ReversePetrogen: A Multiphase Dry Reverse Fractional Crystallization-Mantle Melting Thermobarometer Applied to 13,589 Mid-Ocean Ridge Basalt Glasses

We present a new algorithm, ReversePetrogen (RevPet), to infer mantle melting conditions (pressure, temperature, source composition) using evolved basalts that have experienced multiphase fractional crystallization. RevPet measures and minimizes the compositional distance between experimentally predicted phase saturation boundaries and an erupted basalt and the more primitive liquids that return it to a primary melt. We use RevPet to investigate mantle melting conditions at mid-ocean ridges (MORs) using a global data set of 13,589 basaltic glasses. We find that their average apparent mantle potential temperature (T-P*) is 1322 degrees C +/- 56 degrees C with melting pressures of 13.0 +/- 5 kbars. Inferring the true initial (pre-melted) T-P from T-P* requires knowing the style and degree of melting of the input basalts. If MORB glasses were entirely produced by near-fractional melting of a homogenous source, they would record the cooling of the mantle during melting from an initial T-P = similar to 1380 degrees C (Delta T-P = 0 degrees C) down to T-P = similar to 1270 degrees C. If, instead, they were all fully pooled near-fractional melts of the same source, they would record variations in ambient MOR T-P from similar to 1300 degrees C to 1450 degrees C (Delta T-P = 150 degrees C). However, because MOR basalts are thought to be both near-fractional and variably pooled melts of variable sources, MOR T-P must be intermediate between these two extremes. Our best estimate, consistent with MOR crustal thickness, is that ambient MOR T-P is homogenous (similar to 1350 degrees C-1400 degrees C) except near hotspots where T-P reaches similar to 1600 degrees C. Some primitive glasses found near slow-spreading ridges and back-arcs record very low temperatures (T-P* < 1250 degrees C) and pressures of melting (<10 kbar) and reflect mantle cooling during melting and melt equilibration in the mantle lithosphere.