基于纵横波解耦的三维弹性波逆时偏移

3D elastic reverse time migration based on P-and S-wave decoupling

纵横波波场分离是弹性波偏移方法的必要条件,通过纵横波成像的差异可以获取更多地下介质的信息.目前所用的纵横波波场分离方法多采用Helmholtz分解,这样得到的波场不仅物理意义发生了变化,振幅和相位也会发生改变.本文采用纵横波解耦的弹性波方程,将其应用于三维介质,对比分析了纵横波解耦方法相对传统Helmholtz分解方法在相位、振幅上的优势.将该解耦的波场分离方法应用于弹性波逆时偏移,能得到相位、振幅和物理意义不受改变的偏移结果.但是该解耦方法分离得到的纵横波波场均为矢量场,将该波场分离方法用于弹性波逆时偏移,还需要解决矢量场如何得到标量成像结果的问题.本文引入了Poynting矢量,通过Poynting矢量对矢量波场进行标量化,这样就能得到保振幅、相位,且无极性反转的标量PP和PS成像结果.同时针对S波Poynting矢量求取不准确的问题,采用拟S波应力场和S波速度场得到了更加准确的S波Poynting矢量.理论计算证明了本文采用的3D波场解耦的矢量波场分离方法的正确性和引入Poynting矢量对矢量波场进行标量成像的有效性.

Elastic reverse time migration contains information of not only reflected P-wave but also converted S-waves. Converted S-waves have more information of underground, higher resolution, and wider offset. While to get clean PP and PS images, we need to separate P- and S-waves. The traditional P- and S-wave separation method is based on Helmholtz decomposition. It supposes P-waves are no rotation wavefield and S-waves are no divergence wavefield. So, P-waves are calculated by a gradient operator and S-waves calculated by a curl operator. The phase and amplitude information of decomposed waves are changed, because of a space difference operator. We adopt the P- and S- wave decoupled method to separate P- and S-waves. We extend this decoupled method to 3D media and compare with the Helmholtz decomposition method. We find this decoupled method can maintain the phase and amplitude information of separated P- and S-waves. By this decoupled method, the separated P- and S-waves both are vectors. We need to get scalar images from these vector wavefields if we want to use the decoupled method in elastic reverse time migration. We introduce Poynting vector of P- and S-waves to scalarize vector P- and S-waves. Then we use a traditional acoustic reverse time migration imaging condition to get scalar PP and PS images. These images can maintain phase and amplitude information, because we use P- and S-wave decoupled method to separate them. And the imaging results have no polarity inversal problem. But we find the Poynting vector of S-waves are inaccurate because the S-wave stress are interfered by P-waves. So, we use the S-wave quasi-stress tensor to calculate the S-wave Poynting vector. The S-wave quasi-stress are not interfered by P-waves. Finally, the S-wave Poynting vector calculated by S-wave quasi-stress will be more accurate. Numerical examples illustrate the validity of 3D P- and S-wave decoupled separation method and the accuracy of elastic reverse time migration by the Poynting vector.