Least-Squares Attenuation Compensated Elastic Reverse Time Migration Based on a New Decoupled Viscoelastic Wave Equation

The fractional-order viscoelastic wave equations derived from constant-Q model, possessing decouple amplitude loss and phase dispersion terms, are commonly used for attenuation-compensated elastic reverse time migration (QERTM). However, the substantial computational cost associated with solving fractional-order viscoelastic wave equations using pseudo-spectral method limits its application in industrial production. Moreover, the migrated imaging results obtained by QERTM suffers from low-resolution and migration artefacts. Attenuation-compensated elastic least-squares reverse time migration methods (QELSRTM) can provide high-resolution and clear imaging results, but they merely represent relative perturbations of model parameters rather than iterative update PP and PS images of QERTM. Therefore, we have derived a new viscoelastic wave equation with decoupled amplitude loss and phase dispersion terms, which can be numerically solved using finite-difference method with less computational resources, thereby suitable for QERTM. Furthermore, to enhance the imaging quality of QERTM, we apply the least-squares inversion to the PP and PS images for iteratively updating the images. We refer the imaging method as least-squares attenuation-compensated elastic reverse time migration (LS-QERTM), which is a natural extension of QERTM. Numerical experiments demonstrate the correctness and effectiveness of our newly derived wave equation and newly constructed imaging method.