In a recent global scale seismic study, the correlation between S wave velocity under ridge axes and spreading rate was pointed out. The correlation is strong for depths of about 70 km, but it diminishes below this depth. We present the correlation plots at four depths, 38, 66, 90, 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 for the development of lithosphere and a simple melt percolation. Thermal 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 correlation between S wave velocity and spreading rate, specifically for spreading rate larger than about 3 cm yr-1. This contradicts the correlation observed in the data at shallow depths. The existence of partial melt is thus required to explain the observed behavior at 38 and 66 km depths. We start from four basic equations that govern the distribution of partial melt and derive the relation between the amount of partial melt and the spreading rate.

We adopt a simple power law relation between permeability (k) and porosity (f) by k(f)=k0fn where k0 and n are constants and assume that pores are filled with melt. We then set up an integral relation between S wave velocity and spreading rate. The final formula indicates that the gradient in the correlation plots is the inverse of the power (1/n) in the permeability-porosity relation, thus enabling us to constrain n as well as k0 from seismic data. The data also have some sensitivity to the depth of solidus. We show that (1) the depth to solidus is probably within the range 60--100 km and (2) if the power n is n=2--3, then k0=10-8--10-10 m2. These parameters predict the porosity and fluid velocity are 1--2% and about 0.5 m yr-1, respectively. The depth to solidus is consistent with previous estimates by petrological data but is perhaps the first and direct seismological evidence of partial melt from surface wave data. Analytical forms for the dependence on depth and spreading rate of porosity, fluid velocity within permeable rocks, and ascent times of magma are also obtained.