Joint Inversion of GNSS and InSAR Data for Continuous 3-D Velocity and Strain Rate Fields in Southern California

Mradula Vashishtha, Jeonghyeop Kim, & William E. Holt

Published September 10, 2023, SCEC Contribution #13235, 2023 SCEC Annual Meeting Poster #064 (PDF)

GNSS and InSAR complement each other to provide more information on the spatial gradients of crustal motions. GNSS stations hold precision for the three components of crustal velocities but are spatially limited, while InSAR data provide a more continuous spatial coverage but with inherent ambiguities in the three components owing to surface motions measured along a single line of sight for each pixel.

We present a new joint inversion algorithm for GNSS and InSAR data to obtain a 3-D surface velocity field for Southern California as a product for SCEC CGM. Contrary to prior treatments we generate basis function responses to horizontal body-force equivalent inputs in a spherical treatment. These responses satisfy force-balance equations. Vertical basis function responses are weakly coupled to the horizontal strain rates through the Vr/R term, where Vr is the vertical velocity and R is the radius of the Earth; these vertical responses are applicable to represent motions linked to both elastic and poroelastic processes. This suggests that these basis functions can also serve as fitting functions, and thus we can apply this algorithm to study various surface processes such as groundwater signals. We use UCERF3 velocities as boundary conditions around 1° by 1° areas. The boundary condition solution is added to the optimal set of basis function responses as a linear superposition. Together, these represent an estimate of steady-state deformation. Solutions for 1° by 1° areas are combined to represent a region-wide solution for Southern California.

We investigate both isotropic and anisotropic responses to the body-force equivalent inputs. We use Ridge (L2-norm) regularization and Akaike Bayesian Information Criterion to estimate an optimal damping level as well as a relative weighting of InSAR with respect to GNSS data. We show through tests with synthetic data that the joint inversion provides improved estimates for the surface velocity gradient tensor field, with anisotropic treatment yielding the highest quality match to horizontal velocity gradients. We jointly invert ascending and descending tracks of InSAR data from Xu et al. (2021) with GNSS in ITRF frame to obtain a solution for steady-state horizontal strain rates, rotation rates, vertical velocities, and horizontal gradients in vertical velocities in Southern California. We align adjoining regions together using simple interpolation techniques.

Key Words
Joint inversion, GNSS, InSAR, CGM, Crustal Strain Rates

Citation
Vashishtha, M., Kim, J., & Holt, W. E. (2023, 09). Joint Inversion of GNSS and InSAR Data for Continuous 3-D Velocity and Strain Rate Fields in Southern California. Poster Presentation at 2023 SCEC Annual Meeting.

Related Projects & Working Groups
Tectonic Geodesy