SCEC Award Number 25322 View PDF
Proposal Category Individual Research Project (Single Investigator / Institution)
Proposal Title A Physics-Based Approach for Estimating a StatewideCalifornia 3-D Velocity and Strain Rate Field using GNSS and InSAR Data
Investigator(s)
Name Organization
William Holt Stony Brook University
SCEC Milestones A3-3, A3-5, A3-6 SCEC Groups CEM, Geodesy, SDOT
Report Due Date 03/15/2026 Date Report Submitted 05/06/2026
Project Abstract
 We develop a joint inversion algorithm for continuous surface 3-D velocities and associated horizontal strain rate fields. We employ a physics-based approach based on solutions of the force balance equations on a sphere using the weak formulation in finite elements. The goal of this inversion is to find the best-fit linear combination of these basis functions that predict both GNSS and InSAR measurements. We then apply a damped weighted least squares inversion using Ridge regularization and Akaike Bayesian Information Criterion. We present the interseismic kinematic solution for Southern California. The joint inversion yields a high resolution 3-D velocity field and strain rate field prediction throughout Southern California. We also obtain high resolution predictions of the patterns of the vertical derivative of horizontal shear stress (VDoHS) throughout southern California. The patterns and magnitudes of strain rates and VDoHS enable us to determine the locking depth and slip rates on San Jancito fault and the southern part of San Andreas. Moreover, the vertical velocity field shows strong correlations with groundwater changes in basins, having both natural and anthropogenic sources for the changes.
SCEC Community Models Used Community Fault Model (CFM)
Usage Description The CFM was used to inform about fault strike and fault location. This enables us to know how to project our strain rate and force rate solutions to interpret them in terms of fault locking depths and fault slip rate.
Intellectual Merit This project advances SCEC objectives by shifting from kinematic to physics-based 3D crustal deformation models. By applying horizontal force-balance equations to the joint inversion of GNSS and InSAR data, we resolve the vertical derivative of horizontal shear stress (VDoHS) rates. This creative approach allows for the imaging of fault locking and force-rate distributions at unprecedented resolution across vast regional scales. The research contributes to a deeper understanding of off-fault deformation and stress redistribution, providing a more nuanced physical framework for seismic hazard assessment than traditional slip-rate models.
Broader Impacts This award significantly enhanced research infrastructure by supporting the training of PhD student Mradula Vashishtha, who gained expertise in complex geodetic inversions and geodynamic modeling. The project promotes learning by developing high-resolution, accessible 3D strain and velocity visualizations that clarify complex tectonic interactions for the broader scientific community. Societal benefits include improved earthquake hazard characterization through a more accurate mapping of crustal force rates.
Project Participants William Holt, Mradula Vashishtha
Exemplary Figure Figure 13. Distribution of the spatial gradient of the force rate field (VDoHS rates) across Southern California. The arrows represent the eigenvectors, which map the directions of maximum (increasing) and minimum (decreasing) rates of change of the force rates. The solution demonstrates a characteristic "Mexican-hat" profile across major strike-slip segments, such as the San Jacinto and San Andreas faults. This pattern is physically proportional to the fault locking depth and slip rate, providing a novel method for imaging elastic locking and off-fault deformation without requiring a priori fault geometry. Credit: William Holt and Mradula Vashishtha, Stony Brook University.
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