Error Propagation Analysis in Three-Dimensional Coseismic Displacement Inversion

Using the Bam earthquake as an example, we apply the multiple-aperture interferometry (MAI) algorithm to measure the azimuth (AZI) displacement with multiple mode synthetic aperture radar (SAR) images (ScanSAR and image modes) and further on produce the 3-D coseismic displacement maps using well-known models: multiple independent interferometric SAR (InSAR) with different viewing angles and combining MAI with conventional InSAR. The 3-D displacement maps show that, besides accuracy of SAR observation, inversion model is another major perturbing factor limiting the accuracy of 3-D component reconstruction. That is, in the former model, the smaller the difference of incidence angles is, the more easily influenced by ill-conditioned systems the estimated parameters are. Based on characteristics of error sources of SAR observations, we classify observation errors into random error, systematic error, and gross error. Moreover, their characteristics of error propagation are analyzed in the two models, respectively. Error propagation analysis indicates that random errors only affect variability of inversion result, while systematic error and gross error cause not only variability but also bias or uncertainty in estimated parameters. The presented error analysis method provides a more comprehensive understanding of bias or uncertainty of 3-D estimated components, which will be a useful tool for evaluating errors in displacement fields obtained from SAR observations. In this letter, we also group multiple InSAR and MAI observations to estimate 3-D components using weighted least squares whose weights are given by the Förstner posterior variance estimation, which may avoid an ill-conditioned system, reducing line-of-sight and AZI random noises and improving accuracies of estimated 3-D components.