Causes and consequences of the relation between area and age of the ocean floor

Abstract

The distribution of area of the ocean floor with age, t, is approximately described by dA/dt = C0(1−(t/tm)) where C0 is the rate of crustal generation and tm the maximum age. A linear differential area versus age relation can be explained by a balance between crustal generation and consumption where consumption is uniformly distributed with age. The present distribution of consumption with age was estimated from the isochron map used to derive the area‐age relation and a recently published set of angular velocity vectors describing present plate motions. The rate of consumption per unit age shows considerable scatter about a mean value equal to C0/tm(∼1.7×10−8 km 2/yr 2), but consumption is sufficiently close to being uniformly distributed with age to explain the observed degree of approximation to a linear differential area‐age relation. The trenches appear to be distributed randomly with respect to age provinces in the oceans. It was not possible to discern any trend of mean subduction velocities with age apart from the smaller velocities observed for the two youngest age provinces (0–9 Ma). Changes in the rate of plate generation and the distribution of consumption with age result in shifts in the area‐age distribution. In turn, these shifts produce changes in the plate driving forces which act to restore the rate of plate generation and distribution of consumption to their initial states. The ridge pushing force, for example, decreases as the rate of crustal generation increases. This coupling between driving forces and the area‐age distribution provides a feedback mechanism limiting the extent of any changes. A measure of the magnitude of shifts in the area‐age distribution is given by global changes in sea level. If long‐term changes in sea level are less than 150 m, as suggested by recent estimates, then only small changes (∼12%) in the rate of plate generation and distribution of consumption with age are required. Sea level changes as large as 300 m require about a 50% change in the rate of crustal generation. The above area‐age relation can be combined with simple expressions for depth and heat flow versus age to obtain an empirical hypsometric distribution, parameterized in terms of age, and exact expressions for the heat loss from the ocean floor. The latter is estimated to be 2.9×10 13 W, with 25% of this heat being lost by seafloor younger than 5 Ma. Of the total heat loss from the mantle 26% is estimated to be transported by small‐scale convection.