Mineralogical transformations in the up-welling mantle play a critical role on the dynamics of mass and heat transfers at mid-ocean-ridgeS. The melting event producing ridge basalts occur at 60 km depth below the ridge axis, but because of small amounts of H2O and CO2 in the source region of MOR-basalts, incipient melting can initiate at much greater depth. Such incipient melts concentrate incompatible elements, and are particularly rich in volatile species. These juices evolve from carbonatites, carbonated basalts, to CO2-H2O-rich basalts as recently exposed by petrological surveys; the passage from carbonate to silicate melts is a complex pathway that is strongly non-linear. This picture has recently been complicated further by studies showing that oxygen increasingly partitions into garnet as pressure increases; this implies that incipient melting may be prevented at depth exceeding 200 km because not enough oxygen is available in the system to stabilize carbonate melts. The aim of this work is twofold: - We modelled the complex pathway of mantle melting in presence of C-O-H volatiles by adjusting the thermodynamic properties of mixing in the multi-component C-O-H-melt system. This allows us to calculate the change in melt composition vs. depth following any sortS of adiabat. - We modelled the continuous change in electrical properties from carbonatites, carbonated basalts, to CO2-H2O-rich basalts. We then successfully converted this petrological evolution along a ridge adiabat into electrical conductivity vs. depth signal. The discussion that follows is about comparison of this petrologically-based conductivity profile with the recent profiles obtained by inversion of the long-period electromagnetic signals from the East-Pacific-Rise. These geophysically-based profiles reveal the electrical conductivity structure down to 400 km depth and they show some intriguing highly conductive sections. We will discuss heterogeneity in electrical conductivity of the upper mantle underneath the ridge in terms of melting processes. Our prime conclusion is that the redox melting process, universally predicted by petrological models, might not be universal and that incipient melting can extend down to the transition zone.