<p>Tropospheric delay, comprising stratified and turbulent components, is one of the primary error sources in high-precision surface deformation measurement using Interferometric Synthetic Aperture Radar (InSAR). Thanks to advancements in external data and the developments of the phase-elevation method, stratified delay can be effectively corrected in most cases. However, turbulent delay remains an obstacle for InSAR applications due to its strong spatiotemporal nonlinearity and spatial irregularity. Here, we propose a spatially correlated stochastic model for atmospheric turbulence correction (STOMAC) using a two-step sequential estimation. Firstly, the variance–covariance matrix of each SAR image is constructed via a covariance function and network inversion. Then, the eigenvalue decomposition of the variance–covariance matrix is conducted to isolate the turbulent phase from the residual phase. The effectiveness of the STOMAC method is validated through both simulated and real-data experiments. The root-mean-square error (RMSE) of the differences in displacement time series decreased by 40.5% in the simulated experiments. In a real-data case in Southern California (USA), the mean RMSE decreased from 13.1 to 5.7&#xa0;mm compared with 42 GPS measurements. Our findings highlight the importance of incorporating a stochastic model when mitigating turbulent delays.</p>