  This paper describes how to propagate wavefields for arbitrary numbers of
traditional time steps in a single step, called a superstep. We show how to
construct operators that accomplish this task for finite-difference time domain
schemes, including temporal first-order schemes in isotropic, anisotropic and
elastic media, as well as temporal second-order schemes for acoustic media.
This task is achieved by implementing a computational tradeoff differing from
traditional single step wavefield propagators by precomputing propagator
matrices for each model location for k timesteps (a superstep) and using these
propagator matrices to advance the wavefield k time steps at once. This
tradeoff separates the physics of the propagator matrix computation from the
computer science of wavefield propagation and allows each discipline to provide
their optimal modular solutions.
