TTI介质隐式有限差分平面波偏移

Implicit finite-difference plane wave migration in TTI media

文章研究了TTI介质隐式有限差分(IFD)波场外推算子和TTI介质平面波偏移.与各向同性和VTI介质相比,TTI介质频散关系要复杂的多,很难得到频散关系的显性表达,也不能再只用对称的偶函数表示,需要加入一个奇函数.文中设计TTI介质IFD波场外推算子并用非线性优化方法求解算子系数.将各向同性介质下平面波偏移理论与TTI介质IFD外推算子相结合,实现了TTI介质下平面波偏移.将设计算子的频散关系曲线和偏移脉冲响应与理论解对比,验证了外推算子的精度;将平面波偏移算法用于全波TTI方程拟合并用极化分析得到的P波数据,验证了TTI介质平面波偏移的准确性和高效性.

Implicit finite-difference （IFD） extrapolation operator and plane wave migration in TTI media are studied in this paper. Compared to isotropic and VTI media, the dispersion relation of TTI media is much more complicated. I＇t is difficult to get the explicit expression of the dispersion relations. It needs no longer only a symmetrical even function like isotropic and VTI media but also an odd function to express the dispersion relations. We design TTI medium IFD wave-field extrapolation operator and solve operator coefficients by non-linear optimization method. We combine the theory of plane wave migration in isotropic media with the IFD operator in TTI media and extend plane wave migration to TTI media. Comparing the dispersion curves and migration impulse response of the IFD extrapolation operator with the theoretical solution verifies the high accuracy of the operator. Synthetic P-wave data from full elastic TTI equation modeling followed by polarization analysis verifies the accuracy and effectiveness of the method.