一种基于正则化策略的稳定衰减补偿逆时偏移

地下介质通常具有黏滞性，地震波在地下介质的传播过程中将不可避免地伴随着振幅衰减和速度频散，进而影响地震成像的准确性和分辨率.基于黏滞介质的衰减补偿逆时偏移能沿地震波的传播路径恢复其所经历的振幅衰减和相位畸变，有效提升成像效果.然而，由于地层对地震波的吸收衰减效应呈指数变化，衰减补偿过程中高低频分量的非同步增长易导致补偿算法数值不稳定.为此，本文提出了一种基于正则化策略的稳定衰减补偿逆时偏移方法.该方法基于解耦的常Q分数阶拉普拉斯算子黏滞声波方程描述地震波在地下介质中的传播效应，将振幅正则化因子引入该方程的时间-波数域的解析解中，以确保在补偿过程中地震波场能稳定延拓.二维、三维合成数据以及实际资料的偏移算例均证实了该方法的可行性和有效性，所提出的方法能有效地处理衰减补偿中的不稳定问题，明显提升地震资料的偏移成像质量.

Stable Q-compensated reverse-time migration based on regularization strategy

Viscosity is general in subsurface media, and the seismic waves are inevitably accompanied by amplitude attenuation and velocity dispersion during its propagation, which seriously reduces the accuracy and the resolution of seismic imaging. It is essential to consider attenuation-compensated strategy during seismic imaging, and the attenuation-compensated Reverse-Time Migration (RTM) based on the viscoacoustic wave equation can recover the amplitude attenuation and the phase distortion experienced by seismic waves along the propagation path. However, the attenuation of seismic waves varies exponentially, and the non-synchronous growth of the high and low frequency components during the compensation would face the challenge of numerical instability. For this reason, we propose in this paper a stable attenuation-compensated RTM based on a regularization scheme, which uses the decoupled constant Q fractional-order Laplacian viscoacoustic wave equation to describe the propagation effect of seismic waves in the subsurface media, and introduces an amplitude regularization term into the analytical solution in the time-wavenumber domain of this wave equation to ensure stable extrapolation of seismic wavefield during attenuation-compensated RTM. Migrated images of two- and three-dimensional synthetics and field data have demonstrated the feasibility and effectiveness of the proposed method. It can effectively solve the instability problem during attenuation-compensation and significantly improve the imaging quality of seismic data.