TTI介质有限差分逆时偏移的稳定性探讨

在沉积学中,可假设在相同时期的沉积层具有相近的物理性质和演化过程.因此,沿层传播的地震波和垂直于地层传播的地震波具有各向异性的特点.在纵波资料的处理中,考虑各向异性对逆时偏移的影响,通常假设介质的横波速度为零,这样可以得到纵波在TTI介质中的传播方程,但是该方程在实际计算中仍存在数值稳定性问题.本文加入横波分量可有效解决数值稳定性问题,并选取适当的横波速度减小对纵波成像的影响,实现地震波在TTI介质中的逆时偏移.实际测算表明,P-SV波的方程中包含横波分量,若假设SV的速度为零,则会导致方程的差分格式不稳定;若加入SV波,选择合适的SV波速度可以使SV波的全区各向异性和反射系数达到极小,并可有效的抑制SV波对纵波勘探的影响.本文的方法是一种稳定的TTI介质中的逆时偏移方法.

Stability of reverse time migration in TTI media

The strata in same deposition period have the same physics feature and evolutionary process in sedimentology.So,the anisotropic feature exists between the wave propagating along the strata and the wave propagating vertically along strata.In P wave reverse time migration(PRTM),considering the effect of anisotropic propagation,an hypothesis that share wave velocity should be zero has been generally involved.In this case,the wave equation in TTI media could be obtained,but it suffer from numerical stability problem in practice.In this paper,to get the stable algorithms,the hypothesis of zero shear wave velocity has been discarded.the right SV velocity has been chosen to reduce the affect of SV wave in PRTM.the actual test indicate that If set the velocity of SV wave equal to zero,the differential scheme will be unstable;if not,choosing the right velocity of SV wave can minim the anisotropic feature and reflector coefficients of SV wave.In this way,the effective of SV wave to P wave exploration will be restricted.This is a stable method for P wave Reverse Time Migration in TTI media.