Residual-driven online multiscale methods for acoustic-wave propagation in 2D heterogeneous media

Common applications, such as geophysical exploration, reservoir characterization, and earthquake quantification, in modeling and inversion aim to apply numerical simulations of elastic- or acoustic-wave propagation to increasingly large and complex models, which can provide more realistic and useful results. However, the computational cost of these simulations increases rapidly, which makes them inapplicable to certain problems. We apply a newly developed multiscale finite-element algorithm, the generalized multiscale finite-element method (GMsFEM), to address this challenge in simulating acoustic-wave propagation in heterogeneous media. The wave equation is solved on a coarse grid using multiscale basis functions that are chosen from the most dominant modes among those computed by solving relevant local problems on a fine-grid representation of the model. These multiscale basis functions are computed once in an off-line stage prior to the simulation of wave propagation. Because these calculations are localized to individual coarse cells, one can improve the accuracy of multiscale methods by revising and updating these basis functions during the simulation. These updated bases are referred to as online basis functions. This is a significant extension of previous applications of similar online basis functions to time-independent problems. We tested our new algorithm and numerical results for acoustic-wave propagation using the acoustic Marmousi model. Long-term developments have a strong potential to enhance inversion algorithms because the basis functions need not be regenerated everywhere. In particular, recomputation of basis functions is required only at regions in which the model is updated. Thus, our method allows faster simulations for repeated calculations, which are needed for inversion purpose.