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We calculate the scattering effects associated with the interaction of asurface gravity or {\it f} mode with a thin magnetic flux tube embedded in arealistically 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 tothe incident wave, compared to the values of 0.13% and $40^\circ$ estimatedfrom observations. The extent of scattering into high-order acoustic $p$ modesis too weak to be accurately characterized. We recover the result that thedegree of scattering is enhanced as (a) the frequency of the incident waveincreases and (b) the flux tube becomes magnetically dominated.

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