Adjoint-based inversion for stress and frictional parameters in 3D dynamic earthquake rupture models

Wenqiang Zhang, & Eric M. Dunham

Submitted August 30, 2026, SCEC Contribution #15429, 2026 SCEC Annual Meeting Poster #TBD

Earthquake rupture processes (nucleation, propagation, and arrest) and the stress and frictional conditions that control them are fundamental to seismic and tsunami hazard assessment. Kinematic source inversions recover the space-time evolution of fault slip but do not directly constrain the governing stress and frictional properties. Dynamic rupture inversion targets these parameters, but conventional grid searches and Bayesian sampling require thousands to millions of forward simulations even when the model is reduced to a coarse grid of control points. Adjoint methods overcome this bottleneck by yielding the misfit gradient with respect to all spatially distributed parameters using only one forward and one adjoint simulation, independent of the number of parameters. Adjoint theory for dynamic rupture with rate-and-state friction has recently been established and demonstrated for 2D antiplane ruptures (Stiernstrom et al., 2024). Here we extend this framework to 3D ruptures on geometrically complex faults with either rate-and-state or slip-weakening friction. In 3D, fault slip and shear traction are vectors in the fault surface, so the adjoint friction law acquires a rake-rotation contribution, absent in the scalar antiplane case derived by Fukushima & Dunham (2025), that measures sensitivity to perturbations reorienting the slip vector at fixed magnitude. To this end, we build on DRDG3D (Zhang et al., 2023), a 3D high-order nodal discontinuous Galerkin solver for dynamic rupture on unstructured tetrahedral meshes, including a compressible ocean with gravity. We construct the discrete adjoint as the exact transpose of the nodal scheme, producing gradients that agree with finite-difference tests to machine precision. We further derive adjoint sources for seismic waveforms, geodetic displacements, and ocean-bottom pressure, enabling joint inversion of these data types. Synthetic inversions recover stress and frictional parameters at multiple spatial wavelengths within slipping regions, while resolution remains poor elsewhere, demonstrating the multiscale resolving power and limitations of dynamic rupture inversion. This framework paves the way for computationally tractable, high-dimensional dynamic-rupture inversion with real earthquake data on geometrically complex faults.

Citation
Zhang, W., & Dunham, E. M. (2026, 08). Adjoint-based inversion for stress and frictional parameters in 3D dynamic earthquake rupture models. Poster Presentation at 2026 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)