
There are many applications in which is necessary to solve the acoustic or elastic wave equation in general media repeatedly, such as seismic imaging for seismology and energy resources exploration, optimal design and in general parametric studies such as those necessary to overcome uncertainty. In 3D general media, even with the largest supercomputers, it is still impossible to get timely solutions for the problems listed above. We propose to use a general technique: Model Order Reduction, in order to lessen the size and cost of simulations of large dynamical systems to solve this problem. One such approach is obtained when using he Proper Orthogonal Decomposition or KarhunenLoeve transform, which relies on taking as a basis snapshots of one or just a few full fidelity simulations for use in a Galerkin collocatiom method. We show (in 2D) how this approach can produce reasonably accurate solutions to problems that are perturbations of the ones used for calculating the snapshots, leading to a methodology that can be applied today to solve the above large scale time demanding problems.

