Frequency Domain Q-Compensated Reverse Time Migration Using Anti-Dispersion Acoustic Equation

Reverse time migration (abbreviated as RTM), as a powerful imaging technique, is widely used in many areas such as seismic exploration and ultrasonic nondestructive testing technology. Traditional RTM algorithms do not take the viscosity of media into account so that the final results are degraded because of attenuation of amplitude and dispersion of velocity. To compensate energy loss and correct phase distortion, we propose a Q-compensated RTM algorithm in frequency domain. Wavefields are extrapolated forward and backward by finite difference frequency domain method and cross-correlation is employed as imaging condition. Real-valued velocity is replaced by complex-valued velocity (specifically Kolsky–Futterman model) to incorporate viscosity into acoustic equation. Stabilization is one of the key aspects of Q-compensated RTM, since compensation for the effect of viscosity boosts numerical errors and high-frequency noise as well. To stabilize the process, anti-dispersion acoustic equation is introduced. In this article, we first introduce our algorithm in detail and then carry out two numerical experiments on synthetic data. In each of the two experiments, synthetic acoustic record and viscoacoustic record are displayed to show the effect of viscosity. Secondly, comparison between four results (acoustic RTM on acoustic data, acoustic RTM on viscoacoustic data, unstable Q-compensated RTM on viscoacoustic data and stable Q-compensated RTM on viscoacoustic data) is made to demonstrate the effectiveness of our approach. It is shown that the proposed approach successfully compensates the amplitude attenuation and velocity dispersion while prevent numerical errors and high-frequency noise from growing exponentially.