A model of thick plate deformation and its application to the isostatic movements due to surface, subsurface and internal loadings

Abstract

SUMMARY A model of thick plate deformation is presented without any restriction on stress or strain conditions in the plate. An analytical solution is given for the vertical displacement of a thick elastic plate. The present method is exact and applicable to 3-D plate deformation problems associated with surface, subsurface and internal loadings. The conventional thin plate theory, which ignores the variation of vertical strain of a plate, may not be appropriate to be used as a basic model to study deformation problems of the continental lithosphere, since it is shown that the actual surface isostatic adjustment due to surface loading could reach an amount twice as much as predicted by thin plate theory, even on a relatively thin plate with 30 km thickness and Young’s modulus E = lo00 kbar and Poisson’s ratio Y = 0.25. The isostatic adjustment due to surface load depends on the stress condition at the lower boundary of the elastic lithosphere. If there is an active mantle upwelling or downwelling force acting on the boundary, then the isostatic adjustment, depending on the magnitude of the mantle force, is either greatly hindered or amplified to a degree that is beyond the normal prediction of isostatic movements. In addition, the viscous effect of mantle material on the isostatic movements is shown to be negligible on geological time-scales if the mantle viscosity is below ld4poise. It is also shown that the Airy isostasy of the total sediment load in a surface depression with small wavelength could be achieved only if a considerable period of geological time is allowed for the stress relaxation of viscoelastic or viscous material in the lithosphere. The rheological property of the continental lithosphere has a significant effect on basin subsidence caused by sediment loading alone, while pure elastic lithosphere restricts surface basin development because of the strong basement support throughout the evolution history.