Multiscale finite element modeling of acoustic wave propagation

Numerical simulation of elastic and acoustic wave propagation utilizes increasingly large and complex models, providing more realistic and useful results. However, significant challenges remain in applications such as propagation in fractured media, as complex distributions of fracture systems can be difficult to represent on typical, uniform grids with spacing on the order of 10-20 m. While in some cases, effective medium theories may be useful, in other situations the distribution of fracturing or other heterogeneities may have more complex effects on waves. We describe initial results of a new multiscale finite element algorithm for simulating acoustic wave propagation in heterogeneous media that addresses these problems by combining fine- and coarse-scale grids. The wave equation is solved on a coarse grid using multiscale basis functions, using a global coupling mechanism to to related information between scales. Time stepping is applied on the coarse grid, leading to additional savings. Numerical results demonstrate the utility 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.