稳定Q补偿梯度的黏滞声波全波形反演

Viscoacoustic FWI with a stable Q-compensated gradient

针对衰减介质的全波形反演(FWI)通常采用黏滞声波方程,并通过伴随状态法计算目标函数对介质速度参数的梯度。在梯度计算过程中,由于震源波场和伴随波场都历经衰减,因此梯度随着深度减弱,导致模型参数的修正量变小,降低了反演的收敛速度。为了提升反演效率,研究了基于解耦分数阶拉普拉斯算子(DFL)波动方程的黏滞声波FWI,提出了一种新的基于稳定因子的梯度补偿策略。在补偿梯度过程中设置稳定因子实现稳定补偿,可以在保持正确运动学特征的同时,平衡所恢复梯度的幅度。数值算例表明,与传统的黏滞声波FWI相比,经此梯度补偿的黏滞声波FWI具有更快的收敛速度和更高的反演精度。

The full-waveform inversion(FWI)based on attenuation medium usually adopts the viscoacoustic wave equation,and calculates the gradient of an objective function with respect to the velocity of the media by the adjoint state method.Since both the source wavefield and adjoint wavefield are attenuated,the gradient weakens with depth resulting in reducing the modification of subsurface parameters,which slows down the convergence of the inversion.To speed up the inversion efficiency,this paper develops a viscoacoustic FWI based on the decoupled fractional Laplacian(DFL)wave equation,and provides a new gradient compensation strategy based on a stabilization factor.The new compensation strategy achieves stable compensation by setting one stabilized factor in compensation,balances the amplitudes in the recovered gradient,meanwhile maintains correct kinematics.Compared with the conventional viscoacoustic FWI,the viscoacoustic FWI with this gradient compensation strategy has faster convergence speed and higher inversion accuracy.