  Explicit time stepping schemes are popular for linear acoustic and elastic
wave propagation due to their simple nature which does not require
sophisticated solvers for the inversion of the stiffness matrices. However,
explicit schemes are only stable if the time step size is bounded by the mesh
size in space subject to the so-called CFL condition. In micro-heterogeneous
media, this condition is typically prohibitively restrictive because spatial
oscillations of the medium need to be resolved by the discretization in space.
This paper presents a way to reduce the spatial complexity in such a setting
and, hence, to enable a relaxation of the CFL condition. This is done using the
Localized Orthogonal Decomposition method as a tool for numerical
homogenization. A complete convergence analysis is presented with appropriate,
weak regularity assumptions on the initial data.
