{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T18:43:46Z","timestamp":1776105826424,"version":"3.50.1"},"reference-count":52,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T00:00:00Z","timestamp":1695340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Persistent Scatterer Deformation Pattern Analysis Tool, for short PSDefoPAT, was designed to assign each measuring point of an advanced DInSAR data set a best-fitting time series model based on its displacement time series. In this paper, we will outline the operating principles of the tool. The periodic and trend components of a time series model are separately determined based on hypothesis tests. The periodic component is fitted as a sine function, and for the trend component, linear, quadratic, and piecewise linear regression models are considered. Additionally, the tool assesses the goodness-of-fit for each model in the form of the adjusted coefficient of determination Radj2 value. The tool works fully automatically and thus facilitates the analysis of large data sets, which are becoming more available to the public due to services such as the European Ground Motion Service. Additionally, we demonstrate the capabilities of PSDefoPAT using four case studies characterized by different deformation mechanisms, various extents of active deformation area, and varying density of measuring points. In all cases, we successfully reveal information on the temporal behavior of the deformation not apparent in the typically presented mean deformation velocity maps.<\/jats:p>","DOI":"10.3390\/rs15194646","type":"journal-article","created":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T03:44:42Z","timestamp":1695354282000},"page":"4646","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["PSDefoPAT\u2014Persistent Scatterer Deformation Pattern Analysis Tool"],"prefix":"10.3390","volume":"15","author":[{"given":"Madeline","family":"Evers","sequence":"first","affiliation":[{"name":"Fraunhofer IOSB, Gutleuthausstra\u00dfe 1, 76275 Ettlingen, Germany"},{"name":"Karlsruhe Institute of Technology, Kaiserstra\u00dfe 12, 76131 Karlsruhe, Germany"}]},{"given":"Antje","family":"Thiele","sequence":"additional","affiliation":[{"name":"Fraunhofer IOSB, Gutleuthausstra\u00dfe 1, 76275 Ettlingen, Germany"},{"name":"Karlsruhe Institute of Technology, Kaiserstra\u00dfe 12, 76131 Karlsruhe, Germany"}]},{"given":"Horst","family":"Hammer","sequence":"additional","affiliation":[{"name":"Fraunhofer IOSB, Gutleuthausstra\u00dfe 1, 76275 Ettlingen, Germany"}]},{"given":"Stefan","family":"Hinz","sequence":"additional","affiliation":[{"name":"Karlsruhe Institute of Technology, Kaiserstra\u00dfe 12, 76131 Karlsruhe, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1038\/364138a0","article-title":"The displacement field of the Landers earthquake mapped by radar interferometry","volume":"364","author":"Massonnet","year":"1993","journal-title":"Nature"},{"key":"ref_2","first-page":"397","article-title":"Space geodesy: A revolution in crustal deformation measurements of tectonic processes","volume":"500","author":"Thatcher","year":"2013","journal-title":"Geol. Soc. Am. Spec. Pap."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s12665-013-2422-z","article-title":"Radar interferometry techniques for the study of ground subsidence phenomena: A review of practical issues through cases in Spain","volume":"71","author":"Romero","year":"2014","journal-title":"Environ. Earth Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/36.898661","article-title":"Permanent scatterers in SAR interferometry","volume":"39","author":"Ferretti","year":"2001","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.1109\/TGRS.2002.803792","article-title":"A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms","volume":"40","author":"Berardino","year":"2002","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3460","DOI":"10.1109\/TGRS.2011.2124465","article-title":"A new algorithm for processing interferometric data-stacks: SqueeSAR","volume":"49","author":"Ferretti","year":"2011","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.jappgeo.2009.07.002","article-title":"Practical persistent scatterer processing validation in the course of the Terrafirma project","volume":"69","author":"Adam","year":"2009","journal-title":"J. Appl. Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.culher.2017.01.005","article-title":"Surface deformation data in the archaeological site of Petra from medium-resolution satellite radar images and SqueeSAR\u2122 algorithm","volume":"25","author":"Alberti","year":"2017","journal-title":"J. Cult. Herit."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.rse.2006.01.023","article-title":"A quantitative assessment of the SBAS algorithm performance for surface deformation retrieval from DInSAR data","volume":"102","author":"Casu","year":"2006","journal-title":"Remote Sens. