带正则化校正的TTI介质qP波方程及其逆时偏移方法和应用

各向异性研究对地下介质精确成像有着重要的意义,在当前计算机硬件迅速发展及宽方位地震数据采集日益普遍的情况下,成像必须考虑介质的各向异性.逆时偏移是基于双程波动方程的较为精确的数值解的成像方法,所以相对于其他地震成像方法,它具有很大的优势,譬如不受反射界面的倾角限制、偏移速度结构合适时能够使回转波及多次波正确成像.在各向同性介质中,可使用标量波方程来模拟波场.而在各向异性介质中,P波和SV波是相互耦合的,即不存在单纯的标量波传播,通常利用能代表耦合波场中P波分量运动学特征的拟声波(qP波)进行偏移成像.本文中,我们推导出了TTI介质下qP波控制方程.该方程可采用显式有限差分格式进行求解.通过声学近似,若沿对称轴方向的剪切波速度为零,对于对称轴方向不变且ε≥δ的模型来说,可得到稳定的数值解.但对于TTI介质来说,由于沿对称轴方向各向异性参数是变化的,声学近似会引起波场传播及数值计算的不稳定.因此,我们提出了正则化有限横波的方法,很好地解决了这一问题.最后,给出了Foothill模型的测试结果及某探区实际资料试算结果,展示了采用这个方程进行复杂TTI模型正演和高质量逆时偏移成像结果,证实了该方法的正确性和实际资料应用中的有效性.

A regularized qP-wave equation for TTI media and its application to reverse time migration

The research of anisotropy is significant for subsurface precise imaging. With rapid development of computation capability and gradual generalization of seismic acquisition with wide azimuth, anisotropy should be taken into consideration. The reverse time migration is based on the accurate solution of two-way wave equation, therefore compared with other methods, it has many advantages, such as no dip limitation and the ability to image turning waves and multiples. Scalar wave equation could be used to calculate the wave field in isotropic media. In anisotropic media, however, P and SV waves are coupled and there is no pure scalar wave mode. Consequently, pseudo acoustic wave(qP-waves) which can represent the kinematic property of P-component in the coupled wave field are usually used for imaging in anisotropic media. In this paper, starting with the P-SV coupled dispersion relation for VTI media, we derive qP wave equation for TTI media, which can be solved using an explicit finite difference format. With the help of acoustic approximation, stable numerical solutions can be obtained for a model with vertical symmetric axis, ε≥δ and, if the velocity of shear waves becomes zero along the symmetric axis. However, acoustic approximation will cause the instability of wave field propagation and numerical computation as anisotropic parameters vary in the direction of symmetric axis in TTI media. To solve this problem, we proposed to regularize the finite shear wave equation by adding a regularized term to the original equation. The idea of our method is similar to designing a filter which could attenuate the high wave number components appropriately. We give out the specific form of regularized TTI qP wave equation. Then, the TTI reverse time migration(RTM) method using the regularized wave equation was discussed. In numerical implementation, the computing complexity of our regularized wave equation only increases by one wave field differential and the storage needed only increases by two more wave field. Numerical tests show that by choosing appropriate σ, we can obtain stable wave field even with sharp variation of azimuth and dip of tilted axis.For numerical examples, we give out the modelling and RTM results on the Foothill TTI model and the imaging result of field data from a carbonate rock area. When prorogating time of the wavefield is much longer, the traditional finite shear wave equation shows wavefield instability. In contrast, our method can obtain wavefield without any instabilities. In areas with abrupt changes of model parameters, our method may still produce weak SV wave which are viewed as artificial noise in reverse time migration. But for real seismic data, we didn't find any of these SV wave energy in the final migration profile which may be caused by the quite weaker SV energy compared with P wave energy. The RTM imaging with high quality for field seismic data demonstrates that our method works well and can be applied to field data effectively.