Thermal stresses due to cooling of a viscoelastic oceanic lithosphere

Theories based upon thermal contraction of cooling oceanic lithosphere provide a successful basis for correlating seafloor bathymetry and heat flow. The horizontal components of the contraction of the lithosphere as it cools potentially give rise to large thermal stresses. Current methods to calculate these stresses assume that on the time scales of cooling, the lithosphere initially behaves as an inviscid fluid and instantly freezes into an elastic solid at some critical temperature. These instant-freezing methods inaccurately predict transient thermal stresses in rapidly cooling silicate glass plates because of the temperature dependent rheology of the material. The temperature dependent rheology of the lithosphere may affect the transient thermal stress distribution in a similar way, and for this reason we use a thermoviscoelastic model to estimate thermal stresses in young oceanic lithosphere. This theory is formulated here for linear creep processes that have an Arrhenius rate dependence on temperature. Our results show that the stress differences between instant freezing and linear thermoviscoelastic theory are most pronounced at early times (0–20 m.y.) when the instant freezing stresses may be twice as large. The solutions for the two methods asymptotically approach the same solution with time. A comparison with intraplate seismicity shows that both methods underestimate the depth of compressional stresses inferred from the seismicity in a systematic way.