Retrieving three-dimensional displacement fields of mining areas from a single InSAR pair

This paper presents a novel method for retrieving three-dimensional (3-D) displacement fields of mining areas from a single interferometric synthetic aperture radar (InSAR) pair. This method fully exploits the mechanism of mining subsidence, specifically the proportional relationship between the horizontal displacement and horizontal gradient of vertical displacements caused by underground mining. This method overcomes the limitations of conventional InSAR techniques that can only measure one-dimensional (1-D) deformation of mining area along the radar line-of-sight direction. The proposed method is first validated with simulated 3-D displacement fields, which are obtained by the FLAC$$^{\mathrm{3D}}$$3D software. The root mean square errors of the 3-D displacements retrieved by the proposed method are 13.7, 27.6 and 3.6 mm for the West–East, North–South, and Up–Down components, respectively. We then apply the proposed method to estimate the 3-D displacements of the Qianyingzi and the Xuzhou coal mines in China, respectively, each along with two Advanced Land Observing Satellite (ALOS) Phased Array Type L-band Synthetic Aperture Radar images. Results show that the estimated 3-D displacement is highly consistent with that of the field surveying. This demonstrates that the proposed method is an effective approach for retrieving 3-D mining displacement fields and will play an important role in mining-related hazard prevention and environment assessment under limited InSAR acquisitions.