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

Rikuto Fukushima, & Eric M. Dunham

Submitted September 7, 2025, SCEC Contribution #14408, 2025 SCEC Annual Meeting Poster #TBD

Dynamic source inversion with fault mechanics advances our fundamental understanding of the earthquake source process and helps overcome the difficulties of non-uniqueness or regularization in kinematic inversion. Stiernström et al. (2024) have developed an adjoint-based inversion method to estimate frictional parameters and initial stress from observed waveforms with rate and state friction. We have extended the adjoint framework to slip-weakening friction and linear elastic fracture mechanics (LEFM) for singular cracks.

To better understand adjoint-based source inversion, we analyzed the sensitivity to source parameters with two complementary approaches: the adjoint method and by directly calculating variations of the forward solution. We do this first by deriving closed-form analytical solutions for the spring-slider problem with linear slip-weakening friction. This recovers known results, such as insensitivity to the absolute level of stress, and provides new insights. In particular, sensitivity to source parameters is greatest during the initial instability when strength weakens with slip.

Next we examine propagating ruptures. We start with a variational analysis of the LEFM crack tip equation of motion for a semi-infinite singular crack, which shows that sensitivity to stress drop and fracture energy decrease as rupture velocity approaches the limiting speed. We reproduce these results with the adjoint method, and then turn to slip-weakening friction and nonsingular ruptures. We implemented the adjoint slip-weakening law in 2D dynamic rupture simulations and successfully recovered dynamic source parameters in a synthetic inversion test.

Key Words
fracture mechanics, dynamic source inversion, adjoint method

Citation
Fukushima, R., & Dunham, E. M. (2025, 09). Rupture sensitivity to dynamic source parameters revealed by variational fracture mechanics and adjoint rupture dynamics. Poster Presentation at 2025 SCEC Annual Meeting.

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