  We use numerical simulations to investigate the interaction of an $f$-mode
wave packet with small and large models of a sunspot in a stratified
atmosphere. While a loose cluster model has been largely studied before, we
focus in this study on the scattering from an ensemble of tightly compact
tubes. We showed that the small compact cluster produces a slight distorted
scattered wave field in the transverse direction, which can be attributed to
the simultaneous oscillations of the pairs of tubes within the cluster aligned
in a perpendicular direction to the incoming wave. However, no signature of a
multiple-scattering regime has been observed from this model, while it has been
clearly observable for the large compact cluster model. Furthermore, we pointed
out the importance of the geometrical shape of the monolithic model on the
interaction of $f$-mode waves with a sunspot in a high frequency range ($\nu =$
5 mHz). These results are a contribution to the observational effort to
distinguish seismically between different configurations of magnetic flux tubes
within sunspots and plage.
