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Nearly analytic discrete method (NADM) is a higher accurate method for elastic wave equation that can suppress effectively numerical dispersion caused by discretizing the wave equation. In this paper we investigate the efficient implementation of NADM and present a refinement of the original NADM. Our theoretical analyses show that the modified NADM can improve significantly over the original one in numerous perspectives including numerical errors, storage spaces, and computational costs. Three-component synthetic VSP seismograms in 3-layered transversely isotropic (TI) media generated by the modified NADM are also reported. Theoretical analyses and numerical results show that the modified NADM can reduce storage space about 53 percent and computational costs about 30 percent compared with the original NADM. Moreover the accuracy of the modified NADM in time increases from 2-order of the original NADM to 4-order. Numerical results suggest that the modified NADM is more suitable to large-scale modeling because the modified method has little numerical dispersions even when too-coarse grids are used.
Nearly analytic discrete method (NADM) is a higher accurate method for elastic wave equation that can suppress exactly mass dispersion caused by discretizing the wave equation. In this paper we investigate the efficient implementation of NADM and present a refinement of the original NADM. Our theoretical analyses show that the modified NADM can improve significantly over the original one in numerous perspectives including numerical errors, storage spaces, and computational costs. Three-component synthetic VSP seismograms in 3-layered transversely isotropic (TI) media generated by the modified NADM are also reported. Theoretical analyzes and numerical results show that the modified NADM can reduce storage space about 53 percent and computational costs about 30 percent compared with the original NADM. Moreover the accuracy of the modified NADM in time increases from 2-order of the original NADM to 4-order. Numerical results suggest that the modified NADM is more suitable to larg e-scale modeling because the modified method has little numerical dispersions even when too-coarse grids are used.