Sensitivity and reliability analysis to MSBAS regularization for the estimation of surface deformation over a mine

To systematically and thoroughly analyze the sensitivity and reliability of the MSBAS regularization for the estimation of surface deformation over a mine in combination with an application example, this study processed 101 Sentinel-1A/B SAR images, constructed and solved the 2D deformation models using SVD and Tikhonov regularization methods with different orders and parameters, and estimated the vertical and east-west surface deformation time series in a mine of China. Then, this study collected the leveling-monitoring vertical surface deformation data on three leveling points, and compared and analyzed the sensitivity and reliability of the MSBAS regularization methods for estimating vertical surface deformation. The results indicate that different regularization orders and parameters can lead to thousands of times differences in condition numbers and significant differences in ill-posed degree of the deformation models. The zero-order Tikhonov regularized deformation model with regularization parameter of 0.1 has the minimum condition number and the equation is not ill-posed. The first-order Tikhonov regularized deformation model with regularization parameter of 0.001 has the maximum condition number and the equation is seriously ill-posed. As a result, the estimates of 2D surface deformation models with different parameters and orders are also different in terms of numerical values and accuracy. Compared with the leveling-monitoring data, the first- and second-order MSBAS regularization methods with parameter 0.1 have the minimum fluctuation and the maximum correlation coefficients between the estimated values and the leveling-monitoring values, and are also closest to the leveling-monitoring results with the highest accuracy.