{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T11:07:19Z","timestamp":1771931239521,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T00:00:00Z","timestamp":1662595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Nature Science Foundation of Hunan Province","award":["2020JJ2043"],"award-info":[{"award-number":["2020JJ2043"]}]},{"name":"Nature Science Foundation of Hunan Province","award":["42030112"],"award-info":[{"award-number":["42030112"]}]},{"name":"Nature Science Foundation of Hunan Province","award":["2019CX007"],"award-info":[{"award-number":["2019CX007"]}]},{"name":"National Natural Science Foundation of China","award":["2020JJ2043"],"award-info":[{"award-number":["2020JJ2043"]}]},{"name":"National Natural Science Foundation of China","award":["42030112"],"award-info":[{"award-number":["42030112"]}]},{"name":"National Natural Science Foundation of China","award":["2019CX007"],"award-info":[{"award-number":["2019CX007"]}]},{"name":"Project of Innovation-driven Plan of Central South University","award":["2020JJ2043"],"award-info":[{"award-number":["2020JJ2043"]}]},{"name":"Project of Innovation-driven Plan of Central South University","award":["42030112"],"award-info":[{"award-number":["42030112"]}]},{"name":"Project of Innovation-driven Plan of Central South University","award":["2019CX007"],"award-info":[{"award-number":["2019CX007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>As one of the most prevailing geodetic tools, the interferometric synthetic aperture radar (InSAR) technique can accurately obtain co-seismic displacements, but is limited to the one-dimensional line-of-sight (LOS) measurement. It is therefore difficult to completely reveal the real three-dimensional (3D) surface displacements with InSAR. By employing azimuth displacement observations from pixel offset tracking (POT) and multiple aperture InSAR (MAI) techniques, 3D displacements of large-magnitude earthquakes can be obtained by integrating the ascending and descending data. However, this method cannot be used to accurately realize the 3D surface displacement measurements of small-magnitude earthquakes due to the low accuracies of the POT\/MAI-derived azimuth displacement measurements. In this paper, an alternative method is proposed to calculate co-seismic 3D displacements from ascending and descending InSAR-LOS observations with the dislocation model-based displacement direction constraint. The main contribution lies in the two virtual observation equations that are obtained from the dislocation model-based forward-modeling 3D displacements, which are then combined with the ascending\/descending InSAR observations to calculate the 3D displacements. The basis of the two virtual observation equations is that the directions of the 3D displacement vectors are very similar for real and model-based 3D displacements. In addition, the weighted least squares (WLS) method is employed to solve the final 3D displacements, which aims to consider and balance the possible errors in the InSAR observations as well as the dislocation model-based displacement direction constraint. A simulation experiment demonstrates that the proposed method can achieve more accurate 3D displacements compared with the existing methods. The co-seismic 3D displacements of the 2020 Nima earthquake are then accurately obtained by the proposed method. The results show that co-seismic displacements are dominated by the vertical displacement, the magnitude of the horizontal displacement is relatively small, and the overall displacement pattern fits well with the tensile rupture.<\/jats:p>","DOI":"10.3390\/rs14184481","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T09:51:09Z","timestamp":1662630669000},"page":"4481","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Calculating Co-Seismic Three-Dimensional Displacements from InSAR Observations with the Dislocation Model-Based Displacement Direction Constraint: Application to the 23 July 2020 Mw6.3 Nima Earthquake, China"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5412-2703","authenticated-orcid":false,"given":"Jun","family":"Hu","sequence":"first","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"}]},{"given":"Jianwen","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1528-3771","authenticated-orcid":false,"given":"Jihong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"}]},{"given":"Wanji","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"}]},{"given":"Kang","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Geosciences and Info-Physics, Central South University, Changsha 410083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,8]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1029\/1999GL900138","article-title":"Measuring ground displacements from SAR amplitude images: Application to the Landers earthquake","volume":"26","author":"Michel","year":"1999","journal-title":"Geophys. Res. