An estimate of the magnitude and geometry of the magnetic field within the Earth's core would be valuable for understanding the dynamics of the liquid outer core and for constraining numerical models of the geodynamo. The magnetic field down to the core-mantle boundary can be estimated from surface observations by assuming that the mantle is an insulator, but such estimates cannot be further extrapolated into the conducting core itself. The magnetic field within the core has therefore remained largely unconstrained. Here we construct a simple picture of part of the magnetic field within the core by first showing that the fluid flow at the surface of the core is consistent with the presence of two large waves- 'torsional oscillations' of the type that have been proposed to explain the temporal variation of the magnetic field at the core-mantle boundary. We then use the structure of these waves to calculate a one-dimensional map of the part of the magnetic field that points away from the rotation axis. These results may help distinguish between the different dynamic states proposed for outer-core flow and provide a test for recent numerical models of the geodynamo.
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