Least‐squares reverse‐time migration in a matrix‐based formulation

This paper describes least-squares reverse-time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient-based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high-wavenumber artefacts. It is also shown that least-squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse-time migration. The methodology is currently feasible in 2-D and can naturally be extended to 3-D when computational resources become more powerful.