Geodesy-Informed Deep Learning for InSAR Tropospheric Correction: Adaptive Weighted least squares and STTU-Net

Tropospheric delay is primary limitation for surface deformation retrieval using Synthetic Aperture Radar Interferometry (InSAR), presents challenges due to its spatiotemporal heterogeneity. This study proposes a correction framework integrating geodetic parameter estimation theory with deep learning. It aims to robustly estimate topography-correlated stratified delays while also rigorously applying a new deep learning network to suppress turbulent delays. Initially, a quadtree segmentation method is employed to partition the area of interest. Within each homogeneous segment, the topography-correlated stratified delay phase is robustly estimated using an adaptive-order functional model fitted via weighted least squares. Subsequently, the time-domain differentiation technique is applied to isolate high-frequency turbulent signals, thereby constructing a realistic turbulent sample dataset. Finally, by integrating the strengths of the U-Net architecture and the Convolutional Block Attention Module (CBAM), a Spatio-Temporal Turbulence U-Net (STTU-Net) is designed based on the statistical spatio-temporal characteristics of the real turbulence sample dataset. This network learns the detailed evolution of random turbulent fields, enabling an efficient, data-driven deep learning approach for turbulent delay correction. Applied to Sentinel-1 data over Southern California, the method reduces the average interferogram phase standard deviation by 27% and weakens phase-elevation correlation. After full correction, the RMSE between InSAR and GNSS time series decreases from 4.7 cm to 2.2 cm. The estimated total delays also agree well with GNSS-ZTD (correlation: 0.84; RMSD: 1.94 cm). Results from simulated data confirm that this method effectively suppresses tropospheric delay while fully preserving genuine deformation signals of varying characteristics, thereby providing a systematic and verifiable solution for tropospheric delay correction in InSAR.