基于上下行波分解的分数阶拉普拉斯算子黏滞声波逆时偏移成像方法

Viscoacoustic reverse⁃time migration imaging based on fractional Laplacian with up⁃going and down⁃going wave decomposition

地下介质通常存在黏滞性,使地震波在传播过程中产生能量衰减及(相位)频散效应,降低了偏移成像照明能量。采用互相关成像条件的双程波动方程逆时偏移技术,当速度模型精度不高或存在较强速度梯度时,可能会产生低频噪声和假象。为此,提出一种基于上下行波分解的解耦分数阶拉普拉斯算子黏滞声波逆时偏移成像(Q补偿逆时偏移)方法,采用解耦的分数阶拉普拉斯算子黏滞声波方程分别对震源波场和检波点波场进行外推,在此过程中校正地下介质对地震波产生的衰减效应;引入自适应稳定因子应对地震波衰减补偿过程中数值不稳定问题;采用时间解析波场外推方法,在时间切片上分别对震源、检波点波场的传播方向进行分解;最终运用互相关成像条件对下行的震源波场和上行的检波点波场进行成像。数值测试结果表明,所采用的Q补偿逆时偏移方法可校正由地下介质黏性特性引起的地震波振幅衰减和(相位)频散效应,该成像方法能显著减少传统逆时偏移成像中的低频噪声与假象。

The subsurface media typically exhibit viscosity,which causes energy attenuation and(phase)dispersion effects during seismic wave propagation and in turn reduces the illumination energy of migration imaging.The twoway wave equation reverse‑time migration with cross‑correlation imaging conditions may produce low‑frequency noise and false images when there is no highly accurate velocity models or strong velocity gradients.To this end,this paper proposes a viscoacoustic reverse‑time migration method based on decoupled fractional Laplacian with up and down‑going wave decomposition(Q‑compensated reverse‑time migration method).The viscoacoustic wave equation based on decoupled fractional Laplacian is employed to separately extrapolate the source wavefield and receiver wavefield and correct the attenuation effects generated by subsurface media during the process.An adaptive stability factor is introduced to handle numerical instability arising from the attenuation compensation of seismic waves.The time‑domain analytical wavefield extrapolation method is adopted to separately decompose the propagation directions of the source and receiver wavefields on each time slice.Finally,the cross‑correlation imaging condition is utilized for imaging of the down‑going source wavefield and up‑going receiver wavefield.Numerical tests show that the Q‑compensated reverse‑time migration method can correct the amplitude attenuation and(phase)dispersion effects caused by the viscosity characteristics of subsurface media.This imaging method significantly reduces the low‑frequency noise and false images in traditional reverse‑time migration imaging.