Viscoacoustic VTI Least Square Reverse Time Migration

The attenuation term of viscoacoustic wave quasi-differential equation is extended to VTI wave quasi-differential equations to propose a kind of viscoacoustic VTI wave quasi-differential equations, which care for both viscosity and anisotropy of media. Finite difference method is used to solve the equations, in which attenuation terms are solved in wavenumber domain, while other terms are solved in space domain. Stable regularization operators and a stable reverse time propagation operator are introduced to the equations to eliminate the high frequency instability in the process of backward propagation. On this basis, we derive the viscoacoustic VTI migration operator, demigration operator and gradient formula, to realize the viscoacoustic VTI LSRTM. The test for the modified Marmousi model proved the accuracy and superiority of the viscoacoustic VTI LSRTM.