Numerical simulation of elastic and acoustic wave propagation utilizes increasingly large and complex models, providing more realistic and useful results. However, significant challenges remain as direct simulations on fine grid are computationally prohibitive. While in some cases, effective medium theories may be useful, in other situations the distribution of heterogeneities may have more complex effects on waves. We present our results of a new multiscale finite element algorithm for simulating acoustic wave propagation in heterogeneous media. The wave equation is solved on a coarse grid using multiscale basis functions. These multiscale basis functions are chosen as the most dominant modes among the set of all fine grid basis functions, and thus allowing a coarse representation of complex wave structures. Numerical results demonstrate the performance of the method. Long term developments have strong potential to enhance inversion algorithms, since the basis functions need not be regenerated, allowing faster simulations for repeated calculations needed for inversion.

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