A robust method for 3-D surface displacement fields combining GNSS and single-orbit InSAR measurements with directional constraint from elasticity model

Three‐dimensional (3-D) surface displacement fields are important since they provide the constraint for the optimized earthquake source mechanism and can also be used to reveal the inter-seismic deformation details and assess the seismic risk. In order to obtain a reliable 3-D tectonic displacement field, the general approach integrating geodetic observations and the geophysical property is very desirable. We present a robust method for retrieving the special 3-D crustal deformation field combining high-precision global navigation satellite system (GNSS) and the single-orbit interferometric synthetic aperture radar (InSAR) displacement along the radar line of sight (LOS) with directional constraint from an elasticity model. The strategy is based on the fact that the surface displacement vectors at the adjacent points caused by fault rupture are spatially correlated; in particular, the deformation directions are quite consistent in spatial distribution, which can well correspond to the fault motion modes (thrust, dextral or sinistral strike-slip). In other words, once the main motion feature and the geometry parameters of rupture fault are given preliminarily, the deformation direction trend caused by surface rupture will be confirmed. The preliminary fault slip parameters are inverted only using a simplified elasticity model constrained by a small number of high-precision GNSS observations. The model parameters can then resolve the spatially consistent deformation direction vectors. Constrained by the stable direction information, the InSAR-LOS displacements, which GNSS has calibrated, can be effectively transformed into 3-D deformation components. We reconstruct five representative fault models ranging from the rough to the fine for the 2008 Wenchuan Mw 7.9 earthquake (China) to test the method. Results show that the 3-D deformation trend characteristic from the different models is consistent with field investigation and GNSS observations, although there is a significant discrepancy in the fault model geometry parameters. The correlation coefficients between five model results and GNSS observations are 0.72, 0.64, 0.71, 0.73, 0.78 for horizontal component, and 0.78, 0.64, 0.65, 0.72, 0.85 for vertical component, respectively. The proposed method shows a great advantage when the fault geometry and slip distribution are uncertain or the observation data are insufficient.