Mathematics – Logic
Scientific paper
Nov 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999e%26psl.173..129e&link_type=abstract
Earth and Planetary Science Letters, Volume 173, Issue 1-2, p. 129-141.
Mathematics
Logic
2
Scientific paper
Representation of the lithosphere by an equivalent elastic plate is a common method in Earth sciences, when the mechanical behaviour of the lithosphere is investigated. The equivalent plate is determined by two parameters: thickness and configuration of the middle surface, named as effective elastic thickness (EET) and effective middle surface (EMS) of the lithosphere. EET is related to the flexural deformation of the lithosphere to vertical loading while EMS controls the lithosphere's response to lateral force variations. EET has been well investigated, whereas EMS remains `in the shadow' in geophysics. The present paper proposes a mathematical formulation for the EMS allowing to calculate it theoretically, from a stress-strain distribution. The equilibrium equation of the equivalent elastic plate is derived from the general rheologically independent equilibrium equation for the lithosphere. It contains a member proportional to the EMS curvature, which describes pre-existing flexure of the equivalent elastic plate. It must be included in flexural calculations with non-zero in-plane forces, because it is an integral part of the equilibrium. EMS (like EET) depends on the lithosphere's structure, constitution and thermal state. Contrasting with EET, bending and mechanical layering do not substantially affect EMS. Temperature exerts the strongest influence on EMS: change in thermal regime may shift EMS vertically by 50 km. Possible deflection of EMS, due to variations of other parameters, is usually lower than 10 km. Tectonically, EMS reveals through stress-induced vertical movements. Their amplitude may be detectable even under the action of moderate intraplate force. The most pronounced effect of EMS variation is expected at continental rifts and orogens.
Ershov A. V.
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