Schematic of the cooling oceanic lithosphere
The solid lines are isotherms, T − T0 (K), in the oceanic lithosphere from Equation (4–125). The data points are the thicknesses of the oceanic lithosphere in the Pacific determined from studies of Rayleigh wave dispersion data (Leeds et al., 1974).
High-temperature deformation of rocks in the laboratory indicates that this temperature is about 1600 K. Thus we can think of the lithosphere as the region between the surface and a particular isotherm, as shown in the figure. The depth to this isotherm increases with the age of the lithosphere; that is, the lithosphere thickens as it moves farther from the ridge, since it has more time to cool. We refer to the age of the lithosphere as the amount of time t required to reach the distance x from the ridge (because of symmetry we consider x positive); t = x/u. The temperature of the rock at the ridge crest x = 0 and beneath the plate is T1. The seawater cools the surface to the temperature T0. Thus, a column of mantle is initially at temperature T1, and its surface is suddenly brought to the temperature T0. As the column moves away from the ridge, its surface temperature is maintained at T0, and it gradually cools. This problem is
identical to the sudden cooling of a half-space, treated in Section 4–15, if we
neglect horizontal heat conduction compared with vertical heat conduction.
