instance, magnetic anomalies, and if we assume values for the conductivity and diffusivity, Eq. (5.17) can be used to determine the temperature difference between the top and the bottom of the plate (5.18) Parsons & Sclater did this (JGR, 1977); assuming JK m s , Jkg K , and kgm and using mWm as the best fit to the data they found: C. Comparison to observed heat flow data: Near the ridge crest the observed heat flow is significantly lower than the heat flow predicted from the cooling half-space model. In old oceanic basins the heat flow seems to level off at around 46 mW/m , which suggests that beyond a certain age of the lithosphere the rate of conductive cooling either becomes smaller or the cooling is partly off set by additional heat production. Possible sources of heat which could prevent the half-space cooling are: 1. radioactivity (A is not zero!) 2. shear heating 3. small-scale convection below plate 4. hot upwelings (plumes)
5.4. THERMAL STRUCTURE OF THE OCEANIC LITHOSPHERE 177 Figure 5.11: . Intermezzo 5.2 P LATE - COOLING M ODELS There are two basic models for the description of the cooling oceanic lithosphere, a cooling of a uniform half space and the cooling of a layer with some finite thickness. The former is referred to as the half-space model (first described in this context by Turcotte and Oxburgh, 1967); The latter is also known as the plate model (first described by McKenzie, 1967). Both models assume that the plate moves as a unit, that the surface of the lithosphere is at an isothermal condition of 0 C, and that the main method of heat transfer is conduction (a good assumption, except at the ridge crest). The major difference (apart from the mathematical description) is that in the half-space model the base of the lithosphere is defined by an isotherm (for instance 1300 C) so that plate thickness can grow indefinitely whereas in the plate model the plate thickness is limited by some thickness . The two models give the same results for young plates near the ridge crest, i.e. the thickness is such that the ”bottom” of the lithosphere is not yet ”sensed”. However, they differ significantly after 50 Myr for heat flow predictions and 70 Myr for topography predictions. It was realized early on that at large distances from the ridge (i.e., large ages of the lithosphere) the oceans were not as deep and heat flow not as low as expected from the half-space cooling model (there does not seem to be much thermal difference between lithosphere of 80 and 160 Myr of age). The plate model was proposed to get a better fit to the data, but its conceptual disadvantage is that it does not explain why the lithosphere has a maximum thickness of . The half space model makes more sense physically and its mathematical description is more straightforward. Therefore, we will discuss only the half space cooling model, but we will also give some relevant comparisons with the plate model.