A simple and high-efficient viscoacoustic reverse time migration calculated by finite difference

Abstract

The viscoacoustic wave equation with decoupled amplitude attenuation and phase dispersion terms is convenient for implementing reverse time migration (RTM) in attenuating media. However, the traditional viscoacoustic waves are expressed by the fractional Laplacian, which requires computationally expensive fast Fourier transforms to perform numerical solutions. This is not conducive for commercial applications with seismic data in terabyte, particularly in 3D. Based on the memory-variable-represented viscoacoustic wave equation, we develop new dispersion-dominated and dissipation-dominated wavefield extrapolation operators that can be solved using the economic finite difference method (FDM). In numerical simulation, the staggered grid FDM is used to solve the temporal and spatial derivatives. The computational efficiency analysis shows that, compared to the traditional viscoacoustic wave equation, the new viscoacoustic wave equation has an efficiency improvement of approximately more than two times. The accuracy of simulations of amplitude attenuation and phase dispersion is evaluated in viscoacoustic media with varying Q values. We also extend the proposed viscoacoustic wave equations to Q-compensated RTM. Two synthetic tests and one field data test show that the Q-compensated RTM can produce high-resolution images by correcting phase dispersion and compensating amplitude loss.