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High-order accurate summation-by-parts (SBP) finite difference (FD) methodsconstitute efficient numerical methods for simulating large-scale hyperbolicwave propagation problems. Traditional SBP FD operators that approximatefirst-order spatial derivatives with central-difference stencils often havespurious unresolved numerical wave-modes in their computed solutions. Recentlyderived high order accurate upwind SBP operators based upwind FD stencils havethe potential to suppress these poisonous spurious wave-modes on marginallyresolved computational grids. In this paper, we demonstrate that not all highorder upwind SBP FD operators are applicable. Numerical dispersion relationanalysis shows that odd-order upwind SBP FD operators also support spuriousunresolved high-frequencies on marginally resolved meshes. Meanwhile,even-order upwind SBP FD operators (of order 2, 4, 6) do not support spuriousunresolved high frequency wave modes and also have better numerical dispersionproperties. We discretise the three space dimensional (3D) elastic waveequation on boundary-conforming curvilinear meshes. Using the energy method weprove that the semi-discrete approximation is stable and energy-conserving. Wederive a priori error estimate and prove the convergence of the numericalerror. Numerical experiments for the 3D elastic wave equation in complexgeometries corroborate the theoretical analysis. Numerical simulations of the3D elastic wave equation in heterogeneous media with complex non-planar freesurface topography are given, including numerical simulations of communitydeveloped seismological benchmark problems. Computational results show thateven-order upwind SBP FD operators are more efficient, robust and less prone tonumerical dispersion errors on marginally resolved meshes when compared to theodd-order upwind and traditional SBP FD operators.

Upwind summation by parts finite difference methods for large scale elastic wave simulations in 3D complex geometries