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In situ permeabilities measured within the upper kilometer of oceanic crust in hole 504B on the south flank of the Costa Rica Rift decrease exponentially from 10-13 to 10-14 m2 in layer 2A (the upper 150m) to 10 -15 to 10-17 m2 in layer 2B (150-550 m into basement), and to 10-17 m2 and lower in layer 2C (deeper than 550 m). We estimate the permeability (k) versus depth (z) to vary as k(z)=0.11e(-z/50)x 10-12 m2. If this permeability versus depth function is representative of the oceanic crust in general, then hydrothermal convection would be vertically stratified, with the most vigorous circulation confined to the shallowest pillow basalt layers of the crust. The use of a full suite of geophysical logs (including borehole televiewer imagery; multichannel, full waveform sonic; nuclear; and variable spacing electrical resistivity logs) allows the characterization of the scale and interconnectedness of fractures, and the degree of infilling of these fractures by alteration minerals. At hole 504B, we observe a relationship between permeability and fracture porosity, determined from the geophysical logs. If fractures with similar aspect ratios are encountered at other oceanic sites, then prediction of the permeability of the oceanic crust to within an order of magnitude is possible from geophysical logs. At hole 395A in the Atlantic, for example, in situ permeability measurements yielded values similar to those predicted by the logging relationships established at hole 504B.