Isochrone overturning in steady glacier flow

Bradley P Lipovsky

Ancient ice recovered at Allan Hills extends into the Miocene, but steep layers, age reversals and folds complicate its interpretation. Whether steady glacier flow can overturn initially ordered layers remains uncertain. Here, we track the horizontal order of particles deposited sequentially at the surface. This order is measured by a signed Jacobian that is equivalent to the inverse vertical-thinning factor while layers remain ordered. We find that overturning depends directly on the cumulative competition between vertical shear, which preserves depositional order, and reverse shear, which erodes it. Reverse shear accumulates faster where horizontal speed is small. A layer becomes vertical only after reverse shear has erased both its initial ordering and the ordering accumulated during earlier flow. Full-Stokes mechanics does not guarantee preservation, although shallow-ice flow does. We derive an overturning threshold, bounds for localized obstacles, a cancellation result for periodic bed roughness and a trajectory-based diagnostic for numerical models. Gravity-driven full-Stokes flow with a linear sliding law generates recumbent folding directly from ordered surface deposition, without inherited disturbance or time dependence. Layer curvature and topographic draping can occur without order reversal; the Jacobian provides a test of steady-flow explanations of disturbed stratigraphy at Allan Hills and other old-ice sites.