Evaluating finite-difference operators applied to wave simulation , by John T. Etgen

The continuous wave equation can be Fourier transformed over all spatial variables and over time, and then solved for W as a function of spatial wavenumber. From the dispersion relation, phase velocity or group velocity can be obtained. This procedure can also be applied to discrete, finite-difference approximations to the acoustic or elastic wave equation. Finite-difference solutions to the wave equation have different dispersion relations than the continuous wave equation. The differences between the numerical and exact phase velocities lead to errors commonly observed in finite-difference generated wave fields. Understanding and counteracting these errors will lead to more accurate and efficient techniques for solving wave equations on discrete grids.


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