非均匀VTI介质切比雪夫傅里叶深度偏移方法

Chebyshev Fourier depth migration operator for heterogeneous VTI media

傅里叶法是一类重要的单程波偏移方法.同传统的有限差分类方法相比,傅里叶方法不受数值频散和双向分裂误差的影响,但常因精度要求而计算量较大.在各种多项式展开中,切比雪夫展开与单平方根算子的最大偏差是最小的.我们对单平方根算子的切比雪夫展开,得到一种适用于非均匀VTI介质的深度偏移算子,明显降低了计算量且保持了精度.为了进一步提高算子的整体性能,利用模拟退火法对算子中的常系数进行了优化,使三阶算子的最大精确相位角达到60°.Hess模型的偏移结果证实了算法的有效性.

The Fourier method is an important one-way wave migration method. Compared with conventional finite- difference approaches, it is free from numerical dispersion and two-way splitting error but is computationally intensive as a result of improving its accuracy. The Chebyshev polynomials have the smallest maximum deviation from the single square root operator than other polynomials. We expand the single square root operator by the Chebyshev polynomials and obtain a depth migration operator for heterogeneous VTI media, reducing obviously the order of the expansion whereas maintaining the imaging precision. To improve the overall performance of the operator, we harness the simulated annealing method to optimize constant coefficients of the operator and raise the maximum accurate phase angle to 60 degree. The Hess model is used to manifest the effectiveness of the operator.