  We use 2D numerical simulations and eikonal approximation, to study
properties of MHD waves traveling below the solar surface through the magnetic
structure of sunspots. We consider a series of magnetostatic models of sunspots
of different magnetic field strengths, from 10 Mm below the photosphere to the
low chromosphere. The purpose of these studies is to quantify the effect of the
magnetic field on local helioseismology measurements by modeling waves excited
by sub-photospheric sources. Time-distance propagation diagrams and wave travel
times are calculated for models of various field strength and compared to the
non-magnetic case. The results clearly indicate that the observed time-distance
helioseismology signals in sunspot regions correspond to fast MHD waves. The
slow MHD waves form a distinctly different pattern in the time-distance
diagram, which has not been detected in observations. The numerical results are
in good agreement with the solution in the short-wavelength (eikonal)
approximation, providing its validation. The frequency dependence of the travel
times is in a good qualitative agreement with observations.
