Multidimensional Q-compensated reverse time migration using a high-efficient decoupled viscoacoustic wave equation

Seismic waves propagating through attenuating media induce amplitude loss and phase dispersion. Neglecting the attenuation effects during seismic processing results in the imaging profiles with weakened energy, mispositioned interfaces and reduced resolution. To obtain high-quality imaging results, Q-compensated reverse time migration is developed. The kernel of the Q-compensated reverse time migration algorithm is a viscoacoustic wave equation with decoupled amplitude loss and phase dispersion terms. However, the majority of current decoupled viscoacoustic wave equations are solved using the computationally expensive pseudo-spectral method. To enhance computational efficiency, we initiate our approach from the dispersion relation of a single standard linear solid model. Subsequently, we derive a novel decoupled viscoacoustic wave equation by separating the amplitude loss and phase dispersion terms, previously coupled in the memory variable. The newly derived decoupled viscoacoustic wave equation can be efficiently solved using the finite-difference method. Then, we reverse the sign of the amplitude loss term of the newly derived viscoacoustic wave equation to implement high-efficient Q-compensated reverse time migration based on the finite-difference method. In addition, we design a regularization term to suppress the high-frequency noise for stabilizing the wavefield extrapolation. Forward modelling tests validate the decoupled amplitude loss and phase dispersion characteristics of the newly derived viscoacoustic wave equation. Numerical examples in both two-dimensional and three-dimensional confirm the effectiveness of the Q-compensated reverse time migration based on the finite-difference algorithm in mitigating the attenuation effects in subsurface media and providing high-quality imaging results.