Mid-ocean ridge basalts (MORB) are a consequence of pressure-release melting beneath ocean ridges, and contain much information concerning melt formation, melt migration and heterogeneity within the upper mantle. MORB major element chemical systematics can be divided into global and local aspects, once they have been corrected for low pressure fractionation and interlaboratory biases. Regional average compositions for ridges unaffected by hot spots ("normal" ridges) can be used to define the global correlations among normalized Na20, FeO, TiO2 and Si02 contents, CaO/Al203 ratios, axial depth and crustal thickness. Back-arc basins show similar correlations, but are offset to lower FeO and TiO2 contents. Some hot spots, such as the Azores and Galapagos, disrupt the systematics of nearby ridges and have the opposite relationships between FeO, Na 20 and depth over distances of 1000 km.Local variations in basalt chemistry from slow-and fast-spreading ridges are distinct from one another. On slow-spreading ridges, correlations among the elements cross the global vector of variability at a high angle. On the fast-spreading East Pacific Rise (EPR), correlations among the elements are distinct from both global and slow-spreading compositional vectors, and involve two components of variation. Spreading rate does not control the global correlations, but influences the standard deviations of axial depth, crustal thickness, and MgO contents of basalts.Global correlations are not found in very incompatible trace elements, even for samples far from hot spots. Moderately compatible trace elements for normal ridges, however, correlate with the major elements. Trace element systematics are significantly different for the EPR and the mid-Atlantic Ridge (MAR). Normal portions of the MAR are very depleted in REE, with little variability; hot spots cause large long wavelength variations in REE abundances. Normal EPR basalts are significantly more enriched than MAR basalts from normal ridges, and still more enriched basalts can erupt sporadically along the entire length of the EPR. This leads to very different histograms of distribution for the data sets as a whole, and a very different distribution of chemistry along strike for the two ridges. Despite these differences, the mean Ce/Sm ratios from the two ridges are identical.Existing methods for calculating the major element compositions of mantle melts [Klein and Langmuir, 1987;McKenzie and Bickle, 1988;Niu and Batiza, 1991] are critically examined. New quantitative methods for mantle melting and high pressure fractionation are developed to evaluate the chemical consequences of melting and fractionation processes and mantle heterogeneity. The new methods rely on new equations for partition coefficients for the major elements between mantle minerals and melts. The melting calculations can be used to investigate the chemical compositions produced by small extents of melting or high pressures of melting that cannot yet be determined experimentally. Application of the new models to the ...