The dynamical origin of Hawaiian volcanism

We study the dynamics of melting in the Hawaiian plume using a 3D variable-viscosity convection model outfitted with a melting parameterization that permits calculation of the local melting rate and the distribution of buoyant depleted residual material. From a suite of 45 steady-state numerical experiments, we derive complete scaling laws for the total rate of melting M and the height H and width W of the topographic swell as functions of the lithospheric thickness z(1) and the plume's maximum potential temperature theta(i), thermal buoyancy flux B, and minimum viscosity eta(p). Assuming 1500 degrees C < theta(i) < 1600 degrees C, the observed values of M, H and W can only be matched if z(1) less than or equal to 89 km, 2200 kg s(-1) less than or equal to B less than or equal to 3500 kg s(-1), and eta(p) greater than or equal to 5 x 10(17) Pa s. We study a reference Hawaiian model satisfying these constraints. The depletion anomaly is narrower than the thermal anomaly, and carries 24% of the total (thermal plus depletion) buoyancy flux. Its buoyancy contributes 350 m of the uplift along the swell axis, and reduces the geoid/topography ratio by 16% relative to a model without depletion buoyancy. All the material that melts comes from the hottest central part of the plume, and no direct melting of the asthenosphere or lithosphere occurs. Melting occurs both in a primary melting zone above the plume stem and in a weaker secondary melting zone 300-500 km downstream, separated by an interval where no melting occurs. We propose that the preshield-, shield-, and postshield stages of Hawaiian volcanism are generated by the primary melting zone, and the rejuvenated stage by the secondary melting zone. (C) 1999 Elsevier Science B.V. All rights reserved.