A migration algorithm based on the least-squares formulation will find the correct reflector amplitudes if proper migration weights are applied. The migration weights can be viewed as a pre-conditioner for a gradient-based optimization problem. The pre-conditioner should approximate the pseudo-inverse of the Hessian of the least-squares functional. Usually, an infinite receiver coverage is assumed to derive this approximation, but this may lead to poor amplitude estimates for deep reflectors.
To avoid the assumption of infinite coverage, new amplitude-preserving migration weights are proposed based on a Born approximation of the Hessian. The expressions are tested in the context of frequency-domain finite-difference two-way migration and show improved amplitudes for the deeper reflectors.
