Least-squares attenuation-compensated viscoelastic reverse time migration using a new decoupled viscoelastic wave equation

Abstract

Attenuation-compensated viscoelastic reverse time migration (QERTM) effectively corrects for amplitude loss and reflector mispositioning caused by intrinsic seismic attenuation. However, conventional QERTM implementations based on decoupled fractional Laplacian viscoelastic wave equations require multiple Fourier transforms, resulting in high computational costs. Moreover, QERTM images often suffer from low-wavenumber noise, amplitude imbalance, and acquisition footprints. Although viscoelastic least-squares reverse time migration (QELSRTM) can suppress these artifacts and generate high-quality images with attenuation compensation, it uses elastic parameter perturbations as the imaging targets, which differ from the PP and PS images obtained by QERTM. This difference highlights a discrepancy between QERTM and QELSRTM. To address these limitations, based on the generalized standard linear solid model, we first derive a novel decoupled viscoelastic wave equation with amplitude loss and phase dispersion terms. This equation is efficiently solved using the finite-difference method, making it suitable for QERTM applications. Furthermore, we incorporate a least-squares inversion framework into QERTM to iteratively update the attenuation-compensated PP and PS images. We refer to this method as least-squares QERTM (LS-QERTM), which serves as a natural extension of QERTM. The proposed LS-QERTM method produces high-quality PP and PS images with accurate attenuation compensation. Numerical experiments verify the validity of the derived decoupled viscoelastic wave equation and demonstrate the effectiveness of the proposed LS-QERTM method.