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Low seismic velocities and/or strong seismic anisotropy are often interpreted as being caused by partial melt. To better understand this, we used numerical modelling, varying the shape and amount of melt, to show how seismic phases are affected by melt. We observed that seismic waves are more sensitive to the shape than to the amount of melt. Rayleigh wave velocities were almost always reduced in the presence of melt, while Pn/wide-angle P-wave refraction and Love wave velocities showed low velocity anomalies for vertically aligned melt, but little anomaly for horizontally aligned melt. These data can therefore be used to determine the alignment of melt. Shear wave splitting/receiver functions showed strong anisotropy and can be used to constrain the strike of vertically aligned partial melt. We showed that melt in the mantle beneath Ethiopia is probably stored in low aspect ratio disc-like inclusions, suggesting that the melt is not in textural equilibrium. We estimated that 2–7% of the vertically aligned melt is stored beneath the Main Ethiopian Rift, >6% of the horizontally and vertically aligned melt is stored beneath the Red Sea Rift and 1–6% of the horizontally aligned melt is stored beneath the Danakil microplate. This supports the idea of strong shear-derived segregation of melt in the narrow Main Ethiopian Rift compared with that observed beneath Afar.