Suppression of dispersion in elastic wavefield simulation by FCT of separated P- and S-waves

The finite difference method is widely used in the numerical simulation and propagation of seismic wavefield. The traditional finite difference method uses Taylor series expansion to calculate the spatial partial derivative, but this method will produce numerical dispersion due to grid discretization, which reduces the accuracy of seismic wavefield simulation. The numerical simulation method of optimizing the difference coefficient can suppress some dispersion to a certain extent. However, under the stability condition of the maximum P- wave velocity, due to the large difference of P- and S-wave velocities, the elastic wavefield numerical simulation will lead to obvious numerical dispersion in the shallow low velocity S-wave. To reduce the numerical dispersion coefficient method to and improve the simulation accuracy, this paper first uses the optimized difference grid to reduce part numerical dispersion, and then uses the FCT (Flux-Corrected Transport) further suppress the finite difference numerical dispersion of elastic wavefield. The conventional FCT method directly suppress the elastic wavefield dispersion. But due to the obvious difference in the P- and S-wave velocity, the dispersion of the S-wave is stronger than that of the P-wave. To suppress the S-wave numerical dispersion, it needs to select a larger dispersion suppression parameter, while this will produce artifacts for P-waves. Therefore, this paper proposes a suppression of dispersion method in elastic wavefield simulation by FCT of separated P- and S- waves. By selecting appropriate dispersion suppression parameters for the separated P- and Swave to perform flux correction, the numerical dispersion can be effectively suppressed and the P wave artifacts can be weakened. Through theoretical analysis and numerical examples, it is found that the method in this paper can effectively reduce the numerical dispersion of elastic wave equation finite-difference, and there are no P-wave artifacts compared with the conventional FCT method.