PRIMELT3 MEGA.XLSM software for primary magma calculation: Peridotite primary magma MgO contents from the liquidus to the solidus

An upgrade of the PRIMELT algorithm for calculating primary magma composition is given together with its implementation in PRIMELT3 MEGA.xlsm software. It supersedes PRIMELT2.xls in correcting minor mistakes in melt fraction and computed Ni content of olivine, it identifies residuum mineralogy, and it provides a thorough analysis of uncertainties in mantle potential temperature and olivine liquidus temperature. The uncertainty analysis was made tractable by the computation of olivine liquidus temperatures as functions of pressure and partial melt MgO content between the liquidus and solidus. We present a computed anhydrous peridotite solidus in T-P space using relations amongst MgO, T and P along the solidus; it compares well with experiments on the solidus. Results of the application of PRIMELT3 to a wide range of basalts shows that the mantle sources of ocean islands and large igneous provinces were hotter than oceanic spreading centers, consistent with earlier studies and expectations of the mantle plume model.