提高任意广角波动方程计算效率及压制倏逝波干扰方法

Methods for improving computational efficiency of arbitrarily wide-angle wave equation and suppressing evanescent wave noises

任意广角波动方程(Arbitrarily Wide-angle Wave Equation,AWWE)是一种高精度的时空域单程波动方程,与其他时空域单程波方程相比,具有更大的成像倾角,因此是偏移成像的有力工具之一.本文改进了现有的AWWE有限差分计算方案,避免了原计算方案中对矩阵反复求逆的过程,同时减少了矩阵相乘的次数,显著地提高了AWWE数值计算的效率.数值实验证实,采用改进之后的计算方案,其计算结果与原方案完全一致.此外,本文采用了一种方法,在有倏逝波干扰的情况下,能在频率-波数(f-k)域区分出倏逝波与非倏逝波,为设计f-k滤波器提供合理的视速度门槛信息.偏移实验证实,在深度延拓时仅仅进行数次f-k滤波就能很好地抑制倏逝波干扰,提高偏移成像质量.

Arbitrarily wide-angle wave equation （AWWE） is a high-order spatial domain one-way wave equation （OWWE） with a high accuracy. Compared with the other OWWEs, AWWE can image steeper dips, which enables it to be one of powerful migration tools. In this paper, we slightly modify the existing finite-difference calculation scheme, avoiding repeated matrix inversion and reducing the times of matrix multiplication, thus dramatically improving the computational efficiency. Numerical examples indicate that the calculation results of the developed scheme are completely same as that of the existing one. Besides, a tentative method is presented here to distinguish evanescent waves from non-evanescent waves in frequency-wavenumber domain, thus offering us a reasonable cutoff threshold to design fan-filter to removeevanescent waves. Migration tests indicate that after only several times f-k filtering, the evanescent waves are suppressed obviously and the imaging quality is improved.