地震偏移的最优可分近似算法实现

Implement of optimal separable approximation in seismic migration

针对地震偏移算法中单程波算子的特征函数近似,采用最优可分表示法将该特征函数展开为空间变量(g)和水平波数(k)的可分表达式,以此可分近似表达式为基础,运用正反Fourier变换重新构造单程波算子.为了克服特征函数最优可分近似计算在奇点及其领域产生的数值振荡,引入等价黏性技巧以增强算法的数值计算稳定性,并采用分频最优可分及对空间变量(g)线性插值的方法,不仅提高了计算精度,也节约计算机时.文中具体研究了单程波算子的脉冲响应和二维叠前深度偏移.结果表明,在不甚大步长情况下,本文构造的算子具有适应横向强变速的能力,运用Marmousi模型验证了本文方法适合复杂构造的成像.

An optimal separable approximation（0SA） is applied to the characteristic function of one-way wave operator in the seismic migration algorithm. The characteristic function is expressed as products of functions in space variable（g） and functions in wave number variable（k）. Based on the optimal separable approximation, the mixed domain algorithm with Fourier and inverse Fourier transformation is used to approximate the one-way wave operator. To overcome numerical instability from approximating characteristics function near the singular point, an equivalent sticking skill is adopted to improve algorithmic stability. Moreover, separate frequency computation and linear interpolation for space variables are used to improve precision and save time. The impulse response of one-way wave operator on simples and the complex lateral variable velocity model shows that the optimal separable approximation can apply to lateral the Marmousi model test show the new method can also velocity variation in the case of small steps. Results on be used to image complex structure.