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Geomagnetic field variations as recorded at geomagnetic observatories are important for global electromagnetic studies. However, this data set is rarely used for studying the local electrical conductivity at depths <200 km. The main reasoning being that given a single geomagnetic observatory, one can at most constrain the one-dimensional (1-D) conductivity structure beneath it. At the same time, tippers, magnetic transfer functions resolving these depths, are zero for any 1-D conductivity distribution. We show that the ocean induction effect alleviates these limitations for observatories on islands and develop a method to invert tippers for a 1-D conductivity profile in the presence of three-dimensional conductivity structure due to bathymetry. This allows to recover 1-D upper mantle conductivity profiles at remote oceanic locations where little or no knowledge is available and that would otherwise be difficult to access. We apply the method to Gan in the Indian Ocean and to Tristan da Cunha in the South Atlantic, and the obtained conductivity profiles indicate a normal oceanic mantle and elevated conductivities, respectively, which fits well with their geological settings. [ABSTRACT FROM AUTHOR]