Temperatures in zones of steady-state underthrusting of young oceanic lithosphere

Rapid conduction of heat through the top surface of young oceanic lithosphere can contribute at least some of the heat necessary for high-temperature-low-pressure metamorphism of rock buried in subduction zones and, perhaps, for melting in such environments. We show that the steady-state temperature on a major underthrust fault underlain by a slab of downgoing lithosphere equals the quotient of the temperature that would exist due to the cooling of a slab below the wedge in the absence of advection of heat by the downgoing slab, divided by a dimensionless divisor. This divisor depends only on the speed and dip of subduction, the depth of the fault, the coefficient of thermal diffusivity, and the ratio of coefficients of thermal conductivity in the downgoing slab and in the overlying wedge. This result extends an earlier analysis that did not take into account either the cooling of lithosphere as it is subducted or different coefficients of thermal conductivity in the slab and overlying wedge. For a wide range of geologically common parameters, numerically calculated steady-state temperature fields for two-dimensional heat transfer differ by less than a few percent, and by at most 10%, from those given by this simple analytical approximation. This approximation also concurs with numerical calculations of James et al. [1] that show that temperatures as high as 400°C at a depth of only 10 km in a subduction zone would require the subducted lithosphere to be younger than roughly 1 Ma, if no other source of heat were available. In addition, the formalism presented here permits a simple assessment of the relative importance of the youth of the subducted lithosphere and dissipative heating in the enhancement of temperatures near the fault surface. For example, modest shear stresses of about 50 MPa on faults with high slip rates of 100 mm/yr or more at depths as small as 10 km can contribute as much as 200°C to temperatures on the fault, making temperatures of 400°C at 10 km possible, even when lithosphere as old as 20–30 Ma is subducted.