Rupture sensitivity to dynamic source parameters revealed by variational fracture mechanics and adjoint rupture dynamics

Rikuto Fukushima, & Eric M. Dunham

Submitted August 30, 2026, SCEC Contribution #15444, 2026 SCEC Annual Meeting Poster #TBD

Dynamic source inversion incorporating fault mechanics advances our understanding of earthquake source processes and provides a complementary approach to kinematic slip inversion. Stiernström et al. (2024) introduced adjoint-based dynamic rupture inversion for rate-state friction, in which frictional parameters and initial stress are estimated from observed waveforms. The method appears promising due to the computational efficiency of the adjoint method in evaluating the gradient with respect to a large number of parameters. Here, we extend the adjoint framework to slip-weakening friction. We first perform proof-of-concept inversions for 2D ruptures. The initial stress is well recovered from the observed waveform, except in the unruptured region, which does not affect the observation. Next, we perform a sensitivity analysis separately for (i) the nucleation phase and (ii) dynamic rupture. For nucleation, we use quasi-dynamic elasticity. An analytical solution based on an adjoint spring-slider system reveals extreme sensitivity during the nucleation phase, a consequence of a strong instability; this behavior is further confirmed for nucleation for the 2D continuum problem through an eigenmode expansion analysis. For dynamic rupture, we begin with a variational analysis of the linear elastic fracture mechanics (LEFM) crack-tip equation of motion for a semi-infinite singular crack, which demonstrates that sensitivity to the dynamic parameters depends on rupture propagation speed (with sensitivity decreasing as rupture velocity increases). The adjoint-based sensitivity analysis with slip-weakening rupture reveals that the rupture time is primarily sensitive to fracture energy and stress drop, only weakly sensitive to slip-weakening rate, and insensitive to the absolute stress. Together, these analyses provide a fundamental understanding of the sensitivity underlying dynamic rupture inversion, and inform strategies for future application to real earthquakes.

Key Words
fracture mechanics, dynamic source inversion, adjoint method

Citation
Fukushima, R., & Dunham, E. M. (2026, 08). Rupture sensitivity to dynamic source parameters revealed by variational fracture mechanics and adjoint rupture dynamics. Poster Presentation at 2026 SCEC Annual Meeting.

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