We show that in the presence of a magnetic field that is varying harmonically in space, the fundamental mode, or f-mode, in a stratified layer is altered in such a way that it fans out in the diagnostic k omega diagram, with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014), where a uniform magnetic field was considered, here we employ a non-uniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic field. The expansion of the f-mode is stronger for fields confined to the layer below the surface. In some of those cases, the k omega diagram also reveals a new class of low-frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the f-mode expansion might be a new and sensitive tool to determine subsurface magnetic fields with azimuthal or other horizontal periodicity.