Image-Domain Least-Squares Migration Through Preconditioned Hessian

Abstract

Image-domain least-squares migration (IDLSM), which typically employs a diagonally dominant Hessian with narrow bandwidth for the inverse problem, provides an efficient deconvolution strategy for subsurface reflectivity imaging. Conventional methods often rely on the adjoint of the Born/Kirchhoff modelling operator to compute the Hessian matrix. However, the adjoint-derived Hessian is highly ill-conditioned, leading to slow convergence during linear inversion and resulting in images with undesired resolution and amplitude fidelity. To overcome these limitations, this study introduces a novel IDLSM approach that integrates the state-of-the-art migration operator. We derive and compute the preconditioned Hessian matrix through a Kirchhoff migration engine with source-side and receiver-side illumination. The preconditioned Hessian matrix exhibits identical values along its main diagonal. This illumination compensation will explicitly reduce the condition number of the Hessian matrix and significantly improve the quality of migrated images in terms of amplitude fidelity. In addition, we remove redundant source wavelets from the migrated image and the Hessian matrix. As a result, these improvements will greatly accelerate the convergence of linear inversion solvers while enhancing the resolution and amplitude fidelity of the resulting images. Experiments on synthetic and field datasets demonstrate that the proposed IDLSM method retrieves high-fidelity reflectivity images with superior resolution and amplitude fidelity compared to conventional IDLSM techniques.