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A new directional decomposition of the acoustic 3D wave equation is derived for spherically symmetric geometries,where the wave fields do not need to possess such a symmetry.The wave equation considered incorporates effects from radially varying compressibility and density,but also from an anisotropic compressibility,making the equation applicable for certain so called metafluids.Contrary to previous results on such wave splittings,the new decomposition can be given a very explicit form.