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1029\/2006GL026883","article-title":"Measuring two-dimensional movements using a single InSAR pair","volume":"33","author":"Bechor","year":"2006","journal-title":"Geophys. Res. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2552","DOI":"10.1002\/2016GL067954","article-title":"Three-dimensional displacement field of the 2015 M(w)8.3 Illapel earthquake (Chile) from across- and along-track Sentinel-1 TOPS interferometry","volume":"43","author":"Grandin","year":"2016","journal-title":"Geophys. Res. Lett."},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1109\/LGRS.2010.2051793","article-title":"Mapping Three-Dimensional Surface Deformation by Combining Multiple-Aperture Interferometry and Conventional Interferometry: Application to the June 2007 Eruption of Kilauea Volcano, Hawaii","volume":"8","author":"Jung","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, J., Hu, J., Li, Z., Ma, Z., Shi, J., Xu, W., and Sun, Q. (2022). Three-Dimensional Surface Displacements of the 8 January 2022 Mw6.7 Menyuan Earthquake, China from Sentinel-1 and ALOS-2 SAR Observations. Remote Sens., 14.","DOI":"10.3390\/rs14061404"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1007\/s11430-021-9868-9","article-title":"Complete three-dimensional coseismic displacements related 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_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.earscirev.2014.02.005","article-title":"Resolving three-dimensional surface displacements from InSAR measurements: A review","volume":"133","author":"Hu","year":"2014","journal-title":"Earth-Sci. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3883","DOI":"10.1109\/JSTARS.2016.2577878","article-title":"A Minimum Acceleration Approach for the Retrieval of Multiplatform InSAR Deformation Time Series","volume":"9","author":"Pepe","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Qu, C., Qiao, X., Shan, X., Zhao, D., Zhao, L., Gong, W., and Li, Y. (2020). InSAR 3-D Coseismic Displacement Field of the 2015 Mw 7.8 Nepal Earthquake: Insights into Complex Fault Kinematics during the Event. Remote Sens., 12.","DOI":"10.3390\/rs12233982"},{"key":"ref_12","first-page":"104","article-title":"Deriving 3D coseismic deformation field by combining GPS and InSAR data based on the elastic dislocation model","volume":"57","author":"Song","year":"2017","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1007\/s10291-022-01226-2","article-title":"A robust method for 3-D surface displacement fields combining GNSS and single-orbit InSAR measurements with directional constraint from elasticity model","volume":"26","author":"Xu","year":"2022","journal-title":"GPS Solut."},{"key":"ref_14","first-page":"4000505","article-title":"A New Method for Constructing 3-D Crustal Deformation Field From Single InSAR-LOS Data","volume":"19","author":"Xu","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_15","first-page":"163","article-title":"Recent tectonic activity of Bayanhar fault block and the Kunlun-Wenchuan earthquake series of the Tibetan Plateau","volume":"17","author":"Deng","year":"2010","journal-title":"Earth Sci. Front."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.gr.2011.11.012","article-title":"Structural sequence and geochronology of the Qomo Ri accretionary complex, Central Qiangtang, Tibet: Implications for the Late Triassic subduction of the Paleo-Tethys Ocean","volume":"22","author":"Liang","year":"2012","journal-title":"Gondwana Res."},{"key":"ref_17","first-page":"2297","article-title":"Coseismic deformation characteristics of the 2020 Nima, Xizang Mw6.3 earthquake from Sentinel-1A\/B InSAR data and rupture slip distribution","volume":"64","author":"Li","year":"2021","journal-title":"Chin. J. Geophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"e2021TC006949","DOI":"10.1029\/2021TC006949","article-title":"Coseismic and Postseismic Fault Kinematics of the July 22, 2020, Nima (Tibet) Ms6.6 Earthquake: Implications of the Forming Mechanism of the Active N-S-Trending Grabens in Qiangtang, Tibet","volume":"41","author":"Gao","year":"2022","journal-title":"Tectonics"},{"key":"ref_19","first-page":"173","article-title":"Co-seismic deformation field of the 2020 Nima Tibet Earthquake and fault slip distribution","volume":"2021","author":"Huang","year":"2021","journal-title":"Bull. Surv. Mapp."