Vidar Stiernström: Adjoint-based inversion for stress and frictional parameters in earthquake modeling

Abstract:

Earthquake cycle and dynamic rupture simulations with rate-and-state frictional faults have emerged as promising tools to better understand the processes governing earthquake nucleation and seismicity. In extension, such tools are crucial in order to mitigate earthquake hazards. Modeling the Earth’s subsurface as elastic blocks with faults appearing as frictional interfaces, the governing equations are linear elastodynamics with non-linear interface conditions. The latter are governed by rate-and-state friction - empirically determined equations involving non-linear relations between stresses on the fault and frictional parameters. However, fault stresses and frictional parameters are, in practice, difficult or impossible to constrain. There therefore is a need to connect cycle and dynamic rupture simulations to data measurements. The inversion is a PDE-constrained optimization problem where we seek parameter values that minimize the misfit between model output and data.

We propose a computationally efficient gradient-based optimization method where the gradient of the misfit is computed with only two simulations: one of the forward problem and one of the adjoint problem. To demonstrate the adjoint-based optimization framework we consider a 2D dynamic rupture problem in antiplane shear, discretized using summation-by-parts finite differences and explicit Runge-Kutta time integration. The resulting scheme is dual consistent, ensuring that the discrete adjoint-based gradient is the exact gradient of the discrete misfit functional as well as a consistent approximation of the continuous gradient. The method is applied to inversions for stresses and frictional parameters using synthetic data.