  In order to assess the ability of helioseismology to probe the subsurface
structure and magnetic field of sunspots, we need to determine how helioseismic
travel times depend on perturbations to sunspot models. Here we numerically
simulate the propagation of f, p1, and p2 wave packets through magnetic sunspot
models. Among the models we considered, a ~50 km change in the height of the
Wilson depression and a change in the subsurface magnetic field geometry can
both be detected above the observational noise level. We also find that the
travel-time shifts due to changes in a sunspot model must be modeled by
computing the effects of changing the reference sunspot model, and not by
computing the effects of changing the subsurface structure in the quiet-Sun
model. For p1 modes the latter is wrong by a factor of four. In conclusion,
numerical modeling of MHD wave propagation is an essential tool for the
interpretation of the effects of sunspots on seismic waveforms.
