Addressing InSAR long wavelength errors enhances the reliability of GNSS and InSAR combined 3D deformation estimation: methodology and application to the 2011 Tohoku-Oki earthquake

Summary Interferometric Synthetic Aperture Radar (InSAR) deformation measurements are susceptible to long wavelength errors, yet existing geometric and strain models for estimating three-dimensional (3D) deformation from combined Global Navigation Satellite System (GNSS) and InSAR observations do not explicitly account for these errors. Neglecting long wavelength errors can substantially bias 3D deformation estimates for large earthquakes. We therefore develop a combined adjustment model that introduces additional systematic parameters to represent InSAR long wavelength errors, defines these parameters using GNSS minimum constraints, and optimizes the stochastic model of the heterogeneous observations through least-squares variance component estimation (LS-VCE). We evaluate the model using synthetic tests and observations of the 2011 Tohoku-Oki earthquake. In the synthetic tests, the proposed model constrained the datum deviation to below 1 mm, whereas the corresponding mean datum deviations obtained using the geometric and strain models were 5.40 and 3.80 m, respectively. Relative to the design values, compared with the geometric and strain models, the proposed model reduces the mean absolute error (MAE) for the East (E) and North (N) components by 98.63% and 98.84%, 93.65% and 96.45%, respectively. This indicates that the proposed model can effectively eliminate the interference of long wavelength errors on the 3D deformation parameter estimation. We further applied the proposed model to the 2011 Tohoku-Oki earthquake and compared the resulting deformation with the Jet Propulsion Laboratory (JPL) co-seismic displacement solution. Compared with the geometric and strain models, the proposed model reduces the MAE for the E, N and U components by 89.32% and 89.27%, 83.33% and 85.25%, 37.50% and 82.14%, respectively. Under the adopted fault geometric parameters, the proposed model also recovered candidate strike-slip components that were not resolved by the conventional models. Compared with the geometric and strain models, the proposed model reduces the MAE between forward modeled and JPL co seismic displacements for the E and N components by 98.36% and 98.01%, 95.45% and 94.59%, respectively. Overall, explicitly estimating InSAR long wavelength errors within a combined adjustment framework improves the numerical and physical reliability of GNSS-InSAR 3D deformation estimation.