  In this paper we derive and analyse efficient and stable numerical methods
for accurate numerical simulations of nonlinear dynamic shear ruptures on
non-planar faults embedded in 3D elastic solids using dual-paring (DP)
summation by parts (SBP) finite difference (FD) methods. Specifically, for
nonlinear dynamic earthquake ruptures, we demonstrate that the DP SBP FD
operators [K. Mattsson. J. Comput. Phys., 335:283-310, 2017] generate spurious
catastrophic high frequency wave modes that do not diminish with mesh
refinement. Meanwhile our new dispersion relation preserving (DRP) SBP FD
operators [C. Williams and K Duru, arXiv:2110.04957, 2021] have more accurate
numerical dispersion relation properties and do not support poisonous spurious
high frequency wave modes. Numerical simulations are performed in 3D with
geometrically complex fault surfaces verifying the efficacy of the method. Our
method accurately reproduces community developed dynamic rupture benchmark
problems, proposed by Southern California Earthquake Center, with less
computational effort than standard methods based on traditional SBP FD
operators.
