Spectral-element formulation of multi-transmitting formula and its accuracy and stability in 1D and 2D seismic wave modeling

Application of local artificial boundary conditions in high-efficient spectral element method (SEM) is a problem that needs further study, where difficulties focus on how to design an appropriate numerical scheme of artificial boundaries that is in good accordance with the unequally-spaced grid nodes and high-order property of the element. Liao's local artificial boundary, i.e. multi-transmitting formula (MTF), provides a convenient way of implementing arbitrary-order displacement-type boundaries because it is defined directly in discrete form and can be transformed into numerical schemes by using merely some interpolation approaches. A new set of numerical schemes of MTF is developed and its accuracy and stability are thoroughly discussed in the application of spectral-element simulation of 1D and 2D seismic wave propagation. The new MTF scheme cannot be written into a binomial form like the traditional one does. This fact has a significant influence on numerical properties of high-order boundary, but merely slightly affects the performance of lower-order boundaries which are daily used in practical simulations. Numerical examples compared with viscous-spring or perfectly matched layer (PML) boundary exhibits that stable and quite good accuracy can be achieved by using the proposed method.

Automated summary

The application of local artificial boundary conditions in the high-efficient spectral element method remains a topic for further study. The development of a new set of numerical schemes has shown stable and quite accurate results in spectral-element simulation of seismic wave propagation.