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Space domain derivative calculation

Several derivative algorithms have been implemented in time domain, which includes: 1. Optimized high-order finite-difference methods (up to 32nd order) 2. Compact FD (finite difference) 3. Special pseudo spectrum method (to overcome wrap around artifacts) The above figure displays the dispersion curves in frequency domain for these algorithms. As shown above, Pseudo spectrum has the best dispersion performance (the curve only drops at Nyquist frequency), Compact FD (finite difference) could reach 95 percents, and 32nd FD get 85 percent’s accuracy. A well-defined derivative algorithm enables RTM to apply larger wave propagation grid, which greatly reduces the computation cost. As the pseudo spectrum method, I want to emphasize that our implementation is special, which completely avoid wrap around artifacts.

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