{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:54Z","timestamp":1760242794348,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2016,7,12]],"date-time":"2016-07-12T00:00:00Z","timestamp":1468281600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41404028"],"award-info":[{"award-number":["41404028"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Basic Research Program of China","doi-asserted-by":"publisher","award":["2013CB733300"],"award-info":[{"award-number":["2013CB733300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Spatial and temporal variations in the vertical stratification of the troposphere introduce significant propagation delays in interferometric synthetic aperture radar (InSAR) observations. Observations of small amplitude surface deformations and regional subsidence rates are plagued by tropospheric delays, and strongly correlated with topographic height variations. Phase-based tropospheric correction techniques assuming a linear relationship between interferometric phase and topography have been exploited and developed, with mixed success. Producing robust estimates of tropospheric phase delay however plays a critical role in increasing the accuracy of InSAR measurements. Meanwhile, few phase-based correction methods account for the spatially variable tropospheric delay over lager study regions. Here, we present a robust and multi-weighted approach to estimate the correlation between phase and topography that is relatively insensitive to confounding processes such as regional subsidence over larger regions as well as under varying tropospheric conditions. An expanded form of robust least squares is introduced to estimate the spatially variable correlation between phase and topography by splitting the interferograms into multiple blocks. Within each block, correlation is robustly estimated from the band-filtered phase and topography. Phase-elevation ratios are multiply- weighted and extrapolated to each persistent scatter (PS) pixel. We applied the proposed method to Envisat ASAR images over the Southern California area, USA, and found that our method mitigated the atmospheric noise better than the conventional phase-based method. The corrected ground surface deformation agreed better with those measured from GPS.<\/jats:p>","DOI":"10.3390\/s16071078","type":"journal-article","created":{"date-parts":[[2016,7,12]],"date-time":"2016-07-12T10:01:21Z","timestamp":1468317681000},"page":"1078","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Robust and Multi-Weighted Approach to Estimating Topographically Correlated Tropospheric Delays in Radar Interferograms"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3551-6539","authenticated-orcid":false,"given":"Bangyan","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiancheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengwei","family":"Chu","sequence":"additional","affiliation":[{"name":"Nanjing Institute of Surveying, Mapping and Geotechnical Investigation, Nanjing 210019, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Tang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dawei","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1029\/RS009i010p00803","article-title":"An improved equation for the radio refractive index of air","volume":"9","author":"Thayer","year":"1974","journal-title":"Radio Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1029\/RS020i006p01593","article-title":"Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length","volume":"20","author":"Davis","year":"1985","journal-title":"Radio Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1029\/2000GL000016","article-title":"Influence of ionospheric electron density fluctuations on satellite radar interferometry","volume":"27","author":"Gray","year":"2000","journal-title":"Geophys. Res. Lett."},{"key":"ref_4","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."},{"key":"ref_5","first-page":"43","article-title":"Atmospheric effects on InSAR measurements- A review","volume":"79","author":"Li","year":"2003","journal-title":"Geomat. Res. Australas."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5426","DOI":"10.3390\/s8095426","article-title":"Atmospheric effects on InSAR measurements and their mitigation","volume":"8","author":"Ding","year":"2008","journal-title":"Sensors"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tecto.2011.10.013","article-title":"Recent advances in SAR interferometry time series analysis for measuring crustal deformation","volume":"514\u2013517","author":"Hooper","year":"2012","journal-title":"Tectonophysics"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Onn, F., and Zebker, H.A. (2006). Correction for interferometric synthetic aperture radar atmospheric phase artifacts using time series of zenith wet delay observations from a GPS network. J. Geophy. Res., 111.","DOI":"10.1029\/2005JB004012"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/TGRS.2012.2200901","article-title":"Experimental study on the atmospheric delay based on GPS, SAR interferometry, and numerical weather model data","volume":"51","author":"Mateus","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"11-1","DOI":"10.1029\/2002GL015159","article-title":"Atmospheric models, GPS and InSAR measurements of the atmospheric water vapor field over mount Etna","volume":"29","author":"Wadge","year":"2002","journal-title":"Geophys. Res. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"L16304","DOI":"10.1029\/2006GL026781","article-title":"Mitigating atmospheric noise for InSAR using a high resolution weather model","volume":"33","author":"Foster","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Li, Z. (2005). Interferometric synthetic aperture radar (InSAR) atmospheric correction: GPS, Moderate Resolution Imaging Spectroradiometer (MODIS), and InSAR integration. J. Geophys. Res., 110.","DOI":"10.1029\/2004JB003446"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, Z., Fielding, E.J., Cross, P., and Muller, J.