A main desired attribute from RTM and FD modeling algorithms is their accuracy. A nagging source of significant error in RTM and FD modeling is often dispersion from the discreetized time and space derivatives. One way of eliminating this error is by reducing grid size or time step size, which significantly increases the cost of these already expensive algorithms. I propose methods to eliminate this dispersion error with a more efficient approach. This approach speeds up the algorithms and reduces the temptation to cut corners in the speed-accuracy trade-off. These dispersion errors can be subtle, but because they often affect frequencies for all the data similarly, they constructively interfere and can cause big problems. For example, inversion algorithms such as FWI and iterative migration respond strongly to subtle but consistent parts of the data. I propose that a maximum acceptable error of phase dispersion is PI/20 after 50 wavelengths of propagation, which corresponds to 2 msec error over 4 seconds for all frequencies.


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