the solution of the subnetworks connected to the primary one, involving the entire set of analyzed pixels. To achieve this task, we solve a constrained optimization problem based on the computation of a constrained Delaunay triangulation in the azimuth/range domain. The overall procedure is implemented through two successive processing steps that are both carried out by using the EMCF PhU technique, which has been slightly modified to take into account the Doppler centroid differences of the exploited interferometric SAR data pairs. The experimental results, achieved by applying the proposed approach to a data set consisting of European Remote Sensing (ERS) SAR data acquired from June 1992 to August 2007 over the Napoli (Italy) bay area, confirm the effectiveness of the proposed PhU approach.

In this work we extend the Small BAseline Subset (SBAS) Differential SAR Interferometry approach to allow the generation of deformation time-series by processing long sequences of ERS-1, ERS-2 and ENVISAT SAR data at the full spatial resolution scale. Our idea is to avoid the generation of ERS/ENVISAT cross-interferograms, severely affected by noise phenomena, and to consider single-platform interferograms only (i.e. ERS/ERS and ENVISAT/ENVISAT interferograms), that are properly combined by applying the SVD-based SBAS approach. The presented results, achieved on two dataset relevant to the Napoli Bay area and to the Murge region (Italy), confirm the effectiveness of the presented technique and demonstrate the relevance of deformation analysis carried out at the scale of single buildings with more than 15 years of ERS and ENVISAT acquisitions.

We perform a full exploitation of the Differential SAR Interferometry (DInSAR) algorithm referred to as Small BAseline Subset (SBAS) technique to investigate long term surface deformation occurring in extended, seismogenetic areas. To this aim we benefit of the SBAS technique capability to work in multi-frame and multi-sensor scenarios in order to improve the spatial and temporal coverage, as well as to employ new generation SAR sensors to increase the temporal sampling of the retrieved time series. In this work we apply the SBAS algorithm to analyze the temporal evolution of the detected displacements affecting three different seismogenetic scenarios by means of deformation time series retrieved through data acquired by European (ERS-1/2, ENVISAT) and Italian (COSMO-SkyMed) satellites. In particular, we focus on the analysis of the deformation patterns associated with the activity of the San Andreas (SAF, California, USA), the North Anatolian (NAF, Turkey) and the Paganica (PF, Abruzzo, Central Italy) Faults. The achieved results provide a clear idea of the surface deformation retrieval capability of the SBAS procedure.

We present the results of the first experiment to ¿plug¿ the Small BAseline Subset (SBAS) DInSAR algorithm into a GRID-based system; the key idea is to combine the robustness of the exploited advanced interferometric SAR approach with the high computing capability provided by a GRID environment. In particular, we have exploited the low-resolution SBAS algorithm and we benefited of the availability of the ESA Grid Processing-on-demand environment. The presented results, carried out on ENVISAT data, provide a overview of the main characteristics of the implemented SBAS-GRID processing solution.

In this work we describe the application of the basic small BAseline subset (SBAS) technique, which exploits multilook interferograms, to a number of active volcanic areas. The use of such a technique reduces the amount of data to be processed and simplifies the analysis of geophysical phenomena occurring in extended areas (up to 100 km by 100 km). Moreover, it can be trivially extended in order to combine data acquired by different sensors with similar geometrical and electromagnetic characteristics, i.e., ERS and ENVISAT IS-2 mode, thus allowing an easy extension of the temporal observation window. The selected test sites for this study are Long Valley caldera, Mt. Etna and the Neapolitan Volcanic district (Mt. Vesuvio and Campi Flegrei caldera). Finally, we shortly analyze the implications of the use of forthcoming SAR sensors that operates in L-and X-bands.

We have investigated the deformation affecting the Campi Flegrei caldera (Italy), from 2002 to the end of 2006, by analyzing ENVISAT ASAR IS-2 data. This study has been performed by exploiting the SBAS-DInSAR algorithm that allows us to detect earth surface displacements and to investigate their temporal evolution via the generation of deformation time series. The presented analysis highlighted the renewed volcanic activity that started on mid-2005; moreover, we have combined the ascending and descending data in order to separate the vertical and east-west components of the detected displacements. The obtained results have been confirmed by the leveling data collected by the Osservatorio Vesuviano.

