{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:22:01Z","timestamp":1760149321815,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2023,7,26]],"date-time":"2023-07-26T00:00:00Z","timestamp":1690329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As one of the common techniques for measuring coseismic deformations, optical image correlation techniques are capable of overcoming the drawbacks of inadequate coherence and phase blurring which can occur in radar interferometry, as well as the problem of low spatial resolution in radar pixel offset tracking. However, the scales of the correlation window in optical image correlation techniques typically influence the results; the conventional SAR POT method faces a fundamental trade-off between the accuracy of matching and the preservation of details in the correlation window size. This study regards coseismic deformation as a two-dimensional vector, and develops a new post-processing workflow called VACI-OIC to reduce the dependence of shift estimation on the size of the correlation window. This paper takes the coseismic deformations in both the east\u2013west and north\u2013south directions into account at the same time, treating them as vectors, while also considering the similarity of displacement between adjacent points on the surface. Herein, the angular continuity index of the coseismic deformation vector was proposed as a more reasonable constraint condition to fuse the deformation field results obtained by optical image correlation across different correlation window. Taking the earthquake of 2021 in Maduo, China, as the study area, the deformation with the highest spatial resolution in the violent surface rupture area was determined (which could not be provided by SAR data). Compared to the results of single-scale optical correlation, the presented results were more uniform (i.e., more consistent with published results). At the same time, the proposed index also detected the strip fracture zone of the earthquake with impressive clarity.<\/jats:p>","DOI":"10.3390\/s23156677","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T02:14:48Z","timestamp":1690424088000},"page":"6677","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Vector Angular Continuity in the Fusion of Coseismic Deformations at Multiple Optical Correlation Scales"],"prefix":"10.3390","volume":"23","author":[{"given":"Rui","family":"Guo","sequence":"first","affiliation":[{"name":"Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1020-064X","authenticated-orcid":false,"given":"Qiming","family":"Zeng","sequence":"additional","affiliation":[{"name":"Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shangzong","family":"Lu","sequence":"additional","affiliation":[{"name":"Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1109\/LGRS.2020.2991758","article-title":"Pixel Offset Fusion of SAR and Optical Images for 3-D Coseismic Surface Deformation","volume":"18","author":"Lu","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3486","DOI":"10.1364\/AO.39.003486","article-title":"Measuring earthquakes from optical satellite images","volume":"39","author":"Michel","year":"2000","journal-title":"Appl. Opt."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1029\/2008EO010001","article-title":"Monitoring Earth Surface Dynamics With Optical Imagery","volume":"89","author":"Leprince","year":"2008","journal-title":"Am. Geophys. Union"},{"key":"ref_4","unstructured":"Vadon, H., and Massonnet, D. (2000, January 24\u201328). Earthquake displacement fields mapped by very precise correlation. Complementarity with radar interferometry. Proceedings of the IGARSS 2000. IEEE 2000 International Geoscience and Remote Sensing Symposium. Taking the Pulse of the Planet: The Role of Remote Sensing in Managing the Environment. Proceedings (Cat. No.00CH37120), Honolulu, HI, USA."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Leprince, S., Ayoub, F., Klinger, Y., and Avouac, J.-P. (2007, January 23\u201328). Co-Registration of Optically Sensed Images and Correlation (COSI-Corr): An Operational Methodology for Ground Deformation Measurements. Proceedings of the 2007 IEEE International Geoscience and Remote Sensing Symposium, Barcelona, Spain.","DOI":"10.1109\/IGARSS.2007.4423207"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.isprsjprs.2009.03.005","article-title":"Co-registration and correlation of aerial photographs for ground deformation measurements","volume":"64","author":"Ayoub","year":"2009","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Aati, S., and Avouac, J.-P. (2020). Optimization of Optical Image Geometric Modeling, Application to Topography Extraction and Topographic Change Measurements Using PlanetScope and SkySat Imagery. Remote Sens., 12.","DOI":"10.3390\/rs12203418"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"e2021GC009704","DOI":"10.1029\/2021GC009704","article-title":"Characterizing Near-Field Surface Deformation in the 1990 Rudbar Earthquake (Iran) Using Optical Image Correlation","volume":"22","author":"Ajorlou","year":"2021","journal-title":"Geochem. Geophys. Geosystems"},{"key":"ref_9","first-page":"9","article-title":"Coseismic deformation of 2019 Ridgecrest earthquake sequence obtained by optical images correlation","volume":"30","author":"Wang","year":"2021","journal-title":"Eng. Surv. Mapp."},{"key":"ref_10","first-page":"339","article-title":"Coseismic displacements of 2016 MW 7.8 Kaikoura, New Zealand earthquake, using Sentinel-2 optical images","volume":"48","author":"He","year":"2019","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"L07301","DOI":"10.1029\/2008GL036431","article-title":"Surface displacements in the September 2005 Afar rifting event from satellite image matching: Asymmetric uplift and faulting","volume":"36","author":"Barisin","year":"2009","journal-title":"Geophys. Res. