Constant Q viscoacoustic wave equation with fractional Laplacian operator

Na Fan, Kristopher A. Innanen

The Kjartansson's constant-Q (CQ) model provides an accurate physical description of seismic attenuation in Earth materials. Traditional fractional-Laplacian-based viscoacoustic equations decouple dissipation and dispersion effects but rely on nearly constant-Q (NCQ) approximations. In this study, we propose a new fractional Laplacian viscoacoustic wave equation that theoretically preserves the exact CQ dispersion relation while maintaining the decoupled representation of amplitude loss and phase dispersion. Numerical experiments in homogeneous media demonstrate that the proposed equation achieves superior agreement with analytical solutions compared with previous methods, particularly in strongly attenuating conditions. For heterogeneous media, two numerical strategies - a hybrid pseudospectral/finite-difference scheme and a low-rank approximation method - are employed to efficiently solve the equation under spatially variable Q conditions. Simulations in heterogenous models confirm that the proposed approach provides more accurate attenuation seismograms than existing NCQ equations. Overall, the results show that the proposed CQ viscoacoustic wave equation offers a more accurate and physically consistent framework for seismic wave propagation modeling and enhances its applicability to attenuation-compensated imaging and inversion.