Total-Variation regularised image-domain least-squares migration

SUMMARY

Image-domain least-squares migration (i-LSM) is a powerful imaging tool that estimates a fullbandwidth reflectivity (or perturbation) model from a seismic image by means of a spatially nonstationary deconvolution process with so-called point-spread functions. However, neither a reflectivity nor a perturbation model are a direct representation of any subsurface reservoir property.

In this work, we propose to recast i-LSM to retrieve full-bandwidthmedium properties (e.g., velocity); this is achieved by applying a Total-Variation (TV) regularisation term to the sum of the background velocity model (used to propagate wavefieldsin the Born modeling operator) and the velocity perturbation (used by the Born modeling operator to construct single-scattering seismic data).

By leveraging the property of pre-composition of proximal operators, the proposed TV-regularised inverse problem can be successfully solved using the Primal-Dual algorithm with minimal additional cost to standard leastsquares regularised inversion (or sparsity-promoting inversion when inverting for reflectivity). Numerical results on both synthetic and field datasets are presented to verify the effectiveness of the proposed approach