  Aims. In this paper we analyse numerically the propagation and dispersion of
acoustic waves in the solar-like sub-photosphere with localised non-uniform
magnetic field concentrations, mimicking sunspots with various representative
magnetic field configurations. Methods. Numerical simulations of wave
propagation through the solar sub-photosphere with a localised magnetic field
concentration are carried out using SAC, which solves the MHD equations for
gravitationally stratified plasma. The initial equilibrium density and pressure
stratifications are derived from a standard solar model. Acoustic waves are
generated by a source located at the height approximately corresponding to the
visible surface of the Sun. We analyse the response of vertical velocity to
changes in the interior due to magnetic field at the level corresponding to the
visible solar surface, by the means of local time-distance helioseismology.
Results. The results of numerical simulations of acoustic wave propagation and
dispersion in the solar sub-photosphere with localised magnetic field
concentrations of various types are presented. Time-distance diagrams of the
vertical velocity perturbation at the level corresponding to the visible solar
surface show that the magnetic field perturbs and scatters acoustic waves and
absorbs the acoustic power of the wave packet. For the weakly magnetised case
the effect of magnetic field is mainly thermodynamic, since the magnetic field
changes the temperature stratification. However, we observe the signature of
slow magnetoacoustic mode, propagating downwards, for the strong magnetic field
cases.
