Thermal contraction and the state of stress in the oceanic lithosphere

Abstract

Nonuniform contraction of the oceanic lithosphere as it cools and thickens following its formation at the axis of a spreading center results in a complex three‐dimensional state of deviatoric stress which can be separated into two parts: a thermal bending stress due to changes in the vertical temperature distribution and a thermal contraction stress due to lateral variations in the vertically averaged temperature. We examine thermal contraction stresses due to temperature changes in a thin, semi‐infinite rectangular plate bounded by the spreading center axis. Two stress‐free boundaries, representing transforms or fracture zones, define the plate width or ridge segment length L. With the bottom of the elastic plate defined by a prescribed temperature, the plate thickens as the square root of age, as expected for a thermal boundary layer due to vertical conductive cooling. Above this prescribed temperature, elastic stresses are assumed to relax quickly. Stresses are obtained by properly accounting for the rate of accumulation of the vertically averaged stress as initially stress‐free material is added to bottom of the cooling, thickening plate. The state of thermal contraction stress calculated from this model is characterized by large tensile stresses at the boundaries of the plate and relatively low stresses in the plate interior. At the ridge axis, ridge‐parallel tensile stresses are about 300 MPa, the same as if the plate were not allowed to contract in this direction. Along the transform boundary, the maximum transform‐parallel tensile stress occurs at a distance L/2 from the ridge‐transform intersection, where its magnitude is comparable to the stress at the ridge axis. The tangential stresses at the plate boundary decrease rapidly with distance from the boundary; at a distance of L/4 from the ridge axis the ridge axis parallel stresses are one tenth of their ridge axis magnitude. The stress magnitudes are independent of both spreading rate and ridge segment length. A large transform‐parallel tensile stress may control the length of transform offsets. Thermal bending moments are influenced by the large thermal contraction stresses near the ridge axis. However, a short distance from the ridge these moments attain their free horizontal contraction values which previous studies have shown to cause observable bending of the plate and a geoid anomaly at fracture zones. Flexure due to thermal bending moments will concentrate bending stresses at a distance from the fracture zone determined by the flexural length of the plate, thus providing a natural length scale controlling the spacing of transforms.