  Our previous semi-analytic treatment of f- and p-mode multiple scattering
from ensembles of thin flux tubes (Hanson and Cally, Astrophys. J. 781, 125;
791, 129, 2014) is extended by allowing both sausage and kink waves to freely
escape at the top of the model using a radiative boundary condition there. As
expected, this additional avenue of escape, supplementing downward loss into
the deep solar interior, results in substantially greater absorption of
incident f- and p-modes. However, less intuitively, it also yields mildly to
substantially smaller phase shifts in waves emerging from the ensemble. This
may have implications for the interpretation of seismic data for solar plage
regions, and in particular their small measured phase shifts.
