Noniterative least-squares reverse time migration based on an efficient asymptotic Hessian/point-spread function estimation

Abstract

Although reverse time migration (RTM) is a powerful imaging method, it uses only the adjoint of the wave-propagation operator and produces only a blurred image. Through linearized inversion, least-squares RTM (LSRTM) reduces migration artifacts, balances the amplitudes, and improves the resolution of the imaging results. Compared to data-domain LSRTM, image-domain LSRTM (ID-LSRTM) is a more practical choice because it typically requires one round of RTM and subsequently solves the deblurring problem of the conventional RTM image involving the Hessian matrix. The Hessian matrix can be effectively replaced by a set of point-spread functions (PSFs). PSFs are traditionally obtained through one round of demigration-migration; hence, the traditional PSF estimation has a computational cost that is twice that of the RTM. We have deduced an analytic expression of the Hessian/PSF by using an asymptotic Green’s function and derived an efficient estimation strategy for the Hessian/PSF. The proposed method significantly reduces the computational cost and allows more flexible spatial sampling of PSFs without interference. Based on the explicitly calculated PSFs, ID-LSRTM can be achieved by solving an optimization problem with combined total-variation and curvelet-domain [Formula: see text] regularizations. The total computational cost of the proposed LSRTM is approximately the same as that of the conventional RTM. Numerical examples of synthetic and field data find that the proposed LSRTM significantly improves image quality while being highly efficient.