Isostasy and Flexure of the Lithosphere

Simple analytical solutions exist for the deflection by line loads of thin elastic beams that overlie an inviscid fluid substrate. Deflections for more complex rectangular- and triangular-shaped loads can be evaluated by integration. The deflection of a beam that varies in thickness along its length is best solved, however, by numerical rather than analytical methods. Foremost among them are finite difference techniques, and both two- and three-dimensional codes are now widely available. Thin-plate theory and a flat Earth are good approximations to make in most geological modelling applications.