We present and analyse a Symmetric Interior Penalty Discontinuous Galerkin (SIPDG) method combined with an explicit hybrid Local Time Stepping (LTS) scheme for solving seismic wave problems in heterogeneous anisotropic elastic media. The discontinuous Galerkin method allows for local adjustment of the mesh size and approximation order, and can deal with unstructured non-conforming meshes of mixed types. Furthermore, when using orthogonal basis functions and an explicit time integration scheme, the method becomes fully explicit and inherently parallel, making it an attractive method for seismic applications involving large three-dimensional domains, sharp material contrasts, and detailed internal structures.@en