Least-Squares Kirchhoff Depth Migration With Fast Point-Spread-Function Computation

Seismic migrations are generally formulated as the adjoint operators of linear forward modeling and often lead to images with degraded resolution, unbalanced illumination, and migration artifacts, especially in surveys with geologic complexity and irregular acquisition geometry. Least-squares migration (LSM) is able to mitigate these problems and produce better resolved images that are suitable for subsequent AVO/AVA inversion. However, no matter what domain LSM is implemented in, the computational cost is still several times or even one order of magnitude more than that of the traditional migration. In this article, we present an efficient image-domain least-square Kirchhoff depth migration (LSKDM), in which the Hessian matrix is approximated by a grid of point-spread-functions (PSFs). Traditional PSF computing algorithm requires a nonnegligible cost caused by a successive operation of modeling and migration and has to satisfy a sampling restriction to avoid interference between nearby PSFs. We present in this article that, by using the ray-based Green's functions and the linear traveltime approximation, the PSFs can be constructed explicitly at a significantly reduced computational cost and are able to adapt flexible spatial sampling that is fine enough to detect small-scale illumination variation. With the constructed PSFs, we formulate an image-domain LSKDM to iteratively solve for the optimal reflectivities. Numerical tests on synthetic and field data examples demonstrate that the proposed LSKDM is highly efficient and is capable of producing images with enhanced spatial resolution and amplitude fidelity when compared with the Kirchhoff depth migration (KDM) image.