Model order reduction with oblique projections for large scale wave propagation

There are many applications in which it is necessary to solve large scale parametrized wave propagation problems repeatedly. This is still quite a challenging task, even with the largest available computer clusters. In this paper we will discuss the application of Model Order Reduction (MOR) to problems in seismic petroleum exploration, with the aim of diminishing the necessary computing time by a significant factor. We consider POD and some variants. POD is a Model Order Reduction technique that uses snapshots of a few simulations in order to quickly compute related problems with similar accuracy. The method of lines via a Petrov–Galerkin approximation that uses the snapshots as basis functions is the considered approach. The order reduction comes from projecting the wave equation discretized in space to the subspace spanned by the snapshots. This has been shown earlier to work well in two dimensions. The challenge in three dimensions comes from the size of the spatial meshes required and the fact that the method usually requires a number of snapshots that do not fit in fast memory, even for current high end multicore machines. Parallelization is not an option since it is already used for other aspects of this massive problem.