Plate‐driving forces over the Cenozoic Era

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Abstract
Plate reconstructions are used to estimate plate torques for the Cenozoic Era, assuming a dynamical balance between active torques (slab‐pull and ridge‐push) and plate drag, as the passive torque. In a published one‐dimensional model for the motion of an oceanic plate the plate drag balances slab‐pull and ridge‐push; expressing each of these forces in terms of age and sub‐duction rate and using values at 15 trenches, coefficients are found which give a least squares fit. Here we have retained a common age factor, which gives a greater weight to older, more rapidly moving plates, and the contribution due to ridge‐push is larger than that found in the previous study, but still much smaller than the slab‐pull force. This one‐dimensional force model is generalized to two‐dimensional plates moving over the Earth's surface, and we obtain a torque balance equation in which slab‐pull and ridge‐push torques are proportional to boundary chord vectors, with the weights depending on powers of subduction velocity at the middle of the chords. For each plate we find the unique angular velocity which satisfies the torque balance requirement, and this balance torque is compared with the plate drag torque obtained from the plate's geometry and (reconstructed) angular velocity. Comparison of the torques is made for two published models for present‐day plate motions, as well as six published reconstructions for time intervals spanning the Cenozoic. For the present the mismatch between the balanced torque and drag torque is about the same as the difference between the two alternative published models. Torques are fairly stable throughout the Cenozoic, with the misfit increasing systematically for earlier reconstructions.

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