Viscoacoustic modeling and imaging using low-rank approximation

A constant-Q wave equation involving fractional Laplacians was recently introduced for viscoacoustic modeling and imaging. This fractional wave equation suffers from a mixed-domain problem, because it involves the fractional-Laplacian operators with a spatially varying power. We propose to apply low-rank approximation to the mixed-domain symbol, which allows for an arbitrarily variable fractional power of the Laplacians. Using the new low-rank scheme, we formulate the framework of the Q-compensated reverse-time migration (RTM) and least-squares RTM (LSRTM) for attenuation compensation. Numerical examples using synthetic data demonstrate the advantage of using low-rank wave extrapolation with a constant-Q fractional-Laplacian wave equation for seismic modeling, Q-compensated RTM, as well as LSRTM.