-P. (2006). Interferometric synthetic aperture radar atmospheric correction: Medium Resolution Imaging Spectrometer and Advanced Synthetic Aperture Radar integration. Geophys. Res. Lett., 33.","DOI":"10.1029\/2005GL025299"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.jappgeo.2009.03.010","article-title":"Corrections of stratified atmospheric delays in SAR interferometry: Validation with global atmospheric models","volume":"69","author":"Doin","year":"2009","journal-title":"J. Appl. Geophys."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jolivet, R., Grandin, R., Lasserre, C., Doin, M.P., and Peltzer, G. (2011). Systematic InSAR atmospheric phase delay corrections from global meteorological reanalysis data. Geophys. Res. Lett., 38.","DOI":"10.1029\/2011GL048757"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2849","DOI":"10.1029\/98GL02112","article-title":"Atmospheric corrections of SAR interferograms with strong topography. Application to Etna","volume":"25","author":"Delacourt","year":"1998","journal-title":"Geophys. Res. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1146\/annurev.earth.28.1.169","article-title":"Synthetic aperture radar interferometry to measure Earth\u2019s surface topography and its deformation","volume":"28","author":"Burgmann","year":"2000","journal-title":"Annu. Rev. Earth Planet. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"Q09002","DOI":"10.1029\/2010GC003228","article-title":"A multiscale approach to estimating topographically correlated propagation delays in radar interferograms","volume":"11","author":"Lin","year":"2010","journal-title":"Geochem. Geophys. Geosyst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1002\/2014JB011558","article-title":"A spatially variable powerlaw atmospheric correction technique for InSAR data","volume":"120","author":"Bekaert","year":"2015","journal-title":"J. Geophys. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/s00190-005-0454-1","article-title":"Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness","volume":"79","author":"Xu","year":"2005","journal-title":"J. Geod."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/s00190-009-0361-y","article-title":"Robust estimation for correlated observations: Two local sensitivity-based downweighting strategies","volume":"84","author":"Guo","year":"2010","journal-title":"J. Geod."},{"key":"ref_22","unstructured":"Kampes, B., Hanssen, R., and Perski, Z. (2003, January 1\u20135). Radar interferometry with public domain tools. Proceedings of the Fringe Workshop, Frascati, Italy."},{"key":"ref_23","unstructured":"Hooper, A. (2006). Persistent Scatterer Radar Interferometry for Crustal Deformation Studies and Modeling of Volcanic Deformation, Stanford University."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2737","DOI":"10.1364\/JOSAA.24.002737","article-title":"Phase unwrapping in three dimensions with application to InSAR time series","volume":"24","author":"Hooper","year":"2007","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1029\/EO081i048p00583","article-title":"Shuttle radar topography mission produces a wealth of data","volume":"81","author":"Farr","year":"2000","journal-title":"Eos Trans. AGU"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1029\/2000GL011776","article-title":"Triggered slip: Observations of the 17 August 1999 Izmit (Turkey) earthquake using radar interferometry","volume":"28","author":"Wright","year":"2001","journal-title":"Geophys. Res. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.epsl.2013.02.020","article-title":"Slow slip event in the Mexican subduction zone: Evidence of shallower slip in the Guerrero seismic gap for the 2006 event revealed by the joint inversion of InSAR and GPS data","volume":"367","author":"Cavalie","year":"2013","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hanssen, R.F. (2001). Radar Interferometry: Data Interpretation and Error Analysis, Kluwer Academic Publishers.","DOI":"10.1007\/0-306-47633-9"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"L22309","DOI":"10.1029\/2008GL035806","article-title":"Importance of ocean tidal load corrections for differential InSAR","volume":"35","author":"DiCaprio","year":"2008","journal-title":"Geophys. Res. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1002\/2014JB011557","article-title":"Reassessing the 2006 Guerrero slow slip event, Mexico: Implications for large earthquakes in the Guerrero Gap","volume":"120","author":"Bekaert","year":"2015","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"L15310","DOI":"10.1029\/2012GL052453","article-title":"Seasonal hydrological loading in southern Alaska observed by GPS and GRACE","volume":"39","author":"Fu","year":"2012","journal-title":"Geophys. Res. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"10K","DOI":"10.1007\/BF03655325","article-title":"Robust estimation for dependent observations","volume":"19","author":"Yang","year":"1994","journal-title":"Manuscr. Geod."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s001900050252","article-title":"Robust estimation of systematic errors of satellite laser range","volume":"73","author":"Yang","year":"1999","journal-title":"J. Geod."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Huber, P.J. (1981). Robust Statistics, John Wiley and Sons.","DOI":"10.1002\/0471725250"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1111\/j.1365-246X.2012.05432.x","article-title":"Correcting atmospheric effects on InSAR with MERIS water vapor data and elevation-dependent interpolation model","volume":"189","author":"Li","year":"2012","journal-title":"Geophys. J. Int."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/7\/1078\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:25:58Z","timestamp":1760210758000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/7\/1078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,12]]},"references-count":35,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2016,7]]}},"alternative-id":["s16071078"],"URL":"https:\/\/doi.org\/10.3390\/s16071078","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,7,12]]}}}