Curvelet‐based migration preconditioning

The extreme large size of typical seismic imaging problems has been one of the major stumbling blocks for a successful application of iterative techniques from numerical linear algebra to attain accurate migration amplitudes. These iterative methods are important because they complement theoretically-driven approaches that are hampered by mundane dierences to control problems such as finite-acquisition aperture, source-receiver frequency response, and directivity. To solve this problem, we apply the well-know technique of preconditioning that significantly increases the convergence of iterative solvers, making least-squares migration more tangible. First, we discuss dierent levels of preconditioning that range from corrections for the order of the migration operator to corrections for spherical spreading and position and reflector-dip dependent amplitude errors. While the first two corrections correspond to simple scalings in the Fourier and physical space, the third correction requires an intricate phase-space scaling, which we carry out with curvelets. Aside from providing the appropriate domain for the scaling, curvelets have the additional