Pulse distortions in the FD simulation of elastic wave propagation

The dispersive character of FD schemes when the Courant number is less than one is well known. To study it quantitatively, an analytical description of the global distortion by means of the properties of the pulse momenta is performed. Since, however, local distortions are more meaningful, an analytical calculation of the propagated pulse through its initial components and properly defined transfer coefficients is also performed, in order to predict the detailed features of the simulated pulse. Asymptotic formulas (for very large times) are also obtained in terms of Airy functions. An extensive numerical analysis then confirms the validity of the analytical results and shows in detail the structure of the simulated pulse distortions and their dependence on the relevant parameters. Although the present analysis is limited to the 1-D linear case, it can be useful also for predicting distortions in more complex situations of applicative interest.