Previous techniques for modeling anelastic deformation of the lithosphere have included plane strain models, restricted to two-dimensional problems, and quasi-three-dimensional ''plane stress'' or ''thin plate'' models, that did not accurately include the effects of the shallow frictional layer, or of kinematic detachment of crust from mantle.

This paper presents techniques to remedy these deficiencies of thin plate models. An iteration strategy in which the rheology is linearized using artificial prestress and a particular effective viscosity tensor causes the calculation of horizontal velocities to converge monotonically, even with a frictional layer at the top of the lithosphere. A technique using two planar grids allows deformation and displacement to be different at the crust and mantle levels, at far less cost than that of a three-dimensional grid. A finite element technique is developed for computing the changes in thickness of these layers caused by pure shear, simple shear, and pressure gradients. A technique based on relaxation of perturbation eigenfunctions solves the heat equation in the lithosphere during deformation. Accuracy of component numerical methods is good for simple test problems, but in realistic nonlinear problems utilizing all components, only the precision can be determined because of the lack of analytic solutions. Precision of the combined program is tested with a realistic sample problem and presented as a functional the number of iterations in each velocity solution (convergence factor 0.73 to 0.88), size of time step in the predictor/corrector time integration (convergence as Δt0.8), and number of degrees of freedom in the finite element grid (convergence as N-0.5 to -0.8 for most variables). Overall cost of a simulation varies with the fractional precision &Pgr; as &Pgr;-3.3.

A new consequence of kinematic detachment, a moving wave of crustal thickness, is found; unfortunately, the form of the wave depends on the finite element size. This means that element size must be chosen to approximate the smoothing by flexural rigidity effects that were neglected because of cost. ¿ American Geophysical Union 1989