LAUSR

ABSTRACTReverse time migration (RTM) for attenuating media should take amplitude compensation and phase correction into consideration. However, attenuation compensation during seismic propagation suffers from numerical instability because of the boosted high-frequency ambient noise. We have developed a novel adaptive stabilization method for Q-compensated RTM (Q-RTM), which exhibits superior properties of time variance and Q dependence over conventional low-pass filtering-based method. We derive the stabilization operator by first analytically deriving k-space Green’s functions for a constant-Q wave equation with decoupled fractional Laplacians and its compensated equation. The time propagator of Green’s function for the viscoacoustic wave equation decreases exponentially, whereas that of the compensated equation is exponentially divergent at a high wavenumber, and it is not stable after the wave is extrapolated for a long time. Therefore, the Green’s functions theoretically explain how the numerical inst...