粘弹性介质单程波法非零偏移距地震数值模拟与偏移

地震资料分辨率降低，得不到深层介质的精确信息实际上是由于大地吸收效应的影响.同时与双程波动方程相比单程波动方程避免了多次波的干扰并且计算效率高、占用内存少.本文首先基于开尔芬粘弹性介质模型将品质因子与单程波分步傅立叶法波场延拓算子相结合，实现了粘弹性介质波场延拓，从而将单程波弹性介质波场延拓推广到了粘弹性介质.然后在定位原理，数学检波器原理以及等时叠加原理的基础之上实现了粘弹性介质非零偏移距叠前正演模拟.最后将数值模拟得到的正演记录进行弹性偏移和粘弹性偏移并进行对比分析.通过数值算例可以看出，粘弹性介质叠前正演深层的反射波能量减弱，同相轴变粗，频带变窄，主频减小，分辨率降低；粘弹性偏移不但实现了振幅的恢复，而且同时偏移剖面的垂向空间分辨率也得到了提高.

Numerical simulation and migration of non-zero offset seismic wave in viscoelastic medium by one-way wave equation

Due to absorption of the earth, the seismic data has lower resolution and could not get the precise information. At the same time, one- way wave equation methods have many advantages in seismic forward modeling than full way equation, for example, high calculation efficiency, less memory. In this paper, we combine the quality factor Q with the SSF operator using one-way wave equation to realize wave-field extrapolation arithmetic used for viscoelastic medium. Then, we realize viscoelastic medium nonzero-offset seismic pre-stack forward modeling by one-way equation based on positioning principle, mathematical geophone principle and equal-time stacking principle. Finally, we use elastic and viscoelastic arithmetic to image for viscoelastic forward modeling and comparison. Numerical examples show that viscoelastic medium pre-stack forward decreases the deep reflection wave energy significantly, with the thick axis and narrow band and the lower resolution.Migration with viscoelastic arithmetic has achieved amplitude recovery, and the seismic data resolution also has been enhanced.