A Joint Inversion Algorithm of GNSS and InSAR for Continuous 3-D Surface Velocities and Associated Horizontal Strain Rate Field

Simultaneous analyses of complementary GNSS and InSAR measurements may lead to breakthroughs in our understanding of crustal deformation. We present an algorithm that combines InSAR with GNSS measurements, in which the GNSS data can be used either as original station velocities or as an interpolated and smoothed velocity field, to estimate continuous 3-dimensional surface motions, horizontal strain rates and tilt in a self-consistent way. This damped, weighted least-squares inversion relies on physics-based basis functions and provides a generalized tool for investigating the kinematics and dynamics of surface deformation. Through synthetic tests, we evaluate the performance of the algorithm. The results show that the algorithm reliably recovers a “true” synthetic field representing a complex horizontal interseismic signal mixed with a variable vertical signal in southern California. We also apply this algorithm to real GNSS and InSAR data from the same region to model an interseismic field and assess the final model by comparison with a GNSS-only solution. The joint-inversion model predicts narrower shear zones along faults and higher variations in off-fault dilatational signals than the GNSS-only model. In addition, the joint-inversion model predicts vertical signals pertaining to hydrologic processes and step-overs in small basin areas. We use k-fold cross-validation to determine the optimal smoothness of the joint-inversion model. Although widely used in geophysical inverse problems, it has been less frequently used in surface strain rate inversions. Our results show that the method reliably finds appropriate regularization strength for all tests in this study, indicating its potential for broader application in crustal deformation modeling.