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Crosetto, M., Solari, L., Mr\u00f3z, M., Balasis-Levinsen, J., Casagli, N., Frei, M., Oyen, A., Moldestad, D.A., Bateson, L., and Guerrieri, L. (2020). The evolution of wide-area DInSAR: From regional and national services to the European Ground Motion Service. Remote Sens., 12.","DOI":"10.3390\/rs12122043"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Costantini, M., Minati, F., Trillo, F., Ferretti, A., Passera, E., Rucci, A., Dehls, J., Larsen, Y., Marinkovic, P., and Eineder, M. (2022, January 17\u201322). EGMS: Europe-wide ground motion monitoring based on full resolution InSAR processing of all Sentinel-1 acquisitions. Proceedings of the IGARSS 2022\u20132022 IEEE International Geoscience and Remote Sensing Symposium, Kuala Lumpur, Malaysia.","DOI":"10.1109\/IGARSS46834.2022.9884966"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1945","DOI":"10.5194\/nhess-13-1945-2013","article-title":"Automated classification of Persistent Scatterers Interferometry time series","volume":"13","author":"Berti","year":"2013","journal-title":"Nat. Hazards Earth Syst. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Costantini, M., Zhu, M., Huang, S., Bai, S., Cui, J., Minati, F., Vecchioli, F., Jin, D., and Hu, Q. (2018, January 22\u201327). Automatic detection of building and infrastructure instabilities by spatial and temporal analysis of InSAR measurements. Proceedings of the IGARSS 2018\u20132018 IEEE International Geoscience and Remote Sensing Symposium, Valencia, Spain.","DOI":"10.1109\/IGARSS.2018.8518270"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"147","DOI":"10.5194\/isprs-archives-XLIII-B3-2021-147-2021","article-title":"Concept to Analyze the Displacement Time Series of Individual Persistent Scatterers","volume":"43","author":"Evers","year":"2021","journal-title":"Int. Arch. Photogramm. Remote. Sens. Spat. Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"107","DOI":"10.5194\/isprs-annals-V-3-2022-107-2022","article-title":"Psdefopat\u2013Towards automatic model based psi post-processing","volume":"3","author":"Evers","year":"2022","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"9183","DOI":"10.1029\/JB094iB07p09183","article-title":"Mapping small elevation changes over large areas: Differential radar interferometry","volume":"94","author":"Gabriel","year":"1989","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hanssen, R.F. (2001). Radar Interferometry: Data Interpretation and Error Analysis, Springer Science & Business Media.","DOI":"10.1007\/0-306-47633-9"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7547","DOI":"10.1029\/96JB03804","article-title":"Atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps","volume":"102","author":"Zebker","year":"1997","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2202","DOI":"10.1109\/36.868878","article-title":"Nonlinear subsidence rate estimation using permanent scatterers in differential SAR interferometry","volume":"38","author":"Ferretti","year":"2000","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_20","unstructured":"Hooper, A.J. (2006). Persistent Scatter Radar Interferometry for Crustal Deformation Studies and Modeling of Volcanic Deformation. [Ph.D. Thesis, Stanford University]."},{"key":"ref_21","unstructured":"Werner, C., Wegmuller, U., Strozzi, T., and Wiesmann, A. (2003, January 21\u201325). Interferometric point target analysis for deformation mapping. Proceedings of the IGARSS 2003, 2003 IEEE International Geoscience and Remote Sensing Symposium, Toulouse, France. Proceedings (IEEE Cat. No. 03CH37477)."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2446","DOI":"10.1109\/TGRS.2004.835222","article-title":"Ambiguity resolution for permanent scatterer interferometry","volume":"42","author":"Kampes","year":"2004","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_23","unstructured":"Kampes, B.M. (2006). Radar Interferometry: Persistent Scatterer Technique, Springer Science & Business Media."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.isprsjprs.2015.10.011","article-title":"Persistent scatterer interferometry: A review","volume":"115","author":"Crosetto","year":"2016","journal-title":"ISPRS J. Photogramm. Remote. Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1109\/TGRS.2007.894440","article-title":"Submillimeter accuracy of InSAR time series: Experimental validation","volume":"45","author":"Ferretti","year":"2007","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Kalia, A.C. (2018). Classification of landslide activity on a regional scale using persistent scatterer interferometry at the moselle valley (Germany). Remote Sens., 10.","DOI":"10.3390\/rs10121880"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2883","DOI":"10.1002\/2014GC005307","article-title":"Extent and distribution of aseismic slip on the Ismetpa\u015fa segment of the North Anatolian Fault (Turkey) from Persistent Scatterer InSAR","volume":"15","author":"Cetin","year":"2014","journal-title":"Geochem. Geophys. Geosyst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Solari, L., Ciampalini, A., Raspini, F., Bianchini, S., and Moretti, S. (2016). PSInSAR analysis in the Pisa urban area (Italy): A case study of subsidence related to stratigraphical factors and urbanization. Remote Sens., 8.","DOI":"10.3390\/rs8020120"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.enggeo.2013.01.022","article-title":"Monitoring an earthfill dam using differential SAR interferometry: La Pedrera dam, Alicante, Spain","volume":"157","author":"Cano","year":"2013","journal-title":"Eng. Geol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"659","DOI":"10.5194\/nhess-13-659-2013","article-title":"Multi-temporal SAR interferometry reveals acceleration of bridge sinking before collapse","volume":"13","author":"Sousa","year":"2013","journal-title":"Nat. Hazards Earth Syst. Sci."