The lithosphere-asthenosphere system is fundamental to our understanding of mantle convection and plate tectonics. Seismic and electromagnetic methods are our primary means of determining its structure and physical properties. These independent constraints with different sensitivities to Earth’s properties hold promise for understanding the system. Here we use the shear velocity model from Rayleigh waves and the MT based resistivity model from near the equatorial Mid-Atlantic Ridge. Cross-plots of the models suggest a linear or near-linear trend that is also in agreement with petrophysical predictions. We therefore map the MT model to a new shear-wave starting model using the petrophysical relationship, which is then used to re-invert for shear-wave velocity. The resulting shear-wave velocity model fits the phase velocity data, and the correlation coefficient between the shear velocity and resistivity models is increased. Much of the model can be predicted by expectations for a thermal half-space cooling model, although some regions require a combination of higher temperatures, volatiles, or partial melt. We use the petrophysical predictions to estimate the melt fraction, melt volatile content, and temperature structure of the asthenospheric anomalies. We find up to 4% melt, with the lowest resistivities and shear velocities explained by up to 20% water or 20% CO₂ in the melt or ~1% nearly pure sulfide melt, depending on the set of assumptions used. Melt is required in punctuated anomalies over broad depth ranges, and also in channels at the base of the lithosphere. Melt in the asthenosphere is dynamic, yet persistent on geologic time scales.