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

ABSTRACT 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. A multiscale finite-difference method was developed to solve the frequency-domain counterpart of the wave equation in elastic media, which 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, a multinode coarse element scheme was used, 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 contributed to a significant computational cost reduction in solving the elastic-wave Helmholtz equation without reducing its accuracy. Numerical tests showed 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.