},{"key":"ref_31","unstructured":"Montgomery, D.C., Jennings, C.L., and Kulahci, M. (2015). Introduction to Time Series Analysis and Forecasting, John Wiley & Sons."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Neusser, K. (2016). Time Series Econometrics, Springer.","DOI":"10.1007\/978-3-319-32862-1"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S0169-7439(96)00077-9","article-title":"Noise suppression and signal compression using the wavelet packet transform","volume":"36","author":"Walczak","year":"1997","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Mallat, S. (1999). A Wavelet Tour of Signal Processing, Elsevier.","DOI":"10.1016\/B978-012466606-1\/50008-8"},{"key":"ref_35","unstructured":"Motard, R.L., and Joseph, B. (2013). Wavelet Applications in Chemical Engineering, Springer Science & Business Media."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1109\/29.45554","article-title":"Multifrequency channel decompositions of images and wavelet models","volume":"37","author":"Mallat","year":"1989","journal-title":"IEEE Trans. Acoust. Speech, Signal Process."},{"key":"ref_37","first-page":"1","article-title":"Signal denoising using wavelets","volume":"890","author":"Cohen","year":"2012","journal-title":"Proj. Rep. Dep. Electr. Eng. Tech. Isr. Inst. Technol. Haifa"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1080\/01621459.1995.10476626","article-title":"Adapting to unknown smoothness via wavelet shrinkage","volume":"90","author":"Donoho","year":"1995","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/18.382009","article-title":"De-noising by soft-thresholding","volume":"41","author":"Donoho","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_40","first-page":"54","article-title":"Tests of significance in harmonic analysis","volume":"125","author":"Fisher","year":"1929","journal-title":"Proc. R. Soc. Lond. Ser. A Contain. Pap. Math. Phys. Character"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Ahdesmaki, M., Lahdesmaki, H., and Yli-Harja, O. (2007, January 10\u201312). Robust Fisher\u2019s test for periodicity detection in noisy biological time series. Proceedings of the 2007 IEEE International Workshop on Genomic Signal Processing and Statistics, Tuusula, Finland.","DOI":"10.1109\/GENSIPS.2007.4365817"},{"key":"ref_42","unstructured":"Ott, R.L., and Longnecker, M.T. (2015). An Introduction to Statistical Methods and Data Analysis, Cengage Learning."},{"key":"ref_43","unstructured":"Keogh, E., Chu, S., Hart, D., and Pazzani, M. (2004). Data Mining in Time Series Databases, World Scientific."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.cej.2010.07.059","article-title":"Piecewise linear regression: A statistical method for the analysis of experimental adsorption data by the intraparticle-diffusion models","volume":"163","author":"Malash","year":"2010","journal-title":"Chem. Eng. J."},{"key":"ref_45","first-page":"31","article-title":"Algoritmic methods for segmentation of time series: An overview","volume":"1","year":"2014","journal-title":"J. Contemp. Econ. Bus. Issues"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"5481","DOI":"10.5194\/gmd-15-5481-2022","article-title":"Root-mean-square error (RMSE) or mean absolute error (MAE): When to use them or not","volume":"15","author":"Hodson","year":"2022","journal-title":"Geosci. Model Dev."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.tree.2003.10.013","article-title":"Model selection in ecology and evolution","volume":"19","author":"Johnson","year":"2004","journal-title":"Trends Ecol. Evol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.jvolgeores.2010.05.014","article-title":"Unrest episodes at Campi Flegrei: A reconstruction of vertical ground movements during 1905\u20132009","volume":"195","author":"Aquino","year":"2010","journal-title":"J. Volcanol. Geotherm. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1038\/s41597-022-01849-7","article-title":"Thirty years of volcano geodesy from space at Campi Flegrei caldera (Italy)","volume":"9","author":"Polcari","year":"2022","journal-title":"Sci. Data"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Matano, F., Sacchi, M., Vigliotti, M., and Ruberti, D. (2018). Subsidence trends of volturno river coastal plain (northern campania, southern italy) inferred by sar interferometry data. Geosciences, 8.","DOI":"10.3390\/geosciences8010008"},{"key":"ref_51","unstructured":"Dounias, G., Lazaridou, S., Sakellariou, S., Somakos, L., Skourlis, K., and Mihas, S. (2023, January 20). The behavior of Asteri Dam on Parapeiros River during first filling, Greece. Proceedings of the 91st International Commission of Large Dams Annual Meeting, International Commission of Large Dams, Gothenburg, Sweden."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1002\/stab.200590133","article-title":"Die Netzwerkbogenbr\u00fccke, ein \u00fcberaus effizientes Br\u00fcckentragwerk\u2013tragwirkung und Konstruktion","volume":"74","author":"Teich","year":"2005","journal-title":"Stahlbau"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/19\/4646\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:55:41Z","timestamp":1760129741000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/19\/4646"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,22]]},"references-count":52,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["rs15194646"],"URL":"https:\/\/doi.org\/10.3390\/rs15194646","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,22]]}}}