Numerical simulations of a seismic wavefield are important to analyze seismic wave propagation. Elastic-wave equations are used in data simulation for modeling migration and imaging. In elastic wavefield numerical modeling, the rotated staggered-grid method （RSM） is a modification of the standard staggered-grid method （SSM）. The variable-order method is based on the method of variable-length spatial operators and wavefield propagation, and it calculates the real dispersion error by adapting different finite-difference orders to different velocities. In this study, the variable-order rotated staggered-grid method （VRSM） is developed after applying the variable-order method to RSM to solve the numerical dispersion problem of RSM in low-velocity regions and reduce the computation cost. Moreover, based on theoretical dispersion and the real dispersion error of wave propagation calculated with the wave separation method, the application of the original method is extended from acoustic to shear waves, and the calculation is modified from theoretical to time-varying values. A layered model and an overthrust model are used to demonstrate the applicability of VRSM. We also evaluate the order distribution, wave propagation, and computation time. The results suggest that the VRSM order distribution is reasonable and VRSM produces high-precision results with a minimal computation cost.
