Multiscale model reduction of finite-difference frequency-domain wave modeling in elastic media

Accurate and efficient numerical methods are vital for solving the wave equation in applications such as acoustics, electromagnetics, and seismology. However, large-scale and strongly heterogeneous models give rise to prohibitive computational costs because of large dimensions of the discrete wave equation systems. We develop a multiscale finite-difference method to solve the frequency-domain counterpart of the wave equation in elastic media, that is the elastic wave Helmholtz equation. This multiscale method reduces the dimension of the discrete wave equation system that is assembled using a conventional single-scale finite-difference frequency-domain method. The model reduction is achieved by multiscale basis functions constructed from local elastic Helmholtz problems, and can incorporate the medium heterogeneity at the fine scale into the dimension-reduced discrete wave equation system at the coarse scale. To capture the medium property variations at the fine scale accurately, we employ a multi-node coarse element scheme, which involves more than four coarse nodes in a coarse element, to replace the four-node coarse element designed for the first-order multiscale basis functions. The proposed method contributes to a significant computational cost reduction of solving the elastic wave Helmholtz equation without reducing its accuracy. Numerical tests show that our method can implement finite-difference frequency-domain elastic wave modeling with higher efficiency and lower memory cost than the conventional finite-difference frequency-domain methods.