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.

中文翻译：

---

不规则网格中频域声波方程的色散优化算子

为频域声波建模中的色散优化开发了一种数值技术。优化是使用建模算子的零空间进行的，这减少了高波数建模过程中的色散误差。建模算子的近似和色散误差的优化可以应用于任意定位的节点。为了获得最优的波动算子，使用了灵活的近似，其自由度在算子的零空间的基础上是全函数的。基于这种方法的色散优化算子可以更好地减少数值色散误差。与现有的有限差分和有限元方案相比，数值例子被评估以证明所开发方法的有效性。