Insights and Emerging Directions from Force-Balance Based Joint Inversion of GNSS and InSAR

Mradula Vashishtha, William E. Holt, & Jeonghyeop Kim

Submitted September 7, 2025, SCEC Contribution #14828, 2025 SCEC Annual Meeting Poster #TBD

GNSS (Global Navigation Satellite System) and InSAR (Interferometric Synthetic Aperture Radar) complement each other to provide more information on the spatial gradients of crustal motions. We jointly invert both GNSS and InSAR data for Southern California. We employ a physics-based approach based on solutions of the force balance equations on a sphere using the weak formulation in finite elements. We obtain basis function responses to force rate couples ∅∅, ∅θ and θθ in the horizontal and for Ur/r for the vertical basis function response. For the spherical case the vertical response is weakly coupled to the horizontal. Solutions can also be expressed in terms of the input force rate couples, which are the vertical derivative of horizontal shear stress (VDoHS) rates. This inversion problem is solved using damped-weighted least squares and Ridge regularization. We use this joint inversion algorithm to provide an estimate of a time-averaged strain rate field (15-year average), rotation rates, and vertical gradients of horizontal shear stress (VDoHS) rates (∂σ ̇_xz)/∂z and (∂σ ̇_yz)/∂z . The VDoHS rates, together with the strain rates, can be used to provide new estimates of fault locking depths and slip rates. Gradients of VDoHS rates can enhance our understanding of deformation in 3-D. We also develop a method to determine the velocity field and full strain rate tensor at depth within the crust. The model results for locking depth will be tested through comparison with seismicity data (base of seismogenic zone). Model results of depth-dependent strain rate will be tested through comparison with seismic strain events inferred from over 700,000 earthquake focal mechanisms (Cheng et al., 2023).

Cheng, Y., Hauksson, E., & Ben‐Zion, Y. (2023). Refined Earthquake Focal Mechanism Catalog for Southern California Derived With Deep Learning Algorithms. Journal of Geophysical Research: Solid Earth, 128(2), e2022JB025975. https://doi.org/10.1029/2022JB025975

Key Words
GNSS, InSAR, Strain Rate, 3D deformation,Community Earth Models (CEM), Stress and Deformation Over Time (SDOT)

Citation
Vashishtha, M., Holt, W. E., & Kim, J. (2025, 09). Insights and Emerging Directions from Force-Balance Based Joint Inversion of GNSS and InSAR. Poster Presentation at 2025 SCEC Annual Meeting.

Related Projects & Working Groups
Tectonic Geodesy