Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner
This work addresses the need for accurate and efficient seismic wave simulations with complex topography, offering a hybrid method that balances flexibility and computational efficiency.
The authors combine finite element and finite difference methods for isotropic elastic wave simulations with land topography, achieving an energy-conserving discretization through weakly imposed interface conditions. Numerical examples demonstrate the efficacy of the proposed interface treatment.
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.