We have investigated the phase retrieval capability of the Extended Minimum Cost Flow (EMCF) phase unwrapping (PhU) approach in the framework of the Persistent Scatterers Interferometry (PSI) algorithms for the generation of deformation time-series. The presented technique exploits an appropriate selection of full resolution interferograms obtained via a triangulation step carried out in the Temporal/Perpendicular baseline plane, where the available SAR image sequence is represented. Moreover, the phase unwrapping procedure is implemented via the cascade of two steps, based on the conventional Minimum Cost Flow (MCF) algorithm, that allows us to exploit both the spatial characteristics and the temporal relationships among the produced interferograms. The presented experiments, carried out by analyzing a set of 43 ERS SAR images relevant to an area of the city of Rome (Italy), confirm the effectiveness of the exploited PhU approach.

Accurate subpixel registration of synthetic aperture radar (SAR) images is an issue that is again growing interest since its initial developments related to two-pass interferometry. Recent progress in coherent (multichannel) SAR processing raises the need for accurate registration of data takes acquired with large baseline spans, high temporal coverage, and with different frequency and/or operational modes. In this paper, we discuss a SAR image-registration procedure, based on the use of external measures which allows obtaining a very accurate alignment of SAR images. The presented technique makes use of a digital elevation model and of the precise information about the acquisition flight tracks, to compute the warping functions that map the position of each pixel in the different takes, thus avoiding any approximation. The resulting algorithm is simple, robust, precise, and very efficient; as a matter of fact, it may achieve high accuracy even in critical areas, such as steep topography regions. Moreover, the availability of an analytical and exact model allows performing a detailed sensitivity analysis that can be useful in evaluating the applicability of this technique even to future high-precision satellite systems. Extensive testing, carried out on several real European Remote Sensing and ENVISAT datasets, clearly shows the effectiveness of such algorithm in registering critical SAR images

The Small BAseline Subset (SBAS) approach is a differential synthetic aperture radar interferometry (DIFSAR) technique that allows analyzing deformation phenomena affecting both extended area and localized structures, by exploiting the phase difference of SAR image pairs characterized by small baselines. In this work we process a large set of ERS-1/2 data, acquired from ascending and descending orbits, at both small and large scale resolution and extend the obtained time series with available ENVISAT acquisitions. The results, relevant to the Napoli Bay area (Italy), are compared with geodetic and GPS data in order to achieve a quantitative analysis of the SABS algorithm performances

This paper presents a differential synthetic aperture radar (SAR) interferometry (DIFSAR) approach for investigating deformation phenomena on full-resolution DIFSAR interferograms. In particular, our algorithm extends the capability of the small-baseline subset (SBAS) technique that relies on small-baseline DIFSAR interferograms only and is mainly focused on investigating large-scale deformations with spatial resolutions of about 100/spl times/100 m. The proposed technique is implemented by using two different sets of data generated at low (multilook data) and full (single-look data) spatial resolution, respectively. The former is used to identify and estimate, via the conventional SBAS technique, large spatial scale deformation patterns, topographic errors in the available digital elevation model, and possible atmospheric phase artifacts; the latter allows us to detect, on the full-resolution residual phase components, structures highly coherent over time (buildings, rocks, lava, structures, etc.), as well as their height and displacements. In particular, the estimation of the temporal evolution of these local deformations is easily implemented by applying the singular value decomposition technique. The proposed algorithm has been tested with data acquired by the European Remote Sensing satellites relative to the Campania area (Italy) and validated by using geodetic measurements.

This paper presents a DIFSAR approach that allows us to detect and follow the temporal evolution of surface deformations at different spatial scales. In particular, our solution extends the capability of the algorithm referred to as small baseline subsets (SBAS) technique (Berardino et al., 2002), and allows us to investigate large scale deformation phenomena as well as displacements of single buildings or structures. The proposed technique relies on small baseline DIFSAR interferograms only, in order to mitigate the decorrelation phenomena, and requires two different sets of data generated at low (multi-look) and high (single-look) spatial resolution, respectively. The algorithm has been tested with the data acquired by the European Remote Sensing (ERS) satellites which are relative to the city of Napoli (Italy) and surroundings; the results have been validated by using geodetic data.