Efficient reverse time migration based on fractional Laplacian viscoacoustic wave equation

Abstract

Due to the energy attenuation and phase distortion of seismic waves propagating in viscous media, it is difficult to obtain high resolution and amplitude preserved migration images without compensating the viscous effects. In this paper, we provide a reverse time migration (RTM) scheme based on a viscoacoustic wave equation with fractional Laplacian operators to compensate the viscous effects. First, we develop a high-efficiency method for simulating wave propagation based on the viscoacoustic wave equation. Since the method is independent of the number of different Q values, the numerical simulation examples show that the proposed simulation method is more efficient than the conventional blocked method. When the number of different Q values of a geological model is more than 2, we can obtain a speed-up ratio of about 4.5 with almost the same accuracy as the conventional blocked method. Secondly, we completely split the viscoacoustic wave equation into the amplitude attenuation and phase dispersion equations to achieve a more reasonable Q-compensated RTM algorithm. Finally, we test the Q-compensated reverse time migration approach using a simple graben model and a more realistic modified Marmousi model. We compare our Q-compensated RTM results to those obtained by the conventional RTM method. The compensated migration results are highly close to those obtained by the conventional RTM of seismic data without attenuation. The proposed method is also tested using field seismic data, the result shows that the energy of the deeper part is enhanced, and the events become more continuous.