The thermal-feedback theory of mantle melting proposed by Shaw in 1969 is found to be quantitatively consistent with data pertaining to the evolution of the Hawaiian Ridge. Applicable rate factors are estimated from relations between lava volumes and position along the ridge given in this paper and the radio-metric age distributions given by Jackson and others in 1972. Rate curves derived from these data provide a new method of age extrapolation or interpolation; results indicate that previous methods used to estimate the age of the Hawaiian-Emperor Bend are in error. No definite age is established, but calculations suggest an age greater than 50 m.y. Much more extensive radiometric data are required to define kinematic relations between the Hawaiian Ridge and Emperor Seamount chain.

It appears to be firmly established from the work of Jackson and others and from the present study that the evolution of the Hawaiian Ridge has been episodic, with episodes of several different time scales. Average growth rates of the entire ridge system are divided into two regimes with a discontinuity at a position roughly 1,000 km northwest of Kilauea; the estimated age of this discontinuity is about 10 m.y. Other episodes relate to the durations of eruptive sequences along individual or contiguous lines of volcanoes within the en échelon set of locus lines defined by Jackson and others. The latest of these episodes, beginning about 6 m.y. ago, is marked by accelerating volume rates of eruption and accelerating rates of ridge propagation; this episode appears to be approaching a culminating stage represented by the present activity of Kilauea Volcano. The calculated rate of eruption of Kilauea (0.11 km3 per yr) is virtually identical with a rate independently estimated by Swanson in 1972 using different data. Calculated durations for older locus lines are generally greater than 6 m.y., but major time overlaps occur that are not adequately understood. Episodic behavior of shorter durations also exists relative to growth of individual shields or to synchronous activity on neighboring shields (for example, Mauna Loa and Kilauea). Some of these shorter term effects are partly explained in terms of isostatic factors acting on the lithosphere and asthenosphere. The longer episodes are explained in terms of variations of melting rates in the asthenosphere, governed by viscous heating produced by the interaction of lithosphere translation and both vertical and horizontal shear flows in the subjacent mantle. Accelerations of eruption and propagation rates are explained by melting instabilities in the upper zones of the asthenosphere as a result of thermal feedback. During the latest melting episode, shear stresses in the asthenosphere derived from the rate data as interpreted by the thermal feedback model are in the range 100 to 200 bars; apparent viscosities range from 2 × 1021 to 4 × 1020 poise, decreasing with increasing melting rate.

In general, a thermomechanical model is shown to be consistent with the idea that oceanic melting spots can be fixed relative to the deep mantle, although this invariance is not completely established. The thermal plume model of Morgan is not definitely ruled out but does not seem to be required for internally consistent interpretations of oceanic chains of volcanism. It is concluded that motion vectors of the Pacific plate cannot be inferred directly from rates of propagation of volcanic chains, because these rates reflect local, not average, relative velocities of lithosphere versus mantle flow. During growth of the Hawaiian Ridge, propagation speeds calculated on the basis of rate data for the southeastern Hawaiian Islands ranged from less than 1 cm per yr near the Hawaiian-Emperor Bend to nearly 30 cm per yr at the present ridge front.

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