Model-order reduced full-wavefield migration using proper orthogonal decomposition

Abstract

As seismic migration is increasingly applied to more and more complex media, more sophisticated imaging techniques are required to generate accurate images of the subsurface. Currently, the best results for imaging are achieved by least-squares migration methods, such as least-squares reverse time migration and full-wavefield migration (FWM). These methods iteratively update the image to minimize the misfit between the forward modelled wavefield and the recorded data at the surface. However, a key challenge for these techniques is the speed of convergence. To accelerate the speed of convergence, pre-conditioning is commonly applied. The most common pre-conditioner is the reciprocal of the Hessian operator. However, this operator is computationally expensive to calculate, making it difficult to apply directly. In this paper, we present a novel, alternative, pre-conditioner for FWM. This pre-conditioner is based on applying Galerkin projections to a linear system, which projects the system onto a set of known basis vectors. To find an appropriate set of basis vectors for this approach we apply proper orthogonal decomposition (POD) to a set of partial solutions of the linear system. The resulting method gives an approximation to the pseudo-inverse based on these basis vectors. To test this technique, which we name model-order reduced FWM (MOR-FWM), we apply it to the synthetic Marmousi model as well as to field data from the Vøring basin in Norway. For these examples, we show that MOR-FWM yields an improved data-misfit compared to the standard FWM approach. In addition, we show that the result for the field data case can be improved by normalizing the partial solutions before applying POD.