波动方程有限差分法频散衰减方法研究

Dispersion Attenuation Method Using Wave Equation Finite Difference Method

波动方程式已被广泛用于正演和偏移中波场的数值模拟,但是,空间和时间上的微分近似值的精确才能确保有限差分法结果的精确。传统上,取得精确的数值需要通过使用相对更密集的有限差分网格或很长的有限差分算子;否则,数值误差(即数值频散)将会在很大程度上污染有效信号;然而,以上两种方法将导致大量增加的计算成本。这里提出一种简单和低计算成本的改进的波动方程式用来压制数值频散,当改进的波动方程式数值求解采用有限差分法时,数值频散相对于标准的波动方程式有明显的改善,且几乎没有增加额外的计算。二维数值试验表明,修改后的波动方程式极大地提高了图像质量,而且修改后的计算增量可忽略不计。

Wave equation has been widely used in the forward and migration for numerical simulation.However,the accurate differential approximation space and time would ensure that the results of the finite difference method was accurate.In tradition,to obtain accurate simulation values needed using more denser grid or longer finite difference operator,otherwise numerical error would seriously influence the effective signals.But both of the above methods would result in a substantial increase of cost of calculation.A modified,simple and low cost wave equation is proposed for suppressing numerical dispersion,when the finite differential method was used in the modified wave equation,the numerical dispersion of relative standard wave equation was significantly improved almost without increasing the additional computation.The two-dimensional numerical experiments show that the modified wave equation greatly improves image quality than that of the standard one,and its calculation increment can be ignored.