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

Jeonghyeop Kim, Mradula Vashishtha, William E. Holt, Kyle D. Murray, & Rowena B. Lohman

Published March 9, 2026, SCEC Contribution #15040

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 physicsbased
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.

Key Words
Joint Inversion, GNSS and InSAR Integration, Horizontal Force-Balance, 3-D Surface Velocities, Crustal Deformation Modeling

Citation
Kim, J., Vashishtha, M., Holt, W. E., Murray, K. D., & Lohman, R. B. (2026). A Joint Inversion Algorithm of GNSS and InSAR for Continuous 3‐D Surface Velocities and Associated Horizontal Strain Rate Field. Geochemistry, Geophysics, Geosystems, 27(3). https://doi.org/10.1029/2025GC012682.