Recent Developments In Preconditioning the FWI Hessian - A Dimensionality Reduction Approach

Recent advances based on the mathematical understanding of the Hessian as, under certain conditions, a pseudo-differential operator have resulted in a new preconditioner by L. Demanet et al. Basing their approach on a suitable basis expansion for the Hessian, by suitably 'probing' the Hessian, i.e. applying the Hessian to a small number of randomized model perturbations, one can obtain an approximation to the inverse Hessian in an efficient manner. Building upon this approach, we consider this preconditioner in the context of least-squares migration and Full Waveform Inversion and specifically dimensionality reduction techniques in these domains. By utilizing previous work in simultaneous sources, we are able to develop an efficient Full Waveform Inversion scheme which recovers higher quality images than simply using simultaneous sources alone. As we will see, the preconditioning technique described above will help to regularize much of the noisy crosstalk introduced by the simultaneous sources technique without having to perform significantly more work in order to do so.