  Motivated by the observational results of Braun (1995), we extend the model
of Hanson & Cally (2014) to address the effect of multiple scattering of f and
p-modes by an ensemble of thin vertical magnetic flux tubes in the surface
layers of the Sun. As in observational Hankel analysis we measure the scatter
and phase shift from an incident cylindrical wave in a coordinate system
roughly centred in the core of the ensemble. It is demonstrated that, although
thin flux tubes are unable to interact with high order fluting modes
individually, they can indirectly absorb energy from these waves through the
scatters of kink and sausage components. It is also shown how the distribution
of absorption and phase shift across the azimuthal order m depends strongly on
the tube position, as well as on the individual tube characteristics. This is
the first analytical study into an ensembles multiple scattering regime, that
is embedded within a stratified atmosphere.