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1785\/0220210057","article-title":"The July 2020 Mw 6.3 Nima Earthquake, Central Tibet: A Shallow Normal-Faulting Event Rupturing in a Stepover Zone","volume":"93","author":"Yang","year":"2021","journal-title":"Seismol. Res. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e2021JB022212","DOI":"10.1029\/2021JB022212","article-title":"Joint InSAR and Field Constraints on Faulting During the Mw 6.4, July 23, 2020, Nima\/Rongma Earthquake in Central Tibet","volume":"126","author":"Li","year":"2021","journal-title":"J. Geophys. Res.-Solid Earth"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1093\/gji\/ggt254","article-title":"The 2011 M-W 6.8 Burma earthquake: Fault constraints provided by multiple SAR techniques","volume":"195","author":"Feng","year":"2013","journal-title":"Geophys. J. Int."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"12099","DOI":"10.1029\/2018JB017159","article-title":"Complete Three-Dimensional Coseismic Deformation Field of the 2016 Central Tottori Earthquake by Integrating Left- and Right-Looking InSAR Observations With the Improved SM-VCE Method","volume":"124","author":"Liu","year":"2019","journal-title":"J. Geophys. Res.-Solid Earth"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1038\/nature03425","article-title":"Three-dimensional deformation caused by the Bam, Iran, earthquake and the origin of shallow slip deficit","volume":"435","author":"Fialko","year":"2005","journal-title":"Nature"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/s00190-018-1183-6","article-title":"High-quality three-dimensional displacement fields from new-generation SAR imagery: Application to the 2017 Ezgeleh, Iran, earthquake","volume":"93","author":"He","year":"2019","journal-title":"J. Geod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2007","DOI":"10.1109\/TGRS.2016.2634087","article-title":"Estimation of 3-D Surface Displacement Based on InSAR and Deformation Modeling","volume":"55","author":"Hu","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3271","DOI":"10.1109\/JSTARS.2014.2387865","article-title":"Improved SAR Amplitude Image Offset Measurements for Deriving Three-Dimensional Coseismic Displacements","volume":"8","author":"Wang","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1029\/2005RG000183","article-title":"The shuttle radar topography mission","volume":"45","author":"Farr","year":"2007","journal-title":"Rev. Geophys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4035","DOI":"10.1029\/1998GL900033","article-title":"Radar interferogram filtering for geophysical applications","volume":"25","author":"Goldstein","year":"1998","journal-title":"Geophys. Res. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2192","DOI":"10.1109\/36.868877","article-title":"Probabilistic cost functions for network flow phase unwrapping","volume":"38","author":"Carballo","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7945","DOI":"10.1029\/JB092iB08p07945","article-title":"Detection of a locked zone at depth on the Parkfield, California, segment of the San Andreas Fault","volume":"92","author":"Harris","year":"1987","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2128","DOI":"10.1785\/0120120231","article-title":"Subparallel Dipping Faults that Ruptured during the 2008 Wenchuan Earthquake","volume":"103","author":"Fukuyama","year":"2013","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_33","first-page":"1814","article-title":"Coseismic and postseismic deformation of the 2008 Wenchuan Earthquake from InSAR","volume":"57","author":"Wen","year":"2014","journal-title":"Chin. J. Geophys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1130\/GES00217.1","article-title":"Active structures of the Himalayan-Tibetan orogen and their relationships to earthquake distribution, contemporary strain field, and Cenozoic volcanism","volume":"5","author":"Taylor","year":"2009","journal-title":"Geosphere"},{"key":"ref_35","first-page":"4","article-title":"Conjugate strike-slip faulting along the Bangong-Nujiang suture zone accommodates coeval east-west extension and north-south shortening in the interior of the Tibetan Plateau","volume":"22","author":"Taylor","year":"2003","journal-title":"Tectonics"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/18\/4481\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:27:45Z","timestamp":1760142465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/18\/4481"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,8]]},"references-count":35,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["rs14184481"],"URL":"https:\/\/doi.org\/10.3390\/rs14184481","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,8]]}}}