Image domain least-squares migration with a Hessian matrix estimated by non-stationary matching filters

Abstract

Abstract Assuming that an accurate background velocity is obtained, least-squares migration (LSM) can be used to estimate underground reflectivity. LSM can be implemented in either the data domain or image domain. The data domain LSM (DDLSM) is not very practical because of its huge computational cost and slow convergence rate. The image domain LSM (IDLSM) might be a flexible alternative if estimating the Hessian matrix using a cheap and accurate approach. It has practical potential to analyse convenient Hessian approximation methods because the Hessian matrix is too huge to compute and save. In this paper, the Hessian matrix is approximated with non-stationary matching filters. The filters are calculated to match the conventional migration image to the demigration/remigration image. The two images are linked by the Hessian matrix. An image deblurring problem is solved with the estimated filters for the IDLSM result. The combined sparse and total variation regularisations are used to produce accurate and reasonable inversion results. The numerical experiments based on part of Sigsbee model, Marmousi model and a 2D field data set illustrate that the non-stationary matching filters can give a good approximation for the Hessian matrix, and the results of the image deblurring problem with combined regularisations can provide high-resolution and true-amplitude reflectivity estimations.