Viscoacoustic modeling and imaging using low-rank approximation

Abstract

A constant-[Formula: see text] wave equation involving fractional Laplacians was recently introduced for viscoacoustic modeling and imaging. This fractional wave equation has a convenient mixed-domain space-wavenumber formulation, which involves the fractional-Laplacian operators with a spatially varying power. We have applied the low-rank approximation to the mixed-domain symbol, which enables a space-variable attenuation specified by the variable fractional power of the Laplacians. Using the proposed approximation scheme, we formulated the framework of the [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM) for attenuation compensation. Numerical examples using synthetic data demonstrated the improved accuracy of using low-rank wave extrapolation with a constant-[Formula: see text] fractional-Laplacian wave equation for seismic modeling and migration in attenuating media. Low-rank [Formula: see text]-RTM applied to viscoacoustic data is capable of producing images comparable in quality with those produced by conventional RTM from acoustic data.