A modified beam analysis effect of lateral forces on lithospheric flexure and its implication for post-rift evolution of the Midcontinent Rift system

Abstract

We have use a discretized form of the equation resulting from the elastic Beam Theory to investigate the effect of lateral forces on lithospheric deformation. This technique, the Beam Element Technique (BET), allows the application of a lateral load as a function of distance (i.e., basal shear can be applied in addition to the lateral end forces). Such loading is useful in studying the effects of lithosphere–asthenosphere coupling on lithospheric deformation. The BET also allows for laterally varying the elastic properties and geometry of the beam. By applying laterally varying elastic properties it is possible to investigate the influence an anomalous zone (e.g., rift zone or fault zone) may have on the pattern of lithospheric deformation. Similarly, laterally varying beam geometry (i.e., thickness) permits incorporation of blocks of various ages (older rocks being thicker than younger by virtue of cooling with age) and investigation of their effect on lithospheric deformation. We also derived a beam deflection equation for a laterally varying load. The finite difference formulation of this equation is used to verify the solutions from the BET. Our analysis using the BET shows little difference between the solutions for negative (i.e., opposite to the end load) and positive (i.e., in the direction of the end load) basal tractions. Solutions from the weak zone analysis have allowed investigation of the effect of Grenville tectonism on the post-rift evolution of the Midcontinent Rift system (MCR). We propose that spatially it is possible that compressive forces from the Grenville Tectonic Zone may have caused post-rift thrusting along the MCR. Moreover, it is possible that a single compressive event may have affected both the arms of the MCR, simultaneously.