Investigation of sensitivity to noise in the three-dimensional displacement field retrieval problem, generated by radar interferometry (Case study: Sefidsang and Ezgeleh earthquakes of 21 March and 12 November 2017, respectively)

Document Type : Research


1 Ph.D. Student, Department of Geodesy, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran, Iran

2 Associate Professor, Department of Geodesy, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran, Iran

3 Assistant Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran


In recent decades, Interferometric Synthetic Aperture Radar (InSAR) technology has been an efficient tool in quantitatively measuring of the earth's deformation, influenced by natural and human factors, such as the overexploitation of water from underground aquifers, mining, subsidence, earthquake, and landslide. However, in the nature of the displacement measurement in the satellite's line of sight (LOS) in this technology, the possibility of extracting a three-dimensional displacement field has faced challenges. Especially in the study of many tectonic phenomena requiring a comprehensive understanding of the three-dimensional displacement components. Therefore, at least three independent radar geometries or InSAR-derived LOS displacements are always needed to solve the problem of retrieval of the three-dimensional (3D) displacement field. However, the polar geometry of imaging radar satellites is such that the contribution of the displacement and effect of the noise of the observations on the estimated parameters (Three-dimensional components) will be different, even in some cases, the problem will be unstable. Therefore, in this research, the noise sensitivity of the three-dimensional displacement field retrieval problem in independent and differential radar geometries is investigated and also based on the orbit overlapping method in the Sentinel radar satellite, using simulated and real data, the three-dimensional displacement of the Sefidsang and Ezgeleh earthquakes of 21 March and 12 November 2017 respectively is retrieved and the efficiency of this method is evaluated. In fact, in this study, considering the importance of knowing and measuring the components of the 3D surface displacement field, the problem of three-dimensional displacement field retrieval was investigated using a combination of independent radar geometries. Then, according to the variance-covariance matrix structure of the problem and the principal component analysis (PCA) method, the sensitivity of recovering each component of the displacement field to the input data noise by taking measurements of three independent radar geometries was discussed. The results show that the north-south displacement component has the highest sensitivity to the input data noise and has the least contribution of displacement along with the satellite LOS. Then the east-west and up-down components have approximately the same sensitivity to noise, although, for some specific incidence angles, the sensitivity to noise for the up-down component will be increased. Also, the condition number of the design matrix in the 3D field retrieval problem show that in most cases (except when the incidence angles of the two geometries are equal or have very slight differences), it is a well-established and stable problem and there is no need to solve it with regularization method. In the second part of the paper, remembering that in the Sentinel radar satellite, each sub-swath is imaged at different angles (with a difference of about 10 degrees), so the concept of overlap between the orbits (at least three different geometries) can be used to retrieve the 3D displacement field in most regions. The feasibility and efficiency of this method were evaluated with real and simulated data. The results showed that in the absence of noise components, the orbit overlap interferometry (OOI) method could be well used in 3D field reconstruction.


