SEISMIC CONSTRAINTS ON A MODEL OF PARTIAL MELTS UNDER RIDGE AXES

In a recent global scale seismic study, the correlation between S wave velocity under ridge axes and spreading rate was pointed out. The cor relation is strong for depths to about 70 km, but it diminishes below this depth. We present the correlation plots at four depths, 38, 66, 9 0, and 110 km, for which correlation is strong at 38 and 66 km but is weak at 90 km and is almost nonexistent at 110 km. We present a model to explain this behavior, which includes a thermal conduction model fo r the development of lithosphere and a simple melt percolation. Therma l effects on S wave velocity are assumed to be accounted for entirely by the plate cooling (thermal conduction) model. We point out that the thermal model under this assumption predicts asymptotically no correl ation between S wave velocity and spreading rate, specifically for spr eading rate larger than about 3 cm yr-1. This contradicts the correlat ion observed in the data at shallow depths. The existence of partial m elt is thus required to explain the observed behavior at 38 and 66 km depths. We start from four basic equations that govern the distributio n of partial melt and derive the relation between the amount of partia l melt and the spreading rate. We adopt a simple power law relation be tween permeability (k) and porosity (f) by k(f) = k0f(n), where k0 and n are constants and assume that pores are filled with melt. We then s et up an integral relation between S wave velocity and spreading rate. The final formula indicates that the gradient in the correlation plot s is the inverse of the power (1/n) in the permeability-porosity relat ion, thus enabling us to constrain n as well as k0 from seismic data. The data also have some sensitivity to the depth to solidus. We show t hat (1) the depth to solidus is probably within the range 60-100 km an d (2) if the power n is n = 2-3, then k0 = 10(-8) - 10(-10) m2. These parameters predict that porosity and fluid velocity are 1-2% and about 0.5 m yr-1 respectively. The depth to solidus is consistent with prev ious estimates by petrological data but is perhaps the first and direc t seismological evidence of partial melt from surface wave data. Analy tical forms for the dependence on depth and spreading rate of porosity , fluid velocity within permeable rocks, and ascent times of magma are also obtained.