The electromagnetic data from the Mantle Electromagnetic and Tomography (MELT) experiment are inverted for a two-dimensional transversely anisotropic conductivity structure that incorporates a correction for three-dimensional topographic effects on the magnetotelluric responses. The model space allows for different conductivity values in the along-strike, cross-strike, and vertical directions, along with imposed constraints of model smoothness and closeness among the three directions. Anisotropic models provide a slightly better fit to the data for a given level of model smoothness and are more consistent with other geophysical and laboratory data. The preferred anisotropic model displays a resistive uppermost 60-km-thick mantle independent of plate age, except in the vicinity of the ridge crest. In most inversions, a vertically aligned sheet-like conductor at the ridge crest is especially prominent in the vertical conductivity. Its presence suggests that the melt is more highly concentrated and connected in the vertical direction immediately beneath the rise axis. The melt zone is at least 100 km wide and is asymmetric, having a greater extent to the west. Off-axis, and to the east of the ridge, the mantle is more conductive in the direction of plate spreading at depths greater than 60 km. The flat resistive-conductive boundary at 60 km agrees well with the inferred depth of the dry solidus of peridotite, and the deeper conductive region is consistent with the preferred orientation of olivine inferred from seismic observations. This suggests that the uppermost 60 km represents the region of mantle that has undergone melting at the ridge and has been depleted of water (dissolved hydrogen). By contrast, the underlying mantle has retained a significant amount of water.