Main Subjects

Aflaki, M., Mousavi, Z., Ghods, A., Shabanian, E., Vajedian, S. and Akbarzadeh, M., 2019, The 2017 M w 6 Sefid Sang earthquake and its implication for the geodynamics of NE Iran. Geophysical Journal International, 218(2), 1227-1245.
Babaee, S., Mouavi, Z. and Roostaei, M., 2016, Time Series Analysis of SAR Images Using Small Baseline Subset (SBAS) and Persistent Scatterer (PS) Approaches to Determining Subsidence Rate of Qazvin Plain. Journal of Geomatics Science and Technology, 5(4), 95-111.
Bamler, R. and Hartl, P., 1998, Synthetic aperture radar interferometry. Inverse problems, 14(4), R1.
Berardino, P., Fornaro, G., Lanari, R. and Sansosti, E., 2002, A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms. IEEE Transactions on Geoscience and Remote Sensing, 40(11), 2375-2383.
Feng, W., Samsonov, S., Almeida, R., Yassaghi, A., Li, J., Qiu, Q., Zheng, W., 2018, Geodetic Constraints of the 2017 Mw7. 3 Sarpol Zahab, Iran Earthquake, and Its Implications on the Structure and Mechanics of the Northwest Zagros Thrust‐Fold Belt. Geophysical Research Letters, 45(14), 6853-6861.
Ferretti, A., Prati, C. and Rocca, F., 2001, Permanent scatterers in SAR interferometry. IEEE Transactions on Geoscience and Remote Sensing, 39(1), 8-20.
Fialko, Y., Simons, M. and Agnew, D., 2001, The complete (3‐D) surface displacement field in the epicentral area of the 1999 Mw7. 1 Hector Mine earthquake, California, from space geodetic observations. Geophysical Research Letters, 28(16), 3063-3066.
Hanssen, R. F., 2001, Radar interferometry: data interpretation and error analysis (Vol. 2): Springer Science & Business Media.
He, P., Wen, Y., Xu, C. and Chen, Y., 2018, High-quality three-dimensional displacement fields from new-generation SAR imagery: application to the 2017 Ezgeleh, Iran, earthquake. Journal of Geodesy, 1-19.
Hooper, A., Segall, P. and Zebker, H., 2007, Persistent scatterer interferometric synthetic aperture radar for crustal deformation analysis, with application to Volcán Alcedo, Galápagos. Journal of Geophysical Research: Solid Earth, 112(B7).
Hotelling, H., 1933, Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6), 417.
Hu, J., Li, Z., Ding, X., Zhu, J., Zhang, L. and Sun, Q., 2014, Resolving three-dimensional surface displacements from InSAR measurements: A review. Earth-Science Reviews 17-1, 131.
Kampes, B. M. and Hanssen, R. F., 2004, Ambiguity resolution for permanent scatterer interferometry. IEEE Transactions on Geoscience and Remote Sensing, 42(11), 2446-2453.
Ketelaar, G., Van Leijen, F., Marinkovic, P. and Hanssen, R., 2007, Multi-track PS-InSAR datum connection. Paper presented at the 2007 IEEE International Geoscience and Remote Sensing Symposium.
Mashhadi-Hossainali, M., 2006, A Comprehensive Approach to the Analysis of the 3D-Kinematics of Deformation. Technische Universität.
Massonnet, D., Rossi, M., Carmona, C., Adragna, F., Peltzer, G., Feigl, K. and Rabaute, T., 1993, The displacement field of the Landers earthquake mapped by radar interferometry. Nature, .138 (6433) 364.
Pearson, K., 1901, LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559-572.
Qu, C., Shan, X., Zhao, D., Zhang, G. and Song, X., 2017, Relationships between InSAR Seismic Deformation and Fault Motion Sense, Fault Strike, and Ascending/Descending Modes. Acta Geologica Sinica (English Edition), 91(1), 93-108.
Rodriguez, E. and Martin, J., 1992, Theory and design of interferometric synthetic aperture radars. Paper presented at the IEE Proceedings F (Radar and Signal Processing).
Solari, L., Del Soldato, M., Bianchini, S., Ciampalini, A., Ezquerro, P., Montalti, R., Moretti, S., 2018, From ERS 1/2 to Sentinel-1: subsidence monitoring in Italy in the last two decades. Frontiers in Earth Science, 6, 149.
Solaro, G., Imperatore, P. and Pepe, A., 2016, Satellite SAR Interferometry for Earth’s Crust Deformation Monitoring and Geological Phenomena Analysis Geospatial Technology-Environmental and Social Applications: IntechOpen.
Su, Z., Yang, Y.-H., Li, Y.-S., Xu, X.-W., Zhang, J., Zhou, X. and Zhang, S.-M., 2019, Coseismic displacement of the 5 April 2017 Mashhad earthquake (Mw 6.1) in NE Iran through Sentinel-1A TOPS data: New implications for the strain partitioning in the southern Binalud Mountains. Journal of Asian Earth Sciences, 169, 244-256.
Tarantola, A., 2005, Inverse problem theory and methods for model parameter estimation (Vol. 89): siam.
Vajedian, S. and Motagh, M., 2018, Coseismic displacement analysis of the 12 November 2017 Mw 7.3 Sarpol-e Zahab (Iran) earthquake from SAR Interferometry, burst overlap interferometry and offset tracking. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences 4 (2018), Nr. 3, 4(3), 205-209.
Vajedian, S., Motagh, M., Mousavi, Z., Motaghi, K., Fielding, E., Akbari, B. and Darabi, A., 2018, Coseismic deformation field of the MW 7.3 12 November 2017 Sarpol-e Zahab (Iran) earthquake: A decoupling horizon in the northern Zagros Mountains inferred from InSAR observations. Remote Sensing, 10(10), 1589.
Van Leijen, F. J., 2014, Persistent scatterer interferometry based on geodetic estimation theory.
Wright, T. J., Parsons, B. E. and Lu, Z., 2004, Toward mapping surface deformation in three dimensions using InSAR. Geophysical Research Letters, 31(1).
Xiao, R. and He, X., 2013, GPS and InSAR time series analysis: deformation monitoring application in a hydraulic engineering resettlement zone, Southwest China. Mathematical problems in engineering, 2013.
Xu, G., Xu, C. and Wen, Y., 2018, Sentinel-1 observation of the 2017 Sangsefid earthquake, northeastern Iran: Rupture of a blind reserve-slip fault near the Eastern Kopeh Dagh. Tectonophysics, 731, 131-138.
Yang, C., Han, B., Zhao, C., Du, J., Zhang, D. and Zhu, S., 2019, Co-and post-seismic Deformation Mechanisms of the MW 7.3 Iran Earthquake (2017) Revealed by Sentinel-1 InSAR Observations. Remote Sensing, 11(4), 418.
Zhang, L., Ding, X. and Lu, Z., 2011, Modeling PSInSAR time series without phase unwrapping. IEEE Transactions on Geoscience and Remote Sensing, 49(1), 547-55.