Physics of the flattening of ocean floor depth and heat flow records

Oceanic lithospheric plates form from hot mantle material ascending along the axis of mid-ocean ridges (MORs). As newly formed lithosphere moves away from the ridge, it cools from the surface, leading to progressive deepening of the ocean floor due to thermal contraction and to a decrease in surface heat flow. Turcotte and Oxburgh (1967) proposed a model in which the lithosphere is treated as a cooling half-space with a uniform initial temperature and purely conductive heat transport. Assuming constant thermophysical properties, this model predicts that heat flow and seafloor depth vary linearly with age⁻¹ᐟ² and age¹ᐟ², respectively. Observations of ocean floor topography and heat flow follow these trends up to ages of approximately 50–60 Myr. For older lithosphere, however, the agreement breaks down: observed heat flow is higher and seafloor depth is shallower than predicted by the half-space model.

Several models have been proposed to account for this discrepancy, but all of them are purely kinematic in nature. For example, the widely used “plate model” assumes that temperature is fixed at a certain depth within the mantle. At young ages, the solution coincides with the half-space model, whereas at greater ages it asymptotically approaches the prescribed basal temperature. Although both the basal temperature and the depth of the thermal boundary can be adjusted to fit observations, no known physical mechanism can sustain the boundary condition assumed by this model.

In contrast, we demonstrate that a rheological instability developing within the cooled upper part of the lithospheric plate explains the observations both qualitatively and quantitatively. The key point is that such an instability inevitably arises in a plate cooled from above. Our quantitative analysis is based on experimentally determined non-Newtonian rock viscosity (Hirth and Kohlstedt, 2003) and on the formulation of the Rayleigh number for Arrhenius-type rheology (Solomatov, 1995; Korenaga, 2009). We show that the characteristic Rayleigh number of the instability increases as surface heat flow decreases. Owing to the strong temperature dependence of viscosity, only the lower part of the cooled lithosphere is potentially unstable. For a given heat flow, the thickness of this deformable layer is self-consistently determined by the condition of maximum Rayleigh number. Once the Rayleigh number reaches its critical value, an instability develops that supplies heat to the oceanic lithosphere, inhibits further cooling, and results in the observed flattening of heat flow and seafloor depth records with age.