Viscous Wave Equation Based Attenuation Compensation In Reverse Time Migration

Seismic wave experiences absorption and attenuation effects when traveling through the underground media.Directly migrating the attenuated data would cause poor illumination of the subsurface,thus it is necessary to compensate the attenuated amplitude and correct the distorted phase during seismic data processing.Considering the fact that absorption occurs along wave's travel path,a more convincing approach is to fulfill the compensation during wavefield extrapolation in pre-stack reverse time migration(RTM),namely the Q-compensated RTM(Q-RTM).Conventional Q-RTM methods tend to boost the attenuated energy for compensation.These methods usually suffer from severe numerical instability because of the unlimited amplification of the high-frequency noise.Low-pass filtering is generally used to stabilize the process,nevertheless,at the expense of precision.We develop a stable compensation method in this paper.Based on the decoupled fractional Laplacians wave equation,two compensation operators are obtained by extrapolating wavefields in both dispersion-only and viscous media.Since no explicit amplification is included,these two operators are absolutely stable for implementation.In order to improve the division morbidity for calculating the compensation operators,this paper employs the excitation amplitude criterion and embeds the operators into a new Q-compensated excitation amplitude imaging condition,which results in accurate compensated migration images.We first introduce this method into multicomponent viscoelastic RTM for 2D case,then we apply this method to viscoacoustic RTM for 3D implementation since most seismic explorations use P-wave only.Numerical examples show that the method can recover the attenuated energy and enhance the resolution under the promise of high stability,fidelity,adaptability,and anti-noise performance.