Dispersion optimized operator for frequency-domain acoustic wave equation in an irregular grid

A numerical technique is developed for dispersion optimization in frequency-domain acoustic wave modeling. The optimization is performed using the null space of the modeling operator, which reduces the dispersion error during modeling with a high wavenumber. Approximation of the modeling operator and optimization of the dispersion error can be applied to arbitrarily positioned nodes. To obtain an optimal wave operator, flexible approximation is used, and its degrees of freedom are fully functional with the basis for the nullspace of the operator. A dispersion-optimized operator based on this approach yields an improved reduction in the numerical dispersion error. Numerical examples are evaluated to demonstrate the effectiveness of the developed method. compared with those of the existing finite-difference and finite-element schemes. We have found that the developed approach can produce more accurate results for frequency-domain wave modeling with regular and irregular grids.