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1002\/esp.3383","article-title":"The application of COSI-Corr to determine dune system dynamics in the southern Namib Desert using ASTER data","volume":"38","author":"Scheidt","year":"2013","journal-title":"Earth Surf. Process. Landf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1109\/TGRS.2006.888937","article-title":"Automatic and Precise Orthorectification, Coregistration, and Subpixel Correlation of Satellite Images, Application to Ground Deformation Measurements","volume":"45","author":"Leprince","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","first-page":"102867","article-title":"Polarimetric SAR pixel offset tracking for large-gradient landslide displacement mapping","volume":"112","author":"Cai","year":"2022","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_15","first-page":"15","article-title":"Coseismic surface rupture and seismogenic structure of the 2021-05-22 Maduo (Qinghai) MS 7.4 earthquake","volume":"95","author":"Pan","year":"2021","journal-title":"Acta Geol. Sin."},{"key":"ref_16","first-page":"899","article-title":"Coseismic surface rupture characteristics, causes and significance of the \u201c5.22\u201d MS 7.4 Earthquake in Maduo, Qinghai","volume":"27","author":"Ge","year":"2021","journal-title":"J. Geomech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12639","DOI":"10.1002\/anie.201406854","article-title":"Planet-Satellite Nanostructures Made to Order by RAFT Star Polymers","volume":"53","author":"Rossner","year":"2014","journal-title":"Angew. Chem.-Int. Ed."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1007\/s11430-021-9868-9","article-title":"Complete three-dimensional coseismic displacements due to the 2021 Maduo earthquake in Qinghai Province, China from Sentinel-1 and ALOS-2 SAR images","volume":"65","author":"Liu","year":"2022","journal-title":"Sci. China Earth Sci."},{"key":"ref_19","first-page":"2671","article-title":"Coseismic deformation analysis of the 2021 Qinghai Madoi M7.4 earthquake","volume":"64","author":"Yang","year":"2021","journal-title":"Chin. J. Geophys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2079","DOI":"10.1093\/gji\/ggac311","article-title":"GPS\/BDS precise point positioning with B2b products for high-rate seismogeodesy: Application to the 2021 Mw 7.4 Maduo earthquake","volume":"231","author":"Fang","year":"2022","journal-title":"Geophys. J. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1007\/s12583-021-1556-2","article-title":"The Interpretation of Seismogenic Fault of the Maduo Mw 7.3 Earthquake, Qinghai Based on Remote Sensing Images\u2014A Branch of the East Kunlun Fault System","volume":"33","author":"Ha","year":"2022","journal-title":"J. Earth Sci."},{"key":"ref_22","first-page":"461","article-title":"Distributed characteristics of the surface deformations associated with the 2021 MW 7.4 Madoi earthquake, Qinghai, China","volume":"44","author":"Liu","year":"2022","journal-title":"Seismol. Geol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"229542","DOI":"10.1016\/j.tecto.2022.229542","article-title":"Overall subshear but locally supershear rupture of the 2021 Mw 7.4 Maduo earthquake from high-rate GNSS waveforms and three-dimensional InSAR deformation","volume":"839","author":"Lyu","year":"2022","journal-title":"Tectonophysics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1007\/s12583-022-1637-x","article-title":"Coseismic Slip Distribution of the 2021 Mw 7.4 Maduo, Qinghai Earthquake Estimated from InSAR and GPS Measurements","volume":"33","author":"Xiao","year":"2022","journal-title":"J. Earth Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"229558","DOI":"10.1016\/j.tecto.2022.229558","article-title":"Coseismic slip and early afterslip of the 2021 Mw 7.4 Maduo, China earthquake constrained by GPS and InSAR data","volume":"840","author":"Xiong","year":"2022","journal-title":"Tectonophysics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"229528","DOI":"10.1016\/j.tecto.2022.229528","article-title":"Nucleation mechanism of the 2021 Mw 7.4 Maduo earthquake, NE Tibetan Plateau: Insights from seismic tomography and numerical modeling","volume":"839","author":"Zhang","year":"2022","journal-title":"Tectonophysics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3059","DOI":"10.1016\/j.asr.2022.01.042","article-title":"Research on deformation characteristics of the 2021 Qinghai Maduo MS7.4 earthquake through coseismic dislocation inversion","volume":"69","author":"Zhang","year":"2022","journal-title":"Adv. Space Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1109\/TGRS.2017.2745576","article-title":"A Method for Measuring 3-D Surface Deformations with InSAR Based on Strain Model and Variance Component Estimation","volume":"56","author":"Liu","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"112298","DOI":"10.1016\/j.rse.2021.112298","article-title":"Estimating three-dimensional coseismic deformations with the SM-VCE method based on heterogeneous SAR observations: Selection of homogeneous points and analysis of observation combinations","volume":"255","author":"Hu","year":"2021","journal-title":"Remote Sens. Environ."},{"key":"ref_30","unstructured":"Ayoub, F., Leprince, S., and Avouac, J.-P. (2009). User\u2019s Guide to COSI-CORR Co-Registration of Optically Sensed Images and Correlation, California Institute of Technology."},{"key":"ref_31","first-page":"410","article-title":"A novel kinematics analysis method using quaternion interpolation\u2013a case study in frog jumping","volume":"454","author":"Richards","year":"2018","journal-title":"J. Biol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1029\/2001JB000951","article-title":"Horizontal coseismic deformation of the 1999 Chi-Chi earthquake measured from SPOT satellite images: Implications for the seismic cycle along the western foothills of central Taiwan","volume":"108","author":"Dominguez","year":"2003","journal-title":"J. Geophys. Res. Solid Earth"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/15\/6677\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:19:07Z","timestamp":1760127547000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/15\/6677"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,26]]},"references-count":32,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["s23156677"],"URL":"https:\/\/doi.org\/10.3390\/s23156677","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,7,26]]}}}