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On the Accuracy of the Finite-Difference Schemes: The 1D Elastic Problem

¹ Faculty of Mathematics, Physics and Informatics
Comenius University
Mlynska dolina F1
842 48 Bratislava
Slovak Republic

We present a 1D finite-difference (FD) scheme that is based on the application of Geller and Takeuchi’s (1998) optimally accurate FD operators to the heterogeneous strong-form equation of motion developed by Moczo et al. (2002). We numerically compare the scheme with two other FD schemes that approximate the heterogeneous strong-form equation of motion, one using conventional 2nd-order FD operators, the other using staggered-grid 4th-order FD operators. The numerical comparison is based on the envelope and phase misfits between tested and reference solutions. We discuss the error due to internal interface (primarily controlled by the boundary condition and its numerical approximation) and error due to grid dispersion. We demonstrate the superior accuracy of the scheme based on the application of the optimally accurate operators.