Attenuation compensation in anisotropic least-squares reverse time migration

Abstract

Anisotropic and attenuating properties of subsurface media cause amplitude loss and waveform distortion in seismic wave propagation, resulting in negative influence on seismic imaging. To correct the anisotropy effect and compensate amplitude attenuation, a compensated-amplitude vertical transverse isotropic (VTI) least-squares reverse time migration (LSRTM) method is adopted. In this method, the attenuation term of an attenuated acoustic wave equation is extended to a VTI quasi-differential wave equation, which takes care of effects from anisotropy and attenuation. The finite-difference method is used to solve the equation, in which attenuation terms are solved in the wavenumber domain, and other terms are solved in the space or wavenumber domain. Stable regularization operators are derived and introduced to the equations to eliminate severe numerical noise in high-frequency components during backward propagation. Meanwhile, a demigration operator, migration operator, and gradient formula for attenuated VTI media are derived to implement the amplitude-compensated VTI LSRTM. Test of a homogeneous model proves the accuracy of the attenuated VTI quasi-differential equations and the effectiveness of the regularization operators. A numerical example for a modified Marmousi model verifies the accuracy and superiority to the amplitude-compensated VTI LSRTM. Our results show that the sensitivity to anisotropic parameters is much higher than that to the [Formula: see text] parameters.