Before revision:  On marginally resolved computational grids  , these spurious wave-modes have the potential to destroy the accuracy of numerical solutions for a first-order hyperbolic partial differential equation, such as the elastic wave equation.
After revision:  On marginally resolved computational grids . In this paper, we demonstrate that not all high order upwind SBP FD operators are applicable. Numerical dispersion relation analysis shows that odd-order upwind SBP FD operators also support spurious unresolved high-frequencies on marginally resolved meshes. Meanwhile, even-order upwind SBP FD operators (of order 2, 4 , these spurious wave-modes have the potential to destroy the accuracy of numerical solutions for a first-order hyperbolic partial differential equation, such as the elastic wave equation.