Repeated simulations of large scale wave propagation problems are prevalent in many fields. In oil exploration earth imaging problems, the use of full wave simulations is becoming routine and it is only hampered by the extreme computational resources required. In this contribution, we explore the feasibility of employing reduced-order modeling techniques in an attempt to significantly decrease the cost of these calculations. We consider the acoustic wave equation in two-dimensions for simplicity, but the extension to three-dimensions and to elastic or even anysotropic problems is clear. We use the proper orthogonal decomposition approach to model order reduction and describe two algorithms: the traditional one using the SVD of the matrix of snapshots and a more economical and flexible one using a progressive QR decomposition. We include also two a posteriori error estimation procedures and extensive testing and validation is presented that indicates the promise of the approach.
 D. J. Lucia, P. S. Beran and W. A. Silva, “Reduced-Order Modeling: New Approaches for Computational Physics,” Progress in Aerospace Sciences, Vol. 40, No. 1-2, 2001, pp. 51-117. doi:10.1016/j.paerosci.2003.12.001
 F. Troltzsch, S. Volkwein, L. X. Wang and R. V. N. Melnik, “Model Reduction Applied to Square Rectangular Martensitic Transformations Using Proper Orthogonal Decomposition,” Applied Numerical Mathematics, Vol. 57, No. 5-7, 2007, pp. 510-520. doi:10.1016/j.apnum.2006.07.004
 D. Chapelle, A. Gariah and J. Sainte-Marie, “Galerkin Approximation with Proper Orthogonal Decomposition: New Error Estimates and Illustrative Examples,” ESAIM: Mathematical Modeling and Numerical Analysis, Vol. 46, Cambridge University Press, 2012, pp. 731-757.
 F. Troltzsch and S. Volkwein, “POD A-Posteriori Error Estimates for Linear-Quadratic Optimal Control Problems,” Computational Optimization and Applications, Vol. 44, No. 1, 2009, pp. 83-115. doi:10.1007/s10589-008-9224-3
 P. E. Zadunaisky, “A Method for the Estimation of Errors Propagated in the Numerical Solution of a System of Ordinary Differential Equations,” In: G. I. Kontopoulos, Ed., The Theory of Orbits in the Solar System and in Stellar Systems. Proceedings from Symposium No. 25 Held in Thessaloniki, International Astronomical Union, Academic Press, London, 1964, p. 281.
 M. Rewienski and J. White, “A Trajectory Piecewise-Linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined Devices,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 22, No. 2, 2003, pp. 155-170. doi:10.1109/TCAD.2002.806601
 M. A. Grepl and A. T. Patera, “A Posteriori Error Bounds for Reduced-Basis Approximations of Parametrized Parabolic Partial Differential Equations,” ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 39, No. 1, 2005, pp. 157-181. doi:10.1051/m2an:2005006