{\it f}-mode interactions with thin flux tubes: the scattering matrix

We calculate the scattering effects associated with the interaction of a surface gravity or {\it f} mode with a thin magnetic flux tube embedded in a realistically stratified medium. We find that the dominant scattered wave is an $f$ mode with amplitude and phase of 1.17% and around $49^\circ$ relative to the incident wave, compared to the values of 0.13% and $40^\circ$ estimated from observations. The extent of scattering into high-order acoustic $p$ modes is too weak to be accurately characterized. We recover the result that the degree of scattering is enhanced as (a) the frequency of the incident wave increases and (b) the flux tube becomes magnetically dominated.