Double-grid Chebyshev spectral elements for acoustic wave modeling

Highly accurate algorithms are needed for modeling wave propagation phenomena in realistic media. The spectral element methods, either based on a Chebyshev or a Legendre polynomial basis, have shown their excellent properties of high accuracy and flexibility in describing complex models outperforming other techniques. In contrast with standard grid methods, which use dense spatial meshes, spectral element methods discretize the computational domain in a very coarse mesh. With constant-property elements, this fact may in some cases reduce seriously the computational efficiency. For instance, if the medium is finely heterogeneous, it may need to be described in a much finer way than the acoustic wave field. The double-grid approach presented in this work is a viable way for overcoming this lack of the method and for handling problems where the medium changes continuously or even sharply on the small scale. The variation in the properties is taken into account by using an independent set of shape functions defined on a temporary local grid in such a way that either the small scale fluctuations are accurately handled, without the need of a global finer grid, and the macroscopic wave field propagation is solved with no loose of computational efficiency.